Mathematics · Class 5

Active learning ideas

Identifying Factors and Multiples

Active learning works for identifying factors and multiples because students need to physically manipulate numbers to see the relationships between them, not just memorise rules. Concrete materials like tiles or counters help them visualise division and multiplication in ways that abstract explanations cannot. These activities build confidence as students discover patterns themselves rather than having them told.

• CBSE Learning Outcomes
• NCERT: N-2.2

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 35 min · Small Groups

Hands-On: Tile Grouping

Give each small group 24-48 counters or tiles. Ask them to group in different ways to find factor pairs, like 3x8 or 4x6 for 24. Record pairs on chart paper and discuss why 1x24 works. Extend to predict factors for larger sets.

Compare the characteristics of factors and multiples of a given number.

Facilitation Tip

During Tile Grouping, observe how students arrange tiles to form rectangles, noting if they consider both 1xN and Nx1 as valid groupings to address the misconception that factors must be smaller.

What to look for

Write the number 18 on the board. Ask students to write down: (a) three factors of 18, and (b) three multiples of 18. Review answers as a class, checking for understanding of both concepts.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Simulation Game
• 30 min · Whole Class

Simulation Game: Factor Bingo

Prepare bingo cards with numbers 1-50. Call out a number, students mark its factors on their card. First to complete a line shouts 'Factors!'. Review marked factors as a class to reinforce lists.

Explain why every number is both a factor and a multiple of itself.

Facilitation Tip

For Factor Bingo, circulate to listen for students justifying why a number is or isn’t a factor, reinforcing precise mathematical language.

What to look for

Give each student a card with a number (e.g., 15, 24, 7). Ask them to list all the factors of their number and state whether it is a prime or composite number, explaining their reasoning in one sentence.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 03

• Think-Pair-Share
• 25 min · Pairs

Pairs: Multiples Chain

In pairs, start with a number like 7. One student says next multiple, partner continues up to 100. Switch roles after 10 multiples. Pairs then compare chains and spot patterns with neighbours.

Predict how the number of factors changes as a number increases in value.

Facilitation Tip

In the Multiples Chain activity, step in when pairs struggle to generate multiples beyond 100 to ensure they connect the concept to real-world contexts like counting money or measuring.

What to look for

Pose the question: 'Why is every number a factor and a multiple of itself?' Allow students to discuss in pairs for two minutes, then call on a few pairs to share their explanations with the class, guiding them towards the definitions of factor and multiple.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 04

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Factor Challenges

Set up stations: 1) list factors with divisibility checks, 2) model with drawings, 3) match numbers to factor counts, 4) generate multiples sequences. Groups rotate, recording one insight per station.

Compare the characteristics of factors and multiples of a given number.

Facilitation Tip

During Factor Challenges, provide scaffolding for students who list factors randomly by guiding them to use the smallest factor first to build systematic thinking.

What to look for

Write the number 18 on the board. Ask students to write down: (a) three factors of 18, and (b) three multiples of 18. Review answers as a class, checking for understanding of both concepts.

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

A few notes on teaching this unit

Teachers should approach this topic by first letting students explore without formal definitions, allowing them to discover relationships through hands-on work. Avoid rushing to formalise the concept of factors and multiples before students have a strong intuitive grasp. Research shows that students who struggle often benefit from visual and kinaesthetic methods like arrays and counters, which help bridge the gap between concrete and abstract thinking.

Successful learning looks like students confidently listing factors and multiples for any given number, explaining why 1 and the number itself are always included, and distinguishing between prime and composite numbers without hesitation. They should also articulate the difference between factors of a number and factors of its multiples, showing clear number sense.

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Watch Out for These Misconceptions

• During Tile Grouping, watch for students who exclude a 1xN arrangement when forming rectangles, as this reveals the misconception that factors must always be smaller than the number.

  Use the tile arrays to explicitly show that a single row of N tiles still represents a factor pair (1 and N), reinforcing that every number is a factor of itself by creating a square array when appropriate.

• During Factor Bingo, watch for students who incorrectly mark a number as a factor of its multiple because it appears in the multiple's factor list.

  Have students compare the factor lists of a number and its multiple side-by-side during the game, prompting them to notice that the multiple's factors include additional numbers beyond the original number's factors.

• During the Multiples Chain activity, watch for students who claim prime numbers have no factors after seeing them generate only 1 and themselves.

  Ask students to use counters to form arrays for prime numbers, guiding them to see that the only possible rectangles are 1xN, confirming that primes have exactly two factors: 1 and themselves.

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Methods used in this brief

• Think-Pair-Share
• Simulation Game
• Stations Rotation