NC.4.NF.3

Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Decompose a fraction into a sum of unit fractions and a sum of fractions with the same denominator in more than one way using area models, length models, and equations.
Add and subtract fractions, including mixed numbers with like denominators, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
Solve word problems involving addition and subtraction of fractions, including mixed numbers by writing equations from a visual representation of the problem.

Step 1: Lesson Standards & Learning Goals

Unpacking Clarification

Students explore the meaning of addition and subtraction with fractional amounts using both area and length models. This work is limited to joining, separating, and comparing fractions with like denominators, and the only denominators that should be used are 2, 3, 4, 5, 6, 8, 10, 12, and 100.

The second bullet focuses on using area and length models to decompose a fraction or mixed number into smaller fractional amounts, including unit fractions. A unit fraction is a term that identifies the size of 1 fractional piece in a whole and has a 1 in the numerator. For example, 1/3 is the unit fraction that identifies a whole being divided into 3 equal pieces. Just as there are 3, one-inch units in the length of 3 inches, there are 2, 1/3 units in the fraction 2/3 .

Models should also be used to support students’ work when they add and subtract fractions in the latter two bullets of this standard. The work decomposing fractions, including mixed numbers, in the first two bullets of this standard, is foundational for the last two bullets of this standard. While equivalent fractions are not explicitly mentioned in this standard, students are expected to identify the equivalent fractions of answers to addition and subtraction problems.

Sample Essential Questions

How can fractions be represented as the sum of unit fractions?
Why does the numerator change, but the denominator stays the same when adding and subtracting fractions with like denominators?
What does it mean to add and subtract fractions and mixed numbers with like denominators?
How can fractions and mixed numbers be added and subtracted on a number line?
How can fractions be represented as the sum of unit fractions?
How can fractions and mixed numbers be added and subtracted using visual models?

Vocabulary

Addition
Decompose
Denominator
Equivalent fractions
Fraction
Join
Like denominators
Mixed numbers
Model
Numerator
Separating
Subtraction

Students will be able to...

Explore the meaning of addition and subtraction with fractional amounts using both area and length models.
Join, separate, and compare fractions with like denominators, and the only denominators that should be used are 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Use area and length models to decompose a fraction or mixed number into smaller fractional amounts, including unit fractions.
Use models to add and subtract fractions, including mixed numbers with like denominators.
Identify the equivalent fractions of answers to addition and subtraction problems.
Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

Students will know...

When adding or subtracting fractions with like denominators, you are adding or subtracting portions of the same size. Therefore, the denominator stays the same.
Area and length models can be used to show different ways of adding and subtracting fractions and mixed numbers.
Fractions can be added or subtracted using a number line by moving right to add or left to subtract.
Fractional amounts greater than 1 can be represented using a whole number and a fraction.
A mixed number is composed of a whole number and a fraction.
A fractional amount can be decomposed into a sum of fractions in more than one way.

Step 2: Assessment

Mastery Connect

NC.4.NF.3.A - CO - Howell - Jan. 17, 2023

NC.4.NF.3.B - CO - Howell - Jan. 17, 2023

NC.4.NF.3.C - CO - Howell - Jan. 17, 2023

NC.4 - Cluster 7 Review - CO - Howell - Mar. 6, 2023

Tools 4 NC Teachers

Exit ticket - NF3 Word Problems

Sharing Cake - NF3

Step 3: Lesson Instructions

Possible Activating Strategies

Anchor Chart
- Image: http://mrssomers4th.weebly.com/adding-and-subtracting-fractions.html

Sentence Starters/Prompts
- One thing I already know about addition is ____________________. I need to know this in order to add fractions because ___________________.
- One important thing I know about subtraction is ___________________. I need to know this in order to subtract fractions because ___________________.

Exploration or Experience
Provide students with a set of fraction pieces and ask them to model adding fractions with like denominators.

Teacher Resources

Tools 4 NC Teachers
- Cluster 7 Lessons
Math Expressions - (Barnes and Hearne) - Standards Alignment
Motivation Math
Think Up! Math
Khan Academy - 4th Grade Math
- Unit 8 - Add and Subtract Fractions
Eureka Math/Engage NY Free Resources
- Embarc Online (Eureka Math) -
  - G4 M5 Topic A: Decomposition and Fraction Equivalence
  - G4 M5 Topic D: Fraction Addition and Subtraction
  - G4 M5 Topic E: Extending Fraction Equivalence to Fractions Greater than 1
  - G4 M5 Topic F: Addition and Subtraction of Fractions by Decomposition
- Standards Alignment
- Zearn Math - Online Support Practice for Eureka Math (Requires free account)
- Khan Academy Eureka Math Grade 4
  - Unit Module 5
North Carolina Collaborative for Mathematics Learning - Grade 4 Instructional Framework
NCDPI Resources
- Math Games Grade 4
- Released Math Grade 4 EOG
Thinking Blocks - Word Problem Practice with Bar Diagrams
YouTube Videos
- Math with Mr. J
Fact Practice
- Multiplication.com
- Math Playground Multiplication and Division Games

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