Download Grade 3 Math Modules

Grade 3 Math Modules Module 1: Properties of Multiplication and Division and Solving Problems with Units of 2–5 and 10 Module 2: Place Value and Problem Solving with Units of Measure Module 3: Multiplication and Division with Units of 0, 1, 6–9, and Multiples of 10 Module 4: Multiplication and Area Module 5: Fractions as Numbers on the Number Line Module 6: Collecting and Displaying Data Module 7: Geometry and Measurement Word Problems Summary of Year Third Grade mathematics is about (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-­‐
dimensional shapes. Key Areas of Focus for 3-­‐5: Multiplication and division of whole numbers and fractions—
concepts, skills, and problem solving Required Fluency: 3.OA.7 Multiply and divide within 100. 3.NBT.2 Add and subtract within 1000. Reporting Standards (Report Card) & Proficiency Levels CONCEPTS AND PROCEDURES Represent and solve problems involving multiplication and division Standards: 3.OA.1, 3.0A.2, 3.OA.3, 3.0A.4 Proficiency Level 4 Proficiency Level 3 Proficiency Level 2 a) I
nterpret a
nd r
epresent a) I
nterpret products of a) Interpret and represent products and quotients of whole numbers products and quotients of whole numbers (Factors 0-­‐ whole numbers (Factors 0-­‐ ______________________
10) __________ 12) ______________________ ______________________ ____________ b) Represent a ____________ multiplication situation b) Represent a with materials and a b) Represent a multiplication or division picture. multiplication or division situation as an equation situation as an equation (Factors 0-­‐10) ______________________
(Factors 0-­‐12) ______________________ ______________________ ____________ ____________ ____________ c) Uses multiplication and c) Solve a number story for division within 100 to solve c) Solves a number story word problems involving for a numerical expression a numerical expression using multiplication or equal groups and arrays involving multiplication division within 100 with an unknown product and division within 100 involving equal groups, or quotient (Factors 0-­‐10). involving equal groups, arrays, area, and arrays, area, and measurement quantities measurement quantities other than area with other than area with unknowns in all positions. unknowns in all positions. ______________________
Both factors are less than ____________ Both factors are less than or equal to 10. or equal to 12. d) Determine the unknown ______________________ whole number in a ____________ Proficiency Level 1 a) Given visual models and/or manipulatives, interpet products of whole numbers with factors 2,3,5,10. ______________________
____________ c) Given a visual aid, uses multiplication within 100 to solve word problems involving equal groups and arrays with an unknown product. (Factors 0-­‐10) ______________________
___________ d) Determine the product in a multiplication equation with whole number factors less than Grade 3 Math Modules d) Determine the unknown whole number in a multiplication and division problem by relating multiplication and division. Identifies proper context given a numerical expression and writes a number story involving multiplication and division. ______________________
__________ d) Determine the unknown whole number in a multiplication or division equation relating three whole numbers by relating multiplication and division. Factors are greater than 5 and less than 10. multiplication equation by relating multiplication and division. Limit to factors less than or equal to 5. or equal to 5. Understand properties of multiplication and the relationship between multiplication and division Standards: 3.OA.5, 3.OA.6 Proficiency Level 4 Proficiency Level 3 Proficiency Level 2 Proficiency Level 1 a) Apply properties of a) Apply the commutative a) Given visual models a) Justify the use of operations (commutative, property as a strategy to and/or manipulatives, properties of operations multiply. identify equivalent (commutative, associative, associative, and distributive) as strategies expressions that illustrate and distributive) as to multiply. ______________________ the commutative property strategies to multiply. within 10. ______________________ ______________________ ____________ ____________ _____________________
____________ b) Determine the unknown ____________ whole number in a b) Determine the unknown b) Understand division as an unknown-­‐factor multiplication equation by b) Determine the product whole number in a relating multiplication and in a multiplication multiplication and division problem. For example, find 32÷8 by finding the division. Limit to factors equation with whole problem by relating less than or equal to 5. number factors less than multiplication and division. number that makes 32 when multiplied by 8. or equal to 5. (Factors 0-­‐12) Solve problems involving the four operations and identify and explain patterns in arithmetic Standards: 3.OA.8, 3.OA.9 Proficiency Level 4 Proficiency Level 3 Proficiency Level 2 Proficiency Level 1 a) Solves two-­‐step a) Solves two-­‐step a) Solves two-­‐step a) Solve two-­‐step unscaffolded word scaffolded word problems scaffolded word problems unscaffolded word problems using the four using the four operations using the four operations problems using the four operations, including with drawings, including with concrete materials, operations, including rounding where rounding where and in which the sum, rounding where appropriate, in which the appropriate, in which the difference, product, or appropriate, in which the unknown is in a variety of unknown is in a variety of quotient is always the unknown is in a variety of positions. positions. unknown. positions. ______________________ ______________________ ______________________ ______________________
____________ ____________ ____________ ____________ b) Identify and use b) Identify patterns in the b) Identify and use patterns to determine multiplication chart. patterns to determine products when both products when both factors are less than or factors are less than or equal to 10. equal to 12. Grade 3 Math Modules Develop understanding of fractions as numbers Standards: 3.NF.1, 3.NF.2 Proficiency Level 4 Proficiency Level 3 a) Understands 1/b is a) Understands 1/b is equal to one whole that is equal to one whole that is partitioned into b equal partitioned into b equal parts – limiting the parts – limiting the denominators to 2,3,4,6 denominators to 2,3,4,6 and 8. and 8. _____________________
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____________ ____________ b) Represents 1/b on a b) Represents 1/b on a number line diagram by number line diagram by partitioning the number partitioning the number line between 0-­‐1 into b line between 0-­‐1 into b equal parts recognizing equal parts recognizing that b is the total number that b is the total number of parts. of parts. _____________________
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____________ ___________ c) Demonstrates the c) Demonstrates the understanding of the understanding of the quantity a/b by marking off quantity a/b by marking off a parts of 1/b from 0 a parts of 1/b from 0 on the number line and states on the number line and states that the endpoint that the endpoint locates locates the number a/b. the number a/b. Applies the concepts of 1/b Applies the concepts of 1/b and a/b in real world and a/b in real world situations. situations. Creates the number line that best fits the context. Proficiency Level 2 a) Understands 1/b is equal to one whole that is partitioned into b equal parts – limiting the denominators to 2,4 and 8. ______________________
____________ Represents 1/b on a number line diagram by partitioning the number line between 0-­‐1 into b equal parts recognizing that b is the total number of parts. ______________________
___________ c) Demonstrates the understanding of the quantity a/b by marking off a parts of 1/b from 0 on the number line. Proficiency Level 1 a) Understands 1/b is equal to one whole that is partitioned into b equal parts – limiting the denominators to 2 and 4. _____________________
____________ Represents 1/b on a number line diagram partitioning the number line between 0-­‐1 into b equal parts recognizing that b is the total number of parts. _____________________
____________ c) Represents fractions in the form a/b using a visual model. Proficiency Level 2 a) Given visual models, identify and generate equivalent fractions using denominators of 2,4 and 8. ______________________
____________ b) Express whole numbers as fractions. ______________________
____________ c) Compare two fractions that have the same denominator using Proficiency Level 1 a) Given a visual model and/or manipulatives, identify equivalent fractions for fractions with denominators 2 and 4. Compare fractions by reasoning about their size Standards: 3.NF.3 Proficiency Level 4 Proficiency Level 3 a) Identify and generate a) Compare two fractions equivalent fractions using that interpret, evaluate, denominators of 2,3,4,6 and generate equivalent and 8. fractions using denominators of 2,3,4,6 ______________________
and 8. ___________ ______________________
____________ b) Express whole numbers as fractions, and identify b) Express whole numbers fractions that are as fractions, and generate equivalent to whole fractions that are numbers. equivalent to whole ______________________
numbers, have the same numerator or denominator ___________ using symbols to justify c) Compare two fractions conclusions, determining that have the same _____________________
__________ b) Given a visual model or manipulatives and a fraction 1/b, recognize that b is the total number of equal parts of the whole. _____________________
___________ Grade 3 Math Modules that the two fractions must refer to the same whole in order to compare. Plot the location of equivalent fractions on a number line. numerator or same denominator using symbols, determining that the two fractions must refer to the same whole in order to compare. Identify the location of equivalent fractions on a number line. symbols, determining that the two fractions must refer to the same whole in order to compare. c) Given a visual model and/or manipulatives, compare fractions with the same denominator. Solve problems involving measurement and estimation of time, liquid volumes, and masses of objects Standards: 3.MD.1, 3.MD.2 Proficiency Level 4 Proficiency Level 3 Proficiency Level 2 Proficiency Level 1 a) Tells, writes and a) Tells, writes and a) Tells, writes and a) Tells, writes and measures time to the measures time to the measures time to the measures time to the nearest minute. nearest minute. nearest minute. nearest minute. ______________________
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__________ ___________ ____________ ____________ b) Solves two-­‐step word b) Solves one-­‐step word b) Solves one-­‐step word b) Creates two-­‐step real problems involving problems involving problems involving world problems involving addition or subtraction of addition and subtraction of addition and subtraction of addition or subtraction of time intervals in minutes. time intervals in minutes. time intervals in minutes, time intervals in minutes. with scaffolding, such as a ______________________
_____________________
number line diagram. ______________________
____________ ____________ _____________________
____________ ____________ c) Using grams, kilograms c) Using grams, kilograms c) Using grams, kilograms or liters, measures, or liters, measures and c) Using grams, kilograms or liters, measures, estimates and solves one-­‐
estimates liquid volumes or liters, measures and estimates and solves two-­‐
step word problems and masses of objects estimates liquid volumes step word problems involving l
iquid v
olumes using a
ny o
f t
he f
our b
asic and masses of objects involving liquid volumes and masses of objects operations. using concrete objects and masses of objects using any of the four basic (beakers, measuring cups, using any of the four basic scales) to develop operations. Number values operations. Number values should b
e t
owards t
he estimates. should be towards the higher end of the _____________________
higher end of the ____________ acceptable values for each acceptable values for each operation. operation. ______________________
d) Uses estimated ______________________
____________ measurements to ___________ compare answers to one-­‐
step word problems. d) Evaluates usefulness and d) Uses estimated measurements to compare accuracy of estimations. answers to one-­‐step word problems. Grade 3 Math Modules Understand concepts of area and relate area to multiplication and addition Standards: 3.MD.5, 3.MD.6, 3.MD.7 Proficiency Level 4 Proficiency Level 3 Proficiency Level 2 a) Identify area as an a) Using a visual model, a) Identify area as an attribute of plan figures, affirm that area is attribute of plane figures, and affirm that area is measured using square and affirm that area is measured using square units and can be found by measured using square units and can be found by covering a plan figure with units and can be found by covering a plane figure unit squares, without gaps covering a plane figure with unit squares, without with unit squares, without or overlaps, and counting gaps or overlaps, and them. gaps or overlaps, and counting them. counting them. ______________________ ______________________ ______________________
____________ ____________ ____________ b) Solve real-­‐world and b) Given a visual model b) Solve real-­‐world and mathematical problems and the formula for finding mathematical problems involving rectangular areas area, solve mathematical involving rectangular area by multiplying the side problems by multiplying by multiplying the side lengths. the side lengths. lengths. ______________________ ______________________ ______________________
____________ ____________ ___________ c) Recognize partitioned c) Create a visual model to c) Determine that the number of unit squares rectilinear figures as being show that the number of covering a rectangle is composed of rectangles; unit squares covering a equivalent to multiplying find the areas of some rectangle is equivalent to the side lengths. such rectangles. multiplying the side lengths. ______________________ ______________________
____________ ____________ d) Determine areas of d) Determine areas of rectilinear figures rectilinear figures composed of rectangles by composed of rectangles by adding the areas of the adding the areas of the rectangles. rectangles and applying this technique to solve real-­‐world problems. Use area models to represent the distributive Use area models to property in mathematical represent the distributive reasoning. property in mathematical reasoning. Proficiency Level 1 Grade 3 Math Modules FLUENCY Master addition and subtraction with sums through 1000 using efficient strategies Standards: 3.NBT.2 Proficiency Level 4 Proficiency Level 3 Proficiency Level 2 a) Accurately and quickly a) Accurately in a timely a) Accurately adds and adds and subtracts within manner, adds and subtracts within 1000 1000 using strategies and subtracts within 1000 using strategies and algorithms based on place using strategies and algorithms based on place value, properties of algorithms based on place value, properties of operations, and/or the value, properties of operations, and/or the relationship between operations, and/or the relationship between addition and subtraction. relationship between addition and subtraction. ______________________ addition and subtraction. ____________ ______________________ ______________________
____________ ____________ b) Correctly calculates 100 percent of sums and b) Correctly calculates 100 b) Correctly calculates differences in less than the percent of sums and more than 75 percent and allotted time on items that differences in the allotted less than 100 percent of are timed. time on items that are sums and differences of timed. items that are timed. Proficiency Level 1 a) Adds and subtracts within 1000, using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. ______________________
____________ b) Correctly calculates at least 75 percent of the sums and differences of items that are timed. Master multiplication and division facts with products through 100 Standards: OA.3.7 Proficiency Level 4 Proficiency Level 3 Proficiency Level 2 a) Accurately and quickly a) Accurately in a timely a) Accurately multiplies multiplies and divides manner multiplies and and divides within 100, within 100, using strategies divides within 100, using using strategies relating relating multiplication and strategies relating multiplication and division division or properties of multiplication and division or properties of operations. or properties of operations. ______________________ operations. ______________________
____________ ______________________ ____________ ____________ b) Knows from memory b) Knows from memory 2, 100 percent of the b) Knows from memory 5, 10, 3, 4, 0, 1’s of the multiplication and division 100 percent of the multiplication and division facts within 100 in less multiplication and division facts within 100 on items than the allotted time on facts within 100 in the that are timed. items that are timed. allotted time on items that are timed. Proficiency Level 1 a) Multiplies and divides within 100, using strategies relating multiplication and division or properties of operations. _____________________
____________ b) Knows from memory 2, 5, 10, 3’s.