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

## Number & Operations – Fractions – 4th Grade

#### Build fractions from unit fractions.

CCSS.Math.Content.4.NF.B.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
CCSS.Math.Content.4.NF.B.3.a
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
CCSS.Math.Content.4.NF.B.3.b
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 know a fraction is an expression of a whole divided into parts.
I know that the denominator represents the whole that has been divided into EQUAL sized pieces.
I know that fractions are made up of smaller fractions and can be decomposed.
I know that fractions can be composed and decomposed.
I can use visual models to decompose a fraction. For example, 7/12 = 4/12 + 1/12 + 1/12 + 1/12.
I can justify and record the decomposition of a fraction in more than one way.
I can use models to add and subtract fractions.
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.
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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