Mathematics · Year 7

Active learning ideas

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.

• National Curriculum Attainment Targets
• KS3: Mathematics - Number

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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.

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.

What to look for

Provide students with two problems: 1) Calculate 2/3 + 1/4. 2) Subtract 1 1/2 from 3 1/4. Ask students to show their steps and circle their final answer for each. This checks their ability to find common denominators and manage mixed numbers.

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

Activity 02

• 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.

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.

What to look for

Display the following problem on the board: 'Sarah has 5/8 of a pizza and eats 1/4 of the whole pizza. What fraction of the pizza is left?' Ask students to write down the calculation needed and the common denominator they would use. This assesses their understanding of setting up the problem and identifying the need for a common denominator.

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

Activity 03

• 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.

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.

What to look for

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 explain, perhaps using a visual aid like fraction strips or a diagram, why a common denominator is essential for accurate addition and subtraction.

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

Activity 04

• 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.

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

What to look for

Provide students with two problems: 1) Calculate 2/3 + 1/4. 2) Subtract 1 1/2 from 3 1/4. Ask students to show their steps and circle their final answer for each. This checks their ability to find common denominators and manage mixed numbers.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

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

  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.

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

  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.

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Methods used in this brief

• Collaborative Problem-Solving