Decomposing Fractions Part I: Engage

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

4

Overview

This learning activity introduces the concept of decomposing a whole into fractional parts. Using the book Whole-y Cow Fractions Are Fun by Taryn Souders, students will have fun exploring different fraction-based situations with a friendly little cow who helps guide readers through the story. Prompted by a poem and visual clue, students are encouraged to solve fraction-based problems on each page.

This activity results from the ALEX Resource Development Summit.

Phase

Before/Engage
Mathematics (2019) Grade(s): 4

MA19.4.15

Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.

UP:MA19.4.15

Vocabulary

  • Decomposition
  • Unit fraction
  • Area model
  • Length model
  • Equation
  • Mixed number
  • Visual fraction model
  • Whole
  • Sum
  • Difference
  • Recomposition

Knowledge

Students know:
  • Situation contexts for addition and subtraction problems.
  • A variety of strategies and models to represent addition and subtraction situations.
  • The fraction a/b is equivalent to the unit fraction 1/b being iterated or "copied" the number of times indicated by the numerator, a.
  • A fraction can represent a whole number or fraction greater than 1 and can be illustrated by decomposing the fraction.
    Example: 6/3 = 3/3 + 3/3 = 2 and 5/3 = 3/3 + 2/3 = 1 2/3.

Skills

Students are able to:
  • Decompose fractions as a sum of unit fractions.
  • Model decomposition of fractions as a sum of unit fractions.
  • Add and subtract fractions with like denominators using properties of operations and the relationship between addition and subtraction.
  • Solve word problems involving addition and subtraction using visual models, drawings, and equations to represent the problem.

Understanding

Students understand that:
  • A unit fraction (1/b) names the size of the unit with respect to the whole and that the denominator tells the number of parts the whole is partitioned, and the numerator indicates the number of parts referenced.
  • A variety of models and strategies can be used to represent and solve word situations involving addition and subtraction.
  • The operations of addition and subtraction are performed with quantities expressed in like units, and the sum or difference retains the same unit.

Learning Objectives

Students will decompose a fraction as a sum of fractions with the same denominator in more than one way using equations.

Activity Details

Introduce a fractional conversation to the students by allowing them to share some examples of fractions that they might use or see in their everyday lives (measurements in cooking, half past 3 pm, road signs showing the distance to next exit, etc.) 

Read aloud the book Whole-y Cow Fractions Are Fun by Taryn Souders using a paper copy of the book or the digital copy. Students should record the fractional decompositions as an equation in their math journals. For example: "Moo while her friends paint one half of her blue. What fraction of the cow is blue? What fraction of the cow is white?" Students should record 1/2 + 1/2 = 1

Students will continue to record the fractional decompositions throughout the entire book.

Assessment Strategies

Student recordings of fractional decompositions in their math journals will be used as a formative assessment to check for understanding as students decompose a fraction using an equation as a representation. 

Variation Tips

This book can also be used in a math center. The answers to the questions throughout the book are in the back of the book. 

Background / Preparation

Teachers will need to have access to the book or digital copy of Whole-y Cow Fractions Are Fun by Taryn Souders.

Students should have an understanding that fractions are part of a whole.

http://www.youtube.com/watch?v=a_Famh3Bf58

Approved Date

Owner (Author)

scarver17
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