Mathematics · Year 5

Active learning ideas

Common Factors and Multiples

Active learning works for common factors and multiples because students need repeated, concrete practice to move from memorizing to flexible reasoning. Handling physical tiles, racing through lists, and solving real-world scheduling problems helps students internalize the inverse relationship between factors and multiples without relying only on abstract rules.

• National Curriculum Attainment Targets
• KS2: Mathematics - Multiplication and Division

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

Activity 01

• Stations Rotation
• 35 min · Small Groups

Small Groups: Factor Tile Sort

Provide number tiles (1-20) and two numbers like 12 and 18. Groups sort tiles into factors for each number using Venn diagrams on large paper. Discuss and list common factors. Extend by predicting for new pairs.

Explain how to find the common factors of 12 and 18.

Facilitation Tip

During Factor Tile Sort, circulate to prompt students to explain why 1 and the number itself are always factors.

What to look for

Provide students with two numbers, for example, 15 and 20. Ask them to list all common factors of these two numbers and then list the first three common multiples.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Stations Rotation
• 25 min · Pairs

Pairs: Multiples Relay Race

Pairs generate multiples of two numbers on mini-whiteboards, passing to partner after five each. First pair to list 10 common multiples wins. Review lists as a class, circling shared ones.

Construct a list of the first five common multiples of 3 and 4.

Facilitation Tip

In Multiples Relay Race, time each pair and post their fastest accurate list to celebrate progress and accuracy.

What to look for

Present a word problem: 'Sarah is making party bags. She has 24 sweets and 30 stickers. What is the largest number of party bags she can make so that each bag has the same number of sweets and the same number of stickers?' Ask students to explain how finding a common factor helps solve this problem.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 03

• Stations Rotation
• 45 min · Small Groups

Whole Class: Problem-Solving Carousel

Set up stations with problems needing common factors or multiples, like 'Share 24 cakes between 3 and 4 friends equally.' Groups rotate, solve, and justify. Debrief key strategies.

Analyze a problem where finding a common multiple helps to solve it.

Facilitation Tip

In Problem-Solving Carousel, assign each group a unique pair of numbers to ensure variety and accountability in their discussion.

What to look for

Pose the question: 'When might it be useful to find common multiples in real life?' Encourage students to share examples and explain their reasoning, focusing on scenarios involving cycles or regular intervals.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 04

• Stations Rotation
• 20 min · Individual

Individual: Common Multiple Hunt

Students list first eight multiples of given pairs, highlight commons, then solve a word problem using the smallest common multiple. Share one solution with the class.

Explain how to find the common factors of 12 and 18.

Facilitation Tip

For Common Multiple Hunt, provide graph paper so students can organize their multiples in columns for quick comparison.

What to look for

Provide students with two numbers, for example, 15 and 20. Ask them to list all common factors of these two numbers and then list the first three common multiples.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teach factors and multiples as inverse operations by having students build factor lists and then extend them into multiples. Avoid rushing to algorithms; instead, use repeated listing to build number sense. Research shows that students who physically manipulate objects and discuss their reasoning develop deeper multiplicative thinking than those who only use worksheets or calculators.

Students will confidently list all factors of a number and identify common factors, then generate multiples and spot shared ones. They will explain how factors divide a number and how multiples extend from it, using clear language and examples during group tasks.

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Watch Out for These Misconceptions

• During Factor Tile Sort, watch for students who skip 1 or the number itself when listing factors.

  Prompt them to place all tiles and count how many pairs multiply to the target number, ensuring they see 1 × n and n × 1 as valid pairs.

• During Multiples Relay Race, watch for students who start multiples at zero or omit the first multiple.

  Have them read the rules aloud before racing: multiples begin with the number and continue by repeated addition.

• During Problem-Solving Carousel, watch for students who call factors and multiples the same thing.

  Ask groups to draw a quick Venn diagram on the board comparing factors and multiples, labeling each part with examples from their numbers.

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Methods used in this brief

• Stations Rotation