Adding and Subtracting Fractions

Active learning builds fluency and confidence with fractions by letting students physically manipulate pieces. When they align fraction strips, adjust recipes, or step along number lines, they see why denominators must match before adding or subtracting. These hands-on experiences turn abstract rules into lasting understanding.

• Year 7
• Mathematics
• 4 activities
• 20 min–45 min

Learning Objectives

1. Calculate the sum or difference of two fractions with unlike denominators by finding a common denominator.
2. Convert mixed numbers to improper fractions and vice versa to perform addition and subtraction operations.
3. Explain the necessity of a common denominator for adding and subtracting fractions using a visual model or algebraic reasoning.
4. Analyze the steps required to add or subtract a mixed number and a proper fraction.
5. Predict the sign and approximate magnitude of the result when subtracting fractions, including cases where the subtrahend is larger than the minuend.

Collaborative Problem-Solving

⏱ 30 min·Pairs

Pairs: Fraction Strip Matching

Provide pre-cut fraction strips. Pairs match equivalent fractions, then align strips on a mat to add or subtract by combining or removing lengths. They record sums, simplify, and swap with another pair to check. Discuss why strips of different denominators need equivalents.

Prepare & details

Justify the need for a common denominator when adding or subtracting fractions.

Facilitation Tip: During Fraction Strip Matching, circulate and ask pairs to explain why their matched strips must show equal lengths before they combine numerators.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 45 min·Small Groups

Small Groups: Recipe Adjustment Challenge

Groups receive recipe cards with fractional ingredients, like 1/2 cup flour plus 1/3 cup sugar. They add or subtract to scale for different servings, using drawings or strips to find common denominators. Present adjusted recipes to class and justify steps.

Prepare & details

Analyze the steps involved in adding mixed numbers.

Facilitation Tip: In the Recipe Adjustment Challenge, remind small groups to convert all quantities to eighths or sixteenths first, using measuring cups as visual support.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 25 min·Whole Class

Whole Class: Number Line Relay

Draw a large number line on the board. Teams send one student at a time to plot fractions, add or subtract by jumping intervals, marking results. Class verifies each move aloud, converting mixed numbers as needed. Rotate roles quickly.

Prepare & details

Predict the result of subtracting a larger fraction from a smaller one.

Facilitation Tip: For the Number Line Relay, have each runner mark their starting point and count jumps backward or forward to reinforce the role of the denominator.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 20 min·Individual

Individual: Fraction Puzzle Cards

Students draw cards with fraction problems, solve using personal mini fraction circles, then match to answer cards. Self-check with provided keys, noting tricky steps like common denominators. Share one insight with a partner afterward.

Prepare & details

Justify the need for a common denominator when adding or subtracting fractions.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Teaching This Topic

Teachers should model the process slowly, thinking aloud as they find the least common multiple and convert fractions. Avoid rushing to the algorithm; instead, let students discover the need for common denominators through guided discovery. Research shows that students who struggle benefit from drawing and labeling each step, while advanced learners can explore why the least common multiple works mathematically.

What to Expect

Successful students will explain why fractions need common denominators, perform accurate calculations with mixed numbers, and simplify results appropriately. They will use visual models to justify their steps and communicate their reasoning clearly to peers.

Watch Out for These Misconceptions

Common Misconception

During Fraction Strip Matching, watch for students who try to add numerators and denominators without aligning the strips first.

What to Teach Instead

Prompt them to line up the strips and ask, 'Do these pieces cover the same length?' Have them find strips of equal length before combining, so they see why 1/2 and 1/3 cannot combine without rescaling.

Common Misconception

During Number Line Relay, listen for groups that change the denominator when subtracting fractions.

What to Teach Instead

Ask them to point to the scale on the number line and say, 'What stays the same when we move backward?' Guide them to see that only the numerator changes during subtraction.

Common Misconception

During Recipe Adjustment Challenge, watch for students who subtract mixed numbers without converting to improper fractions.

What to Teach Instead

Provide measuring cups and ask them to show how many whole cups and fractional cups they have before and after. Have them model borrowing visually to clarify the conversion step.

Assessment Ideas

Exit Ticket

After Fraction Strip Matching, give each student two problems to solve: 2/3 + 1/4 and 3 1/2 - 1 3/4. Ask them to show their steps and circle their final answers, including any simplification.

Quick Check

During Recipe Adjustment Challenge, circulate and ask each group to explain how they converted their recipe fractions to a common denominator. Listen for correct use of the least common multiple and proper handling of mixed numbers.

Discussion Prompt

After Number Line Relay, pose the question, 'Why can’t we just add the numerators and denominators of 1/3 and 1/2 to get 2/5?' Facilitate a class discussion where students use their number line diagrams to explain why a common denominator is essential.

Extensions & Scaffolding

• Challenge early finishers to design a fraction recipe challenge for the class using three mixed numbers.
• For students struggling, provide pre-cut fraction pieces and a template for drawing their own number lines with labeled jumps.
• Deeper exploration: Have students research and present why ancient civilizations used unit fractions and how our current methods compare.

Key Vocabulary

Common Denominator	A shared denominator for two or more fractions, which is typically a multiple of the original denominators. It allows for the addition or subtraction of fractions.
Equivalent Fraction	Fractions that represent the same value or proportion, even though they have different numerators and denominators. For example, 1/2 is equivalent to 2/4.
Improper Fraction	A fraction where the numerator is greater than or equal to the denominator, indicating a value of one or more. For example, 5/4 is an improper fraction.
Mixed Number	A number consisting of a whole number and a proper fraction. For example, 2 1/2 is a mixed number.
Least Common Multiple (LCM)	The smallest positive integer that is a multiple of two or more integers. It is often used to find the least common denominator.