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Download Content Area: Math Grade/Course: Kindergarten Count orally to 100
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Content Area: Math Grade/Course: Kindergarten Strand Mathematics Standard 1: Count orally to 100 by ones. Count to 30 by 2’s, 5’s and 10’s using grouped objects as needed. Topic Counting Benchmark N.ME.00.01, N.ME.00.04 Count objects in sets up to 30. Read and write numbers to 30 and connect them to the quantities they represent. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently count objects in set Usually count objects in set Sometimes count objects in set Rarely count objects in set up to 30. Read and write numbers up to 30. Read and write numbers up to 30. Read and write numbers up to 30. Read and write numbers to 30 and connect them to the to 30 and connect them to the to 30 and connect them to the to 30 and connect them to the quantities they represent. quantities they represent. quantities they represent. quantities they represent. Differentiation of Instruction Strand Mathematics Standard 1: Count orally to 100 by ones. Count to 30 by 2’s, 5’s and 10’s using grouped objects as needed. Topic Counting Benchmark N.ME.00.02, N.ME.00.03 Use one-to-one correspondence to compare and order sets of objects to 30 using such phrases as “same number”, “more than”, or “less than”; use counting and matching. Compare and order numbers to 30. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently use one to one Usually use one to one Sometimes use one to one Rarely use one to one correspondence to compare and order correspondence to compare and order correspondence to compare and order correspondence to compare and sets of objects to 30 using such sets of objects to 30 using such sets of objects to 30 using such order sets of objects to 30 using phrases as “same number”, "more phrases as “same number”, "more phrases as “same number”, "more such phrases as “same number”, than" or “less than”; use counting than" or “less than”; use counting than" or “less than”; use counting "more than" or “less than”; use and matching. Compare and and matching. Compare and and matching. Compare and counting and matching. Compare and order numbers to 30. order numbers to 30. order numbers to 30. order numbers to 30. Differentiation of Instruction Strand Mathematics Standard 2: Make drawings and write simple addition and subtraction sentences for situations/stories involving putting together and taking apart for totals up to 10; use finger and object counting to solve. Topic Counting Benchmark N.MR.00.08, N.MR.00.09 Compose and decompose numbers from 2 to 10, e.g., 5 = 4 + 1 = 2 + 3, with attention to the additive structure of number systems, e.g., 6 is 1 more than 5, 7 is one more than 6. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently compose and decompose Usually compose and decompose Sometimes compose and decompose Rarely compose and decompose numbers from 2 to 10, numbers from 2 to 10, numbers from 2 to 10, numbers from 2 to 10, , e.g., 5 = 4 + 1 = 2 + 3, with attention , e.g., 5 = 4 + 1 = 2 + 3, with attention , e.g., 5 = 4 + 1 = 2 + 3, with attention , e.g., 5 = 4 + 1 = 2 + 3, with attention to the additive structure of to the additive structure of to the additive structure of to the additive structure of of number systems, e.g., 6 is 1 more of number systems, e.g., 6 is 1 more of number systems, e.g., 6 is 1 more of number systems, e.g., 6 is 1 more than 5, 7 is one more than 6. than 5, 7 is one more than 6. than 5, 7 is one more than 6. than 5, 7 is one more than 6. Differentiation of Instruction Strand Mathematics Standard 2: Make drawings and write simple addition and subtraction sentences for situations/stories involving putting together and taking apart for totals up to 10; use finger and object counting to solve. Topic Counting Benchmark N.MR.00.10 Create, describe, and extend simple number patterns. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently create, describe, and Usually create, describe, and Sometimes create, describe, and Rarely create, describe, and extend simple number patterns. extend simple number patterns. extend simple number patterns. extend simple number patterns. Differentiation of Instruction Strand Mathematics Standard 3: Compare length and weight of objects by comparing to reference objects, and use terms such as shorter, longer, taller, lighter, heavier. Topic Counting Benchmark M.PS.00.05 Compare two or more objects by length, weight and capacity, e.g., which is shorter, longer, taller? Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently compare two or more Usually compare two or more Sometimes compare two or more Rarely compare two or more objects bylength, weight, objects bylength, weight, objects bylength, weight, objects bylength, weight, and capacity. and capacity. and capacity. and capacity. Differentiation of Instruction Strand Mathematics Standard 4: Relate familiar three-dimensional objects inside and outside the classroom to their geometric name, e.g., ball/sphere, box/cube, soup can/cylinder, ice cream cone/cone, refrigerator/prism. Topic Counting Benchmark G.GS.00.01 Identify, sort and classify objects by attribute and identify objects that do not belong in a particular group. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify, sort and Usually identify, sort and Sometimes identify, sort and Rarely identify, sort and classify objects by attitudes classify objects by attitudes classify objects by attitudes classify objects by attitudes and identify objects that do not and identify objects that do not and identify objects that do not and identify objects that do not belong in a particular group. belong in a particular group. belong in a particular group. belong in a particular group. Differentiation of Instruction Strand Mathematics Standard 4: Relate familiar three-dimensional objects inside and outside the classroom to their geometric name, e.g., ball/sphere, box/cube, soup can/cylinder, ice cream cone/cone, refrigerator/prism. Topic Counting Benchmark G.GS.00.01 Create, describe, and extend simple geometric patterns. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently create, describe, Usually create, describe, Sometimes create, describe, Rarely create, describe, and extend simple geometric patterns. and extend simple geometric patterns. and extend simple geometric patterns. and extend simple geometric patterns. Differentiation of Instruction Strand Mathematics Standard 4: Relate familiar three-dimensional objects inside and outside the classroom to their geometric name, e.g., ball/sphere, box/cube, soup can/cylinder, ice cream cone/cone, refrigerator/prism. Topic Counting Benchmark G.GS.00.01 Understand the numbers 1 to 30 as having one, or two, or three groups of ten and some ones. Also count by tens with objects in ten-groups to 100. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand the numbers Usually understand the numbers Sometimes understand the numbers Rarely understand the numbers 1 to 30 as having one, or two, or 1 to 30 as having one, or two, or 1 to 30 as having one, or two, or 1 to 30 as having one, or two, or three groups of ten and some ones. three groups of ten and some ones. three groups of ten and some ones. three groups of ten and some ones. Also counrt by tens with objects in Also counrt by tens with objects in Also counrt by tens with objects in Also counrt by tens with objects in ten-groups to 100. ten-groups to 100. ten-groups to 100. ten-groups to 100. Differentiation of Instruction Strand Mathematics Standard 4: Relate familiar three-dimensional objects inside and outside the classroom to their geometric name, e.g., ball/sphere, box/cube, soup can/cylinder, ice cream cone/cone, refrigerator/prism. Topic Counting Benchmark M.UN.00.01 Know and use the common words for the parts of the day (morning, afternoon, evening, night) and relative time (yesterday, today, tomorrow, last week, next year). Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently begins to know and use Usually begins to know and use Sometimes begins to know and use Rarely begins to know and use common words for the parts of the common words for the parts of the common words for the parts of the common words for the parts of the day and relative time. day and relative time. day and relative time. day and relative time. Differentiation of Instruction Content Area: Math Grade/Course: 1st Strand Mathematics Standard 1: Count to 110 by 1s, 2s, 5s, and 10s, starting from any number in the sequence; count to 500 by 100s and 10s; use ordinals to identify position in a sequence, e.g., 1st, 2nd, 3rd. Topic Counting Benchmark N.ME.01.02, N.ME.01.03 Read and write numbers to 110 and relate them to the quantities they represent. Order numbers to 110; compare using phrases such as same as, more than, greater than, fewer than, and use = symbol. Arrange small sets of numbers in increasing or decreasing order, e.g., write the following from smallest to largest: 21, 16, 35, 8 Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently read and write numbers Usually read and write numbers Sometimes read and write numbers Rarely read and write numbers to 110. Order numbers to 110; to 110. Order numbers to 110; to 110. Order numbers to 110; to 110. Order numbers to 110; Arrange small sets of numbers in Arrange small sets of numbers in Arrange small sets of numbers in Arrange small sets of numbers in increasing or decreasing order. increasing or decreasing order. increasing or decreasing order. increasing or decreasing order. Differentiation of Instruction Strand Mathematics Standard 1: Count to 110 by 1s, 2s, 5s, and 10s, starting from any number in the sequence; count to 500 by 100s and 10s; use ordinals to identify position in a sequence, e.g., 1st, 2nd, 3rd. Topic Counting Benchmark N.ME.01.04, N.ME.01.05 Identify one more than, one less than, 10 more than and 10 less than for any number up to 100. Understand that a number to the right of another number on the number line is bigger and that a number to the left is smaller. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify one more than, Usually identify one more than, Sometimes identify one more than, Rarely identify one more than, one less than, 10 more than and 10 one less than, 10 more than and 10 one less than, 10 more than and 10 one less than, 10 more than and 10 less than for any number up to 100. less than for any number up to 100. less than for any number up to 100. less than for any number up to 100. Understand that a number to the Understand that a number to the Understand that a number to the Understand that a number to the right on the number line is bigger and right on the number line is bigger and right on the number line is bigger and right on the number line is bigger and to the left is smaller. to the left is smaller. to the left is smaller. to the left is smaller. Differentiation of Instruction Strand Mathematics Standard 1: Count to 110 by 1s, 2s, 5s, and 10s, starting from any number in the sequence; count to 500 by 100s and 10s; use ordinals to identify position in a sequence, e.g., 1st, 2nd, 3rd. Topic Counting Benchmark N.ME.01.06 Count backward by 1s starting from any number between 1 and 100. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently count backward by Usually count backward by Sometimes count backward by Rarely count backward by 1's starting from any number 1's starting from any number 1's starting from any number 1's starting from any number between 1 and 100. between 1 and 100. between 1 and 100. between 1 and 100. Differentiation of Instruction Strand Mathematics Standard 1: Count to 110 by 1s, 2s, 5s, and 10s, starting from any number in the sequence; count to 500 by 100s and 10s; use ordinals to identify position in a sequence, e.g., 1st, 2nd, 3rd. Topic Counting Benchmark N.ME.01.07 Compose and decompose numbers to 30 using bundles of tens and some ones. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently compose and Usually compose and Sometimes compose and Rarely compose and decompose numbers to 30 using decompose numbers to 30 using decompose numbers to 30 using decompose numbers to 30 using bundles of tens and some ones. bundles of tens and some ones. bundles of tens and some ones. bundles of tens and some ones. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 10 to solve problems. Topic Counting Benchmark N.MR.01.10 Model addition and subtraction for numbers through 30 for a given contextual situation using objects or pictures; explain in words; record using numbers and symbols; solve. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently model addition and Usually model addition and Sometimes model addition and Rarely model addition and subtraction for numbers through 30 subtraction for numbers through 30 subtraction for numbers through 30 subtraction for numbers through 30 for a given contextural situation using for a given contextural situation using for a given contextural situation using for a given contextural situation using objects or pictures; explain in words; objects or pictures; explain in words; objects or pictures; explain in words; objects or pictures; explain in words; record using numbers and symbols; record using numbers and symbols; record using numbers and symbols; record using numbers and symbols; solve. solve. solve. solve. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 10 to solve problems. Topic Counting Benchmark N.ME.01.08 List number facts (partners inside of numbers) for 2 through 10; e.g., 8 = 7 + 1 = 6 + 2 = 5 + 3 = 4 + 4; 10 = 8 + 2 = 2 + 8. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently list number facts Usually list number facts Sometimes list number facts Rarely list number facts for 2 through 8. for 2 through 8. for 2 through 8. for 2 through 8. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 10 to solve problems. Topic Counting Benchmark N.FL.01.12, N.MR.01.13 Know all the addition facts up to 10 + 10, and solve the related subtraction problems fluently. Apply knowledge of fact families to solve simple open sentences for addition and subtraction, such as: ? + 2 = 7 and 10 - ? = 6. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently know all the addition Usually know all the addition Sometimes know all the addition Rarely know all the addition facts up to 10 + 10, and solve the facts up to 10 + 10, and solve the facts up to 10 + 10, and solve the facts up to 10 + 10, and solve the related subtraction problems related subtraction problems related subtraction problems related subtraction problems fluently. Apply knowledge of fact fluently. Apply knowledge of fact fluently. Apply knowledge of fact fluently. Apply knowledge of fact families to solve open sentences for families to solve open sentences for families to solve open sentences for families to solve open sentences for addition and subtraction. addition and subtraction. addition and subtraction. addition and subtraction. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 10 to solve problems. Topic Counting Benchmark N.FL.01.14 Add three one-digit numbers. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently add three one Usually add three one Sometimes add three one Rarely add three one digit numbers. digit numbers. digit numbers. digit numbers. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 10 to solve problems. Topic Counting Benchmark N.MR.01.09 Compare two or more sets in terms of the difference in number of elements. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently compare two or more Usually compare two or more Sometimes compare two or more Rarely compare two or more sets in terms of the difference in sets in terms of the difference in sets in terms of the difference in sets in terms of the difference in number of elements. number of elements. number of elements. number of elements. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 10 to solve problems. Topic Counting Benchmark N.MR.01.11 Understand the inverse relationship between addition and subtraction, e.g., subtraction “undoes” addition: because 3 + 5 = 8, we know that 8 - 3 = 5 and 8 - 5 = 3; recognize that some problems involving combining, “taking away,” or comparing can be solved by either operation. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand the inverse Usually understand the inverse Sometimes understand the inverse Rarely understand the inverse relationship between addition and relationship between addition and relationship between addition and relationship between addition and subtraction; recognize that some subtraction; recognize that some subtraction; recognize that some subtraction; recognize that some problems involving combining, problems involving combining, problems involving combining, problems involving combining, "taking away', or comparing can "taking away', or comparing can "taking away', or comparing can "taking away', or comparing can be solved by either operation. be solved by either operation. be solved by either operation. be solved by either operation. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 10 to solve problems. Topic Counting Benchmark N.MR.01.15 Calculate mentally sums and differences involving: a two-digit number and a one-digit number without regrouping; a two-digit number and a multiple of 10. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently calculate mentally sums Usually calculate mentally sums Sometimes calculate mentally sums Rarely calculate mentally sums differences involving; a two-digit differences involving; a two-digit differences involving; a two-digit differences involving; a two-digit number and a one-digit number number and a one-digit number number and a one-digit number number and a one-digit number without regrouping; a two-digit without regrouping; a two-digit without regrouping; a two-digit without regrouping; a two-digit number abd a multiole of 10. number abd a multiole of 10. number abd a multiole of 10. number abd a multiole of 10. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 10 to solve problems. Topic Counting Benchmark N.MR.01.16 Compute sums and differences through 30 using number facts and strategies, number without regrouping; a two-digit number and a multiple of 10. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently compute sums and Usually compute sums and Sometimes compute sums and Rarely compute sums and differences through 30 using differences through 30 using differences through 30 using differences through 30 using number facts and strategies, number facts and strategies, number facts and strategies, number facts and strategies, number without regrouping; a two- number without regrouping; a two- number without regrouping; a two- number without regrouping; a two- digit number and a multiple of 10. digit number and a multiple of 10. digit number and a multiple of 10. digit number and a multiple of 10. Differentiation of Instruction Strand Mathematics Standard 3: Solve one-step word problems involving addition and subtraction of length and including “how much more/less,” without mixing units. Topic Measuring Benchmark M.UN.01.01 Measure the lengths of objects in non-standard units, e.g., pencil lengths, shoe lengths, to the nearest whole unit. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently measure the Usually measure the Sometimes measure the Rarely measure the lengths of objects in non-standard lengths of objects in non-standard lengths of objects in non-standard lengths of objects in non-standard units to the nearest whole. units to the nearest whole. units to the nearest whole. units to the nearest whole. Differentiation of Instruction Strand Mathematics Standard 3: Solve one-step word problems involving addition and subtraction of length and including “how much more/less,” without mixing units. Topic Comparing Measurements Benchmark M.UN.01.02 Compare measured lengths using the words shorter, shortest, longer, longest, taller, tallest, etc Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently compared measured Usually compared measured Sometimes compared measured Rarely compared measured lengths using key words. lengths using key words. lengths using key words. lengths using key words. Differentiation of Instruction Strand Mathematics Standard 3: Solve one-step word problems involving addition and subtraction of length and including “how much more/less,” without mixing units. Topic Money Benchmark M.UN.01.04 Identify the different denominations of coins and bills Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify the Usually identify the Sometimes identify the Rarely identify the different denominations of coins different denominations of coins different denominations of coins different denominations of coins and bills. and bills. and bills. and bills. Differentiation of Instruction Strand Mathematics Standard 3: Solve one-step word problems involving addition and subtraction of length and including “how much more/less,” without mixing units. Topic Money Benchmark M.UN.01.05 Match one coin or bill of one denomination to an equivalent set of coins/bills of other denominations, e.g., 1 quarter = 2 dimes and 1 nickel. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently match one coin or Usually match one coin or Sometimes match one coin or Rarely match one coin or bill of one denomination to an bill of one denomination to an bill of one denomination to an bill of one denomination to an equivalent set of coins/bill of other equivalent set of coins/bill of other equivalent set of coins/bill of other equivalent set of coins/bill of other denomination. denomination. denomination. denomination. Differentiation of Instruction Strand Mathematics Standard 3: Solve one-step word problems involving addition and subtraction of length and including “how much more/less,” without mixing units. Topic Money Benchmark M.UN.01.06 Tell the amount of money: in cents up to $1, in dollars up to $100. Use the symbols $ and ¢. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently tell the amount of Usually tell the amount of Sometimes tell the amount of Rarely tell the amount of money; in cents up to $1, in dollars up money; in cents up to $1, in dollars up money; in cents up to $1, in dollars up money; in cents up to $1, in dollars up to $100. Use the symbol $ and ¢. to $100. Use the symbol $ and ¢. to $100. Use the symbol $ and ¢. to $100. Use the symbol $ and ¢. Differentiation of Instruction Strand Mathematics Standard 3: Solve one-step word problems involving addition and subtraction of length and including “how much more/less,” without mixing units. Topic Money Benchmark M.UN.01.07 Add and subtract money in dollars only or in cents only. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently add and subtract Usually add and subtract Sometimes add and subtract Rarely add and subtract money in dollars only or in cents money in dollars only or in cents money in dollars only or in cents money in dollars only or in cents only. only. only. only. Differentiation of Instruction Strand Mathematics Standard 4: Create and describe patterns, such as repeating patterns and growing patterns using number, shape, and size. Topic Patterns Benchmark G.SR.01.04 Distinguish between repeating and growing patterns. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently distinguish between Usually distinguish between Sometimes distinguish between Rarely distinguish between repeating and growing patterns. repeating and growing patterns. repeating and growing patterns. repeating and growing patterns. Differentiation of Instruction Strand Mathematics Standard 4: Create and describe patterns, such as repeating patterns and growing patterns using number, shape, and size. Topic Patterns Benchmark G.SR.01.05 Predict the next element in a simple repeating pattern. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently predict the next Usually predict the next Sometimes predict the next Rarely predict the next element in a simple repeating pattern. element in a simple repeating pattern. element in a simple repeating pattern. element in a simple repeating pattern. Differentiation of Instruction Strand Mathematics Standard 4: Create and describe patterns, such as repeating patterns and growing patterns using number, shape, and size. Topic Patterns Benchmark G.SR.01.06 Describe ways to get to the next element in simple repeating patterns. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently describe the ways Usually describe the ways Sometimes describe the ways Rarely describe the ways to get to the next element in to get to the next element in to get to the next element in to get to the next element in simple reoeating patterns. simple reoeating patterns. simple reoeating patterns. simple reoeating patterns. Differentiation of Instruction Strand Mathematics Standard 5: Make pictographs to represent simple sets of data. Topic Pictographs Benchmark . D.RE.01.01 Collect and organize data to use in pictographs. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently collect and organize Usually collect and organize Sometimes collect and organize Rarely collect and organize data to use pictographs. data to use pictographs. data to use pictographs. data to use pictographs. Differentiation of Instruction Strand Mathematics Standard 5: Make pictographs to represent simple sets of data. Topic Pictographs Benchmark D.RE.01.02 Read and interpret pictographs. ect and organize data to use in pictographs. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently read and interpret Usually read and interpret Sometimes read and interpret Rarely read and interpret pictographs and organize data pictographs and organize data pictographs and organize data pictographs and organize data to use pictographs. to use pictographs. to use pictographs. to use pictographs. Differentiation of Instruction Strand Mathematics Standard 5: Make pictographs to represent simple sets of data. Topic Pictographs Benchmark D.RE.01.03 Make pictographs of given data using both horizontal and vertical forms of graphs; scale Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently make pictographs of Usually make pictographs of Sometimes make pictographs of Rarely make pictographs of given data using both horizontal given data using both horizontal given data using both horizontal given data using both horizontal and vertical forms of graphs; scale and vertical forms of graphs; scale and vertical forms of graphs; scale and vertical forms of graphs; scale Differentiation of Instruction Strand Mathematics Standard 5: Make pictographs to represent simple sets of data. Topic Pictographs Benchmark G.SR.01.06 Describe ways to get to the next element in simple repeating patterns. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently describe ways to Usually describe ways to Sometimes describe ways to Rarely describe ways to get to the next element in get to the next element in get to the next element in get to the next element in simple repeating patterns. simple repeating patterns. simple repeating patterns. simple repeating patterns. Differentiation of Instruction Strand Mathematics Standard 5: Also in 1st Grade Topic Telling Time Benchmark M.UN.01.03 Tell time on a twelve-hour clock face to the hour and half-hour. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently tell time on a Usually tell time on a Sometimes tell time on a Rarely tell time on a twelve-hour clock face to the twelve-hour clock face to the twelve-hour clock face to the twelve-hour clock face to the hour and half-hour. hour and half-hour. hour and half-hour. hour and half-hour. Differentiation of Instruction Strand Mathematics Standard 5: Also in 1st Grade Topic Geometrical Shapes Benchmark G.GS.01.01 Create and describe common two- and three-dimensional shapes. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently create and describe Usually create and describe Sometimes create and describe Rarely create and describe common two-and-three common two-and-three common two-and-three common two-and-three dimensional shapes. dimensional shapes. dimensional shapes. dimensional shapes. Differentiation of Instruction Content Area: Math Grade/Course:2nd Strand Mathematics Standard 1: Express numbers through 999 using place value. Topic Ordering Numbers Benchmark N.ME.02.03 Compare and order numbers to 1000; use the symbols > and <. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently compare and order Usually compare and order Sometimes compare and order Consistently compare and order numbers to 1000; numbers to 1000; numbers to 1000; numbers to 1000; use the symbols > and <. use the symbols > and <. use the symbols > and <. use the symbols > and <. Differentiation of Instruction Strand Mathematics Standard 1: Express numbers through 999 using place value. Topic Reading and Writing Numbers Benchmark N.ME.02.02 Read and write numbers to 1000 in numerals and words, and relate them to the quantities they represent. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently read and write to Usually read and write to Sometimes read and write to Rarely read and write to 1000 in numerals and words, and 1000 in numerals and words, and 1000 in numerals and words, and 1000 in numerals and words, and relate them to the quantities they relate them to the quantities they relate them to the quantities they relate them to the quantities they represent. represent. represent. represent. Differentiation of Instruction Strand Mathematics Standard 1: Express numbers through 999 using place value. Topic Counting Benchmark N.ME.02.01 Count to 1000 by 1s, 10s and 100s starting from any number in the sequence. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently count to 1000 by Usually count to 1000 by Sometimes count to 1000 by Rarely count to 1000 by 1s, 10s and 100s starting from 1s, 10s and 100s starting from 1s, 10s and 100s starting from 1s, 10s and 100s starting from any number in the sequence. any number in the sequence. any number in the sequence. any number in the sequence. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 99 to solve problems, using strategies including formal algorithms. Topic Modeling Benchmark N.MR.02.09 Given a contextual situation that involves addition and subtraction for numbers through 99, model using objects or pictures, explain in words, record using numbers and symbols; solve Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently give a contextual Usually give a contextual Sometimes give a contextual Rarely give a contextual situation that involves addition and situation that involves addition and situation that involves addition and situation that involves addition and subtraction for numbers through 99, subtraction for numbers through 99, subtraction for numbers through 99, subtraction for numbers through 99, model using objects or pictures, model using objects or pictures, model using objects or pictures, model using objects or pictures, explain in words, record using explain in words, record using explain in words, record using explain in words, record using numbers and symbols; solve numbers and symbols; solve numbers and symbols; solve numbers and symbols; solve Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 99 to solve problems, using strategies including formal algorithms. Topic Adding and Subtracting Benchmark N.MR.02.10 Add fluently two numbers through 99, using strategies including formal algorithms; subtract fluently two numbers through 99. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently add fluently two Usually add fluently two Sometimes add fluently two Rarely add fluently two numbers through 99, using strategies numbers through 99, using strategies numbers through 99, using strategies numbers through 99, using strategies inckuding formal algorithms; inckuding formal algorithms; inckuding formal algorithms; inckuding formal algorithms; subtract fluently two numbers subtract fluently two numbers subtract fluently two numbers subtract fluently two numbers through 99. through 99. through 99. through 99. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 99 to solve problems, using strategies including formal algorithms. Topic Missing Numbers Benchmark N.MR.02.08 Find missing values in open sentences, e.g., 42 + _ = 57; use relationship between addition and subtraction. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find missing values Usually find missing values Sometimes find missing values Rarely find missing values in open sentences; use relationship in open sentences; use relationship in open sentences; use relationship in open sentences; use relationship between addition and subtraction. between addition and subtraction. between addition and subtraction. between addition and subtraction. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 99 to solve problems, using strategies including formal algorithms. Topic Estimate Benchmark N.MR.02.11 Estimate the sum of two numbers with three digits. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently estimate the sum Usually estimate the sum Sometimes estimate the sum Rarely estimate the sum of two numbers with three digits. of two numbers with three digits. of two numbers with three digits. of two numbers with three digits. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 99 to solve problems, using strategies including formal algorithms. Topic Mental Addition and Subtraction Benchmark N.MR.02.12 Calculate mentally sums and differences involving: three-digit numbers and ones; threedigit numbers and tens; three-digit numbers and hundreds. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently calculate mentally Usually calculate mentally Sometimes calculate mentally Rarely calculate mentally sums and differences involving sums and differences involving sums and differences involving sums and differences involving three-digit numbers and ones; three three-digit numbers and ones; three three-digit numbers and ones; three three-digit numbers and ones; three digit numbers and tens; three-digit digit numbers and tens; three-digit digit numbers and tens; three-digit digit numbers and tens; three-digit numbers and hundreds. numbers and hundreds. numbers and hundreds. numbers and hundreds. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 99 to solve problems, using strategies including formal algorithms. Measuring Topic Benchmark N.MR.02.10 M.UN.02.01 Measure lengths in meters, centimeters, inches, feet, and yards approximating to the nearest M.PS.02.02 whole unit using abbreviations: cm, m, in, ft, yd.; compare lengths; add and subtract lengths (no conversion of units). ; solve simple word problems involving length (and money). Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently measure lengths and Usually measure lengths and Sometimes measure lengths and Rarely measure lengths and approximate to the nearest whole approximate to the nearest whole approximate to the nearest whole approximate to the nearest whole unit using abbreviations: compare unit using abbreviations: compare unit using abbreviations: compare unit using abbreviations: compare lenghts; add and subtract lengths; lenghts; add and subtract lengths; lenghts; add and subtract lengths; lenghts; add and subtract lengths; solve simple word problems solve simple word problems solve simple word problems solve simple word problems involving length. involving length. involving length. involving length. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 99 to solve problems, using strategies including formal algorithms. Topic Distance Benchmark M.TE.02.11 Determine perimeters of rectangles and triangles by adding lengths of sides, recognizing the meaning of perimeter. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently determine perimeters Usually determine perimeters Sometimes determine perimeters Rarely determine perimeters of rectangles and triangles by of rectangles and triangles by of rectangles and triangles by of rectangles and triangles by adding lengths of sides, recognizing adding lengths of sides, recognizing adding lengths of sides, recognizing adding lengths of sides, recognizing the meaning of perimeter. the meaning of perimeter. the meaning of perimeter. the meaning of perimeter. Differentiation of Instruction Strand Mathematics Standard 2: Add and subtract fluently with numbers up to 99 to solve problems, using strategies including formal algorithms. Topic Addition Pairs Benchmark N.FL.02.06 Decompose 100 into addition pairs, e.g., 100 = 99 + 1 = 98 + 2... Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently decompose 100 Usually decompose 100 Sometimes decompose 100 Rarely decompose 100 into addition pairs. into addition pairs. into addition pairs. into addition pairs. Differentiation of Instruction Strand Mathematics Standard 3: Recognize simple multiplication and division situations up to 5x5, represent them with objects, words and symbols; solve using strategies. Topic Relating Multiplication to Addition Benchmark N.MR.02.13 Understand multiplication as the result of counting the total number of objects in a set of equal groups, e.g., 3 x 5 gives the number of objects in 3 groups of 5 objects, ie., 3 x 5 = 5 + 5 + 5 = 15. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand multiplication Usually understand multiplication Simetimes understand multiplication Rarely understand multiplication as the result of counting the total as the result of counting the total as the result of counting the total as the result of counting the total number of objects in a set of equal number of objects in a set of equal number of objects in a set of equal number of objects in a set of equal groups. groups. groups. groups. Differentiation of Instruction Strand Mathematics Standard 3: Recognize simple multiplication and division situations up to 5x5, represent them with objects, words and symbols; solve using strategies. Topic Multiplication Models Benchmark N.MR.02.14 Represent multiplication using area and array models. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently represent multiplication Usually represent multiplication Sometimes represent multiplication Rarely represent multiplication using area and array models. using area and array models. using area and array models. using area and array models. Differentiation of Instruction Strand Mathematics Standard 3: Recognize simple multiplication and division situations up to 5x5, represent them with objects, words and symbols; solve using strategies. Topic Fact Families Benchmark N.MR.02.15 Understand division (÷) as another way of expressing multiplication, using fact families within the 5 x 5 multiplication table; emphasize that division “undoes” multiplication, e.g., 2 x 3 = 6 can be rewritten as 6 ÷ 2 = 3 or 6 ÷ 3 = 2. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand division Usually understand division Sometimes understand division Rarely understand division as another way of expressing as another way of expressing as another way of expressing as another way of expressing multiplication, using fact families. multiplication, using fact families. multiplication, using fact families. multiplication, using fact families. Differentiation of Instruction Strand Mathematics Standard 3: Recognize simple multiplication and division situations up to 5x5, represent them with objects, words and symbols; solve using strategies. Topic Equal Sharing Benchmark N.MR.02.16 Given a situation involving groups of equal size or of sharing equally, represent with objects, words, and symbols; solve. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently able to represent Usually able to represent Sometimes able to represent Rarely able to represent with objects, words, and symbols with objects, words, and symbols with objects, words, and symbols with objects, words, and symbols a given situation involving groups a given situation involving groups a given situation involving groups a given situation involving groups of equal size or of sharing equally. of equal size or of sharing equally. of equal size or of sharing equally. of equal size or of sharing equally. Differentiation of Instruction Strand Mathematics Standard 3: Recognize simple multiplication and division situations up to 5x5, represent them with objects, words and symbols; solve using strategies. Topic Multiplying Benchmark N.MR.02.17 Develop strategies for fluently multiplying numbers up to 5 x 5. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently develop strategies Usually develop strategies Sometimes develop strategies Rarely develop strategies for fluently multiplying numbers for fluently multiplying numbers for fluently multiplying numbers for fluently multiplying numbers up to 5x5. up to 5x5. up to 5x5. up to 5x5. Differentiation of Instruction Strand Mathematics Standard 3: Recognize simple multiplication and division situations up to 5x5, represent them with objects, words and symbols; solve using strategies. Topic Area of Rectangle Benchmark N.MR.02.17 Find the area of a rectangle with whole number side lengths by covering with unit squares and counting, or by using a grid of unit squares; write the area as a product. Measure area using non-standard units to the nearest whole unit. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find the area of a Usually find the area of a Sometimes find the area of a Rarely find the area of a rectangle with whole number side rectangle with whole number side rectangle with whole number side rectangle with whole number side lengths by covering with unit squares lengths by covering with unit squares lengths by covering with unit squares lengths by covering with unit squares and counting, or by using a grid of and counting, or by using a grid of and counting, or by using a grid of and counting, or by using a grid of unit squares; write the area as a unit squares; write the area as a unit squares; write the area as a unit squares; write the area as a product. product. product. product. Differentiation of Instruction Strand Mathematics Standard 4: Recognize, name, and write commonly used fractions: 1/2, 1/3, 2/3, 1/4, 2/4, 3/4. Topic Recognizing Fractions Benchmark N.ME.02.18 Recognize, name, and represent commonly used unit fractions with denominators 12 or less; model 1/2, 1/3, and 1/4 by folding strips. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently recognize, name Usually recognize, name Sometimes recognize, name Rarely recognize, name and represent commonly used and represent commonly used and represent commonly used and represent commonly used fractions with denominators 12 or fractions with denominators 12 or fractions with denominators 12 or fractions with denominators 12 or less; model 1/2, 1/3, and 1/4 by less; model 1/2, 1/3, and 1/4 by less; model 1/2, 1/3, and 1/4 by less; model 1/2, 1/3, and 1/4 by folding strips. folding strips. folding strips. folding strips. Differentiation of Instruction Strand Mathematics Standard 4: Recognize, name, and write commonly used fractions: 1/2, 1/3, 2/3, 1/4, 2/4, 3/4. Topic Recognizing Halves Benchmark N.ME.02.20 Place 0 and halves, e.g., ½, 1 ½, 2 ½, on the number line; relate to a ruler. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently place 0 and halves Usually place 0 and halves Sometimes place 0 and halves Rarely place 0 and halves on the number line; related to a on the number line; related to a on the number line; related to a on the number line; related to a ruler. ruler. ruler. ruler. Differentiation of Instruction Strand Mathematics Standard 4: Recognize, name, and write commonly used fractions: 1/2, 1/3, 2/3, 1/4, 2/4, 3/4. Topic Inverse Relationships Benchmark N.ME.02.21 For unit fractions from 1/12 to 1/2, understand the inverse relationship between the size of the denominator; compare unit fractions from 1/12 to 1/2. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand the Usually understand the Sometimes understand the Rarely understand the inverse relationship between the inverse relationship between the inverse relationship between the inverse relationship between the size of the denominator for unit size of the denominator for unit size of the denominator for unit size of the denominator for unit fractions from 1/12 to 1/2. fractions from 1/12 to 1/2. fractions from 1/12 to 1/2. fractions from 1/12 to 1/2. Compare unit fractions from Compare unit fractions from Compare unit fractions from Compare unit fractions from 1/12 to 1/2. 1/12 to 1/2. 1/12 to 1/2. 1/12 to 1/2. Differentiation of Instruction Strand Mathematics Standard 4: Recognize, name, and write commonly used fractions: 1/2, 1/3, 2/3, 1/4, 2/4, 3/4. Topic Fractions as a Whole (1) Benchmark N.ME.02.22 Recognize that fractions such as 2/2, 3/3 and 4/4 are equal to the whole (one). Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently recognize that Usually recognize that Sometimes recognize that Rarely recognize that fractions such as 2/2 are equal fractions such as 2/2 are equal fractions such as 2/2 are equal fractions such as 2/2 are equal to the whole (1). to the whole (1). to the whole (1). to the whole (1). Differentiation of Instruction Strand Mathematics Standard 5: Add and subtract money in mixed units, e.g., $2.50 + 60 cents and $5.75 - $3, but not $2.50 + $3.10. Topic Money Benchmark M.UN.02.07 Read and write amounts of money using decimal notations, e.g., $1.15. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently read and write Usually read and write Sometimes read and write Rarely read and write amounts of money using decimal amounts of money using decimal amounts of money using decimal amounts of money using decimal notations. notations. notations. notations. Differentiation of Instruction Strand Mathematics Standard 5: Add and subtract money in mixed units, e.g., $2.50 + 60 cents and $5.75 - $3, but not $2.50 + $3.10. Topic Money Benchmark M.UN.02.10 Solve simple word problems involving (length and) money. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve simple word Usually solve simple word Sometimes solve simple word Rarely solve simple word problems involving length and problems involving length and problems involving length and problems involving length and money. money. money. money. Differentiation of Instruction Strand Mathematics Standard 6: Tell and write time from the clock face in 5 minute intervals and from digital clocks to the minute. Topic Time Benchmark M.UN.02.05 Using both A.M. and P.M., tell and write time from the clock face in 5 minute intervals and from digital; include reading time: “9:15” as “nine-fifteen” and “9:50” as nine-fifty interpret time both as minutes after the hour and minutes before the next hour, e.g., 8:50 as eight-fifty and ten to nine. Show times by drawing hands on clock face. Sample Performance Assessment (SPA) Rubric Advanced Partially Proficient Novice Consistently using both A.M. and P.M., Usually using both A.M. and P.M., Sometimes using both A.M. and P.M., Rarely using both A.M. and P.M., tell and write time from the clock face tell and write time from the clock face tell and write time from the clock face tell and write time from the clock face in 5 minute intervals; include reading in 5 minute intervals; include reading in 5 minute intervals; include reading in 5 minute intervals; include reading time: “9:15” as “nine-fifteen”; time: “9:15” as “nine-fifteen”; time: “9:15” as “nine-fifteen”; time: “9:15” as “nine-fifteen”; interpret time both as minutes after interpret time both as minutes after interpret time both as minutes after interpret time both as minutes after the hour and minutes before the hour. the hour and minutes before the hour. the hour and minutes before the hour. the hour and minutes before the hour. Differentiation of Instruction Proficient Strand Mathematics Standard 6: Tell and write time from the clock face in 5 minute intervals and from digital clocks to the minute. Topic Time Benchmark M.UN.02.06 Use the concept of duration of time, e.g., determine what time it will be half an hour from 10:15. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently use the concept of Usually use the concept of Sometimes use the concept of Rarely use the concept of duration of time. duration of time. duration of time. duration of time. e.g., determine what time it will e.g., determine what time it will e.g., determine what time it will e.g., determine what time it will be half an hour from 10:15. be half an hour from 10:15. be half an hour from 10:15. be half an hour from 10:15. Differentiation of Instruction Strand Mathematics Standard 7: Describe and construct various two- and three-dimensional geometric shapes Topic Geometric Shapes Benchmark G.GS.02.04 Distinguish between curves and straight lines and between curved surfaces and flat surfaces. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently distnguish between Usually distnguish between Sometimes distnguish between Rarely distnguish between curves and straight lines and curves and straight lines and curves and straight lines and curves and straight lines and between curved surface and between curved surface and between curved surface and between curved surface and flat surfaces. flat surfaces. flat surfaces. flat surfaces. Differentiation of Instruction Strand Mathematics Standard 7: Describe and construct various two- and three-dimensional geometric shapes Topic Geometric Shapes Benchmark G.SR.02.05 Classify familiar plane and solid objects, e.g., square, rectangle, rhombus, cube, pyramid, prism, cone, cylinder, and sphere, by common attributes such as shape, size, color, roundness, or number of corners and explain which attributes are being used for classification. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently classify familiar Usually classify familiar Sometimes classify familiar Rarely classify familiar plane and solid objects by common plane and solid objects by common plane and solid objects by common plane and solid objects by common attributes such as shape, size, color attributes such as shape, size, color attributes such as shape, size, color attributes such as shape, size, color roundness, or number of corners and roundness, or number of corners and roundness, or number of corners and roundness, or number of corners and explain which attributes are being explain which attributes are being explain which attributes are being explain which attributes are being used for classification. used for classification. used for classification. used for classification. Differentiation of Instruction Strand Mathematics Standard 7: Describe and construct various two- and three-dimensional geometric shapes Topic Geometric Shapes Benchmark G.SR.02.05 Recognize that shapes that have been slid, turned or flipped are the same shape, e.g., a square rotated 45° is still a square. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently recognize that Usually recognize that Sometimes recognize that Rarely recognize that shapes that have been slid, turned or shapes that have been slid, turned or shapes that have been slid, turned or shapes that have been slid, turned or flipped are the same shape. flipped are the same shape. flipped are the same shape. flipped are the same shape. Content Area: Math Grade/Course:3rd Strand Mathematics Standard 1: Fluently add and subtract whole numbers up to 999 with regrouping and up to 9999 without regrouping. Topic Ordering Numbers Benchmark N.ME.03.01, N.ME.03.03 Read, write, compare and order numbers to 10,000 in both numerals and words, and relate them to the quantities they represent, e.g., relate numeral or written word to a display of dots or objects. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently read, write, compare Usually read, write, compare Sometimes read, write, compare Rarely read, write, compare and order numbers to 10,000 in both and order numbers to 10,000 in both and order numbers to 10,000 in both and order numbers to 10,000 in both numerals and words, and relate them numerals and words, and relate them numerals and words, and relate them numerals and words, and relate them to the quantities they represent. to the quantities they represent. to the quantities they represent. to the quantities they represent. Differentiation of Instruction Strand Mathematics Standard 1: Fluently add and subtract whole numbers up to 999 with regrouping and up to 9999 without regrouping. Topic Mental Math Benchmark N.FL.03.08 Use mental strategies to fluently add and subtract two-digit numbers. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently use mental strategies Usually use mental strategies Sometimes use mental strategies Rarely use mental strategies to fluently add and subtract two- to fluently add and subtract two- to fluently add and subtract two- to fluently add and subtract two- digit numbers. digit numbers. digit numbers. digit numbers. Differentiation of Instruction Strand Mathematics Standard 1: Fluently add and subtract whole numbers up to 999 with regrouping and up to 9999 without regrouping. Topic Place Values Benchmark N.ME.03.02 Identify the place value of a digit in a number, e.g., in 3,241, 2 is in the hundreds place. Recognize and use expanded notation for numbers using place value through 9,999, e.g., 2,517 is 2000+ 500+10+ 7; 4 hundreds and 2 ones is 402. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify the place Usually identify the place Sometimes identify the place Rarely identify the place value of a digit in a number. value of a digit in a number. value of a digit in a number. value of a digit in a number. Recognize and use expanded Recognize and use expanded Recognize and use expanded Recognize and use expanded notation for numbers using place notation for numbers using place notation for numbers using place notation for numbers using place value through 9,999. value through 9,999. value through 9,999. value through 9,999. Differentiation of Instruction Strand Mathematics Standard 1: Fluently add and subtract whole numbers up to 999 with regrouping and up to 9999 without regrouping. Topic Estimating Benchmark N.FL.03.07 Estimate the sum and difference of two numbers with three digits (sums up to 1,000), and judge reasonableness of estimates. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently estimate the sum and Usually estimate the sum and Sometimes estimate the sum and Rarely estimate the sum and difference of two number with three difference of two number with three difference of two number with three difference of two number with three digits and judge reasonableness digits and judge reasonableness digits and judge reasonableness digits and judge reasonableness of estimates. of estimates. of estimates. of estimates. Differentiation of Instruction Strand Mathematics Standard 2: Multiply fluently up to 10x10 and use related quotients to solve problems. Topic Recognizing Use of Multiplication Benchmark N.MR.03.10 Recognize situations that can be solved using multiplication and write mathematical statements to represent those situations. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently recognize situations Usually recognize situations Sometimes recognize situations Rarely recognize situations that can be solved using that can be solved using that can be solved using that can be solved using multiplication and write mathematical multiplication and write mathematical multiplication and write mathematical multiplication and write mathematical statements to represent those statements to represent those statements to represent those statements to represent those situations. situations. situations. situations. Differentiation of Instruction Strand Mathematics Standard 2: Multiply fluently up to 10x10 and use related quotients to solve problems. Topic Fact Families Benchmark N.MR.03.09 Use multiplication and division fact families to understand the inverse relationship of these two operations; e.g., because 3 x 8 = 24, we know that 24 ÷ 8 = 3 or 24 ÷ 3 = 8. Express a multiplication statement as an equivalent division statement. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently use multiplication and Usually use multiplication and Sometimes use multiplication and Rarely use multiplication and division fact families to understand division fact families to understand division fact families to understand division fact families to understand the inverse relationship these two the inverse relationship these two the inverse relationship these two the inverse relationship these two operations. operations. operations. operations. Differentiation of Instruction Strand Mathematics Standard 2: Multiply fluently up to 10x10 and use related quotients to solve problems. Topic Repetetive Counting Benchmark N.ME.03.04 Count orally by 6s, 7s, 8s and 9s starting with 0, making the connection between repeated addition and multiplication. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently count makes orally the by Usually count makes orally by the Sometimes count makes orally theby Rarely count orally makesbythe connection between repeated connection between repeated connection between repeated connection between repeated addition and multiplication by counting addition and multiplication by counting addition and multiplication by counting addition and multiplication by counting orally by 6s, 7s, 8s and 9s orally by 6s, 7s, 8s and 9s orally by 6s, 7s, 8s and 9s orally by 6s, 7s, 8s and 9s starting with 0. starting with 0. starting with 0. starting with 0. Differentiation of Instruction Strand Mathematics Standard 2: Multiply fluently up to 10x10 and use related quotients to solve problems. Topic Open ended sentences Benchmark N.MR.03.12 Find solutions to open sentences such as 7 x ? = 42 or 12 ÷ ? = 4, using the inverse relationship between multiplication and division. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find solutions to open Usually find solutions to open Sometimes find solutions to open Rarely find solutions to open sentences such as 7 x ? = 42, sentences such as 7 x ? = 42, sentences such as 7 x ? = 42, sentences such as 7 x ? = 42, using the inverse relationship using the inverse relationship using the inverse relationship using the inverse relationship between multiplication and division. between multiplication and division. between multiplication and division. between multiplication and division. Differentiation of Instruction Strand Mathematics Standard 2: Multiply fluently up to 10x10 and use related quotients to solve problems. Topic Odd and Even Numbers Benchmark N.ME.03.05 Understand even numbers as divisible by two, odd numbers as not. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand even Usually understand even Sometimes understand even Rarely understand even numbers as divisible by two, odd numbers as divisible by two, odd numbers as divisible by two, odd numbers as divisible by two, odd numbers are not. numbers are not. numbers are not. numbers are not. Differentiation of Instruction Strand Mathematics Standard 2: Multiply fluently up to 10x10 and use related quotients to solve problems. Topic Mental Math Benchmark N.FL.03.13 Mentally calculate simple products and quotients up to a three-digit number by a one digit number involving multiples of 10, e.g., 500 x 6, or 400 ÷ 8. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently use mental skills to Usually use mental skills to Sometimes use mental skills to Rarely use mental skills to calculate simple products and calculate simple products and calculate simple products and calculate simple products and quotients up to three-digit number quotients up to three-digit number quotients up to three-digit number quotients up to three-digit number by a one digit number involving by a one digit number involving by a one digit number involving by a one digit number involving multioples of 10. multioples of 10. multioples of 10. multioples of 10. Differentiation of Instruction Strand Mathematics Standard 2: Multiply fluently up to 10x10 and use related quotients to solve problems. Topic Story Problems Benchmark N.FL.03.15 Given problems that use any one of the four operations with appropriate numbers, represent with objects, words (including “product” and “quotient”), and mathematical statements, and solve. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently able to represent and Usually able to represent and Sometimes able to represent and Rarely able to represent and objects, words and mathematical objects, words and mathematical objects, words and mathematical objects, words and mathematical statements, problems that use' statements, problems that use' statements, problems that use' statements, problems that use' any of the four operations with any of the four operations with any of the four operations with any of the four operations with appropriate numbers. appropriate numbers. appropriate numbers. appropriate numbers. Differentiation of Instruction Strand Mathematics Standard 3: Solve and interpret division problems involving remainders. Topic Division Benchmark N.MR.03.10 Recognize situations that can be solved using division including finding “How many groups?” and “How many in a group?” and write mathematical statements to represent those situations. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently recognize situations Usually recognize situations Sometimes recognize situations Rarely recognize situations that can be solved using division and that can be solved using division and that can be solved using division and that can be solved using division and write mathematical statements to write mathematical statements to write mathematical statements to write mathematical statements to represent those situations. represent those situations. represent those situations. represent those situations. Differentiation of Instruction Strand Mathematics Standard 4: Find equivalent fractions with denominators 2, 4, and 8; place fractions on the number line. Topic Fractions Benchmark N.ME.03.16 Understand that fractions may represent a portion of a whole unit that has been partitioned into parts of equal area or length; use the terms “numerator” and “denominator.” Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand that Usually understand that Sometimes understand that Rarely understand that fractions may represent a portion of fractions may represent a portion of fractions may represent a portion of fractions may represent a portion of a whole unit that has been a whole unit that has been a whole unit that has been a whole unit that has been partitioned into parts of equal area partitioned into parts of equal area partitioned into parts of equal area partitioned into parts of equal area or length; use terms "numerator" or length; use terms "numerator" or length; use terms "numerator" or length; use terms "numerator" and "denominator". and "denominator". and "denominator". and "denominator". Differentiation of Instruction Strand Mathematics Standard 4: Find equivalent fractions with denominators 2, 4, and 8; place fractions on the number line. Topic Equivalent Fractions Benchmark N.ME.03.17 Recognize, name and use equivalent fractions with denominators 2, 4, and 8, using strips, circle fraction pieces, and number lines. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently recognize, name and Usually recognize, name and Sometimes recognize, name and Rarely recognize, name and use equivalent fractions with use equivalent fractions with use equivalent fractions with use equivalent fractions with denominators 2,4, and 8, using strips denominators 2,4, and 8, using strips denominators 2,4, and 8, using strips denominators 2,4, and 8, using strips circles fraction pieces, and circles fraction pieces, and circles fraction pieces, and circles fraction pieces, and number lines. number lines. number lines. number lines. Differentiation of Instruction Strand Mathematics Standard 4: Find equivalent fractions with denominators 2, 4, and 8; place fractions on the number line. Topic Comparing Fractions Benchmark N.ME.03.17 Place fractions with denominators of 2, 4, and 8 on the number line; relate the number line to a ruler; compare and order up to three fractions with denominators 2, 4, and 8. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently able to place fractions Usually able to place fractions Sometimes able to place fractions Rarely able to place fractions with denominators of 2, 4, and 8 on with denominators of 2, 4, and 8 on with denominators of 2, 4, and 8 on with denominators of 2, 4, and 8 on the number line; relate the number the number line; relate the number the number line; relate the number the number line; relate the number line to a ruler; compare and order up line to a ruler; compare and order up line to a ruler; compare and order up line to a ruler; compare and order up to three fractions with denominators to three fractions with denominators to three fractions with denominators to three fractions with denominators 2,4, and 8. 2,4, and 8. 2,4, and 8. 2,4, and 8. Differentiation of Instruction Strand Mathematics Standard 5: Add and subtract fractions with like denominators. Topic Adding Fractions Benchmark N.ME.03.19 Understand that any fraction can be written as a sum of unit fractions. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand that any Usually understand that any Sometimes understand that any Rarely understand that any fraction can be written as a sum fraction can be written as a sum fraction can be written as a sum fraction can be written as a sum of unit fractions. of unit fractions. of unit fractions. of unit fractions. Differentiation of Instruction Strand Mathematics Standard 5: Add and subtract fractions with like denominators. Topic Modeling Fractions Benchmark N.ME.03.20 Recognize that addition and subtraction of fractions with equal denominators can be modeled by adjoining or taking away segments on the number line. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently recognizes that addition Usually recognizes that addition Sometimes recognizes that addition Rarely recognizes that addition and subtraction of fractions with and subtraction of fractions with and subtraction of fractions with and subtraction of fractions with equal denominators can be modeled' equal denominators can be modeled' equal denominators can be modeled' equal denominators can be modeled' by adjoining or taking away segments by adjoining or taking away segments by adjoining or taking away segments by adjoining or taking away segments on the number line. on the number line. on the number line. on the number line. Differentiation of Instruction Strand Mathematics Standard 6: Know and use common units of measurements in length, weight, time; solve problems involving money. Topic Measurement Benchmark M.UN.03.02 Measure in mixed units within the same measurement system for length, weight and time: feet and inches, meters and centimeters, kilograms and grams, pounds and ounces, liters and milliliters, hours and minutes, minutes and seconds, years and months. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently measure in mixed Usually measure in mixed Sometimes measure in mixed Rarely measure in mixed units within the same measurement units within the same measurement units within the same measurement units within the same measurement system for length, weight and time. system for length, weight and time. system for length, weight and time. system for length, weight and time. Differentiation of Instruction Strand Mathematics Standard 6: Know and use common units of measurements in length, weight, time; solve problems involving money. Topic Relationships between Measurement Benchmark M.UN.03.03 Understand relationships between sizes of standard units, e.g., feet and inches, meters and centimeters. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand the Usually understand the Sometimes understand the Rarely understand the relationship between sizes of relationship between sizes of relationship between sizes of relationship between sizes of standard measurement; feet and standard measurement; feet and standard measurement; feet and standard measurement; feet and inches, etc. inches, etc. inches, etc. inches, etc. Differentiation of Instruction Strand Mathematics Standard 6: Know and use common units of measurements in length, weight, time; solve problems involving money. Topic Benchmark Temperature Benchmark M.UN.03.04 Know benchmark temperatures such as freezing, 32ºF, 0ºC; boiling, 212ºF, 100ºC; and compare temperatures to these, e.g., cooler, warmer. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently know benchmark Usually know benchmark Sometimes know benchmark Rarely know benchmark temperature such as freezing, boiling temperature such as freezing, boiling temperature such as freezing, boiling temperature such as freezing, boiling and compare temperatures using and compare temperatures using and compare temperatures using and compare temperatures using cooler, warmer, etc. cooler, warmer, etc. cooler, warmer, etc. cooler, warmer, etc. Differentiation of Instruction Strand Mathematics Standard 6: Know and use common units of measurements in length, weight, time; solve problems involving money. Topic Adding and Subtracting Units Benchmark M.PS.03.10 Add and subtract lengths, weights and times using mixed units within the same measurement system. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently add and subtract Usually add and subtract Sometimes add and subtract Rarely add and subtract lengths, weights and times using lengths, weights and times using lengths, weights and times using lengths, weights and times using mixed units within the same mixed units within the same mixed units within the same mixed units within the same measurement system. measurement system. measurement system. measurement system. Differentiation of Instruction Strand Mathematics Standard 6: Know and use common units of measurements in length, weight, time; solve problems involving money. Topic Relate Decimal to Dollar Benchmark N.ME.03.21 Relate decimal fractions to fractional parts of a dollar (¼ of a $1 = $0.25). Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently relate decimal Usually relate decimal Sometimes relate decimal Rarely relate decimal fractions to fractional parts of a fractions to fractional parts of a fractions to fractional parts of a fractions to fractional parts of a dollar. dollar. dollar. dollar. Differentiation of Instruction Strand Mathematics Standard 6: Know and use common units of measurements in length, weight, time; solve problems involving money. Topic Money Benchmark M.PS.03.11 Add and subtract money in dollars and cents. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently add and subtract Usually add and subtract Sometimes add and subtract Rarely add and subtract money in dollars and cents. money in dollars and cents. money in dollars and cents. money in dollars and cents. Differentiation of Instruction Strand Mathematics Standard 6: Know and use common units of measurements in length, weight, time; solve problems involving money. Topic Solving Problems Benchmark M.PS.03.12 Solve applied problems involving money, length and time. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve applied Usually solve applied Sometimes solve applied Rarely solve applied problems involving money, length problems involving money, length problems involving money, length problems involving money, length and time. and time. and time. and time. Differentiation of Instruction Strand Mathematics Standard 7: Solve applied problems involving the perimeter and area of squares and rectangular regions. Topic Defining Area and Perimeter Benchmark M.UN.03.05 Know the definition of area and perimeter and calculate the perimeter of a square and rectangle given whole number side lengths. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently know the definition Usually know the definition Sometimes know the definition Rarely know the definition of area and perimeter and can of area and perimeter and can of area and perimeter and can of area and perimeter and can calculate the perimeter of a square calculate the perimeter of a square calculate the perimeter of a square calculate the perimeter of a square and rectangle with whole numbers and rectangle with whole numbers and rectangle with whole numbers and rectangle with whole numbers as lengths. as lengths. as lengths. as lengths. Differentiation of Instruction Strand Mathematics Standard 7: Solve applied problems involving the perimeter and area of squares and rectangular regions. Topic Calculating Area Benchmark M.UN.03.06 Use square units in calculating area by covering the region and counting the number of square units. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently use square units Usually use square units Sometimes use square units Rarely use square units in calculating area by covering the in calculating area by covering the in calculating area by covering the in calculating area by covering the area and counting the number of area and counting the number of area and counting the number of area and counting the number of squares. squares. squares. squares. Differentiation of Instruction Strand Mathematics Standard 7: Solve applied problems involving the perimeter and area of squares and rectangular regions. Topic Distinguish between units Benchmark M.UN.03.07 Distinguish between units of length and area and choose a unit appropriate in the context. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently distinguish between Usually distinguish between Sometimes distinguish between Rarely distinguish between units of length and area units of length and area units of length and area units of length and area and choose a unit appropriate and choose a unit appropriate and choose a unit appropriate and choose a unit appropriate in the context. in the context. in the context. in the context. Differentiation of Instruction Strand Mathematics Standard 7: Solve applied problems involving the perimeter and area of squares and rectangular regions. Topic Compare sizes Benchmark M.UN.03.08 Visualize and describe the relative sizes of one square inch and one square centimeter. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently visualize and describe Usually visualize and describe Sometimes visualize and describe Rarely visualize and describe the relative sizes of one square the relative sizes of one square the relative sizes of one square the relative sizes of one square inch and one square centimeter. inch and one square centimeter. inch and one square centimeter. inch and one square centimeter. Differentiation of Instruction Strand Mathematics Standard 7: Solve applied problems involving the perimeter and area of squares and rectangular regions. Topic Estimate Perimeter and Area Benchmark M.TE.03.09 Estimate the perimeter of a square and rectangle in inches and centimeters; estimate the area of a square and rectangle in square inches and square centimeters. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently estimate the Usually estimate the Sometimes estimate the Rarely estimate the area and perimeter of a rectangle area and perimeter of a rectangle area and perimeter of a rectangle area and perimeter of a rectangle and square in inches and and square in inches and and square in inches and and square in inches and centimeters. centimeters. centimeters. centimeters. Differentiation of Instruction Strand Mathematics Standard 7: Solve applied problems involving the perimeter and area of squares and rectangular regions. Topic Problem Solving Benchmark M.PS.03.13 Solve contextual problems about perimeters of rectangles and areas of rectangular regions. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve contextual Usually solve contextual Sometimes solve contextual Rarely solve contextual problems about perimeters of problems about perimeters of problems about perimeters of problems about perimeters of rectangles and areas of rectangular rectangles and areas of rectangular rectangles and areas of rectangular rectangles and areas of rectangular regions. regions. regions. regions. Differentiation of Instruction Strand Mathematics Standard 8: Describe and classify two- and three-dimensional shapes. Topic Geometric Terms Benchmark G.GS.03.01 Identify points, line segments, lines and distance. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify points, Usually identify points, Sometimes identify points, Rarely identify points, line segments, lines and distances. line segments, lines and distances. line segments, lines and distances. line segments, lines and distances. Differentiation of Instruction Strand Mathematics Standard 8: Describe and classify two- and three-dimensional shapes. Topic Geometric Terms Benchmark G.GS.03.02 Identify perpendicular lines and parallel lines in familiar shapes and in the classroom. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify perpendicular Usually identify perpendicular Sometimes identify perpendicular Rarely identify perpendicular lines and parallel lines in familiar lines and parallel lines in familiar lines and parallel lines in familiar lines and parallel lines in familiar shapes and in the classroom. shapes and in the classroom. shapes and in the classroom. shapes and in the classroom. Differentiation of Instruction Strand Mathematics Standard 8: Describe and classify two- and three-dimensional shapes. Topic Geometric Shapes Benchmark G.GS.02.01, G.GS.02.02, Describe, construct and transform various geometric shapes G.GS.02.04, G.SR.02.05 Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently describe, construct Usually describe, construct Sometimes describe, construct Rarely describe, construct and transform various geometric and transform various geometric and transform various geometric and transform various geometric shape. shape. shape. shape. Differentiation of Instruction Strand Mathematics Standard 8: Describe and classify two- and three-dimensional shapes. Topic Two dimensional Shapes Benchmark G.GS.03.04 Identify, describe, compare and classify two-dimensional shapes, e.g., parallelogram, trapezoid, circle, rectangle, square and rhombus, based on their component parts (angles, sides, vertices, line segment) and the number of sides and vertices. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify, describe Usually identify, describe Sometimes identify, describe Rarely identify, describe compare and classify two- compare and classify two- compare and classify two- compare and classify two- dimensional shapes based on their dimensional shapes based on their dimensional shapes based on their dimensional shapes based on their component parts and the number component parts and the number component parts and the number component parts and the number of sides and vertices. of sides and vertices. of sides and vertices. of sides and vertices. Differentiation of Instruction Strand Mathematics Standard 8: Describe and classify two- and three-dimensional shapes. Topic Two dimensional Shapes Benchmark G.GS.03.05 Compose and decompose triangles and rectangles to form other familiar two-dimensional shapes, e.g., form a rectangle using two congruent right triangles, or decompose a parallelogram into a rectangle and two right triangles. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently compose and Usually compose and Sometimes compose and Rarely compose and decompose triangles and rectangles decompose triangles and rectangles decompose triangles and rectangles decompose triangles and rectangles to form other familiar two-dimensional to form other familiar two-dimensional to form other familiar two-dimensional to form other familiar two-dimensional shapes. shapes. shapes. shapes. Differentiation of Instruction Strand Mathematics Standard 8: Describe and classify two- and three-dimensional shapes. Topic Three dimensional Shapes Benchmark G.GS.03.06 Identify, describe, build and classify familiar three-dimensional solids, e.g., cube, rectangular prism, sphere, pyramid, cone, based on their component parts (faces, surfaces, bases, edges, vertices). Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify, describe Usually identify, describe Sometimes identify, describe Rarely identify, describe build and classify familiar three- build and classify familiar three- build and classify familiar three- build and classify familiar three- dimensional solids. dimensional solids. dimensional solids. dimensional solids. Differentiation of Instruction Strand Mathematics Standard 8: Describe and classify two- and three-dimensional shapes. Topic Geometric Shapes Benchmark G.GS.03.07 Represent front, top, and side views of solids built with cubes. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently represent front, Usually represent front, Sometimes represent front, Rarely represent front, top, and views of solids built top, and views of solids built top, and views of solids built top, and views of solids built with cubes. with cubes. with cubes. with cubes. Differentiation of Instruction Content Area: Math Grade/Course:4th Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Ordering Numbers Benchmark N.ME.04.01 Read and write numbers to 1,000,000; relate them to the quantities they represent; compare and order. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently read, write, compare Usually read, write, compare Sometimes read, write, compare Rarely read, write, compare and order numbers to 100,000. and order numbers to 100,000. and order numbers to 100,000. and order numbers to 100,000. Differentiation of Instruction Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Place Value Benchmark N.ME.04.02 Compose and decompose numbers using place value to 1,000,000s, e.g., 25,068 is 2 ten thousands, 5 thousands, 0 hundreds, 6 tens, and 8 ones. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently compose and decompose Usually compose and decompose Sometimes compose and decompose Rarely compose and decompose numbers using placr value to numbers using placr value to numbers using placr value to numbers using placr value to 1, 000,000's. 1, 000,000's. 1, 000,000's. 1, 000,000's. Differentiation of Instruction Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Place Values Benchmark N.ME.04.03 Understand the magnitude of numbers up to 1,000,000; recognize the place values of numbers, and the relationship of each place value to the place to its right, e.g., 1,000 is 10 hundreds. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand numbers Usually understand numbers Sometimes understand numbers Rarely understand numbers up to 1,000,000; recognize the up to 1,000,000; recognize the up to 1,000,000; recognize the up to 1,000,000; recognize the place value and the relationship of place value and the relationship of place value and the relationship of place value and the relationship of each place value to the place to its each place value to the place to its each place value to the place to its each place value to the place to its right. right. right. right. Differentiation of Instruction Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Multiples Benchmark N.ME.04.05 List the first ten multiples of a given one-digit whole number; determine if a whole number is a multiple of a given one-digit whole number. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently list the first ten Usually list the first ten Sometimes list the first ten Rarely list the first ten multiples of a given one-digit multiples of a given one-digit multiples of a given one-digit multiples of a given one-digit number; determine if a whole number number; determine if a whole number number; determine if a whole number number; determine if a whole number is a multiple of a given one-digit is a multiple of a given one-digit is a multiple of a given one-digit is a multiple of a given one-digit number. number. number. number. Differentiation of Instruction Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Factors Benchmark N.ME.04.04 Find all factors of any whole number through 50, list factor pairs, and determine if a onedigit number is a factor of a given whole number. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find all factors Usually find all factors Sometimes find all factors Rarely find all factors of any whole numbers through 50, of any whole numbers through 50, of any whole numbers through 50, of any whole numbers through 50, list factor pairs, and determine if list factor pairs, and determine if list factor pairs, and determine if list factor pairs, and determine if a one-digir number is a factor of a a one-digir number is a factor of a a one-digir number is a factor of a a one-digir number is a factor of a given whole number. given whole number. given whole number. given whole number. Differentiation of Instruction Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Prime Numbers Benchmark N.ME.04.6 Know that some numbers including 2, 3, 5, 7, and 11 have exactly two factors (1 and the number itself) and are called prime numbers. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently know that some Usually know that some Sometimes know that some Rarely know that some numbers have exactly two factors numbers have exactly two factors numbers have exactly two factors numbers have exactly two factors and referred to them as prime and referred to them as prime and referred to them as prime and referred to them as prime numbers. numbers. numbers. numbers. Differentiation of Instruction Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Multiples and Factors Benchmark N.ME.04.07 Use factors and multiples to compose and decompose whole numbers Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently use factors and Usually use factors and Sometimes use factors and Rarely use factors and multiples to compose and multiples to compose and multiples to compose and multiples to compose and decompose whole numbers. decompose whole numbers. decompose whole numbers. decompose whole numbers. Differentiation of Instruction Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Distributive Property Benchmark N.ME.04.09 Multiply two-digit numbers by 2, 3, 4, and 5, using the distributive property, e.g., 21 x 3 = (1 + 20) x 3 = (1 x 3) + (20 x 3) = 3 + 60 = 63. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently multiply two-digit Usually multiply two-digit Sometimes multiply two-digit Rarely multiply two-digit numbers by 2, 3, 4, and 5 using numbers by 2, 3, 4, and 5 using numbers by 2, 3, 4, and 5 using numbers by 2, 3, 4, and 5 using distributive property. distributive property. distributive property. distributive property. Differentiation of Instruction Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Multiplication (Distributive Property) Benchmark N.FL.04.10 Multiply fluently any whole number by a one-digit number, and a three-digit number by a two-digit number; for a two-digit by one-digit multiplication, use distributive property to develop meaning for the algorithm. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently multiply any whole Usually multiply any whole Sometimes multiply any whole Rarely multiply any whole number by a one-digit number, and a number by a one-digit number, and a number by a one-digit number, and a number by a one-digit number, and a three-digit number by a two-digit three-digit number by a two-digit three-digit number by a two-digit three-digit number by a two-digit number; and use distributive number; and use distributive number; and use distributive number; and use distributive property to multiply a two-digit by property to multiply a two-digit by property to multiply a two-digit by property to multiply a two-digit by one-digit. one-digit. one-digit. one-digit. Differentiation of Instruction Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Multiplication (Distributive Property) Benchmark N.FL.04.12 Find the value of the unknowns in equations such as a ÷ 10 = 25; 125 ÷ b = 25. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find the value Usually find the value Sometimes find the value Rarely find the value of the unknowns in equations. of the unknowns in equations. of the unknowns in equations. of the unknowns in equations. Differentiation of Instruction Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Simplify and Check Computations Benchmark N.MR.04.13 Use the relationship between multiplication and division to simplify computations and check results. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently use the relationship Usually use the relationship Sometimes use the relationship Rarely use the relationship between multiplication and division between multiplication and division between multiplication and division between multiplication and division to simply and check results of to simply and check results of to simply and check results of to simply and check results of various computations. various computations. various computations. various computations. Differentiation of Instruction Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Problem Solving Benchmark N.MR.04.14 Solve contextual problems involving whole number multiplication and division. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve contextual Usually solve contextual Sometimes solve contextual Rarely solve contextual between multiplication and division between multiplication and division between multiplication and division between multiplication and division problems involving whole number problems involving whole number problems involving whole number problems involving whole number multiplication and division. multiplication and division. multiplication and division. multiplication and division. Differentiation of Instruction Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Estimate Benchmark N.FL.04.34 Estimate the answers to calculations involving addition, subtraction, or multiplication. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently estimate the answers Usually estimate the answers Sometimes estimate the answers Rarely estimate the answers to calculations involving addition, to calculations involving addition, to calculations involving addition, to calculations involving addition, subtraction, or multiplication. subtraction, or multiplication. subtraction, or multiplication. subtraction, or multiplication. Differentiation of Instruction Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Approximation Benchmark N.FL.04.35 Know when approximation is appropriate and use it to check the reasonableness of answers; be familiar with common place-value errors in calculations. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently know when it is Usually know when it is Sometimes know when it is Rarely know when it is appropriate to approximate and use appropriate to approximate and use appropriate to approximate and use appropriate to approximate and use it to check if answers are reasonable. it to check if answers are reasonable. it to check if answers are reasonable. it to check if answers are reasonable. Understand common place-value Understand common place-value Understand common place-value Understand common place-value errors in calculations. errors in calculations. errors in calculations. errors in calculations. Differentiation of Instruction Strand Mathematics Standard 1: Multiply whole numbers fluently up to 3 digits by 2 digits and divide numbers up to 4 digits by 1 digit and by 10 to solve problems. Topic Estimate using Mental Math Benchmark N.ME.04.36 Make appropriate estimations and calculations fluently with whole numbers using mental math Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently make appropriate Usually make appropriate Sometimes make appropriate Rarely make appropriate estimation and use mental math to estimation and use mental math to estimation and use mental math to estimation and use mental math to calculate with whole numbers. calculate with whole numbers. calculate with whole numbers. calculate with whole numbers. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving adding and subtracting fractions where one denominator is a multiple of the other. Topic Understanding Fractions Benchmark N.ME.04.20 Understand fractions as parts of a set of objects. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand fractions Usually understand fractions Sometimes understand fractions Rarely understand fractions as parts of a set of objects. as parts of a set of objects. as parts of a set of objects. as parts of a set of objects. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving adding and subtracting fractions where one denominator is a multiple of the other. Topic Equivalent Fractions Benchmark N.MR.04.21 Explain why equivalent fractions are equal, using models such as fraction strips, or the number line, for fractions with denominators of 12 or less, or equal to 100. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently explain why equivalent Usually explain why equivalent Sometimes explain why equivalent Rarely explain why equivalent fractions are equal, using models fractions are equal, using models fractions are equal, using models fractions are equal, using models for fractions with denominators of for fractions with denominators of for fractions with denominators of for fractions with denominators of 12 or less or equal to 100. 12 or less or equal to 100. 12 or less or equal to 100. 12 or less or equal to 100. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving adding and subtracting fractions where one denominator is a multiple of the other. Topic Understanding Fractions Benchmark N.MR.04.22 Locate fractions with denominators of 12 or less on the number line; include mixed numbers. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently locate fractions Usually locate fractions Sometimes locate fractions Rarely locate fractions with denominators of 12 or less on with denominators of 12 or less on with denominators of 12 or less on with denominators of 12 or less on the number line, including mixed the number line, including mixed the number line, including mixed the number line, including mixed numbers. numbers. numbers. numbers. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving adding and subtracting fractions where one denominator is a multiple of the other. Topic Understanding Improper Fractions Benchmark N.ME.04.24 Know that fractions of the form m/n where m is greater than n, are greater than 1 and are called improper fractions; locate improper fractions on the number line. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently know that an improper Usually know that an improper Sometimes know that an improper Rarely know that an improper fraction the numerator is larger fraction the numerator is larger fraction the numerator is larger fraction the numerator is larger than the denominator; locate improper than the denominator; locate improper than the denominator; locate improper than the denominator; locate improper fraction on the number line. fraction on the number line. fraction on the number line. fraction on the number line. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving adding and subtracting fractions where one denominator is a multiple of the other. Topic Coverting Improper Fractions Benchmark N.ME.04.24 Write improper fractions as mixed numbers, and understand that a mixed number represents the number of “wholes” and the part of a whole remaining, e.g., 5/4 = 1 + 1/4 = 1 1/4. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently write improper Usually write improper Sometimes write improper Rarely write improper fraction as mixed numbers, and fraction as mixed numbers, and fraction as mixed numbers, and fraction as mixed numbers, and understand that a mixed number understand that a mixed number understand that a mixed number understand that a mixed number represent the number of wholes and represent the number of wholes and represent the number of wholes and represent the number of wholes and the part of a whole remaining. the part of a whole remaining. the part of a whole remaining. the part of a whole remaining. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving adding and subtracting fractions where one denominator is a multiple of the other. Topic Compare and Order Fractions Benchmark N.ME.04.26 Compare and order up to three fractions with denominators 2, 4, and 8, and 3, 6, and 12, including improper fractions and mixed numbers. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently compare and order Usually compare and order Sometimes compare and order Rarely compare and order up to three fractions with up to three fractions with up to three fractions with up to three fractions with denominators 2, 4, and 8, denominators 2, 4, and 8, denominators 2, 4, and 8, denominators 2, 4, and 8, and 3, 6, and 12, including improper and 3, 6, and 12, including improper and 3, 6, and 12, including improper and 3, 6, and 12, including improper fractions and mixed numbers. fractions and mixed numbers. fractions and mixed numbers. fractions and mixed numbers. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving adding and subtracting fractions where one denominator is a multiple of the other. Topic Add and Subtract Fractions Benchmark N.ME.04.27 Add and subtract fractions less than 1 with denominators through 12 and/or 100, in cases where the denominators are equal or when one denominator is a multiple of the other, e.g., 1/12 + 5/12 = 6/12; 1/6 + 5/12 = 7/12; 3/10 - 23/100 = 7/100. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently add and subtract Usually add and subtract Sometimes add and subtract Rarely add and subtract fractions less then 1 with fractions less then 1 with fractions less then 1 with fractions less then 1 with denominators that are common and denominators that are common and denominators that are common and denominators that are common and multiples of each other. multiples of each other. multiples of each other. multiples of each other. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving adding and subtracting fractions where one denominator is a multiple of the other. Topic Problem Solving Benchmark N.ME.04.28 Solve contextual problems involving sums and differences for fractions where one denominator is a multiple of the other (denominators 2 through 12, and 100). Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve problems Usually solve problems Sometimes solve problems Rarely solve problems involving sums and differences involving sums and differences involving sums and differences involving sums and differences for fractin where one denominator for fractin where one denominator for fractin where one denominator for fractin where one denominator is a multiple of the other. is a multiple of the other. is a multiple of the other. is a multiple of the other. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving adding and subtracting fractions where one denominator is a multiple of the other. Topic Finding the Unknown Benchmark N.ME.04.29 Find the value of an unknown in equations such as 1/8 + x = 5/8 or 3/4 - y = 1/2. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find the value of Usually find the value of Sometimes find the value of Rarely find the value of an unknown in equations. an unknown in equations. an unknown in equations. an unknown in equations. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving adding and subtracting fractions where one denominator is a multiple of the other. Topic Multiplying Fractions Benchmark N.ME.04.30 Multiply fractions by whole numbers, using repeated addition and area or array models. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently multiply fractions by Usually multiply fractions by Sometimes multiply fractions by Rarely multiply fractions by whole numbers, using repeated whole numbers, using repeated whole numbers, using repeated whole numbers, using repeated addition and area or array models. addition and area or array models. addition and area or array models. addition and area or array models. Differentiation of Instruction Strand Mathematics Standard 3: Add and subtract decimals through hundredths. Topic Multiplying Fractions Benchmark N.ME.04.15 N.ME.04.18 Read, write, interpret, and compare decimals up to two decimal places; relate to money and place value decomposition. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently read, write, interpret Usually read, write, interpret Sometimes read, write, interpret Rarely read, write, interpret and compare decimals up tp two and compare decimals up tp two and compare decimals up tp two and compare decimals up tp two decimal places; relate it to money and decimal places; relate it to money and decimal places; relate it to money and decimal places; relate it to money and place value. place value. place value. place value. Differentiation of Instruction Strand Mathematics Standard 3: Add and subtract decimals through hundredths. Topic Decimals as Fractions Benchmark N.ME.04.16 Know that terminating decimals represents fractions whose denominators are 10, 10x10, 10x10x10, etc., e.g., powers of 10. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently know that Usually know that Sometimes know that Rarely know that terminating decimals represents terminating decimals represents terminating decimals represents terminating decimals represents fractions whose denominators are 10. fractions whose denominators are 10. fractions whose denominators are 10. fractions whose denominators are 10. Differentiation of Instruction Strand Mathematics Standard 3: Add and subtract decimals through hundredths. Topic Locating Decimals on Number Line Benchmark N.ME.04.17 Locate tenths and hundredths on a number line. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently locate tenths and Usually locate tenths and Sometimes locate tenths and Rarely locate tenths and hundredths on a number line. hundredths on a number line. hundredths on a number line. hundredths on a number line. Differentiation of Instruction Strand Mathematics Standard 3: Add and subtract decimals through hundredths. Topic Adding and Subtracting Decimals Benchmark N.MR.04.31 For problems that use addition and subtraction of decimals through hundredths, represent equivalents for halves and fourths. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently represent equivalents Usually represent equivalents Sometimes represent equivalents Rarely represent equivalents for halves and fourths for addition for halves and fourths for addition for halves and fourths for addition for halves and fourths for addition and subtraction problems of decimals and subtraction problems of decimals and subtraction problems of decimals and subtraction problems of decimals through hundredths. through hundredths. through hundredths. through hundredths. Differentiation of Instruction Strand Mathematics Standard 3: Add and subtract decimals through hundredths. Topic Writing Decimals and Fractions Benchmark N.MR.04.19 Write tenths and hundredths in decimal and fraction forms, and know the decimal equivalents for halves and fourths. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently write tenths and Usually write tenths and Sometimes write tenths and Rarely write tenths and hundredths in decimal and fraction hundredths in decimal and fraction hundredths in decimal and fraction hundredths in decimal and fraction forms and know the decimal forms and know the decimal forms and know the decimal forms and know the decimal equivalent for halves and fourths. equivalent for halves and fourths. equivalent for halves and fourths. equivalent for halves and fourths. Differentiation of Instruction Strand Mathematics Standard 3: Add and subtract decimals through hundredths. Topic Multiplying and Dividing with Decimals Benchmark N.FL.04.33 Multiply and divide decimals up to two decimal places by a one-digit whole number where the result is a terminating decimal.. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently multiply and divide Usually multiply and divide Sometimes multiply and divide Rarely multiply and divide decimals up to two decimal places decimals up to two decimal places decimals up to two decimal places decimals up to two decimal places by a one-digit whole number where by a one-digit whole number where by a one-digit whole number where by a one-digit whole number where the result is a terminating decimal. the result is a terminating decimal. the result is a terminating decimal. the result is a terminating decimal. Differentiation of Instruction Strand Mathematics Standard 4: Understand and solve problems involving perimeter, area and surface area of basic geometric shapes. Topic Measuring Surface Area Benchmark M.TE.04.04 Measure surface area of cubes and rectangular prisms by covering and counting area of the faces. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently measure surface area Usually measure surface area Sometimes measure surface area Rarely measure surface area of cubes and rectangular prisms of cubes and rectangular prisms of cubes and rectangular prisms of cubes and rectangular prisms by covering and counting area by covering and counting area by covering and counting area by covering and counting area of the faces. of the faces. of the faces. of the faces. Differentiation of Instruction Strand Mathematics Standard 4: Understand and solve problems involving perimeter, area and surface area of basic geometric shapes. Topic Formulas for Perimeter and Area Benchmark M.TE.04.06 Know and understand the formulas for perimeter and area of a square and a rectangle; calculate the perimeters and areas of these shapes and combinations of these shapes using the formulas. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently know, understand and Usually know, understand and Sometimes know, understand and Rarely know, understand and calculate the formulas for perimeter calculate the formulas for perimeter calculate the formulas for perimeter calculate the formulas for perimeter and area of a square and a and area of a square and a and area of a square and a and area of a square and a rectangle and combinations of these rectangle and combinations of these rectangle and combinations of these rectangle and combinations of these shapes. shapes. shapes. shapes. Differentiation of Instruction Strand Mathematics Standard 4: Understand and solve problems involving perimeter, area and surface area of basic geometric shapes. Topic Finding Dimensions Benchmark M.TE.04.07 Find one dimension of a rectangle given the other dimension and its perimeter or area. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find one dimension Usually find one dimension Sometimes find one dimension Rarely find one dimension of a rectangle given the other of a rectangle given the other of a rectangle given the other of a rectangle given the other dimension and its perimeter or dimension and its perimeter or dimension and its perimeter or dimension and its perimeter or area. area. area. area. Differentiation of Instruction Strand Mathematics Standard 4: Understand and solve problems involving perimeter, area and surface area of basic geometric shapes. Topic Determining Size of a Square Benchmark M.TE.04.08 Find the side of a square given its perimeter or area. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find the size Usually find the size Sometimes find the size Rarely find the size of a square given its perimeter of a square given its perimeter of a square given its perimeter of a square given its perimeter or area. or area. or area. or area. Differentiation of Instruction Strand Mathematics Standard 4: Understand and solve problems involving perimeter, area and surface area of basic geometric shapes. Topic Problem Solving Benchmark M.PS.04.09 Solve contextual problems about perimeter and area of squares and rectangles in compound shapes. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve contextual Usually solve contextual Sometimes solve contextual Rarely solve contextual problems about perimeter and area problems about perimeter and area problems about perimeter and area problems about perimeter and area of a squares and rectangles in of a squares and rectangles in of a squares and rectangles in of a squares and rectangles in compound shapes. compound shapes. compound shapes. compound shapes. Differentiation of Instruction Strand Mathematics Standard 4: Understand and solve problems involving perimeter, area and surface area of basic geometric shapes. Topic Problem Solving Benchmark M.PS.04.11 Solve contextual problems about surface area. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve contextual Usually solve contextual Sometimes solve contextual Rarely solve contextual problems about surface area problems about surface area problems about surface area problems about surface area Strand Mathematics Standard 5: Recognize plane figures that have line symmetry and sketch flips, slides and turns of two-dimensional figures. Topic Identifying and Drawing Lines Benchmark G.GS.04.01 Identify and draw perpendicular, parallel, and intersecting lines using a ruler and a tool or object with a square (90º) corner. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify and draw Usually identify and draw Sometimes identify and draw Rarely identify and draw perpendicular, parallel, and perpendicular, parallel, and perpendicular, parallel, and perpendicular, parallel, and intersecting lines using a ruler and a intersecting lines using a ruler and a intersecting lines using a ruler and a intersecting lines using a ruler and a tool or object with a square corner. tool or object with a square corner. tool or object with a square corner. tool or object with a square corner. Strand Mathematics Standard 5: Recognize plane figures that have line symmetry and sketch flips, slides and turns of two-dimensional figures. Topic Right Angles Benchmark M.TE.04.10 Identify right angles and compare angles to right angles. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify right angles Usually identify right angles Sometimes identify right angles Rarely identify right angles and compare them to other angles. and compare them to other angles. and compare them to other angles. and compare them to other angles. Strand Mathematics Standard 5: Recognize plane figures that have line symmetry and sketch flips, slides and turns of two-dimensional figures. Topic Geometric Shapes Benchmark G.GS.04.02 Identify basic geometric shapes including isosceles, equilateral and right triangles, and use their properties to solve problems. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify basic geometric Usually identify basic geometric Sometimes identify basic geometric Rarely identify basic geometric shapes including isosoceles, shapes including isosoceles, shapes including isosoceles, shapes including isosoceles, equilateral, and right triangles and equilateral, and right triangles and equilateral, and right triangles and equilateral, and right triangles and use their properties to solve problems. use their properties to solve problems. use their properties to solve problems. use their properties to solve problems. Strand Mathematics Standard 5: Recognize plane figures that have line symmetry and sketch flips, slides and turns of two-dimensional figures. Topic Three-Dimensional Shapes Benchmark G.SR.04.03 Identify and count the faces, edges, and vertices of basic three-dimensional geometric solids including cubes, rectangular prisms, and pyramids; describe the shape of their faces. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify and count the Usually identify and count the Sometimes identify and count the Rarely identify and count the faces, edges, and vertices of basic faces, edges, and vertices of basic faces, edges, and vertices of basic faces, edges, and vertices of basic three-dimensional geometric solids three-dimensional geometric solids three-dimensional geometric solids three-dimensional geometric solids and describe the shape of their face. and describe the shape of their face. and describe the shape of their face. and describe the shape of their face. Strand Mathematics Standard 6: Use bar graphs and find the median and range of a set of data. Topic Constructing Tables and Bar Graphs Benchmark D.RE.04.01 Construct tables and bar graphs from given data. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently construct table Usually construct table Sometimes construct table Rarely construct table and bar graphs from given data. and bar graphs from given data. and bar graphs from given data. and bar graphs from given data. Strand Mathematics Standard 6: Use bar graphs and find the median and range of a set of data. Topic Median and Range Benchmark D.RE.04.02 Order a given set of data, find the median, and specify the range of values. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently order, find the median Usually order, find the median Sometimes order, find the median Rarely order, find the median and specify the range of value for and specify the range of value for and specify the range of value for and specify the range of value for a given set of data. a given set of data. a given set of data. a given set of data. Strand Mathematics Standard 6: Use bar graphs and find the median and range of a set of data. Topic Problem Solving Benchmark D.RE.04.03 Solve problems using data presented in tables and bar graphs, e.g., compare data represented in two bar graphs and read bar graphs showing two data sets. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve problems using Usually solve problems using Sometimes solve problems using Rarely solve problems using data from tables and bar graphs. data from tables and bar graphs. data from tables and bar graphs. data from tables and bar graphs. Content Area: Math Grade/Course:5th Strand Mathematics Standard 1: Divide fluently up to a four-digit number by a two-digit number and solve applied problems involving multiplication and division of whole numbers. Topic Ordering Numbers Benchmark N.MR.05.01 Understand the meaning of division of whole numbers, with and without remainders; relate division to fractions and to repeated subtraction. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand division with Usually understand division with Sometimes understand division with Rarely understand division with and without remainders; relate and without remainders; relate and without remainders; relate and without remainders; relate division to fractions and to division to fractions and to division to fractions and to division to fractions and to repeated subtraction. repeated subtraction. repeated subtraction. repeated subtraction. Differentiation of Instruction Strand Mathematics Standard 1: Divide fluently up to a four-digit number by a two-digit number and solve applied problems involving multiplication and division of whole numbers. Topic Writing Mathematical Statements Benchmark N.MR.05.03 Write mathematical statements involving division for given situations. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently write mathematical Usually write mathematical Sometimes write mathematical Rarely write mathematical statements involving division for statements involving division for statements involving division for statements involving division for given situations. given situations. given situations. given situations. Differentiation of Instruction Strand Mathematics Standard 1: Divide fluently up to a four-digit number by a two-digit number and solve applied problems involving multiplication and division of whole numbers. Topic Division with Remainders Benchmark N.MR.05.02 Relate division of whole numbers with remainders to the form a = bq + r, e.g., 34 ÷ 5 = 6 r 4, so 5 • 6 + 4 = 34; note remainder (4) is less than divisor (5). Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently relate division of Usually relate division of Sometimes relate division of Rarely relate division of whole numbers with remainders to whole numbers with remainders to whole numbers with remainders to whole numbers with remainders to the form that a=bq+r the form that a=bq+r the form that a=bq+r the form that a=bq+r Differentiation of Instruction Strand Mathematics Standard 1: Divide fluently up to a four-digit number by a two-digit number and solve applied problems involving multiplication and division of whole numbers. Topic Multiplication Benchmark N.FL.05.04 Multiply a multi-digit number by a two-digit number; recognize and be able to explain common computational errors such as not accounting for place value. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently multiply a multi-digit Usuaslly multiply a multi-digit Sometimes multiply a multi-digit Rarely multiply a multi-digit number by a two-digit number and number by a two-digit number and number by a two-digit number and number by a two-digit number and recognizes common computational recognizes common computational recognizes common computational recognizes common computational errors. errors. errors. errors. Differentiation of Instruction Strand Mathematics Standard 1: Divide fluently up to a four-digit number by a two-digit number and solve applied problems involving multiplication and division of whole numbers. Topic Prime Factorization Benchmark N.MR.05.07 Find the prime factorization of numbers from 2 through 50, express in exponential notation, and understand that every whole number greater than 1 is either prime or can be expressed as a product of primes. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find the prime Usually find the prime Sometimes find the prime Rarely find the prime factorization of numbers from 2 factorization of numbers from 2 factorization of numbers from 2 factorization of numbers from 2 through 50, express in exponential through 50, express in exponential through 50, express in exponential through 50, express in exponential notation and understand any whole notation and understand any whole notation and understand any whole notation and understand any whole number greater than 1 is either prime number greater than 1 is either prime number greater than 1 is either prime number greater than 1 is either prime or expressed as a oroduct of primes or expressed as a oroduct of primes or expressed as a oroduct of primes or expressed as a oroduct of primes Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving sums and differences of fractions with unlike denominators. Topic Relationship between Fractions and Decimals Benchmark N.ME.05.10 Understand a fraction as a statement of division, e.g., 2 ÷ 3 = 2/3 using simple fractions and pictures to represent. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand a fraction Usually understand a fraction Sometimes understand a fraction Rarely understand a fraction as a statement of division using as a statement of division using as a statement of division using as a statement of division using simple fractions and pictures to simple fractions and pictures to simple fractions and pictures to simple fractions and pictures to represent. represent. represent. represent. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving sums and differences of fractions with unlike denominators. Topic Common Denominators Benchmark N.ME.05.11 Given two fractions, e.g., 1/2 and 1/4 , express them as fractions with a common denominator, but not necessarily a least common denominator, e.g., 1/2 = 4/8 and 3/4 = 6/8 ; use denominators less than 12 or factors of 100. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently express two given Usually express two given Sometimes express two given Rarely express two given fractions with unlike denominators fractions with unlike denominators fractions with unlike denominators fractions with unlike denominators as fractions with common as fractions with common as fractions with common as fractions with common denominators. denominators. denominators. denominators. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving sums and differences of fractions with unlike denominators. Topic Multiplying Fractions Benchmark N.ME.05.12 Find the product of two unit fractions with small denominators using an area model. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find the product Usually find the product Sometimes find the product Rarely find the product of two unit fractions with small of two unit fractions with small of two unit fractions with small of two unit fractions with small denominators using an area model. denominators using an area model. denominators using an area model. denominators using an area model. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving sums and differences of fractions with unlike denominators. Topic Dividing Fractions Benchmark N.MR.05.13 Divide a fraction by a whole number and a whole number by a fraction, using simple unit fractions. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently divide a fraction Usually divide a fraction Sometimes divide a fraction Rarely divide a fraction by a whole number and a whole by a whole number and a whole by a whole number and a whole by a whole number and a whole number by a fraction, using simple number by a fraction, using simple number by a fraction, using simple number by a fraction, using simple unit fractions. unit fractions. unit fractions. unit fractions. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving sums and differences of fractions with unlike denominators. Topic Adding and Subtracting Fractions Benchmark N.FL.05.14 Add and subtract fractions with unlike denominators through 12 and/or 100, using the common denominator that is the product of the denominators of the 2 fractions, e.g., for 3/8 + 7/10, use 80 as the common denominator. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently add and subtract Usually add and subtract Sometimes add and subtract Rarely add and subtract fractions with unlike denominators fractions with unlike denominators fractions with unlike denominators fractions with unlike denominators through 12 and/or 100, using the through 12 and/or 100, using the through 12 and/or 100, using the through 12 and/or 100, using the common denominator. common denominator. common denominator. common denominator. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving sums and differences of fractions with unlike denominators. Topic Mathematical Statements Benchmark N.FL.05.18 Use mathematical statements to represent an applied situation involving addition and subtraction of fractions. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently use mathematical Usually use mathematical Sometimes use mathematical Rarely use mathematical statements to represent an statements to represent an statements to represent an statements to represent an applied situation involving applied situation involving applied situation involving applied situation involving addition and subtraction of fractions. addition and subtraction of fractions. addition and subtraction of fractions. addition and subtraction of fractions. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving sums and differences of fractions with unlike denominators. Topic Problem Solving Benchmark N.MR.05.19 Solve contextual problems that involve finding sums and differences of fractions with unlike denominators using knowledge of equivalent fractions. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve contextual Usually solve contextual Sometimes solve contextual Rarely solve contextual problems that involve finding sums problems that involve finding sums problems that involve finding sums problems that involve finding sums and differences of fractions with and differences of fractions with and differences of fractions with and differences of fractions with unlike denominators using the unlike denominators using the unlike denominators using the unlike denominators using the knowledge of common denomimnators. knowledge of common denomimnators. knowledge of common denomimnators. knowledge of common denomimnators. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving sums and differences of fractions with unlike denominators. Topic Problem Solving Benchmark N.FL.05.20 Solve applied problems involving fractions and decimals; include rounding of answers and checking reasonableness. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve applied Usually solve applied Sometimes solve applied Rarely solve applied problems that involve fractions problems that involve fractions problems that involve fractions problems that involve fractions and decimals; including rounding and decimals; including rounding and decimals; including rounding and decimals; including rounding of answers and checking of answers and checking of answers and checking of answers and checking reasonableness. reasonableness. reasonableness. reasonableness. Differentiation of Instruction Strand Mathematics Standard 2: Solve contextual problems involving sums and differences of fractions with unlike denominators. Topic Problem Solving Benchmark N.MR.05.21 Solve for the unknown in equations such as 1/4 + x = 7/12 Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve for the Usually solve for the Sometimes solve for the Rarely solve for the unknown in equations. unknown in equations. unknown in equations. unknown in equations. Differentiation of Instruction Strand Mathematics Standard 3: Express fractions and decimals as percentages, and vice versa. Topic Place Value Benchmark N.ME.05.08 Understand the relative magnitude of ones, tenths, and hundredths and the relationship of each place value to the place to its right, e.g., 1 is 10 tenths, one tenth is 10 hundredths. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand the Usually understand the Sometimes understand the Rarely understand the relative magnitude of ones, tenths, relative magnitude of ones, tenths, relative magnitude of ones, tenths, relative magnitude of ones, tenths, and hundredths and the relationship and hundredths and the relationship and hundredths and the relationship and hundredths and the relationship of each place value to the place to of each place value to the place to of each place value to the place to of each place value to the place to its right. its right. its right. its right. Differentiation of Instruction Strand Mathematics Standard 3: Express fractions and decimals as percentages, and vice versa. Topic Percentages Benchmark N.ME.05.09 Understand percentages as parts out of 100, use % notation, and express a part of a whole as a percentage. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand Usually understand Sometimes understand Rarely understand percentage as part out of 100, use % percentage as part out of 100, use % percentage as part out of 100, use % percentage as part out of 100, use % notation, and express a part of a notation, and express a part of a notation, and express a part of a notation, and express a part of a whole as a percentage. whole as a percentage. whole as a percentage. whole as a percentage. its right. its right. its right. its right. Differentiation of Instruction Strand Mathematics Standard 3: Express fractions and decimals as percentages, and vice versa. Topic Multiply by Powers of 10 Benchmark N.MR.05.15 Multiply a whole number by powers of 10: 0.01, 0.1, 1, 10, 100, 1,000 and identify patterns. each place value to the place to its right, e.g., 1 is 10 tenths, one tenth is 10 hundredths. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently multiply whole number Usually multiply whole number Sometimes multiply whole number Rarely multiply whole number by powers of 10 and identify the by powers of 10 and identify the by powers of 10 and identify the by powers of 10 and identify the pattern of tenths. pattern of tenths. pattern of tenths. pattern of tenths. Differentiation of Instruction Strand Mathematics Standard 3: Express fractions and decimals as percentages, and vice versa. Topic Division Benchmark N.FL.05.16 Divide numbers by 10s, 100s, 1,000s using mental strategies. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently use mental strategies Usually use mental strategies Sometimes use mental strategies Rarely use mental strategies to divide numbers by to divide numbers by to divide numbers by to divide numbers by 10s, 100s, 1,000s. 10s, 100s, 1,000s. 10s, 100s, 1,000s. 10s, 100s, 1,000s. Differentiation of Instruction Strand Mathematics Standard 3: Express fractions and decimals as percentages, and vice versa. Topic Multiplying Decimals Benchmark N.MR.05.17 Multiply one- and two-digit whole numbers by decimals up to two decimal places. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently multiply one- and Usually multiply one- and Sometimes multiply one- and Rarely multiply one- and two digit whole numbers by decimals two digit whole numbers by decimals two digit whole numbers by decimals two digit whole numbers by decimals up to two places. up to two places. up to two places. up to two places. Differentiation of Instruction Strand Mathematics Standard 4: Convert measurements of length, weight, area, volume, and time within a given system using easily manipulable numbers. Topic Equivalent Measurements Benchmark M.UN.05.01 Recognize the equivalence of 1 liter, 1000 ml and 1000 cm (cubed) and include conversions among liters, milliliters, and cubic centimeters. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently recognize the Usually recognize the Sometimes recognize the Rarely recognize the equivalence of 1 liter, 1000ml and equivalence of 1 liter, 1000ml and equivalence of 1 liter, 1000ml and equivalence of 1 liter, 1000ml and 1000 cm (cubed) and include 1000 cm (cubed) and include 1000 cm (cubed) and include 1000 cm (cubed) and include conversions. conversions. conversions. conversions. Differentiation of Instruction Strand Mathematics Standard 4: Convert measurements of length, weight, area, volume, and time within a given system using easily manipulable numbers. Topic Equivalent Measurements Benchmark M.UN.05.01 Know the units of measure of volume: cubic centimeter, cubic meter, cubic inches, feet, cubic yards, and use their abbreviations (cm3, m3, in3, ft3, yd3). (cubed) Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently know the units Usually know the units Sometimes know the units Rarely know the units of measure volume and their of measure volume and their of measure volume and their of measure volume and their abbreviations. abbreviations. abbreviations. abbreviations. Differentiation of Instruction Strand Mathematics Standard 4: Convert measurements of length, weight, area, volume, and time within a given system using easily manipulable numbers. Topic Comparison Benchmark M.UN.05.03 Compare the relative sizes of one cubic inch to one cubic foot, and one cubic centimeter to one cubic meter. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently compare the relative Usually compare the relative Sometimes compare the relative Rarely compare the relative sizes of one cubic inch to one cubic sizes of one cubic inch to one cubic sizes of one cubic inch to one cubic sizes of one cubic inch to one cubic feet, and centimeter to meter. feet, and centimeter to meter. feet, and centimeter to meter. feet, and centimeter to meter. Differentiation of Instruction Strand Mathematics Standard 4: Convert measurements of length, weight, area, volume, and time within a given system using easily manipulable numbers. Topic Conversion Benchmark M.UN.05.04 Convert measurements of length, weight, area, volume, and time within a given system using easily manipulable numbers. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently convert measurements Usually convert measurements Sometimes convert measurements Rarely convert measurements of length, weight, area, volume and of length, weight, area, volume and of length, weight, area, volume and of length, weight, area, volume and time within a given system using time within a given system using time within a given system using time within a given system using easily manipulable numbers. easily manipulable numbers. easily manipulable numbers. easily manipulable numbers. Differentiation of Instruction Strand Mathematics Standard 5: Use area formulas for triangles and parallelograms and understand volume. Topic Relationships between Areas Benchmark M.PS.05.05 Represent relationships between areas of rectangles, triangles, and parallelograms using models. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently represent relationships Usually represent relationships Sometimes represent relationships Rarely represent relationships between areas of rectangles, between areas of rectangles, between areas of rectangles, between areas of rectangles, triangles and parallelograms using triangles and parallelograms using triangles and parallelograms using triangles and parallelograms using models. models. models. models. Differentiation of Instruction Strand Mathematics Standard 5: Use area formulas for triangles and parallelograms and understand volume. Topic Area of Triangle Benchmark M.TE.05.06 Understand and know how to use the area formula of a triangle: A = 1/2 bh (where b is length of the base and h is the height), and represent using models and manipulatives. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand and Usually understand and Sometimes understand and Rarely understand and know how to use the formula of know how to use the formula of know how to use the formula of know how to use the formula of a triangle: A=1/2bh. a triangle: A=1/2bh. a triangle: A=1/2bh. a triangle: A=1/2bh. Represent using models and Represent using models and Represent using models and Represent using models and manipulatives. manipulatives. manipulatives. manipulatives. Differentiation of Instruction Strand Mathematics Standard 5: Use area formulas for triangles and parallelograms and understand volume. Topic Relationships between Areas Benchmark M.TE.05.07 Understand and know how to use the area formula for a parallelogram: A = bh, and represent using models and manipulatives. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand and Usually understand and Sometimes understand and Rarely understand and know how to use the formula of know how to use the formula of know how to use the formula of know how to use the formula of a parallelogram: A= bh. a parallelogram: A= bh. a parallelogram: A= bh. a parallelogram: A= bh. Represent using models and Represent using models and Represent using models and Represent using models and manipulatives. manipulatives. manipulatives. manipulatives. Differentiation of Instruction Strand Mathematics Standard 5: Use area formulas for triangles and parallelograms and understand volume. Topic Solids Benchmark M.TE.05.08 Build solids with unit cubes and state their volumes. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently build solids with Usually build solids with Sometimes build solids with Rarely build solids with unit cubes and state their volumes. unit cubes and state their volumes. unit cubes and state their volumes. unit cubes and state their volumes. Differentiation of Instruction Strand Mathematics Standard 5: Use area formulas for triangles and parallelograms and understand volume. Topic Finding Volume Benchmark M.TE.05.09 Use filling (unit cubes or liquid) and counting or measuring to find the volume of a cube and rectangular prism. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently use filling and Usually use filling and Sometimes use filling and Rarely use filling and counting or measuring to find the counting or measuring to find the counting or measuring to find the counting or measuring to find the volume of a cube and rectangular volume of a cube and rectangular volume of a cube and rectangular volume of a cube and rectangular prism. prism. prism. prism. Differentiation of Instruction Strand Mathematics Standard 5: Use area formulas for triangles and parallelograms and understand volume. Topic Problem Solving Benchmark M.TE.05.10 Solve applied problems about the volumes of rectangular prisms using multiplication and division and using the appropriate units. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve applied Usually solve applied Sometimes solve applied Rarely solve applied problems about the volumes of problems about the volumes of problems about the volumes of problems about the volumes of rectangular prisms using multiplication rectangular prisms using multiplication rectangular prisms using multiplication rectangular prisms using multiplication and division and using the and division and using the and division and using the and division and using the appropriate units. appropriate units. appropriate units. appropriate units. Differentiation of Instruction Strand Mathematics Standard 6: Measure angles and understand angle relationships in geometric figures. Topic Angle Degrees Benchmark G.TR.05.01 Associate an angle with a certain amount of turning; know that angles are measured in degrees; understand that 90°, 180°, 270°, and 360° are associated, respectively, with 1/4, 1/2, and 3/4 and full turns. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently associate an angle Usually associate an angle Sometimes associate an angle Rarely associate an angle with a certain amount of turning; with a certain amount of turning; with a certain amount of turning; with a certain amount of turning; know that angles are measured in know that angles are measured in know that angles are measured in know that angles are measured in degrees. Understand certain degrees degrees. Understand certain degrees degrees. Understand certain degrees degrees. Understand certain degrees are associated with a respective are associated with a respective are associated with a respective are associated with a respective fraction and full turns. fraction and full turns. fraction and full turns. fraction and full turns. Differentiation of Instruction Strand Mathematics Standard 6: Measure angles and understand angle relationships in geometric figures. Topic Measure Degrees Benchmark G.GS.05.02 Measure angles with a protractor, and classify them as acute, right, obtuse, or straight. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently measure angles Usually measure angles Sometimes measure angles Rarely measure angles with a protractor, and classify them with a protractor, and classify them with a protractor, and classify them with a protractor, and classify them as acute, right, obtuse or straight. as acute, right, obtuse or straight. as acute, right, obtuse or straight. as acute, right, obtuse or straight. Differentiation of Instruction Strand Mathematics Standard 6: Measure angles and understand angle relationships in geometric figures. Topic Identify Angles Benchmark G.GS.05.03, G.GS.05.05 Identify & name angles on a straight line & vertical angles. Know that angles on a straight line add up to 180° and angles surrounding a point add up to 360°; justify informally by “surrounding” a point with angles. Find unknown angles in problems involving angles on a straight line, angles surrounding a point and vertical angles. G.GS.05.04 Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify & name angles Usually identify & name angles Sometimes identify & name angles Rarely identify & name angles on a straight line & vertical line. Know on a straight line & vertical line. Know on a straight line & vertical line. Know on a straight line & vertical line. Know the sum of angles for straight and the sum of angles for straight and the sum of angles for straight and the sum of angles for straight and angles surrounding a point. Find angles surrounding a point. Find angles surrounding a point. Find angles surrounding a point. Find unknown angles in problems. unknown angles in problems. unknown angles in problems. unknown angles in problems. Differentiation of Instruction Strand Mathematics Standard 6: Measure angles and understand angle relationships in geometric figures. Topic Angle Sums Benchmark G.GS.05.06 Understand why the sum of the interior angles of a triangle is 180° and the sum of the interior angles of a quadrilateral is 360°, and use these properties to solve problems. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand why the Usually understand why the Sometimes understand why the Rarely understand why the sum of the interior angles of a sum of the interior angles of a sum of the interior angles of a sum of the interior angles of a triangle is 180 degrees and the sum triangle is 180 degrees and the sum triangle is 180 degrees and the sum triangle is 180 degrees and the sum of the interior angles of a of the interior angles of a of the interior angles of a of the interior angles of a quadrilateral is 360 degrees, and use quadrilateral is 360 degrees, and use quadrilateral is 360 degrees, and use quadrilateral is 360 degrees, and use these problems to solve problems. these problems to solve problems. these problems to solve problems. these problems to solve problems. Differentiation of Instruction Strand Mathematics Standard 6: Measure angles and understand angle relationships in geometric figures. Topic Finding Unknown Angle Benchmark G.GS.05.07 Find unknown angles using the properties of triangles, including right, isosceles, and equilateral triangles; parallelograms, including rectangles and rhombuses; and trapezoids. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find an unknown Usually find an unknown Sometimes find an unknown Rarely find an unknown angles using properties of triangles; angles using properties of triangles; angles using properties of triangles; angles using properties of triangles; including right, isosceles, and including right, isosceles, and including right, isosceles, and including right, isosceles, and equilateral triangles; parallelograms, equilateral triangles; parallelograms, equilateral triangles; parallelograms, equilateral triangles; parallelograms, including rectangles and rhombuses; including rectangles and rhombuses; including rectangles and rhombuses; including rectangles and rhombuses; and trapezoids. and trapezoids. and trapezoids. and trapezoids. Differentiation of Instruction Strand Mathematics Standard 7: Find the mean of a set of data. Topic Finding the Mean and Mode Benchmark D.AN.05.03 D.AN.05.04 Given a set of data, find and interpret the mean (using the concept of fair share) and mode. Solve multi-step problems involving means. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find the mean and Usually find the mean and Sometimes find the mean and Rarely find the mean and mode of a given set of a data. mode of a given set of a data. mode of a given set of a data. mode of a given set of a data. Solve multi-step problems Solve multi-step problems Solve multi-step problems Solve multi-step problems involving means. involving means. involving means. involving means. Differentiation of Instruction Content Area: Math Grade/Course: 6th Strand Mathematics Standard 1: Understand and use negative numbers. Topic Understanding Integer Benchmark N.ME.06.19 Understand that 0 is an integer that is neither negative nor positive. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand that 0 is Usually understand that 0 is Sometimes understand that 0 is Rarely understand that 0 is an integer that is neither negative an integer that is neither negative an integer that is neither negative an integer that is neither negative nor positive. nor positive. nor positive. nor positive. Differentiation of Instruction Strand Mathematics Standard 1: Understand and use negative numbers. Topic Understanding Integer Benchmark N.ME.06.17 Locate negative rational numbers (including integers) on the number line; know that numbers and their negatives add to 0 and are on opposites sides and at equal distance from 0 on a number line. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently locate negative rational Usually locate negative rational Sometimes locate negative rational Rarely locate negative rational numbers on the number line; know numbers on the number line; know numbers on the number line; know numbers on the number line; know that numbers and their negatives add that numbers and their negatives add that numbers and their negatives add that numbers and their negatives add to 0 and are on opposite sides and to 0 and are on opposite sides and to 0 and are on opposite sides and to 0 and are on opposite sides and at equal distance from 0 on the at equal distance from 0 on the at equal distance from 0 on the at equal distance from 0 on the number line. number line. number line. number line. Differentiation of Instruction Strand Mathematics Standard 1: Understand and use negative numbers. Topic Absolute Value Benchmark N.ME.06.20 Know that the absolute value of a number is the value of the number, ignoring the sign, or is the distance of the number from 0. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently know that the Usually know that the Sometimes know that the Rarely know that the absolute value of a number is the absolute value of a number is the absolute value of a number is the absolute value of a number is the value of the number, ignoring the value of the number, ignoring the value of the number, ignoring the value of the number, ignoring the sign, or is the distance of the sign, or is the distance of the sign, or is the distance of the sign, or is the distance of the number from 0. number from 0. number from 0. number from 0. Differentiation of Instruction Strand Mathematics Standard 1: Understand and use negative numbers. Topic Inverse Operation Benchmark N.MR.06.08 Understand integer subtraction as the inverse of integer addition. Understand integer division as the division as the inverse of integer multiplication. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand the inverse Usually understand the inverse Sometimes understand the inverse Rarely understand the inverse of interger subtraction and integer of interger subtraction and integer of interger subtraction and integer of interger subtraction and integer division. division. division. division. Differentiation of Instruction Strand Mathematics Standard 1: Understand and use negative numbers. Topic Integers Benchmark N.FL.06.09 Add and multiply integers between -10 and 10; subtract and divide integers using the related facts. Use the number line and chip models for addition and subtraction. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently add and multiply Usually add and multiply Sometimes add and multiply Rarely add and multiply integers between -10 and 10; integers between -10 and 10; integers between -10 and 10; integers between -10 and 10; subtract and divide integers. Use the subtract and divide integers. Use the subtract and divide integers. Use the subtract and divide integers. Use the number line and chip models for number line and chip models for number line and chip models for number line and chip models for addition and subtraction. addition and subtraction. addition and subtraction. addition and subtraction. Differentiation of Instruction Strand Mathematics Standard 2: Multiply and divide any two fractions fluently to solve applied problems. Topic Understanding Fractions as Integers Benchmark N.ME.06.07 Understand that a fraction or a negative fraction is a quotient of two integers, e.g., - 8/3 is -8 divided by 3. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand that a fraction Usually understand that a fraction Sometimes understand that a fraction Rarely understand that a fraction or a negative fraction is a quotient or a negative fraction is a quotient or a negative fraction is a quotient or a negative fraction is a quotient of two integers. of two integers. of two integers. of two integers. Differentiation of Instruction Strand Mathematics Standard 2: Multiply and divide any two fractions fluently to solve applied problems. Topic Finding the Product Benchmark N.ME.05.12 Find the product of two unit fractions with small denominators using an area model. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find the product of Usually find the product of Sometimes find the product of Rarely find the product of two unit fractions with small two unit fractions with small two unit fractions with small two unit fractions with small denominators using an area model. denominators using an area model. denominators using an area model. denominators using an area model. Differentiation of Instruction Strand Mathematics Standard 2: Multiply and divide any two fractions fluently to solve applied problems. Topic Solving for Unknown Benchmark N.MR.06.03 Solve for the unknown in equations such as:¼ ÷ _ = 1, ¾ ÷ _ = ¼ and ½ = 1 • _ . Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve for the Usually solve for the Sometimes solve for the Rarely solve for the unknown in equations. unknown in equations. unknown in equations. unknown in equations. Differentiation of Instruction Strand Mathematics Standard 2: Multiply and divide any two fractions fluently to solve applied problems. Topic Dividing Fractions Benchmark N.MR.05.13 Divide a fraction by a whole number and a whole number by a fraction, using simple unit fractions Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently divide a fraction Usually divide a fraction Sometimes divide a fraction Rarely divide a fraction by a whole number and a whole by a whole number and a whole by a whole number and a whole by a whole number and a whole number by a fraction. number by a fraction. number by a fraction. number by a fraction. Differentiation of Instruction Strand Mathematics Standard 2: Multiply and divide any two fractions fluently to solve applied problems. Topic Understanding Fractions as Integers Benchmark N.MR.06.01 Understand division of fractions as the inverse of multiplication, e.g., if 4/5 ÷ 2/3 = _, then 2/3 • _ = 4/5 , so _ = 4/5 • 3/2 = 12/10. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand division Usually understand division Sometimes understand division Rarely understand division of fractions as the inverse of of fractions as the inverse of of fractions as the inverse of of fractions as the inverse of multiplication. multiplication. multiplication. multiplication. Differentiation of Instruction Strand Mathematics Standard 2: Multiply and divide any two fractions fluently to solve applied problems. Topic Writing Mathematical Statements Benchmark N.FL.06.02 Given an applied situation involving dividing fractions, write a mathematical statement to represent the situation. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently writes a mathematical Usually writes a mathematical Sometimes writes a mathematical Rarely writes a mathematical statement when given an applied statement when given an applied statement when given an applied statement when given an applied situation involving dividing fractions. situation involving dividing fractions. situation involving dividing fractions. situation involving dividing fractions. Differentiation of Instruction Strand Mathematics Standard 2: Multiply and divide any two fractions fluently to solve applied problems. Topic Multiply and Divide Benchmark N.FL.06.04 Multiply and divide any two fractions fluently. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently multiply and Usually multiply and Sometimes multiply and Rarely multiply and divide two fractions fluently. divide two fractions fluently. divide two fractions fluently. divide two fractions fluently. Differentiation of Instruction Strand Mathematics Standard 3: Solve applied problems that use the four operations with appropriate decimal numbers and percentages. Topic Rational Numbers as Fraction or Decimals Benchmark N.ME.06.06, N.ME.06.05 Represent rational numbers as fractions or terminating decimals when possible and translate between these representations. Order rational numbers and place them on the number line. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently represents rational Usually represents rational Sometimes represents rational Rarely represents rational numbers as fractions or terminating numbers as fractions or terminating numbers as fractions or terminating numbers as fractions or terminating decimals. Order rational numbers decimals. Order rational numbers decimals. Order rational numbers decimals. Order rational numbers and place them on the number line. and place them on the number line. and place them on the number line. and place them on the number line. Differentiation of Instruction Strand Mathematics Standard 3: Solve applied problems that use the four operations with appropriate decimal numbers and percentages. Topic Multiply 1 and 2 Digits Benchmark N.MR.05.17, N.FL.06.14 Multiply one- and two-digit whole numbers by decimals up to two decimal places. For applied situations, estimate the answers to calculations involving operations with rational numbers. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently multiply one and two Usually multiply one and two Sometimes multiply one and two Rarely multiply one and two digit whole numbers by decimals up digit whole numbers by decimals up digit whole numbers by decimals up digit whole numbers by decimals up to two decimal places. Estimate to two decimal places. Estimate to two decimal places. Estimate to two decimal places. Estimate for applied situations. for applied situations. for applied situations. for applied situations. Differentiation of Instruction Strand Mathematics Standard 3: Solve applied problems that use the four operations with appropriate decimal numbers and percentages. Benchmark N.ME.05.09 Understand percentages as parts out of 100, use % notation, and express a part of a whole as a percentage. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand Usually understand Sometimes understand Rarely understand percentage as part out of 100, use % percentage as part out of 100, use % percentage as part out of 100, use % percentage as part out of 100, use % notation, and express a part of a notation, and express a part of a notation, and express a part of a notation, and express a part of a whole as a percentage. whole as a percentage. whole as a percentage. whole as a percentage. its right. its right. its right. its right. Differentiation of Instruction Strand Mathematics Standard 3: Solve applied problems that use the four operations with appropriate decimal numbers and percentages. Topic Fractions and Decimals to Percentages Benchmark N.MR.05.22 Express fractions and decimals as percentages and vice versa. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently express fractions and Usually express fractions and Sometimes express fractions and Rarely express fractions and decimals as percentages and decimals as percentages and decimals as percentages and decimals as percentages and vice versa. vice versa. vice versa. vice versa. Differentiation of Instruction Strand Mathematics Standard 3: Solve applied problems that use the four operations with appropriate decimal numbers and percentages. Topic Finding the Unknown Benchmark N.FL.06.12 Calculate part of a number given the percentage and the number. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently calculate part of Usually calculate part of Sometimes calculate part of Rarely calculate part of a number given the percentage a number given the percentage a number given the percentage a number given the percentage and the number. and the number. and the number. and the number. Differentiation of Instruction Strand Mathematics Standard 4: Use ratios and rates in problem situations. Topic Express Ratios Benchmark N.ME.05.23 Express ratios in several ways given applied situations, e.g., 3 cups to 5 people, 3:5, 3/5 cups per person; recognize and find equivalent ratios. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently express ratios in Usually express ratios in Sometimes express ratios in Rarely express ratios in several ways; recognize and several ways; recognize and several ways; recognize and several ways; recognize and find equivalent ratios. find equivalent ratios. find equivalent ratios. find equivalent ratios. Differentiation of Instruction Strand Mathematics Standard 4: Use ratios and rates in problem situations. Topic Scaling Benchmark N.ME.06.11 Find equivalent ratios by scaling up or scaling down. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find equivalent ratios Usually find equivalent ratios Sometimes find equivalent ratios Rarely find equivalent ratios by scaling up or scaling down. by scaling up or scaling down. by scaling up or scaling down. by scaling up or scaling down. Differentiation of Instruction Strand Mathematics Standard 4: Use ratios and rates in problem situations. Topic Problem Solving Benchmark A.PA.06.01 Solve applied problems involving rates including speed, e.g., if a car is going 50 mph, how far will it go in 3 ½ hours? Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve applied Usually solve applied Sometimes solve applied Rarely solve applied problems involving rates including problems involving rates including problems involving rates including problems involving rates including speed. speed. speed. speed. Differentiation of Instruction Strand Mathematics Standard 5: Represent situations using algebraic expressions and solve simple equations. Topic Using Variables Benchmark A.FO.06.03 Use letters, with units, to represent quantities in a variety of contexts, e.g., y lbs., k minutes, x cookies. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently use letters, with Usually use letters, with Sometimes use letters, with Rarely use letters, with units, to represent quantities in units, to represent quantities in units, to represent quantities in units, to represent quantities in a variety of contexts. a variety of contexts. a variety of contexts. a variety of contexts. Differentiation of Instruction Strand Mathematics Standard 5: Represent situations using algebraic expressions and solve simple equations. Topic Using Variables Benchmark A.FO.06.05 Use standard conventions for writing algebraic expressions, e.g., 2x + 1 means “two times x, plus 1” and 2(x + 1) means “two times the quantity (x + 1).” Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently use standard Usually use standard Sometimes use standard Rarely use standard conventions for writing algebraic conventions for writing algebraic conventions for writing algebraic conventions for writing algebraic expressions. expressions. expressions. expressions. Differentiation of Instruction Strand Mathematics Standard 5: Represent situations using algebraic expressions and solve simple equations. Topic Creating Algebraic Expressions and Equations Benchmark A.FO.06.06 Represent information given in words using algebraic expressions and equations. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently represent information Usually represent information Sometimes represent information Rarely represent information given in words using algebraic given in words using algebraic given in words using algebraic given in words using algebraic expressions and equations. expressions and equations. expressions and equations. expressions and equations. Differentiation of Instruction Strand Mathematics Standard 5: Represent situations using algebraic expressions and solve simple equations. Topic Algebraic Expressions and Equations Benchmark A.FO.06.04 Distinguish between an algebraic expression and an equation. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently distinguish between Usually distinguish between Sometimes distinguish between Rarely distinguish between algebraic expressions and algebraic expressions and algebraic expressions and algebraic expressions and equations. equations. equations. equations. Differentiation of Instruction Strand Mathematics Standard 5: Represent situations using algebraic expressions and solve simple equations. Topic Simplifying Benchmark A.FO.06.07 Simplify expressions of the first degree by combining like terms, and evaluate using specific values. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently simplify expressions Usually simplify expressions Sometimes simplify expressions Rarely simplify expressions by combining like teems and evaluate by combining like teems and evaluate by combining like teems and evaluate by combining like teems and evaluate using specific values. using specific values. using specific values. using specific values. Differentiation of Instruction Strand Mathematics Standard 5: Represent situations using algebraic expressions and solve simple equations. Topic Solving Linear Equations Benchmark A.FO.06.11 Relate simple linear equations with integer coefficients, e.g., 3x = 8 or x + 5 = 10, to particular contexts and solve. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently relate simple linear Usually relate simple linear Sometimes relate simple linear Rarely relate simple linear equations with integer coefficents equations with integer coefficents equations with integer coefficents equations with integer coefficents and solve. and solve. and solve. and solve. Differentiation of Instruction Strand Mathematics Standard 5: Represent situations using algebraic expressions and solve simple equations. Topic Creating New Equations Benchmark A.FO.06.12 Understand that adding or subtracting the same number to both sides of an equation creates a new equation that has the same solution. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand that adding Usually understand that adding Sometimes understand that adding Rarely understand that adding and subtracting the same number and subtracting the same number and subtracting the same number and subtracting the same number to both sides of an equation creates to both sides of an equation creates to both sides of an equation creates to both sides of an equation creates a new equation with the same a new equation with the same a new equation with the same a new equation with the same solution. solution. solution. solution. Differentiation of Instruction Strand Mathematics Standard 5: Represent situations using algebraic expressions and solve simple equations. Topic Creating New Equations Benchmark A.FO.06.13 Understand that multiplying or dividing the same number to both sides of an equation creates a new equation that has the same solution. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand that Usually understand that Sometimes understand that Rarely understand that multiplying or dividing the same multiplying or dividing the same multiplying or dividing the same multiplying or dividing the same number to both sides of an equation number to both sides of an equation number to both sides of an equation number to both sides of an equation creates a new equation with creates a new equation with creates a new equation with creates a new equation with the same solution. the same solution. the same solution. the same solution. Differentiation of Instruction Strand Mathematics Standard 6 Represent linear relationships using verbal descriptions, tables, graphs, and formulas; be able to translate among the representations. Topic Plotting Ordered Pairs Benchmark A.RP.06.02 Plot ordered pair of integers and use ordered pairs of integers to identify points in all four quadrants of the coordinate plane. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently plot and use ordered Usually plot and use ordered Sometimes plot and use ordered Rarely plot and use ordered pair of integers to identify points in pair of integers to identify points in pair of integers to identify points in pair of integers to identify points in all four quadrants of a all four quadrants of a all four quadrants of a all four quadrants of a coordinate plane. coordinate plane. coordinate plane. coordinate plane. Differentiation of Instruction Strand Mathematics Standard 6 Represent linear relationships using verbal descriptions, tables, graphs, and formulas; be able to translate among the representations. Topic Plotting Ordered Pairs Benchmark A.RP.06.08 Understand that relationships between quantities can be suggested by graphs and tables. of the coordinate plane. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand that Usually understand that Sometimes understand that Rarely understand that relationships between quantities relationships between quantities relationships between quantities relationships between quantities can be suggested by graphs and can be suggested by graphs and can be suggested by graphs and can be suggested by graphs and tables of the coordinate planes. tables of the coordinate planes. tables of the coordinate planes. tables of the coordinate planes. Differentiation of Instruction Strand Mathematics Standard 6 Represent linear relationships using verbal descriptions, tables, graphs, and formulas; be able to translate among the representations. Topic Problem Solving Benchmark A.RP.06.09 Solve problems involving linear functions whose input values are integers; write the equation; graph the resulting ordered pairs of integers, e.g., given c chairs, the “leg function” is 4c; if you have 5 chairs, how many legs?; if you have 12 legs, how many chairs? Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve problems involving Usually solve problems involving Sometimes solve problems involving Rarely solve problems involving linear functions whose input values linear functions whose input values linear functions whose input values linear functions whose input values are integers; write the equation and are integers; write the equation and are integers; write the equation and are integers; write the equation and graph the results. graph the results. graph the results. graph the results. Differentiation of Instruction Strand Mathematics Standard 6 Represent linear relationships using verbal descriptions, tables, graphs, and formulas; be able to translate among the representations. Topic Relationships between Quantities Benchmark A.RP.06.02 Represent simple relationships between quantities using verbal descriptions, formulas or equations, tables, and graphs, e.g., perimeter-side relationship for a square, conversions distance-time graphs, such as feet to inches. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently represent simple Usually represent simple Sometimes represent simple Rarely represent simple relationships between quantities relationships between quantities relationships between quantities relationships between quantities using verbal description, formulas using verbal description, formulas using verbal description, formulas using verbal description, formulas or equations, tables and graphs. or equations, tables and graphs. or equations, tables and graphs. or equations, tables and graphs. Differentiation of Instruction Strand Mathematics Standard 7 Understand and apply properties of lines, angles, and triangles. Topic Geometric Construction Benchmark G.SR.06.05 Use paper folding to perform basic geometric constructions of perpendicular lines, midpoints of line segments and angle bisectors; justify informally. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently performs basic Usually performs basic Sometimes performs basic Rarely performs basic geometric constructions of geometric constructions of geometric constructions of geometric constructions of perpendicular lines, midpoinrts of perpendicular lines, midpoinrts of perpendicular lines, midpoinrts of perpendicular lines, midpoinrts of line segments and angle bisectors by line segments and angle bisectors by line segments and angle bisectors by line segments and angle bisectors by folding paper. folding paper. folding paper. folding paper. Differentiation of Instruction Strand Mathematics Standard 7 Understand and apply properties of lines, angles, and triangles. Topic Applying Properties Benchmark G.SR.06.01 Understand and apply basic properties of lines, angles, and triangles (See Below) Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand and apply Usually performs basic Sometimes performs basic Rarely performs basic basic properties of lines,angles geometric constructions of geometric constructions of geometric constructions of and triangle perpendicular lines, midpoinrts of perpendicular lines, midpoinrts of perpendicular lines, midpoinrts of line segments and angle bisectors by line segments and angle bisectors by line segments and angle bisectors by line segments and angle bisectors by folding paper. folding paper. folding paper. folding paper. Differentiation of Instruction - triangle inequality relationships of vertical angles, complementary angles, supplementary angles congruence of corresponding and alternate interior angles when parallel lines are cut by a transversal, and that such congruences imply parallel lines locate interior and exterior angles of any triangle, and use the property that an exterior angle of a triangle is equal to the sum of the remote (opposite) interior angles know that the sum of the exterior angles of a convex polygon is 360º. Strand Mathematics Standard 7 Understand and apply properties of lines, angles, and triangles. Topic Congruent Polygons Benchmark G.SR.06.02 Understand that for polygons, congruence means corresponding sides and angles have equal measures. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understands that Usually understands that Sometimes understands that Rarely understands that congruent polygons have congruent polygons have congruent polygons have congruent polygons have corresponding sides and angles corresponding sides and angles corresponding sides and angles corresponding sides and angles that have equal measures. that have equal measures. that have equal measures. that have equal measures. Differentiation of Instruction Strand Mathematics Standard 8 Compute the volume and surface area of cubes and rectangular prisms given the lengths of their sides using formulas. Topic Congruent Polygons Benchmark M.PS.06.02 Draw patterns (of faces) for a cube and rectangular prism that, when cut, will cover the solid exactly (nets). Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently draw patterns for Usually draw patterns for Sometimes draw patterns for Rarely draw patterns for cubes and rectangular prisms that cubes and rectangular prisms that cubes and rectangular prisms that cubes and rectangular prisms that when cut will cover the solid exactly. when cut will cover the solid exactly. when cut will cover the solid exactly. when cut will cover the solid exactly. Differentiation of Instruction Content Area: Math Grade/Course: 7th Strand Mathematics Standard 1: Solve problems involving operations with integers, including solving linear equations Topic Understanding Integer Benchmark N.ME.06.19 Understand that 0 is an integer that is neither negative nor positive. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand that 0 is Usually understand that 0 is Sometimes understand that 0 is Rarely understand that 0 is an integer that is neither negative an integer that is neither negative an integer that is neither negative an integer that is neither negative nor positive. nor positive. nor positive. nor positive. Differentiation of Instruction Strand Mathematics Standard 1: Solve problems involving operations with integers, including solving linear equations Topic Understanding Integer Benchmark N.ME.06.17 Locate negative rational numbers (including integers) on the number line; know that numbers and their negatives add to 0 and are on opposites sides and at equal distance from 0 on a number line. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently locate negative rational Usually locate negative rational Sometimes locate negative rational Rarely locate negative rational numbers on the number line; know numbers on the number line; know numbers on the number line; know numbers on the number line; know that numbers and their negatives add that numbers and their negatives add that numbers and their negatives add that numbers and their negatives add to 0 and are on opposite sides and to 0 and are on opposite sides and to 0 and are on opposite sides and to 0 and are on opposite sides and at equal distance from 0 on the at equal distance from 0 on the at equal distance from 0 on the at equal distance from 0 on the number line. number line. number line. number line. Differentiation of Instruction Strand Mathematics Standard 1: Solve problems involving operations with integers, including solving linear equations Topic Integers Benchmark N.FL.06.09 Add and multiply integers between -10 and 10; subtract and divide integers using the related facts. Use the number line and chip models for addition and subtraction. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently add and multiply Usually add and multiply Sometimes add and multiply Rarely add and multiply integers between -10 and 10; integers between -10 and 10; integers between -10 and 10; integers between -10 and 10; subtract and divide integers. Use the subtract and divide integers. Use the subtract and divide integers. Use the subtract and divide integers. Use the number line and chip models for number line and chip models for number line and chip models for number line and chip models for addition and subtraction. addition and subtraction. addition and subtraction. addition and subtraction. Differentiation of Instruction Strand Mathematics Standard 1: Solve problems involving operations with integers, including solving linear equations Topic Inverse Operation Benchmark N.MR.06.08 Understand integer subtraction as the inverse of integer addition. Understand integer division as the division as the inverse of integer multiplication. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand the inverse Usually understand the inverse Sometimes understand the inverse Rarely understand the inverse of interger subtraction and integer of interger subtraction and integer of interger subtraction and integer of interger subtraction and integer division. division. division. division. Differentiation of Instruction Strand Mathematics Standard 1: Solve problems involving operations with integers, including solving linear equations Topic Poperties of Real Numbers Benchmark A.PA.07.11 Understand and use basic properties of real numbers: additive and multiplicative identities, additive and multiplicative inverses, commutativity, associativity, and the distributive property of multiplication over addition. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand and use Usually understand and use Sometimes understand and use Rarely understand and use basic properties of real numbers basic properties of real numbers basic properties of real numbers basic properties of real numbers Differentiation of Instruction Strand Mathematics Standard 1: Solve problems involving operations with integers, including solving linear equations Topic Problem Solving Benchmark N.FL.07.07 Solve problems involving operations with integers. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve problems Usually solve problems Sometimes solve problems Rarely solve problems involving operations with integers. involving operations with integers. involving operations with integers. involving operations with integers. Differentiation of Instruction Strand Mathematics Standard 2: Solve problems involving rates, ratios, and proportions using various methods. Topic Express Ratios Benchmark N.ME.05.23 Express ratios in several ways given applied situations, e.g., 3 cups to 5 people, 3:5, 3/5 cups per person; recognize and find equivalent ratios. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently express ratios in Usually express ratios in Sometimes express ratios in Rarely express ratios in several ways; recognize and several ways; recognize and several ways; recognize and several ways; recognize and find equivalent ratios. find equivalent ratios. find equivalent ratios. find equivalent ratios. Differentiation of Instruction Strand Mathematics Standard 2: Solve problems involving rates, ratios, and proportions using various methods. Topic Scaling Benchmark N.ME.06.11 Find equivalent ratios by scaling up or scaling down. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find equivalent ratios Usually find equivalent ratios Sometimes find equivalent ratios Rarely find equivalent ratios by scaling up or scaling down. by scaling up or scaling down. by scaling up or scaling down. by scaling up or scaling down. Differentiation of Instruction Strand Mathematics Standard 2: Solve problems involving rates, ratios, and proportions using various methods. Topic Problem Solving Benchmark A.PA.06.01 Solve applied problems involving rates including speed, e.g., if a car is going 50 mph, how far will it go in 3 ½ hours? Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve applied Usually solve applied Sometimes solve applied Rarely solve applied problems involving rates including problems involving rates including problems involving rates including problems involving rates including speed. speed. speed. speed. Differentiation of Instruction Strand Mathematics Standard 2: Solve problems involving rates, ratios, and proportions using various methods. Topic Problem Solving Benchmark N.MR.07.02 Solve problems involving derived quantities such as density, velocity, and weighted averages. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve problems Usually solve problems Sometimes solve problems Rarely solve problems involving derived quantities such involving derived quantities such involving derived quantities such involving derived quantities such as density, velocitty, and as density, velocitty, and as density, velocitty, and as density, velocitty, and weighted averages. weighted averages. weighted averages. weighted averages. Differentiation of Instruction Strand Mathematics Standard 2: Solve problems involving rates, ratios, and proportions using various methods. Topic Problem Solving Benchmark N.FL.07.03 Calculate rates of change including speed. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently calculate rates Usually calculate rates Sometimes calculate rates Rarely calculate rates of change including speed. of change including speed. of change including speed. of change including speed. Differentiation of Instruction Strand Mathematics Standard 2: Solve problems involving rates, ratios, and proportions using various methods. Topic Converting between Units Benchmark N.MR.07.04 Convert ratio quantities between different systems of units such as feet per second to miles per hour. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently covert ratio quantities Usually covert ratio quantities Sometimes covert ratio quantities Rarely covert ratio quantities between different systems of units. between different systems of units. between different systems of units. between different systems of units. Differentiation of Instruction Strand Mathematics Standard 2: Solve problems involving rates, ratios, and proportions using various methods. Topic Problem Solving Benchmark N.FL.07.05 Solve proportion problems using such methods as unit rate, scaling, finding equivalent fractions, and solving the proportion equation a/b = c/d; know how to see patterns about proportional situations in tables. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve proportion Usually solve proportion Sometimes solve proportion Rarely solve proportion problems using different methods; problems using different methods; problems using different methods; problems using different methods; know how to see patterns about know how to see patterns about know how to see patterns about know how to see patterns about proportional situations in tables. proportional situations in tables. proportional situations in tables. proportional situations in tables. Differentiation of Instruction Strand Mathematics Standard 2: Solve problems involving rates, ratios, and proportions using various methods. Topic Problem Solving Benchmark G.TR.07.04 Solve problems about similar figures and scale drawings. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve problems Usually solve problems Sometimes solve problems Rarely solve problems about similar figures and scale about similar figures and scale about similar figures and scale about similar figures and scale drawings. drawings. drawings. drawings. Differentiation of Instruction Strand Mathematics Standard 3: From applied situations, generate and solve linear equations of the form ax + b = c and ax + b = cx + d, and interpret solutions. Topic Solving Linear Equations Benchmark A.FO.06.11 A.FO.06.14 Relate simple linear equations with integer coefficients, e.g., 3x = 8 or x + 5 = 10, to particular contexts and solve. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently relate simple linear Usually relate simple linear Sometimes relate simple linear Rarely relate simple linear equations with integer coefficents equations with integer coefficents equations with integer coefficents equations with integer coefficents and solve. and solve. and solve. and solve. Differentiation of Instruction Strand Mathematics Standard 3: From applied situations, generate and solve linear equations of the form ax + b = c and ax + b = cx + d, and interpret solutions. Topic Poperties of Real Numbers Benchmark A.PA.07.11 Understand and use basic properties of real numbers: additive and multiplicative identities, additive and multiplicative inverses, commutativity, associativity, and the distributive property of multiplication over addition. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand and use Usually understand and use Sometimes understand and use Rarely understand and use basic properties of real numbers basic properties of real numbers basic properties of real numbers basic properties of real numbers Differentiation of Instruction Strand Mathematics Standard 3: From applied situations, generate and solve linear equations of the form ax + b = c and ax + b = cx + d, and interpret solutions. Topic Solving Linear Equations Benchmark A.FO.07.12 N.FL.07.08 Add, subtract, and multiply simple algebraic expressions of the first degree and justify using properties of real numbers. Be able to add, subtract, multiply, and divide positive and negative rational numbers fluently in algebraic expressions. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently add, subtract, and Usually add, subtract, and Sometimes add, subtract, and Rarely add, subtract, and multiply simple algebraic expressions multiply simple algebraic expressions multiply simple algebraic expressions multiply simple algebraic expressions of real numbers; add, subtract, of real numbers; add, subtract, of real numbers; add, subtract, of real numbers; add, subtract, multiply and divide rational numbers multiply and divide rational numbers multiply and divide rational numbers multiply and divide rational numbers in algebraic expressions in algebraic expressions in algebraic expressions in algebraic expressions Differentiation of Instruction Strand Mathematics Standard 4: Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations. Topic Linear Relationships Benchmark A.PA.07.01 Recognize when information given in a table, graph, or formula suggests a directly proportional or linear relationship. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently recognize when Usually recognize when Sometimes recognize when Rarely recognize when information in a table, graph or information in a table, graph or information in a table, graph or information in a table, graph or formula suggests a directly formula suggests a directly formula suggests a directly formula suggests a directly proportional or linear relationship. proportional or linear relationship. proportional or linear relationship. proportional or linear relationship. Differentiation of Instruction Strand Mathematics Standard 4: Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations. Topic Linear Relationships Benchmark A.PA.07.02 Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas and translate among these representations. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently represent proportional Usually represent proportional Sometimes represent proportional Rarely represent proportional and linear relationships using and linear relationships using and linear relationships using and linear relationships using verbal descriptions. verbal descriptions. verbal descriptions. verbal descriptions. Differentiation of Instruction Strand Mathematics Standard 4: Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations. Topic Linear Relationships Benchmark A.PA.07.03 Given a directly proportional or other linear situation, graph and interpret the slope and and intercept(s) in terms of the original situation; evaluate y = mx + b for specific x values. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently graph and interpret Usually graph and interpret Sometimes graph and interpret Rarely graph and interpret the slope and intercepts given a the slope and intercepts given a the slope and intercepts given a the slope and intercepts given a directly proportional or other directly proportional or other directly proportional or other directly proportional or other linear situation. linear situation. linear situation. linear situation. Differentiation of Instruction Strand Mathematics Standard 4: Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations. Topic Problem Solving Benchmark A.PA.07.04 For directly proportional or linear situations, solve applied problems using graphs and equations. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve applied Usually solve applied Sometimes solve applied Rarely solve applied problems using graphs and equations problems using graphs and equations problems using graphs and equations problems using graphs and equations for directly proportional or linear for directly proportional or linear for directly proportional or linear for directly proportional or linear situations. situations. situations. situations. Differentiation of Instruction Strand Mathematics Standard 4: Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations. Topic Linear Relationships Benchmark A.PA.07.05 Recognize and use directly proportional relationships of the form y = mx, and distinguish from linear relationships of the form y = mx + b, b non-zero; understand that in a directly proportional relationship between two quantities, one quantity is a constant multiple of the other quantity. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently represent proportional Usually represent proportional Sometimes represent proportional Rarely represent proportional and linear relationships of the form and linear relationships of the form and linear relationships of the form and linear relationships of the form y=mx and distingusih from linear y=mx and distingusih from linear y=mx and distingusih from linear y=mx and distingusih from linear relationships of the form y=mx+b relationships of the form y=mx+b relationships of the form y=mx+b relationships of the form y=mx+b where b is non 0. where b is non 0. where b is non 0. where b is non 0. Differentiation of Instruction Strand Mathematics Standard 4: Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations. Topic Linear Relationships Benchmark A.PA.07.06 Calculate the slope from the graph of a linear function as the ratio of “rise/run” for a pair of points on the graph, and express the answer as a fraction and a decimal; understand that linear functions have slope that is a constant rate of change Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently calculate the slope Usually calculate the slope Sometimes calculate the slope Rarely calculate the slope as the ratio rise/run for a pair of as the ratio rise/run for a pair of as the ratio rise/run for a pair of as the ratio rise/run for a pair of points on the graph and express points on the graph and express points on the graph and express points on the graph and express answer as a fraction and decimal; answer as a fraction and decimal; answer as a fraction and decimal; answer as a fraction and decimal; understand that a slope is a constant understand that a slope is a constant understand that a slope is a constant understand that a slope is a constant rate of change. rate of change. rate of change. rate of change. Differentiation of Instruction Strand Mathematics Standard 4: Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations. Topic Linear Functions Benchmark A.PA.07.07 Represent linear functions in the form y = x + b, y = mx, and y = mx + b, and graph, interpreting slope and y-intercept. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently represent linear Usually represent linear Sometimes represent linear Rarely represent linear functions in the form y=x+b, functions in the form y=x+b, functions in the form y=x+b, functions in the form y=x+b, y+mx+b, and y=mx, and graph, y+mx+b, and y=mx, and graph, y+mx+b, and y=mx, and graph, y+mx+b, and y=mx, and graph, interpret slope and y-intercept. interpret slope and y-intercept. interpret slope and y-intercept. interpret slope and y-intercept. Differentiation of Instruction Strand Mathematics Standard 4: Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations. Topic X and Y Intercept Benchmark A.PA.07.02 Find and interpret the x and/or y-intercepts of a linear equation or function. Know that the solution to a linear equation of the form ax + b = 0 corresponds to the point at which the graph of y = ax + b crosses the x-axis. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find and interpret the Usually find and interpret the Sometimes find and interpret the Rarely find and interpret the x and/or y-intercepts of a linear x and/or y-intercepts of a linear x and/or y-intercepts of a linear x and/or y-intercepts of a linear equation or function. Know that equation or function. Know that equation or function. Know that equation or function. Know that the solution to a linear equation the solution to a linear equation the solution to a linear equation the solution to a linear equation corresponds to the point where the corresponds to the point where the corresponds to the point where the corresponds to the point where the y=ax+b crosses the x-axis. y=ax+b crosses the x-axis. y=ax+b crosses the x-axis. y=ax+b crosses the x-axis. Differentiation of Instruction Strand Mathematics Standard 5: Solve problems about similar figures and scale drawings (using concepts of proportionality related to M7.2). Topic Similar Figures and Scale Factors Benchmark G.TR.07.03 Understand that in similar polygons, corresponding angles are congruent and the ratios of corresponding sides are equal; understand the concepts of similar figures and scale factor. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand that in Usually understand that in Sometimes understand that in Rarely understand that in similar polygons, corresponding similar polygons, corresponding similar polygons, corresponding similar polygons, corresponding angles and the ratios of the sides angles and the ratios of the sides angles and the ratios of the sides angles and the ratios of the sides are congruent. Understand the are congruent. Understand the are congruent. Understand the are congruent. Understand the concept of similar figures and concept of similar figures and concept of similar figures and concept of similar figures and scale factor. scale factor. scale factor. scale factor. Differentiation of Instruction Strand Mathematics Standard 5: Solve problems about similar figures and scale drawings (using concepts of proportionality related to M7.2). Topic Similar Triangles Benchmark G.TR.07.05 Show that two triangles are similar using the criteria: corresponding angles are congruent (AAA similarity); the ratios of two pairs of corresponding sides are equal and the included angles are congruent (SAS similarity); ratios of all pairs of corresponding sides are (SSS similarity); use these criteria to solve problems and to justify arguments. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently show that two Usually show that two Sometimes show that two Rarely show that two triangles are similar use the triangles are similar use the triangles are similar use the triangles are similar use the AAA, SAS, and SSS criterias. AAA, SAS, and SSS criterias. AAA, SAS, and SSS criterias. AAA, SAS, and SSS criterias. Strand Mathematics Standard 5: Solve problems about similar figures and scale drawings (using concepts of proportionality related to M7.2). Topic Similar Figures and Scale Factors Benchmark G.TR.07.06 Understand and use the fact that when two triangles are similar with scale factor of r, their areas are related by a factor of r to the second power. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand that when Usually understand that when Sometimes understand that when Rarely understand that when two triangles are similar with the two triangles are similar with the two triangles are similar with the two triangles are similar with the scale factor r, their areas are related scale factor r, their areas are related scale factor r, their areas are related scale factor r, their areas are related by a factor of r to the second power. by a factor of r to the second power. by a factor of r to the second power. by a factor of r to the second power. Strand Mathematics Standard 6: Represent and interpret data using appropriate graphs. Topic Interpreting Data Benchmark D.RE.07.01 Represent and interpret data using circle graphs, stem and leaf plots, histograms, and box-and-whisker plots and select appropriate representation to address specific questions. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently interpret data using Usually interpret data using Sometimes interpret data using Rarely interpret data using appropriate representation to appropriate representation to appropriate representation to appropriate representation to address specific questions. address specific questions. address specific questions. address specific questions. Strand Mathematics Standard 6: Represent and interpret data using appropriate graphs. Topic Interpreting Data Benchmark D.AN.07.02 Create and interpret scatter plots and use an estimated line of best fit to answer questions about the data. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently create and interpret Usually create and interpret Sometimes create and interpret Rarely create and interpret scatter plots and use an estimated scatter plots and use an estimated scatter plots and use an estimated scatter plots and use an estimated line of best fit to answer questions line of best fit to answer questions line of best fit to answer questions line of best fit to answer questions about data. about data. about data. about data. Strand Mathematics Standard 6: Represent and interpret data using appropriate graphs. Topic Relative Frequencies Benchmark D.AN.07.03 Calculate and interpret relative frequencies and cumulative frequencies for given data sets. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently calculate and interpret Usually calculate and interpret Sometimes calculate and interpret Rarely calculate and interpret relative frequencies and cumulative relative frequencies and cumulative relative frequencies and cumulative relative frequencies and cumulative frequencies dfoe given data sets. frequencies dfoe given data sets. frequencies dfoe given data sets. frequencies dfoe given data sets. Strand Mathematics Standard 6: Represent and interpret data using appropriate graphs. Topic Median, Quartile and Interquartile Benchmark D.AN.07.04 Find and interpret the median, quartiles, and interquartile range of a given set of data Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find and interpret Usually find and interpret Sometimes find and interpret Rarely find and interpret the median, quartiles, and the median, quartiles, and the median, quartiles, and the median, quartiles, and interquartile range of a given set interquartile range of a given set interquartile range of a given set interquartile range of a given set of data. of data. of data. of data. Content Area: Math Grade/Course: 8th Strand Mathematics Standard 1: Solve problems involving everyday arithmetic calculations, including percent increases and decreases, weighted averages, and problems involving ratio units (e.g. miles per hour, dollars per pound, etc.) Topic Understanding Integer Benchmark N.MR.08.07 Understand percent increase and percent decrease in both sum and product form, e.g., 3% increase of a quantity x is x + .03x = 1.03x. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand percent Usually understand percent Sometimes understand percent Rarely understand percent increase and percent decrease. increase and percent decrease. increase and percent decrease. increase and percent decrease. Differentiation of Instruction Strand Mathematics Standard 1: Solve problems involving everyday arithmetic calculations, including percent increases and decreases, weighted averages, and problems involving ratio units (e.g. miles per hour, dollars per pound, etc.) Topic Problem Solving Benchmark N.MR.08.09 Solve problems involving compounded interest or multiple discounts. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve problems Usually solve problems Sometimes solve problems Rarely solve problems invoving compound integers or invoving compound integers or invoving compound integers or invoving compound integers or multiple discounts. multiple discounts. multiple discounts. multiple discounts. Differentiation of Instruction Strand Mathematics Standard 2: Set up and solve applied problems involving linear inequalities, linear equations, quadratic equations, and simultaneous equations (system of equations) in two variables. Topic Problem Solving Benchmark A.FO.08.10 Understand that to solve the equation f(x) = g(x) means to find all values of x for which the equation is true. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand that Usually understand that Sometimes understand that Rarely understand that to solve the equation f(x) = g(x) to solve the equation f(x) = g(x) to solve the equation f(x) = g(x) to solve the equation f(x) = g(x) you must find the value of x. you must find the value of x. you must find the value of x. you must find the value of x. Differentiation of Instruction Strand Mathematics Standard 2: Set up and solve applied problems involving linear inequalities, linear equations, quadratic equations, and simultaneous equations (system of equations) in two variables. Topic Problem Solving Benchmark (A.FO.08.11, A.FO.08.13 Set up and solve applied problems involving simultaneous linear equations in two variables by graphing, by substitution, and by linear combination; estimate solutions using graphs; include examples with no solutions and infinitely many solutions. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently set and solve applied Usually set and solve applied Sometimes set and solve applied Rarey set and solve applied problems involving simultaneous problems involving simultaneous problems involving simultaneous problems involving simultaneous linear equations with 2 variables by linear equations with 2 variables by linear equations with 2 variables by linear equations with 2 variables by graphing, substitution, linear graphing, substitution, linear graphing, substitution, linear graphing, substitution, linear combination; estimate. combination; estimate. combination; estimate. combination; estimate. Differentiation of Instruction Strand Mathematics Standard 2: Set up and solve applied problems involving linear inequalities, linear equations, quadratic equations, and simultaneous equations (system of equations) in two variables. Topic Problem Solving Benchmark A.FO.08.12, A.FO.08.13 Set up and solve applied problems involving linear inequalities in one and two variables, and graph the solution sets. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently set and solve applied Usually set and solve applied Sometimes set and solve applied Rarely set and solve applied problems involving linear problems involving linear problems involving linear problems involving linear inequalities with one and two inequalities with one and two inequalities with one and two inequalities with one and two varibles, and graph the solution. varibles, and graph the solution. varibles, and graph the solution. varibles, and graph the solution. Differentiation of Instruction Strand Mathematics Standard 2: Set up and solve applied problems involving linear inequalities, linear equations, quadratic equations, and simultaneous equations (system of equations) in two variables. Topic Problem Solving Benchmark A.FO.08.07 Recognize and apply the common formulas: and represent these geometrically Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently recognize and Usually recognize and Sometime recognize and Rarely recognize and apply the common formulas and apply the common formulas and apply the common formulas and apply the common formulas and represent these geometrically. represent these geometrically. represent these geometrically. represent these geometrically. Differentiation of Instruction Strand Mathematics Standard 2: Set up and solve applied problems involving linear inequalities, linear equations, quadratic equations, and simultaneous equations (system of equations) in two variables. Topic Factoring Benchmark A.FO.08.8 Factor simple quadratic expressions with integer coefficients; solve simple quadratic equations; verify solutions by evaluation. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently factor simple Usually factor simple Soemtimes factor simple Rarely factor simple quadratic expressions with integer quadratic expressions with integer quadratic expressions with integer quadratic expressions with integer coefficienrts; solve equations and coefficienrts; solve equations and coefficienrts; solve equations and coefficienrts; solve equations and verify solution by evaluation. verify solution by evaluation. verify solution by evaluation. verify solution by evaluation. Differentiation of Instruction Strand Mathematics Standard 2: Set up and solve applied problems involving linear inequalities, linear equations, quadratic equations, and simultaneous equations (system of equations) in two variables. Topic Problem Solving Benchmark A.FO.08.9 Solve applied problems involving simple quadratic equations. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve applied Usually solve applied Sometimes solve applied Rarely solve applied problems involving simple problems involving simple problems involving simple problems involving simple quadratic equations. quadratic equations. quadratic equations. quadratic equations. Differentiation of Instruction Strand Mathematics Standard 3: Identify and represent families of functions using tables, graphs, and equations; how changes in one variable affect the other. Topic Identify Different Functions Benchmark A.RP.08.01 Identify and represent linear functions, quadratic functions, and other simple functions including inversely proportional relationships; cubics; roots; and exponentials; using tables, graphs, and equations. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify and represent Usually identify and represent Sometimes identify and represent Rarely identify and represent linear functions, quadratic functions, linear functions, quadratic functions, linear functions, quadratic functions, linear functions, quadratic functions, and other simple functions including and other simple functions including and other simple functions including and other simple functions including inversely proportional relationships. inversely proportional relationships. inversely proportional relationships. inversely proportional relationships. Differentiation of Instruction Strand Mathematics Standard 3: Identify and represent families of functions using tables, graphs, and equations; how changes in one variable affect the other. Topic Problem Solving Benchmark A.PA.08.02 For basic functions, e.g., simple quadratics, direct and indirect variation, and population growth, describe how changes in one variable affect the others. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently describe how changes Usually describe how changes Sometimes describe how changes Rarely describe how changes in one variable affect the others for in one variable affect the others for in one variable affect the others for in one variable affect the others for basic functions. basic functions. basic functions. basic functions. Differentiation of Instruction Strand Mathematics Standard 3: Identify and represent families of functions using tables, graphs, and equations; how changes in one variable affect the other. Topic Problem Solving Benchmark A.RP.08.01 Recognize basic functions in problem context; e.g., area of a circle is pr2, inversely proportional relationships; cubics; roots; and exponentials; using tables, graphs, and equations. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently identify and represent Usually identify and represent Sometimes identify and represent Rarely identify and represent linear functions, quadratic functions, linear functions, quadratic functions, linear functions, quadratic functions, linear functions, quadratic functions, and other simple functions including and other simple functions including and other simple functions including and other simple functions including inversely proportional relationships. inversely proportional relationships. inversely proportional relationships. inversely proportional relationships. Differentiation of Instruction Strand Mathematics Standard 3: Identify and represent families of functions using tables, graphs, and equations; how changes in one variable affect the other. Topic quadratic function. Benchmark A.RP.08.05 Relate quadratic functions in factored form and vertex form to their graphs and vice versa; in particular, note that solutions of a quadratic equation are the x-intercepts of the corresponding quadratic function. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently relate quadratic Usually relate quadratic Sometimes relate quadratic Rarely relate quadratic functions is factored form and functions is factored form and functions is factored form and functions is factored form and vertex form to their graph and vice vertex form to their graph and vice vertex form to their graph and vice vertex form to their graph and vice versa. versa. versa. versa. Differentiation of Instruction Strand Mathematics Standard 3: Identify and represent families of functions using tables, graphs, and equations; how changes in one variable affect the other. Topic Problem Solving Benchmark A.RP.08.06 Graph factorable quadratic functions, finding where the graph intersects the x axis and the coordinates of the vertex; use words “parabola” and “roots”; include functions in vertex form and those with leading coefficient -1. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently graph quadratic functions Usually graph quadratic functions Sometimes graph quadratic functions Rarely graph quadratic functions use words parabola and roots use words parabola and roots use words parabola and roots use words parabola and roots include functions in vertex form include functions in vertex form include functions in vertex form include functions in vertex form and those with leading coefficient -1 and those with leading coefficient -1 and those with leading coefficient -1 and those with leading coefficient -1 Differentiation of Instruction Strand Mathematics Standard 4: Solve problems involving area of triangles, quadrilaterals and complex figures; area and circumference of circles; surface area and volume. Topic Problem Solving Benchmark G.GS.08.01 Use the Pythagorean Theorem and its converse to solve applied problems including perimeter, area, and volume problems. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently use the Usually use the Sometimes use the Rarely use the Pythagorean Theorem and its Pythagorean Theorem and its Pythagorean Theorem and its Pythagorean Theorem and its converse to solve applied problems, converse to solve applied problems, converse to solve applied problems, converse to solve applied problems, Differentiation of Instruction Strand Mathematics Standard 4: Solve problems involving area of triangles, quadrilaterals and complex figures; area and circumference of circles; surface area and volume. Topic Distance Formula Benchmark G.LO.08.02 Find the distance between two points on the coordinate plane using the distance formula; recognize that the distance formula is an application of the Pythagorean Theorem. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find the distance Usually find the distance Sometimes find the distance Rarely find the distance between two points on the between two points on the between two points on the between two points on the coordinate plane using the distancw coordinate plane using the distancw coordinate plane using the distancw coordinate plane using the distancw formula. formula. formula. formula. Differentiation of Instruction Strand Mathematics Standard 4: Solve problems involving area of triangles, quadrilaterals and complex figures; area and circumference of circles; surface area and volume. Topic Problem Solving Benchmark G.SR.08.03 Understand the definition of a circle; know and use the formulas for circumference and area of a circle to solve problems. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently know and use the Usually know and use the Sometimes know and use the Rarely know and use the formula for circumference and formula for circumference and formula for circumference and formula for circumference and area of a circle to solve problems. area of a circle to solve problems. area of a circle to solve problems. area of a circle to solve problems. Differentiation of Instruction Strand Mathematics Standard 4: Solve problems involving area of triangles, quadrilaterals and complex figures; area and circumference of circles; surface area and volume. Topic Problem Solving Benchmark G.SR.08.04 Find area and perimeter of complex figures by sub-dividing them into basic shapes (quadrilaterals, triangles, circles). Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently find the area and Usually find the area and Sometimes find the area and Rarely find the area and perimeter of complex figures by perimeter of complex figures by perimeter of complex figures by perimeter of complex figures by sub-dividing them into basic shapes. sub-dividing them into basic shapes. sub-dividing them into basic shapes. sub-dividing them into basic shapes. Differentiation of Instruction Strand Mathematics Standard 4: Solve problems involving area of triangles, quadrilaterals and complex figures; area and circumference of circles; surface area and volume. Topic Problem Solving Benchmark G.SR.08.05 Solve applied problems involving areas of triangles, quadrilaterals, and circles. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently solve applied Usually solve applied Sometimes solve applied Rarely solve applied problems involving areas of problems involving areas of problems involving areas of problems involving areas of triangles, quadrilateralas, and circles. triangles, quadrilateralas, and circles. triangles, quadrilateralas, and circles. triangles, quadrilateralas, and circles. Differentiation of Instruction Strand Mathematics Standard 4: Solve problems involving area of triangles, quadrilaterals and complex figures; area and circumference of circles; surface area and volume. Topic Sketching Benchmark G.SR.08.08 Sketch a variety of two-dimensional representations of three dimensional solids including orthogonal views (top, front, and side), picture views (projective or isometric), and nets, use such two-dimensional representations to help solve problems. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently sketch a variety Usually sketch a variety Sometimes sketch a variety Rarely sketch a variety of two-dimensional representations of two-dimensional representations of two-dimensional representations of two-dimensional representations of three-dimensional solids and use of three-dimensional solids and use of three-dimensional solids and use of three-dimensional solids and use them to help solve problems. them to help solve problems. them to help solve problems. them to help solve problems. Differentiation of Instruction Strand Mathematics Standard 4: Solve problems involving area of triangles, quadrilaterals and complex figures; area and circumference of circles; surface area and volume. Topic Problem Solving Benchmark G.SR.08.06 Know the volume formulas for generalized cylinders (bh), generalized cones and pyramids (1/3bh) and spheres (4/3pr3) and apply them to solve problems. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently know the volume Usually know the volume Sometimes know the volume Rarely know the volume formulas for generalized cylinders, formulas for generalized cylinders, formulas for generalized cylinders, formulas for generalized cylinders, cones and pyramids, and spheres cones and pyramids, and spheres cones and pyramids, and spheres cones and pyramids, and spheres and apply them to solve problems. and apply them to solve problems. and apply them to solve problems. and apply them to solve problems. Differentiation of Instruction Strand Mathematics Standard 4: Solve problems involving area of triangles, quadrilaterals and complex figures; area and circumference of circles; surface area and volume. Topic Surface Area Benchmark G.SR.08.07 Understand the concept of surface area, and find the surface area of prisms, cones, spheres, pyramids, and cylinders. Sample Performance Assessment (SPA) Rubric Advanced Proficient Partially Proficient Novice Consistently understand the Usually understand the Sometimes understand the Rarely understand the concept of surface area and concept of surface area and concept of surface area and concept of surface area and find the surface area of prisms, find the surface area of prisms, find the surface area of prisms, find the surface area of prisms, cones, spheres, pyramids, and cones, spheres, pyramids, and cones, spheres, pyramids, and cones, spheres, pyramids, and cylinders. cylinders. cylinders. cylinders. Differentiation of Instruction
