# Teaching 4.NF.B.3 .a.b – Decomposing Fractions – Adding & Subtracting Fractions

## Number & Operations – Fractions – 4th Grade

**Build fractions from unit fractions.**

Understand a fraction

*a*/

*b*with

*a*> 1 as a sum of fractions 1/

*b*.

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.

*Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8*.

**Teacher Notes**

Students need to develop an understanding and skill of manipulating whole numbers and fractions. Decomposing whole numbers is a great way to retrieve prior knowledge or develop new knowledge.

Fractions can be composed and decomposed and be able to compose (join) and decompose (separate) fractions referring to the same whole.

Composing and decomposing fractions is the basis for adding and subtracting fractions. We are joining or separating parts within the same whole.

**Student Knowledge Goals**

I can use visual models to decompose a fraction. For example, 7/12 = 4/12 + 1/12 + 1/12 + 1/12.

I can add or subtract mixed numbers.

I can solve word problems with fractions.

**Vocabulary**

compose

decompose

denominator

fraction

numerator

parts

whole

justify

**Lessons**

Fraction Bars – Equivalent fractions for Smart Board Viewing

Building Fractions from Unit Fractions – MA DOE lesson unit with free printables

Engage NY Module 5 A-1 – Decompose fractions as a sum of unit fractions using tape diagrams.

Engage NY Module 5 A-2 – Decompose fractions as a sum of unit fractions using tape diagrams.

Engage NY Module 5 A-3 – Decompose non-unit fractions and represent them as a whole number times a unit fraction using tape diagrams.

Engage NY Module 5 A-4 – Decompose fractions into sums of smaller unit fractions using tape diagrams.

Engage NY Module 5 A-5 – Decompose unit fractions using area models to show equivalence.

Engage NY Module 5 A-6 – Decompose fractions using area models to show equivalence.

—–

Engage NY Module 5 D-16 – Use visual models to add and subtract two fractions with the same units.

Engage NY Module 5 D-17 – Use visual models to add and subtract two fractions with the same units, including subtracting from one whole.

Engage NY Module 5 D-18 – Add and subtract more than two fractions.

Engage NY Module 5 D-19 – Solve word problems involving addition and subtraction of fractions. *(4.NF.B.3.d)*

Engage NY Module 5 D-20 – Use visual models to add two fractions with related units using the denominators 2, 3, 4, 5, 6, 8, 10, and 12.

**Student Video Lessons**

Decomposing Whole Numbers – Important review/background for concept

Learn Zillion – Understand and explain equivalent fractions using visual models

Virtual Nerd – Understand a fraction a/b with a > 1 as a sum of fractions 1/b

Study Jams – Add & Subtract fractions with same denominator

**Online Problems and Assessments**

Khan Academy – Questions and Video Lessons

Add fractions with like denominators using number lines

Subtract fractions with like denominators using number lines

Add and subtract fractions with like denominators using number lines

Add and subtract fractions with like denominators

Compare sums and differences of fractions with like denominators

Add 3 or more fractions with like denominators

Compare sums of unit fractions

Compare differences of unit fractions

Compare sums and differences of unit fractions

Decompose fractions into unit fractions

Decompose fractions

Decompose fractions multiple ways

Add and subtract fractions with like denominators

Add 3 or more fractions with like denominators

** Online Games**

Decompose Fractions

Adding Subtracting Fractions Like Denominators

Adding Subtracting Fractions Like Denominators

**Printables**

Fraction Bars

Benchmark Fraction Strips

Decompose Whole Numbers – Teaching decomposing starts with whole numbers

Decompose Fractions

Adding Fractions/Subtracting Fractions – Like Denominator

Adding Fractions/Subtracting Fractions – Unlike Denominator

Assessment Task 1

Assessment Task 2

Assessment Task 3

Assessment Task 4

Assessment Task 9

Assessment Task 10

Assessment Task 13