SADLIER New York Progress Mathematics New York State … · 2015. 11. 13. · SADLIER New York...

SADLIER

New York Progress Mathematics

William H. Sadlier, Inc.www.sadlierschool.com800-221-5175

2 Module 1: Properties of Multiplication and Division and Solving Problems with Units of 2–5 and 10

10 Module 2: Place Value and Problem Solving with Units of Measure

15 Module 3: Multiplication and Division with Units of 0, 1, 6–9, and Multiples of 10

26 Module 4: Multiplication and Area

31 Module 5: Fractions as Numbers on the Number Line

37 Module 6: Collecting and Displaying Data

38 Module 7: Geometry and Measurement Word Problems

Contents

Correlated to the

New York State Common CoreMathematics Curriculum

Grade 3

New York Sta te Common Core Mathemat i c s Cur r i cu lum – NYS CC S tanda rds f o r Mathemat i c s – Sad l ie r New York Prog res s Mathemat i c s Cor re la t ion

Copyright © William H. Sadlier, Inc. All rights reserved. 2

Module 1 • Properties of Multiplication and Division and Solving Problems with Units of 2–5 and 10 NYS COMMON CORE MATHEMATICS CURRICULUM, GRADE 3 NYS COMMON CORE STANDARDS FOR MATHEMATICS, GRADE 3 SADLIER NEW YORK PROGRESS MATHEMATICS, GRADE 3

Topic A: Multiplication and the Meaning of the Factors

Instructional Days: 3

Lesson 1: Understand equal groups of as multiplication.

Lesson 2: Relate multiplication to the array model.

Lesson 3: Interpret the meaning of factors—the size of the group or the number of groups.

3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

Lesson 1 Interpret Products of Whole Numbers—pp. 10–17

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.

Lesson 3 Problem Solving: Multiplication/Division and Equal Groups—pp. 26–33

Lesson 4 Problem Solving: Multiplication/Division and Arrays—pp. 34–41

Lesson 32 Problem Solving: Measurement—pp. 288–295

Topic B: Division as an Unknown Factor

Problem


Lesson 4: Understand the meaning of the unknown as the size of the group in division.

Lesson 5: Understand the meaning of the unknown as the number of groups in division.

Lesson 6: Interpret the unknown in division using the array model.

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. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

Lesson 2 Interpret Quotients of Whole Numbers—pp. 18–26

3.OA.6 Understand division as an unknown‐factor

problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. Multiply and divide within 100.

Lesson 8 Divide by Finding an Unknown Factor—pp. 66–73








3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ÷ 3, 6 × 6 = ?.

Lesson 5 Find Unknown Numbers in Multiplication and Division Equations—pp. 42–49

Topic C: Multiplication Using Units of 2 and 3


Lessons 7–8: Demonstrate the commutativity of multiplication, and practice related facts by skip‐counting objects in array models.

Lesson 9: Find related multiplication facts by adding and subtracting equal groups in array models.

Lesson 10: Model the distributive property with arrays to decompose units as a strategy to multiply.



3.OA.5 Apply properties of operations as strategies to multiply and divide.3 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) 3The associative property is addressed in Module 3.

Lesson 6 Apply Commutative and Associative Properties to Multiply—pp. 50–57

Lesson 7 Apply the Distributive Property to Multiply—pp. 58–65










Mid‐Module Assessment: Topics A–C (assessment ½ day, return ½ day, remediation or further applications 1 day)

Days: 2

Topic D: Division Using Units of 2 and 3


Lesson 11: Model division as the unknown factor in multiplication using arrays and tape diagrams.

Lesson 12: Interpret the quotient as the number of groups or the number of objects in each group using units of 2.

Lesson 13: Interpret the quotient as the number of groups or the number of objects in each group using units of 3.



3.OA.4 Determine the unknown whole number in a

multiplication or division equation relating three – continued on next page





– continued from previous page –

whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ÷ 3, 6 × 6 = ?.




3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 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. Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Lesson 9 Multiply and Divide Fluently within 100—pp. 80–87





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. (This standard is limited to problems posed with whole numbers and having whole‐number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order, i.e, Order of Operations.)

Lesson 10 Problem Solving: Two‐Step Problems—pp. 88–95

Lesson 11 Problem Solving: Use Equations—pp. 96–103




Topic E: Multiplication and Division Using Units of 4


Lesson 14: Skip‐count objects in models to build fluency with multiplication facts using units of 4.

Lesson 15: Relate arrays to tape diagrams to model the commutative property of multiplication.

Lesson 16: Use the distributive property as a strategy to find related multiplication facts.

Lesson 17: Model the relationship between multiplication and division.








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

– continued on next page –






equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.










Topic F: Distributive Property and Problem

Solving Using Units of 2–5 and 10


Lessons 18–19: Apply the distributive property to decompose units.

Lesson 20: Solve two‐step word problems involving multiplication and division, and assess the reasonableness of answers.








Lesson 21: Solve two‐step word problems involving all four operations, and assess the reasonableness of answers.






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. (This standard is limited to problems posed with whole numbers and having whole‐number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order, i.e, Order of Operations.)















End‐of‐Module Assessment: Topics A–F (assessment ½ day, return ½ day, remediation or further application 1 day)

Days: 2

Total Number of Instructional Days: 25



Module 2 • Place Value and Problem Solving with Units of Measure NYS COMMON CORE MATHEMATICS CURRICULUM, GRADE 3 NYS COMMON CORE STANDARDS FOR MATHEMATICS, GRADE 3 SADLIER NEW YORK PROGRESS MATHEMATICS, GRADE 3

Topic A: Time Measurement and Problem Solving


Lesson 1: Explore time as a continuous measurement using a stopwatch.

Lesson 2: Relate skip‐counting by fives on the clock and telling time to a continuous measurement model, the number line.

Lesson 3: Count by fives and ones on the number line as a strategy to tell time to the nearest minute on the clock.

Lesson 4: Solve word problems involving time intervals within 1 hour by counting backward and forward using the number line and clock.

Lesson 5: Solve word problems involving time intervals within 1 hour by adding and subtracting on the number line.

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.

Lesson 14 Add and Subtract Fluently within 1000—pp. 120–127

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.

Lesson 24 Problem Solving: Time—pp. 218–225

Topic B: Measuring Weight and Liquid Volume

in Metric Units


Lesson 6: Build and decompose a kilogram to reason about the size and weight of 1 kilogram, 100 grams, 10 grams, and 1 gram.







Lesson 7: Develop estimation strategies by reasoning about the weight in kilograms of a series of familiar objects to establish mental benchmark measures.

Lesson 8: Solve one‐step word problems involving metric weights within 100 and estimate to reason about solutions.

Lesson 9: Decompose a liter to reason about the size of 1 liter, 100 milliliters, 10 milliliters, and 1 milliliter.

Lesson 10: Estimate and measure liquid volume in liters and milliliters using the vertical number line.

Lesson 11: Solve mixed word problems involving all four operations with grams, kilograms, liters, and milliliters given in the same units.

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.

Lesson 25 Problem Solving: Volumes and Masses—pp. 226–233


Mid‐Module Assessment: Topics A–B (assessment ½ day, return ½ day, remediation or further applications 1 day)

Days: 2

Topic C: Rounding to the Nearest Ten and

Hundred


Lesson 12: Round two‐digit measurements to the nearest ten on the vertical number line.

3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.

Lesson 13 Round Whole Numbers to the Nearest 10 or 100—pp. 112–119




Lesson 13: Round two‐ and three‐digit numbers to the nearest ten on the vertical number line.

Lesson 14: Round to the nearest hundred on the vertical number line.






Topic D: Two‐ and Three‐Digit Measurement

Addition Using the Standard Algorithm


Lesson 15: Add measurements using the standard algorithm to compose larger units once.

Lesson 16: Add measurements using the standard algorithm to compose larger units twice.

Lesson 17: Estimate sums by rounding and apply to solve measurement word problems.








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.

Topic E: Two‐ and Three‐Digit Measurement

Subtraction Using the Standard Algorithm


Lesson 18: Decompose once to subtract measurements including three‐digit minuends with zeros in the tens or ones place.

Lesson 19: Decompose twice to subtract measurements including three‐digit minuends with zeros in the tens and ones places.

Lesson 20: Estimate differences by rounding and apply to solve measurement word problems.

Lesson 21: Estimate sums and differences of measurements by rounding, and then solve mixed word problems.














End‐of‐Module Assessment: Topics A–E (assessment ½ day, return ½ day, remediation or further applications 1 day)

Days: 2




Module 3 • Multiplication and Division with Units of 0, 1, 6–9, and Multiples of 10 NYS COMMON CORE MATHEMATICS CURRICULUM, GRADE 3 NYS COMMON CORE STANDARDS FOR MATHEMATICS, GRADE 3 SADLIER NEW YORK PROGRESS MATHEMATICS, GRADE 3

Topic A: The Properties of Multiplication and Division


Lesson 1: Study commutativity to find known facts of 6, 7, 8, and 9.

Lesson 2: Apply the distributive and commutative properties to relate multiplication facts 5 × n + n to 6 × n and n × 6 where n is the size of the unit.

Lesson 3: Multiply and divide with familiar facts using a letter to represent the unknown.

3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ÷ 3, 6 × 6 = ?.


3.OA.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)





3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Lesson 12 Identify and Explain Arithmetic Patterns—pp. 104–111














Lesson 8 Divide by Finding an Unknown Factor—pp. 66–

73

Topic B: Multiplication and Division Using Units

of 6 and 7


Lesson 4: Count by units of 6 to multiply and divide using number bonds to decompose.

Lesson 5: Count by units of 7 to multiply and divide using number bonds to decompose.








Lesson 6: Use the distributive property as a strategy to multiply and divide using units of 6 and 7.

Lesson 7: Interpret the unknown in multiplication and division to model and solve problems using units of 6 and 7.





















73

Topic C: Multiplication and Division Using Units

up to 8


Lesson 8: Understand the function of parentheses and apply to solving problems.

Lesson 9: Model the associative property as a strategy to multiply.

Lesson 10: Use the distributive property as a strategy to multiply and divide

Lesson 11: Interpret the unknown in multiplication and division to model and solve problems.







3.OA.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 =








40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)










73

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. This standard is limited to problems posed with whole numbers and having whole‐number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order, i.e., Order of Operations).

Mid‐Module Assessment: Topics A–C (assessment ½ day, return ½ day, remediation or further applications 1 day)

Days: 2

Topic D: Multiplication and Division Using Units

of 9


Lesson 12: Apply the distributive property and the fact 9 = 10 – 1 as a strategy to multiply.

Lessons 13–14: Identify and use arithmetic patterns to multiply.

Lesson 10: Interpret the unknown in multiplication and division to model and solve problems.















73

Topic E: Analysis of Patterns and Problem

Solving Including Units of 0 and 1


Lesson 16: Reason about and explain arithmetic patterns using units of 0 and 1 as they relate to multiplication and division.

Lesson 17: Identify patterns in multiplication and division facts using the multiplication table.

Lesson 18: Solve two‐step word problems involving all four operations and assess the reasonableness of solutions.







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. This standard is limited to problems posed with whole numbers and having whole‐number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order, i.e., Order of Operations).















73

Topic F: Multiplication of Single‐Digit Factors

and Multiples of 10


Lesson 19: Multiply by multiples of 10 using the place value chart.

Lesson 20: Use place value strategies and the associative property n × (m × 10) = (n × m) × 10 (where n and m are less than 10) to multiply by multiples of 10.

Lesson 21: Solve two‐step word problems involving multiplying single‐digit factors and multiples of 10.




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. This standard is limited to problems posed with whole numbers and having whole‐number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order, i.e., Order of Operations).








3.NBT.3 Multiply one‐digit whole numbers by multiples of

10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Lesson 15 Multiply One‐Digit Whole Numbers by

Multiples of 10—pp. 128–135



End‐of‐Module Assessment: Topics A–F (assessment ½ day, return ½ day, remediation or further application 1 day)

Days: 2




Module 4 • Multiplication and Area NYS COMMON CORE MATHEMATICS CURRICULUM, GRADE 3 NYS COMMON CORE STANDARDS FOR MATHEMATICS, GRADE 3 SADLIER NEW YORK PROGRESS MATHEMATICS, GRADE 3

Topic A: Foundations for Understanding Area


Lesson 1: Understand area as an attribute of plane figures.

Lesson 2: Decompose and recompose shapes to compare areas.

Lesson 3: Model tiling with centimeter and inch unit squares as a strategy to measure area.

Lesson 4: Relate side lengths with the number of tiles on a side.

3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.

3.MD.5a 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.

Lesson 28 Understand Concepts of Area Measurement—

pp. 256–263

3.MD.5b A plane figure which can be covered without

gaps or overlaps by n unit squares is said to have an area of n square units.


pp. 256–263

3.MD.6 Measure areas by counting unit squares (square

cm, square m, square in, square ft, and improvised units).


pp. 256–263

3.MD.7 Relate area to the operations of multiplication and addition.

3.MD.7a 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.

Lesson 29 Find Areas of Rectangles: Tile and Multiply—

pp. 264–271

3.MD.7b 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.

Lesson 29 Find Areas of Rectangles: Tile and Multiply—pp. 264–271

3.MD.7c 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 × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

Lesson 30 Find Areas of Rectangles: Use the Distributive Property—pp. 272–279





3.MD.7d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non‐overlapping rectangles and adding the areas of the non‐overlapping parts, applying this technique to solve real world problems.

Lesson 31 Find Areas: Decompose Figures into Rectangles—pp. 280–287


Topic B: Concepts of Area Measurement


Lesson 5: Form rectangles by tiling with unit squares to make arrays.

Lesson 6: Draw rows and columns to determine the area of a rectangle given an incomplete array.

Lesson 7: Interpret area models to form rectangular arrays.

Lesson 8: Find the area of a rectangle through multiplication of the side lengths.





pp. 256–263




pp. 256–263




pp. 256–263





pp. 264–271









Mid‐Module Assessment: Topics A–B (assessment 1 day, return ½ day, remediation or further applications ½ day)

Days: 2

Topic C: Arithmetic Properties Using Area

Models


Lesson 9: Analyze different rectangles and reason about their area.

Lesson 10: Apply the distributive property as a strategy to find the total area of a large rectangle by adding two products.

Lesson 11: Demonstrate the possible whole number side lengths of rectangles with areas of 24, 36, 48, or 72 square units using the associative property.





pp. 256–263




pp. 256–263





pp. 264–271












Topic D: Applications of Area Using Side

Lengths of Figures


Lesson 12: Solve word problems involving area.

Lessons 13–14: Find areas by decomposing into rectangles or completing composite figures to form rectangles.

Lessons 15–16: Apply knowledge of area to determine areas of rooms in a given floor plan.




pp. 256–263





pp. 264–271













3.MD.5a 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.


pp. 256–263

3.MD.5b A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.


pp. 256–263

End‐of‐Module Assessment: Topics A–D (assessment 1 day, return ½ day, remediation or further applications ½ day)

Days: 2




Module 5 • Fractions as Numbers on the Number Line NYS COMMON CORE MATHEMATICS CURRICULUM, GRADE 3 NYS COMMON CORE STANDARDS FOR MATHEMATICS, GRADE 3 SADLIER NEW YORK PROGRESS MATHEMATICS, GRADE 3

Topic A: Partitioning a Whole into Equal Parts


Lesson 1: Specify and partition a whole into equal parts, identifying and counting unit fractions using concrete models.

Lesson 2: Specify and partition a whole into equal parts, identifying and counting unit fractions by folding fraction strips.

Lesson 3: Specify and partition a whole into equal parts, identifying and counting unit fractions by drawing pictorial area models.

Lesson 4: Represent and identify fractional parts of different wholes.

3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For 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.

Lesson 36 Partition Shapes to Make Equal Areas—pp. 320–327

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 a parts of size 1/b.

Lesson 16 Understand Unit Fractions as Quantities—pp. 142–149

Lesson 17 Understand Fractions as Quantities—pp. 150–157

Topic B: Unit Fractions and Their Relation to

the Whole


Lesson 5: Partition a whole into equal parts and define the equal parts to identify the unit fraction numerically.

Lesson 6: Build non‐unit fractions less than one whole from unit fractions.

Lesson 7: Identify and represent shaded and non‐shaded parts of one whole as fractions.

Lesson 8: Represent parts of one whole as fractions with number bonds.

Lesson 9: Build and write fractions greater than one whole using unit fractions.




3.NF.3 Explain equivalence of fractions in special cases,

and compare fractions by reasoning about their size.

3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

Lesson 21 Relate Whole Numbers and Fractions—pp. 182–189






Topic C: Comparing Unit Fractions and

Specifying the Whole


Lesson 10: Compare unit fractions by reasoning about their size using fraction strips.

Lesson 11: Compare unit fractions with different‐sized models representing the whole.

Lesson 12: Specify the corresponding whole when presented with one equal part.

Lesson 13: Identify a shaded fractional part in different ways depending on the designation of the whole.



3.NF.3d Compare two fractions with the same numerator or the same denominator by reasoning about 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.

Lesson 22 Compare Fractions: Same Denominator—pp. 190–197

Lesson 23 Compare Fractions: Same Numerator—pp. 198–205






3.NF.3a Understand two fractions as equivalent (equal) if

they are the same size, or the same point on a number line.

Lesson 19 Understand Equivalent Fractions—pp. 166–173




3.NF.3b 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.

Lesson 20 Write Equivalent Fractions—pp. 174–181





Mid‐Module Assessment: Topics A–C (assessment 1 day, return 1 day, remediation or further applications 1 day)

Days: 3

Topic D: Fractions on the Number Line


Lesson 14: Place fractions on a number line with endpoints 0 and 1.

Lesson 15: Place any fraction on a number line with endpoints 0 and 1.

Lesson 16: Place whole number fractions and fractions between whole numbers on the number line.

3.NF.2 Understand a fraction as a number on the

number line; represent fractions on a number line diagram.

3.NF.2a 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.

Lesson 18 Understand Fractions on the Number Line—pp. 158–165




Lesson 17: Practice placing various fractions on the number line.

Lesson 18: Compare fractions and whole numbers on the number line by reasoning about their distance from 0.

Lesson 19: Understand distance and position on the number line as strategies for comparing fractions. (Optional.)

3.NF.2b Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

Lesson 18 Understand Fractions on the Number Line—pp. 158–165








Topic E: Equivalent Fractions


Lesson 20: Recognize and show that equivalent fractions have the same size, though not necessarily the same shape.

Lesson 21: Recognize and show that equivalent fractions refer to the same point on the number line.



3.NF.3a Understand two fractions as equivalent (equal) if

they are the same size, or the same point on a number line.

Lesson 19 Understand Equivalent Fractions—pp. 166–173




Lessons 22–23: Generate simple equivalent fractions by using visual fraction models and the number line.

Lesson 24: Express whole numbers as fractions and recognize equivalence with different units.

Lesson 25: Express whole number fractions on the number line when the unit interval is 1.

Lesson 26: Decompose whole number fractions greater than 1 using whole number equivalence with various models.

Lesson 27: Explain equivalence by manipulating units and reasoning about their size.

3.NF.3b 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.

Lesson 20 Write Equivalent Fractions—pp. 174–181

3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.


Topic F: Comparison, Order, and Size of

Fractions


Lesson 28: Compare fractions with the same numerator pictorially.

Lesson 29: Compare fractions with the same numerator using <, >, or =, and use a model to reason about their size.

Lesson 30: Partition various wholes precisely into equal parts using a number line method.









End‐of‐Module Assessment: Topics A–F (assessment 1 day, return 1 day, remediation or further applications 1 day)

Days: 3




Module 6 • Collecting and Displaying Data NYS COMMON CORE MATHEMATICS CURRICULUM, GRADE 3 NYS COMMON CORE STANDARDS FOR MATHEMATICS, GRADE 3 SADLIER NEW YORK PROGRESS MATHEMATICS, GRADE 3

Topic A: Generate and Analyze Categorical Data


Lesson 1: Generate and organize data.

Lesson 2: Rotate tape diagrams vertically.

Lesson 3: Create scaled bar graphs.

Lesson 4: Solve one‐ and two‐step problems involving graphs.

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. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

Lesson 26 Draw Graphs to Represent Categorical Data—pp. 234–241

Topic B: Generate and Analyze Measurement

Data


Lesson 5: Create ruler with 1‐inch, 1/2‐inch, and 1/4‐inch intervals and generate measurement data.

Lesson 6: Interpret measurement data from various line plots.

Lessons 7–8: Represent measurement data with line plots.

Lesson 9: Analyze data to problem solve.

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.

Lesson 27 Generate and Graph Measurement Data—pp. 242–249

End‐of‐Module Assessment: Topics A–B (assessment ½ day, return ¼ day, remediation or further applications ¼ day)

Days: 1




Module 7 • Geometry and Measurement Word Problems NYS COMMON CORE MATHEMATICS CURRICULUM, GRADE 3 NYS COMMON CORE STANDARDS FOR MATHEMATICS, GRADE 3 SADLIER NEW YORK PROGRESS MATHEMATICS, GRADE 3

Topic A: Solving Word Problems


Lessons 1– 2: Solve word problems in varied contexts using a letter to represent the unknown.

Lesson 3: Share and critique peer solution strategies to varied word problems.

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. (This standard is limited to problems posed with whole numbers and having whole‐number 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].)



Topic B: Attributes of Two‐Dimensional Figures


Lesson 4: Compare and classify quadrilaterals.

Lesson 5: Compare and classify other polygons.

Lesson 6: Draw polygons with specified attributes to solve problems.

Lesson 7: Reason about composing and decomposing polygons using tetrominoes.

Lesson 8: Create a tangram puzzle and observe relationships among the shapes.

Lesson 9: Reason about composing and decomposing polygons using tangrams.

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.

Lesson 35 Understand Shapes and Attributes—pp. 312–319




Topic C: Problem Solving with Perimeter


Lesson 10: Decompose quadrilaterals to understand perimeter as the boundary of a shape.

Lesson 11: Tessellate to understand perimeter as the boundary of a shape. (Optional.)

Lesson 12: Measure side lengths in whole number units to determine the perimeter of polygons.

Lesson 13: Explore perimeter as an attribute of plane figures and solve problems.

Lesson 14: Determine the perimeter of regular polygons and rectangles when whole number measurements are missing.

Lesson 15: Solve word problems to determine perimeter with given side lengths.

Lesson 16: Use string to measure the perimeter of various circles to the nearest quarter inch.

Lesson 17: Use all four operations to solve problems involving perimeter and missing measurements.

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 exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Lesson 33 Problem Solving: Perimeter—pp. 296–303

Lesson 34 Problem Solving: Compare Perimeter and Area—pp. 304–311



Mid‐Module Assessment: Topics A–C (assessment 1 day, return 1 day, remediation or further applications 1 day)

Days: 3




Topic D: Recording Perimeter and Area Data on Line Plots


Lesson 18: Construct rectangles from a given number of unit squares and determine the perimeters.

Lesson 19: Use a line plot to record the number of rectangles constructed from a given number of unit squares.

Lessons 20–21: Construct rectangles with a given perimeter using unit squares and determine their areas.

Lesson 22: Use a line plot to record the number of rectangles constructed in Lessons 20 and 21.

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.

Lesson 27 Generate and Graph Measurement Data—pp. 242–249

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 exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.





Topic E: Problem Solving with Perimeter and

Area


Lesson 23: Solve a variety of word problems with perimeter.

3.MD.8 Solve real world and mathematical problems

involving perimeters of polygons, including – continued on next page –






Lessons 24–27: Use rectangles to draw a robot with specified perimeter measurements, and reason about the different areas that may be produced.

Lessons 28–29: Solve a variety of word problems involving area and perimeter using all four operations.

Lesson 30: Share and critique peer strategies for problem solving.


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 quadri‐laterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.


End‐of‐Module Assessment: Topics A–E (assessment 1 day, return 1 day, remediation or further applications 1 day)

Days: 3

Topic F: Year in Review


Lessons 31–32: Explore and create unconventional representations of one‐half.

Lesson 33: Solidify fluency with Grade 3 skills.

Lesson 34: Create resource booklets to support fluency with Grade 3 skills.


SADLIER New York Progress Mathematics New York State … · 2015. 11. 13. · SADLIER New York...

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