4.NF.3: Adding and Subtracting Fractions

Visual Models for Adding and Subtracting Fractions

1. Fraction Strips

Use fraction strips to visually represent adding and subtracting fractions with the same denominator. For example, to show 2/6 + 3/6, use two 1/6 strips and three 1/6 strips, then combine them to see they equal 5/6.

2. Number Lines

Use a number line divided into equal parts to show adding and subtracting fractions. For example, to show 3/8 + 2/8, start at 0, move right 3/8, then move right another 2/8 to land at 5/8.

3. Area Models

Draw rectangles or circles divided into equal parts to represent fractions. Shade different sections to show addition or subtraction. For example, shade 2/4 of a circle blue and 1/4 red to show that 2/4 + 1/4 = 3/4.

Decomposing Fractions into Unit Fractions

Show how any fraction can be broken down into a sum of unit fractions:

• 2/3 = 1/3 + 1/3
• 4/5 = 1/5 + 1/5 + 1/5 + 1/5
• 7/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8

Everyday Applications

1. Cooking and Recipes

Practice adding fractions when combining ingredients:

• If a recipe calls for 2/3 cup of flour for the crust and 1/3 cup for the topping, how much flour is needed in total? (2/3 + 1/3 = 3/3 = 1 cup)
• If you've used 3/4 cup of sugar and the recipe calls for 1 cup, how much more do you need? (1 - 3/4 = 1/4 cup)

2. Time Management

Use fractions to discuss time:

• If homework takes 1/6 of an hour for math, 2/6 for reading, and 1/6 for science, how much time is spent on homework? (1/6 + 2/6 + 1/6 = 4/6 = 2/3 of an hour)
• If you've spent 3/8 of your study time on history, how much time is left for other subjects? (1 - 3/8 = 5/8 of your study time)

3. Crafts and Construction

Apply fractions to measuring and building:

• If you need pieces of ribbon that are 2/3 foot, 1/3 foot, and 3/3 foot long, how much ribbon do you need in total? (2/3 + 1/3 + 3/3 = 6/3 = 2 feet)
• If you have a board that's 8/8 foot long and you cut off a piece that's 3/8 foot, how much is left? (8/8 - 3/8 = 5/8 foot)

When Your Child Struggles

1. Focus on the Denominator

Remind your child that when adding or subtracting fractions with the same denominator, the denominator stays the same and only the numerators are added or subtracted. Use the analogy of adding or subtracting the same type of object (e.g., 2 apples + 3 apples = 5 apples).

2. Use Visual Models

If your child is having trouble understanding fraction operations conceptually, use visual models like fraction strips, area models, or number lines to help them see what's happening when fractions are added or subtracted.

3. Practice Unit Fractions First

Start by breaking down fractions into unit fractions (fractions with numerator 1). For example, show that 3/4 = 1/4 + 1/4 + 1/4. This helps build a strong foundation for understanding fraction operations.

4. Connect to Whole Numbers

Help your child see the connection between adding fractions and adding whole numbers. Just as 2 + 3 = 5, similarly 2/8 + 3/8 = 5/8. The denominator tells us what kind of pieces we're counting.

5-Minute Activities

Activity 1: Fraction Cards

Create a set of cards with various fractions. Have your child pick two cards with the same denominator and add or subtract them. For more challenge, include cards with mixed numbers.

Activity 2: Fraction Scavenger Hunt

Hide fraction problems around the house. When your child finds a problem, they solve it and then look for the next clue. For example, "Find 2/6 + 3/6 and look under something that's this fraction of a foot tall."

Activity 3: Decompose the Fraction

Give your child a fraction (like 5/8) and ask them to decompose it in as many different ways as possible (e.g., 1/8 + 4/8, 2/8 + 3/8, 1/8 + 1/8 + 3/8, etc.).

Activity 4: Fraction Word Problems

Create simple word problems based on everyday situations:

• "If you ate 2/8 of a pizza and your sister ate 3/8, how much did you eat together?"
• "If you've completed 5/6 of your homework and take a break, how much is left to do?"

Mid-Year Expectations

By the middle of the school year, your child should be able to:

• Decompose fractions into unit fractions (e.g., 3/4 = 1/4 + 1/4 + 1/4)
• Add fractions with the same denominator (e.g., 2/5 + 1/5 = 3/5)
• Subtract fractions with the same denominator (e.g., 4/6 - 1/6 = 3/6)
• Represent fraction addition and subtraction using visual models
• Solve simple word problems involving fractions with like denominators

End-of-Year Expectations

By the end of the school year, your child should be able to:

• Decompose fractions in multiple ways (e.g., 5/8 = 2/8 + 3/8 = 1/8 + 4/8)
• Add and subtract fractions and mixed numbers with like denominators
• Solve multi-step word problems involving fractions with like denominators
• Explain their reasoning when adding and subtracting fractions
• Apply fraction addition and subtraction to real-world contexts

Signs of Mastery

Your child has mastered this standard when they can:

• Consistently and accurately add and subtract fractions with like denominators
• Decompose fractions into unit fractions and explain their reasoning
• Represent fraction operations using multiple models (number lines, area models, etc.)
• Solve complex word problems involving fractions with like denominators
• Explain the relationship between whole numbers and fractions in addition and subtraction
• Apply fraction concepts to solve real-world problems

Questions to Check Understanding:

• "How can you write 4/7 as a sum of unit fractions?"
• "What is 3/8 + 2/8? Can you show me using a visual model?"
• "If you have 5/6 of a pizza and eat 2/6, how much is left? How do you know?"
• "Can you decompose 7/10 in three different ways?"

Below Grade Level

For students who need additional support with basic fraction concepts and simple fraction addition and subtraction.

📥 Download Practice Worksheet

At Grade Level

For students who need practice with grade-level fraction addition and subtraction concepts.

📥 Download Grade Level Worksheet

Above Grade Level

For students ready for more challenging fraction addition and subtraction concepts and applications.

📥 Download Challenge Worksheet