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COURSE CONTENT MATHEMATICS THIRD GRADE CCRS EVIDENCE OF STUDENT ATTAINMENT CONTENT STANDARDS RESOURCES FIRST SIX WEEKS 8 [3.OA.8] Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3 (3This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) 9 [3.OA.9] Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Example: Observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. Students: Given a variety of two-step word problems involving all four operations, Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities, Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions, (e.g., "The answer had to be around 125 because it's a put together problem, and 72 is close to 75, and 56 is close to 50, and 75 plus 50 is 125."). Students: Go Math Chapter 1 AMSTI Year One Units Collections and Travel Stories Inv. 1: Sess. 1.4-1.5, Inv. 2: Sess. 2.1-2.2, 2.4, Inv. 3: 3.43.7, Inv. 4: 4.1-4.4 Year Two Units How Many Hundreds?: Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, Inv. 3: Sess. 3.63.9 Solids and Boxes: CC 4A.3 Other Units Trading Stickers: Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, 2.5, 2.7-2.8 Go Math Chapter 1 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. (e.g., observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends). AMSTI Year One Units Collections and Travel Stories: Inv. 1: Sess. 1.1-1.2, 1.5-1.6, Inv. 2: Sess. 2.3-2.7, Inv. 3: Sess. 3.3, Inv. 4: Sess. 4.4 Equal Groups: Inv. 1: Sess. 1.3, Inv. 2: Sess. 2.1-2.6, Inv. 3: Sess. 3.13.4 CC 3.5A, 3.5B, 3.7A Year Two Units How Many Hundreds?: Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.1-2.5, Inv. 3: Sess. 3.1-3.9 Other Units 1 COURSE CONTENT MATHEMATICS THIRD GRADE 10 [3.NBT.1] Use place value understanding to round whole numbers to the nearest 10 or 100. Students: Given any number less than 1,000, 11 [3.NBT.2] Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Round it to the nearest 10 or 100 and justify the answer using place value vocabulary, (e.g., "Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150). Students: Fluently add and subtract within 1000, using strategies based on place values, properties of operations, and/or the relationship between addition and subtraction, Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning. Trading Stickers, Combining Coins: Inv. 1: Sess. 1.2, 1.4, Inv. 2: Sess. 2.2-2.3, 2.6 Stories, Tables, & Graphs: TMM Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.1-2.3, Inv. 3: Sess. 3.1-3.7 Go Math Chapter 1 AMSTI Year One Units Collections and Travel Stories: CC 1.7A Perimeter, Angles, & Area: CC 2.5A Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.4-2.5, Inv. 3: Sess. 3.5-3.6 Year Two Units Finding Fair Shares: Inv. 1: Sess. 1.1-1.3, Inv. 2: Sess. 2.1-2.4 CC 1.4A, 1.4B Solids and Boxes: Inv. 2: Sess. 2.1-2.3 CC 4A.1, 4A.2, 4A.3 Other Units Stories, Tables, & Graphs: Inv. 2: Sess. 2.2, Inv. 3: Sess. 3.1, 3.3-3.4 Go Math Chapter 1 AMSTI Year One Units Collections and Travel Stories: Inv. 1: Sess. 1.1-1.6, Inv. 2: Sess. 2.1-2.7, Inv. 3: Sess. 3.2-3.7, Inv. 4: Sess. 4.1-4.6 Perimeter, Angles, & Area: Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.4-2.5, Inv. 3: Sess. 3.2, 3.5-3.6 CC2.5A Year Two Units Finding Fair Shares: Inv. 1: Sess. 1.1-1.3, Inv. 2: Sess. 2.1-2.4 2 COURSE CONTENT MATHEMATICS THIRD GRADE 18 19 [3.MD.3] Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. Example: Draw a bar graph in which each square in the bar graph might represent 5 pets. Students: [3.MD.4] Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units- whole numbers, halves, or quarters. Students: CC1.4A, 1.4B How Many Hundreds?: Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.1-2.5, Inv. 3: Sess. 3.1-3.9 Solids and Boxes: Inv. 2: Sess. 2.1-2.3 CC 4A.1, 4A.2, 4A.3 Other Units Trading Stickers, Combining Coins: Inv. 1: Sess. 1.1-1.9, Inv. 2: Sess. 2.2-2.8 Stories, Tables, & Graphs: TMM Inv. 1: Sess. 1.2-1.4, Inv. 2: Sess. 2.1-2.3, Inv. 3: Sess. 3.1-3.4 Go Math Chapter 2 Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1, Reason quantitatively to answer one- and twostep "how many more?" and "how many less?" problems using information presented in the scaled pictographs and bar graph. AMSTI Other Units Surveys and Line Plots: Inv. 1: Sess. 1.2-1.8, Inv. 2: Sess. 2.1-2.2, Inv. 3: Sess. 3.5 CC 2.3A Go Math Chapter 2 Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch, half inch, or quarter inch) of several objects (e.g., measure the length of all class members' fingers) or by making repeated measurements (e.g., measuring how far a marble rolls under certain conditions), Communicate questions and descriptions related to the data display AMSTI Other Units Surveys and Line Plots: Inv. 3: Sess. 3.1-3.4 3 COURSE CONTENT MATHEMATICS THIRD GRADE 1 [3.OA.1] Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. Example: Describe a context in which a total number of objects can be expressed as 5 x 7. Students: Given any multiplication problem in the form a x b = c, 3 5 Represent the problem physically or pictorially and describe the relationship between the factors and the product in the equation and the attributes of the representation (i.e., given 3 x 5 = 15, students make 3 piles of buttons with 5 buttons in each pile. They explain that 15 represents the total number of buttons, 3 is the number of piles and 5 is the number of buttons in each pile) , Write a corresponding word problems containing a multiplication context. [3.OA.3] Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Students: Given a variety of multiplication and division word problems within 100, [3.OA.5] Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication) Knowing that 8 x 5 = 40 and 8 Students: Given multiplication and division problems within 100, Explain and justify solutions and solution paths using connections among a variety of representations (e.g., place value blocks, drawings, open arrays, and equations with a symbol for the unknown). Use the properties of operations and descriptive language for the property to justify their products and quotients (e.g., If I know that 8 x 5 is 40, and two more groups of 8 would be 16, then 8 x 7 must be 40 + 16 or Go Math Chapter 3 AMSTI Year One Units Equal Groups: Inv. 1: Sess. 1.1-1.4, Inv. 2: Sess. 2.1-2.6, Inv. 3: Sess. 3.1-3.4, 3.6, Inv. 4: Sess. 4.7 Year Two Units How Many Hundreds? Inv. 3.5 Go Math Chapter 3 AMSTI Year One Units Equal Groups: Inv. 1: Sess. 1.1-1.4, Inv. 2: Sess. 2.3-2.6, Inv. 3: Sess. 3.1, 3.3-3.4, Inv. 4: Sess. 4.1-4.3, 4.5-4.7 Year Two Units Finding Fair Shares: Inv. 1: Sess. 1.1, Inv. 2: Sess. 2.1 Other Units Stories, Tables, & Graphs: Inv. 3: Sess. 3.1-3.7 Go Math Chapter 3 AMSTI Year One Units Equal Groups: Inv. 1: Sess. 1.4, Inv. 2: Sess. 2.2-2.6, Inv. 3: Sess. 3.13.4, 3.6 CC3.5A, 3.5B, 3.7A 4 COURSE CONTENT MATHEMATICS THIRD GRADE 56). x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive property) 8 [3.OA.8] Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Students: Given a variety of two-step word problems involving all four operations, Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities, Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions, (e.g., "The answer had to be around 125 because it's a put together problem, and 72 is close to 75, and 56 is close to 50, and 75 plus 50 is 125."). Other Units Ten-Minute Math Unit 6 Stories, Tables, & Graphs: Inv. 2: Sess. 2.1-2.3, Inv. 3: Sess. 3.1-3.6 Go Math Chapter 3 AMSTI Year One Units Collections and Travel Stories Inv. 1: Sess. 1.4-1.5, Inv. 2: Sess. 2.1-2.2, 2.4, Inv. 3: 3.43.7, Inv. 4: 4.1-4.4 Year Two Units How Many Hundreds?: Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, Inv. 3: Sess. 3.63.9 Solids and Boxes: CC 4A.3 Other Units Trading Stickers: Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, 2.5, 2.7-2.8 SECOND SIX WEEKS 3 5 [3.OA.3] Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Students: Given a variety of multiplication and division word problems within 100, [3.OA.5] Apply properties of operations as strategies to multiply and divide.2 Students: Given multiplication and division problems within 100, Explain and justify solutions and solution paths using connections among a variety of representations (e.g., place value blocks, drawings, open arrays, and equations with a symbol for the unknown). Go Math Chapter 4 AMSTI Year One Units Equal Groups: Inv. 1: Sess. 1.1-1.4, Inv. 2: Sess. 2.3-2.6, Inv. 3: Sess. 3.1, 3.3-3.4, Inv. 4: Sess. 4.1-4.3, 4.5-4.7 Year Two Units Finding Fair Shares: Inv. 1: Sess. 1.1, Inv. 2: Sess. 2.1 Other Units Stories, Tables, & Graphs: Inv. 3: Sess. 3.1-3.7 Go Math Chapter 4 5 COURSE CONTENT MATHEMATICS THIRD GRADE Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive property) 7 8 Use the properties of operations and descriptive language for the property to justify their products and quotients (e.g., If I know that 8 x 5 is 40, and two more groups of 8 would be 16, then 8 x 7 must be 40 + 16 or 56). [3.OA.7] Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Students: Given any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient, [3.OA.8] Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Students: Given a variety of two-step word problems involving all four operations, Use an efficient strategy (e.g., recall, inverse operations, arrays, derived facts, properties of operations, etc.) to name the product or quotient. Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities, Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions, (e.g., "The answer had to be around 125 because it's a put together problem, and 72 is close to 75, and 56 is close to 50, and 75 plus AMSTI Year One Units Equal Groups: Inv. 1: Sess. 1.4, Inv. 2: Sess. 2.2-2.6, Inv. 3: Sess. 3.13.4, 3.6 CC3.5A, 3.5B, 3.7A Other Units Ten-Minute Math Unit 6 Stories, Tables, & Graphs: Inv. 2: Sess. 2.1-2.3, Inv. 3: Sess. 3.1-3.6 Go Math Chapter 4 AMSTI Year One Units Equal Groups: Inv. 3: Sess. 3.4, 3.6, Inv. 4: Sess. 4.5-4.6 CC 3.5A, 3.5B, 3.7A Year Two Units Finding Fair Shares: CC 1.4A How Many Hundreds?: Inv. 1: Sess. 1.4 Go Math Chapter 4 AMSTI Year One Units Collections and Travel Stories Inv. 1: Sess. 1.4-1.5, Inv. 2: Sess. 2.1-2.2, 2.4, Inv. 3: 3.43.7, Inv. 4: 4.1-4.4 Year Two Units How Many Hundreds?: Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, Inv. 3: Sess. 3.63.9 Solids and Boxes: CC 4A.3 Other Units Trading Stickers: Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, 2.5, 2.7-2.8 6 COURSE CONTENT MATHEMATICS THIRD GRADE 50 is 125."). 9 4 9 [3.OA.9] Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Example: Observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. Students: [3.OA.4] Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Example: Determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = _ ÷ 3, 6 x 6 = ?. Students: [3.OA.9] Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Example: Observe that 4 times a number is Students: Go Math Chapter 4 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. (e.g., observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends). Solve single operation multiplication/division equations containing a single unknown (e.g. 8x? = 48, 5= __ ÷3, 6x6 = ___). Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. (e.g., observe that 4 times a AMSTI Year One Units Collections and Travel Stories: Inv. 1: Sess. 1.1-1.2, 1.5-1.6, Inv. 2: Sess. 2.3-2.7, Inv. 3: Sess. 3.3, Inv. 4: Sess. 4.4 Equal Groups: Inv. 1: Sess. 1.3, Inv. 2: Sess. 2.1-2.6, Inv. 3: Sess. 3.13.4 CC 3.5A, 3.5B, 3.7A Year Two Units How Many Hundreds?: Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.1-2.5, Inv. 3: Sess. 3.1-3.9 Other Units Trading Stickers, Combining Coins: Inv. 1: Sess. 1.2, 1.4, Inv. 2: Sess. 2.2-2.3, 2.6 Stories, Tables, & Graphs: TMM Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.1-2.3, Inv. 3: Sess. 3.1-3.7 Go Math Chapter 5 AMSTI Year One Units Equal Groups: Inv. 1: Sess. 1.3-1.4, Inv. 2: Sess. 2.6, Inv. 4: Sess. 4.14.6 CC3.5A, 3.5B, 3.7A Go Math Chapter 5 AMSTI Year One Units Collections and Travel Stories: 7 COURSE CONTENT MATHEMATICS THIRD GRADE always even, and explain why 4 times a number can be decomposed into two equal addends 3 number is always even, and explain why 4 times a number can be decomposed into two equal addends). [3.NBT.3] Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. Students: [3.OA.2] Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. Example: Describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. Students: Given any division problem in the form a ÷ b = c, Efficiently use strategies based on place value and properties of operations to multiply onedigit numbers by multiples of 10 (from 10-90) and justify their answers. Inv. 1: Sess. 1.1-1.2, 1.5-1.6, Inv. 2: Sess. 2.3-2.7, Inv. 3: Sess. 3.3, Inv. 4: Sess. 4.4 Equal Groups: Inv. 1: Sess. 1.3, Inv. 2: Sess. 2.1-2.6, Inv. 3: Sess. 3.13.4 CC 3.5A, 3.5B, 3.7A Year Two Units How Many Hundreds?: Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.1-2.5, Inv. 3: Sess. 3.1-3.9 Other Units Trading Stickers, Combining Coins: Inv. 1: Sess. 1.2, 1.4, Inv. 2: Sess. 2.2-2.3, 2.6 Stories, Tables, & Graphs: TMM Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.1-2.3, Inv. 3: Sess. 3.1-3.7 Go Math Chapter 5 Year One Units Equal Groups: CC 3.7A THIRD SIX WEEKS 2 Represent the problem physically or pictorially and describe the relationship between the dividend, divisor, and quotient in the equation and the attributes of the representation (e.g., given 15 ÷ 3 = 5, students make 3 piles of buttons with 5 buttons in each pile and explain that 15 represents the total number of buttons, 3 is the number of piles the total was shared among and 5 is the number of buttons in each pile), Write a corresponding word problem Go Math Chapter 6 AMSTI Year One Units Equal Groups: Inv. 4: Sess. 4.1-4.7 8 COURSE CONTENT MATHEMATICS THIRD GRADE containing a division context. 3 5 [3.OA.3] Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem Students: Given a variety of multiplication and division word problems within 100, [3.OA.5] Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive property) Students: Given multiplication and division problems within 100, Explain and justify solutions and solution paths using connections among a variety of representations (e.g., place value blocks, drawings, open arrays, and equations with a symbol for the unknown). Use the properties of operations and descriptive language for the property to justify their products and quotients (e.g., If I know that 8 x 5 is 40, and two more groups of 8 would be 16, then 8 x 7 must be 40 + 16 or 56). Go math Chapter 6 AMSTI Year One Units Equal Groups: Inv. 1: Sess. 1.1-1.4, Inv. 2: Sess. 2.3-2.6, Inv. 3: Sess. 3.1, 3.3-3.4, Inv. 4: Sess. 4.1-4.3, 4.5-4.7 Year Two Units Finding Fair Shares: Inv. 1: Sess. 1.1, Inv. 2: Sess. 2.1 Other Units Stories, Tables, & Graphs: Inv. 3: Sess. 3.1-3.7 Go Math Chapter 6 AMSTI Year One Units Equal Groups: Inv. 1: Sess. 1.4, Inv. 2: Sess. 2.2-2.6, Inv. 3: Sess. 3.13.4, 3.6 CC3.5A, 3.5B, 3.7A Other Units Ten-Minute Math Unit 6 Stories, Tables, & Graphs: Inv. 2: Sess. 2.1-2.3, Inv. 3: Sess. 3.1-3.6 (2Students need not use formal terms for these properties.) 6 [3.OA.6] Understand division as an unknownfactor problem. Example: Find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. Students: Given a division problem with an unknown quotient, Use a pictorial or physical model to explain the connection between the division problem Go Math Chapter 6 AMSTI Year One Units Equal Groups: Inv. 4: Sess. 4.1-4.6 9 COURSE CONTENT MATHEMATICS THIRD GRADE and the related unknown factor equation. 7 4 7 8 [3.OA.7] Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Students: Given any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient, [3.OA.4] Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Example: Determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = _ ÷ 3, 6 x 6 = ?. Students: [3.OA.7] Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Students: Given any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient, [3.OA.8] Solve two-step word problems using the four operations. Represent these problems Students: Given a variety of two-step word problems involving all Use an efficient strategy (e.g., recall, inverse operations, arrays, derived facts, properties of operations, etc.) to name the product or quotient. Solve single operation multiplication/division equations containing a single unknown (e.g. 8x? = 48, 5= __ ÷3, 6x6 = ___). Use an efficient strategy (e.g., recall, inverse operations, arrays, derived facts, properties of operations, etc.) to name the product or quotient. Go Math Chapter 6 AMSTI Year One Units Equal Groups: Inv. 3: Sess. 3.4, 3.6, Inv. 4: Sess. 4.5-4.6 CC 3.5A, 3.5B, 3.7A Year Two Units Finding Fair Shares: CC 1.4A How Many Hundreds?: Inv. 1: Sess. 1.4 Go Math Chapter 7 AMSTI Year One Units Equal Groups: Inv. 1: Sess. 1.3-1.4, Inv. 2: Sess. 2.6, Inv. 4: Sess. 4.14.6 CC3.5A, 3.5B, 3.7A Go Math Chapter 7 AMSTI Year One Units Equal Groups: Inv. 3: Sess. 3.4, 3.6, Inv. 4: Sess. 4.5-4.6 CC 3.5A, 3.5B, 3.7A Year Two Units Finding Fair Shares: CC 1.4A How Many Hundreds?: Inv. 1: Sess. 1.4 Go Math Chapter 7 10 COURSE CONTENT MATHEMATICS THIRD GRADE using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3 (3This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) four operations, Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities, Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions, (e.g., "The answer had to be around 125 because it's a put together problem, and 72 is close to 75, and 56 is close to 50, and 75 plus 50 is 125."). AMSTI Year One Units Collections and Travel Stories Inv. 1: Sess. 1.4-1.5, Inv. 2: Sess. 2.1-2.2, 2.4, Inv. 3: 3.43.7, Inv. 4: 4.1-4.4 Year Two Units How Many Hundreds?: Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, Inv. 3: Sess. 3.63.9 Solids and Boxes: CC 4A.3 Other Units Trading Stickers: Inv. 1: Sess. 1.1-1.5, Inv. 2: Sess. 2.3, 2.5, 2.7-2.8 FOURTH SIX WEEKS 13 [3.NF.1] Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by aparts of size 1/b. Students: Given any fraction in the form a/b, Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1). (e.g., 3/5 = 1/5 + 1/5 + 1/5). Go Math Chapter 8 AMSTI Year Two Units Finding Fair Shares: Inv.1: Sess. 1.1-1.6, Inv. 2: Sess. 2.1-2.4, Inv. 3: Sess. 3.1-3.4 Given a model of a fraction, 14 [3.NF.2] Understand a fraction as a number on the number line; represent fractions on a number line diagram. Write the corresponding fraction and explain the relationship of the numerator and denominator to the model. Students: Given any common fraction a/b between 0 and 1 (denominators of 2, 3, 4, 6, 8), Go Math Chapter 8 AMSTI 11 COURSE CONTENT MATHEMATICS THIRD GRADE a. b. 15 Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. Represent a fraction a/b on a number line diagram by marking off a lengths 1/bfrom 0. Recognize that the resulting interval has size a/band that its endpoint locates the number a/b on the number line. [3.NF.3] [3.NF.3] Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. b. c. d. Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line. Recognize and generate simple equivalent fractions, e.g., 1/2= 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 =3/1; recognize that6/1 = 6; locate 4/4and 1 at the same point of a number line diagram. Compare two fractions with the same numerator or the same denominator by reasoning about Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction. Students: Year Two Units Finding Fair Shares: CC 1.4A, 1.4B Go Math Chapter 8-9 Use visual models (e.g., fraction manipulatives, number lines, or pictures) to generate simple equivalent fractions including fractions equivalent to whole numbers, Given two fractions, use logical reasoning and a variety of models to represent and order the fractions (using <, =, >) and justify their answers, Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (e.g., why it may not be valid to say 1/2 >1/4 if the 1/2 refers to a small pizza and the 1/4 refers to an extra-large pizza or "Susie said her 1/6 pizza was bigger than my 1/2 pizza, is she correct?"). AMSTI Year Two Units Finding Fair Shares: a. Finding Fair Shares: Inv.1: Sess. 1.1-1.2, 1.4-1.6, Inv. 2: Sess. 2.1-2.4, Inv. 3: Sess. 3.1-3.4 CC 1.4A, 1.4B b. Finding Fair Shares: Inv.1: Sess. 1.5, Inv. 2: Sess. 2.1-2.4, Inv. 3: Sess. 3.1-3.4 c. Finding Fair Shares: Inv.1: Sess. 1.3, Inv. 2: Sess. 2.1-2.4, Inv. 3: Sess. 3.4 CC 1.4A, 1.4B d. Finding Fair Shares: Inv.1: Sess. 1.2-1.3 CC 1.4B 12 COURSE CONTENT MATHEMATICS THIRD GRADE their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. FIFTH SIX WEEKS 16 [3.MD.1] Tell and write time to the nearest minute, and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. Students: 17 [3.MD.2] Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.7 (6Excludes compound units such as cm3 and finding the geometric volume of a container.) (7Excludes multiplicative comparison Go Math Chapter 10 Tell and write time to the nearest minute using analog and digital clocks, Use strategies (e.g., watch the movement of a second or minute hand, count the changing of digits) to estimate and measure time intervals in minutes, Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines. Students: Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales, graduated cylinders, beakers, and measuring cups to determine measures to the nearest whole unit. AMSTI Year One Units Collections and Travel Stories: Inv. 3: Sess. 3.2-3.7, Inv. 4: Sess. 4.1-4.6 CC 1.7A Equal Groups: Inv. 1: Sess. 1.1-1.4, Inv. 3: Sess. 3.1-3.3, Inv. 4: Sess. 4.1-4.7 CC 3.1A Year Two Units Finding Fair Shares: Inv. 1: Sess. 1.4-1.6, Inv. 3: Sess. 3.1-3.4 Other Units Stories, Tables, & Graphs: TMM Go Math Chapter 10 AMSTI Year Two Units Solids and Boxes: CC 4A.1, 4A.2, 4A.3 Given a variety of one-step word problems involving 13 COURSE CONTENT MATHEMATICS THIRD GRADE problems (problems involving notions of "times as much").) same unit volume or mass measurements, 19 [3.MD.4] Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units- whole numbers, halves, or quarters. Explain and justify solutions using a variety of representations. Students: Go Math Chapter 10 Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch, half inch, or quarter inch) of several objects (e.g., measure the length of all class members' fingers) or by making repeated measurements (e.g., measuring how far a marble rolls under certain conditions), Communicate questions and descriptions related to the data display AMSTI Other Units Surveys and Line Plots: Inv. 3: Sess. 3.1-3.4 SIXTH SIX WEEKS 20 [3.MD.5] Recognize area as an attribute of plane figures, and understand concepts of area measurement. a. b. 21 Students: A square with side length 1 unit called "a unit square," is said to have "one square unit" of area and can be used to measure area. A plane figure which can be covered without gaps or overlaps byn unit squares is said to have an area of n square units. [3.MD.6] Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). Go Math Chapter 11 Explain the result of measuring the area of a plane figure as a number of "unit squares" needed to cover the object without gaps or overlaps. Students: Given a variety of plane figures, Accurately measure area by counting standard AMSTI Year One Units Perimeter, Angles, and Area: Inv. 2 a. Perimeter, Angles, and Area: Inv. 2: Sess. 2.2-2.6, Inv. 3: Sess. 3.6 CC 2.5A b. Perimeter, Angles, and Area: Inv. 2: Sess. 2.1-2.6, Inv. 3: Sess. 3.6 CC 2.5A Go Math Chapter 11 AMSTI 14 COURSE CONTENT MATHEMATICS THIRD GRADE (square centimeter, square meter, square inch, and square foot) and non-standard unit squares (e.g., orange pattern blocks, floor tiles, etc.). 22 [3.MD.7] Relate area to the operations of multiplication and addition. a. b. c. d. 23 Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b +c is the sum of a xb and a x c. Use area models to represent the distributive property in mathematical reasoning. Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real-world problems. [3.MD.8] Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and Students: Given a polygon that may be decomposed into 2 or more rectangles, Find the total area by decomposing the figure into non-overlapping rectangles, finding the area of each, and find the sum of the areas. Given a rectangle with whole number length sides, Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width). Using array cards or tiles, Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c. (the Distributive Property). Students: Year One Units Perimeter, Angles, and Area: Inv. 2: Sess. 2.1-2.6, Inv. 3: Sess. 3.6 CC 2.5A Go Math Chapter 11 AMSTI Year One Units Perimeter, Angles, and Area: Inv. 2 Equal Groups: Inv. 3 a. Perimeter, Angles, and Area: Inv. 2: Sess. 2.4 Equal Groups: Inv. 3: Sess. 3.1-3.4 CC 3.1A, 3.5A b. Perimeter, Angles, and Area: Inv. 2: Sess. 2.4 Equal Groups: Inv.3: Sess. 3.1, 3.3-3.4, 3.6 CC 3.1A, 3.5A c. Equal Groups: CC 3.1A, 3.5A d. Perimeter, Angles, & Area: Inv. 2: Sess. 2.3-2.5 CC 2.5A Equal Groups: CC 3.1A, 3.5A Go Math Chapter 11 Find and justify solutions to real world and AMSTI 15 COURSE CONTENT MATHEMATICS THIRD GRADE exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. 24 25 mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas, or with the same area and different perimeters. [3.G.1] Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Students: [3.G.2] Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. Example: Partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape. Students: Given squares, rectangles, or circles, Year One Units Perimeter, Angles, and Area: Inv. 1: Sess. 1.2-1.5 CC 2.5A Go Math Chapter 12 Justify their identification/sorting of shapes (triangles, quadrilaterals, pentagons, hexagons, squares, rectangles, rhombuses) by referring to their shared attributes, Draw corresponding shapes when given a list of attributes. Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about equal area, Express the area of each part as a unit fraction of the whole (e.g., partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape). AMSTI Year One Units Perimeter, Angles, and Area: Inv. 3: Sess. 3.1-3.6 Year Two Units Solids & Boxes Inv. 1 Go Math Chapter 12 AMSTI Year Two Units Finding Fair Shares: Inv.1: Sess. 1.1-1.6, Inv. 2: Sess. 2.1-2.4, Inv. 3: Sess. 3.1-3.4 Getting Ready Lessons 1 – 20 16