New York State Common Core 3 GRADE Mathematics Curriculum GRADE 3 • MODULE 5 Table of Contents GRADE 3 • MODULE 5 Fractions as Numbers on the Number Line Module Overview ........................................................................................................... i Topic A: Partition a Whole into Equal Parts: Identify and Count Unit Fractions as 1 Half, 1 Third, 1 Fourth, etc.; Specify the Whole as 2, 3, and 4 Equal Parts, etc. ................................................................................................. 5.A.1 Topic B: Identify Unit Fractions and Clarify Their Relation to the Whole .............. 5.B.1 Topic C: Compare Unit Fractions and Specify the Whole by Reasoning About Size .................................................................................................................. 5.C.1 Topic D: Represent and Compare Fractions on Number Line Diagrams ................ 5.D.1 Topic E: Equivalent Fractions ................................................................................. 5.E.1 Topic F: Compare and Order Fractions and Reason About Their Size .................... 5.F.1 Module Assessments ............................................................................................... 5.S.1 Module 5: Fractions as Numbers on the Number Line Date: 2/3/13 i © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Module Overview 3 Grade 3 • Module 5 Fractions as Numbers on the Number Line OVERVIEW In this 35‐day Grade 3 module, students extend and deepen second grade practice with “equal shares” to understanding fractions as equal partitions of a whole (2.G.3). Their knowledge becomes more formal as they work with area models and the number line. Topic A opens Module 5 with students actively partitioning different models of wholes into equal parts (e.g., concrete models, fraction strips, drawn pictorial area models on paper). They identify and count equal parts as 1 half, 1 fourth, 1 third, 1 sixth, and 1 eighth in unit form before an introduction to the unit fraction (3.NF.1). In Topic B, students compare unit fractions and learn to build non‐unit fractions with unit fractions as basic building blocks (3.NF.3d). This parallels the understanding that the number 1 is the basic building block of whole numbers. In Topic C, students practice comparing unit fractions with fraction strips, specifying the whole and labeling fractions in relation to the number of equal parts in that whole (3.NF.3d). In Topic D, students transfer their work to the number line. They begin by using the interval from 0 to 1 as the whole. Continuing beyond the first interval, they partition, place, count, and compare fractions on the number line (3.NF.2a, 3.NF.2b, 3.NF.3d). In Topic E, they notice that some fractions with different units are placed at the exact same point on the number line, and therefore are equal (3.NF.3a). For example , , and are equivalent fractions (3.NF.3b). Students recognize that whole numbers can be written as fractions, as exemplified on the number lines below (3.NF.3c). Topic F concludes the module with comparing fractions that have the same numerators. As they compare fractions by reasoning about their size, students understand that fractions with the same numerator and a larger denominator are actually smaller pieces of the whole (3.NF.3d). Topic F leaves students with a new method for precisely partitioning a number line into unit fractions of any size without using a ruler. Module 5: Fractions as Numbers on the Number Line Date: 2/3/13 ii © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Module Overview 3 Focus Grade Level Standards Develop understanding of fractions as numbers. 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. 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. 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. b. 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. Module 5: Fractions as Numbers on the Number Line Date: 2/3/13 iii © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Module Overview 3 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. 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. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form of 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. d. 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. Represent and interpret data. 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. Reason with shapes and their attributes.1 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. Foundational Standards 2.G.2 Partition a rectangle into rows and columns of same‐size squares and count to find the total number of them. 2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. 2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters. 1 3.G.1 is taught in Module 7. Module 5: Fractions as Numbers on the Number Line Date: 2/3/13 iv © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Module Overview 3 Focus Standards for Mathematical Practice MP.2 Reason abstractly and quantitatively. Students represent fractions concretely, pictorially and abstractly and move back and forth between representations. Students also represent word problems involving fractions pictorially and then express the answer in the context of the problem. MP.3 Construct viable arguments and critique the reasoning of others. Students reason about the area of a shaded region to decide what fraction of the whole it represents. MP.6 Attend to precision. Students specify the whole amount when referring to a unit fraction and explain what is meant by “equal parts” in their own words. MP.7 Look for and make use of structure. Students understand and use the unit fraction as the basic building block or structure of all fractions on the number line. Module 5: Fractions as Numbers on the Number Line Date: 2/3/13 v © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM Module Overview 3 Overview of Module Topics and Lesson Focus Standards Module Topics Days 3.G.2 A Partition a Whole into Equal Parts: Identify and Count Unit Fractions as 1 Half, 4 3.NF.1 1 Third, 1 Fourth, etc.; Specify the Whole as 2, 3, and 4 Equal Parts, etc. 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: Explore: Represent and Identify Fractional Parts of Different Wholes 3.NF.1 B Identify Unit Fractions and Clarify Their Relation to the Whole 5 3.NF.3c Lesson 5: Partition a Whole Into Equal Parts and Define the Equal Parts to 3.G.2 Identify the Unit Fraction Numerically Lesson 6: Build Non‐Unit Fractions Less than One 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.3d C Compare Unit Fractions and Specify the Whole by Reasoning About Size 4 3.NF.1 Lesson 10: Compare Unit Fractions by Reasoning About Their Size Using 3.NF.3a Fraction Strips 3.NF.3b Lesson 11: Compare Unit Fractions with Different Sized Models Representing 3.NF.3c the Whole 3.G.2 Lesson 12: Specify the Corresponding Whole When Presented with One Equal Part, E.g., “This is 1/3, draw a picture of the whole.” Lesson 13: Identify a Shaded Fractional Part in Different Ways Depending on the Designation of the Whole Mid‐Module Assessment: Topics A through C (assessment 1 day, return 1 day, 3 remediation or further applications 1 day) Module 5: Fractions as Numbers on the Number Line Date: 2/3/13 vi © 2012 Common Core, Inc.