Mastering Mathematical Thinking: 4th Class · 4th Class

Active learning ideas

Factors and Multiples

Active learning shifts the abstract ideas of factors and multiples into hands-on experiences where students can see, touch, and manipulate numbers. When students work in pairs, small groups, or individually with visual tools like cards and arrays, they build mental models that last beyond the lesson.

• NCCA Curriculum Specifications
• NCCA: Primary - Number

• 15–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 25 min · Pairs

Pairs: Factor Pair Cards

Prepare cards with numbers from 1 to 50 and their potential factors. Pairs match factor pairs that multiply to the target number, like 3 and 8 for 24. After matching, pairs justify choices to the class.

Differentiate between a factor and a multiple of a number.

Facilitation Tip

During Factor Pair Cards, listen for students to articulate why 1 and the number itself belong in every pair, reinforcing the definition through conversation.

What to look for

Write the number 36 on the board. Ask students to write down: 1) Three factors of 36. 2) Two multiples of 36. 3) One factor pair for 36.

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

Activity 02

• Stations Rotation
• 35 min · Small Groups

Small Groups: Array Builders

Provide counters and grid paper. Groups build rectangular arrays for given numbers, such as 24 as 4x6 or 3x8, then list all dimensions as factors. Groups share arrays on the board.

Construct a list of all factors for a given number like 24.

Facilitation Tip

While Array Builders, circulate to ask groups how changing one dimension of the array affects the other, guiding them to see factors as dimensions.

What to look for

Pose this question to small groups: 'If 5 is a factor of a number, what do you know about that number? If 20 is a multiple of a number, what do you know about that number?' Have groups share their reasoning.

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

Activity 03

• Stations Rotation
• 20 min · Whole Class

Whole Class: Multiples Skip Count

Students stand in a circle. Teacher calls a number like 7; class counts multiples aloud while passing a beanbag. Speed up rounds to practice fluency, noting patterns.

Explain the relationship between multiplication and finding factors and multiples.

Facilitation Tip

For Multiples Skip Count, stand back during the opening round to let students self-correct rhythm errors, then model the correct skip pattern on the board.

What to look for

Give each student a card with two numbers, for example, 8 and 12. Ask them to write: 1) Three factors of 8. 2) Three multiples of 12. 3) One common multiple of 8 and 12.

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

Activity 04

• Stations Rotation
• 15 min · Individual

Individual: Factor Lists Challenge

Give numbers 12 to 36. Students list all factors systematically, checking with multiplication. Collect sheets for feedback and class discussion of complete lists.

Differentiate between a factor and a multiple of a number.

Facilitation Tip

During Factor Lists Challenge, provide blank grids for students who rush to slow down and list systematically from smallest to largest.

What to look for

Write the number 36 on the board. Ask students to write down: 1) Three factors of 36. 2) Two multiples of 36. 3) One factor pair for 36.

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

A few notes on teaching this unit

Teachers introduce factors and multiples through concrete materials before moving to symbolic notation. Use arrays and skip counting to bridge multiplication facts to new concepts, avoiding premature abstract rules. Research shows that students who physically arrange objects develop stronger number sense than those who only see written lists.

By the end of these activities, students should confidently list factors and multiples without prompting, explain how they are related to multiplication tables, and identify common factors and multiples with minimal support. Their explanations should include precise language such as 'divides evenly' and 'whole number multiples.'

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Watch Out for These Misconceptions

• During Factor Pair Cards, watch for students to claim factors must be larger than 1 and smaller than the number.

  Prompt pairs to include the card with 1 and the card with the target number, modeling the pair (1, number) and (number, 1) to show these are always valid factors.

• During Array Builders, watch for students to exclude 1 as a factor when building arrays.

  Challenge groups to build a 1-by-n array for any n, then ask them to identify the corresponding factor pair, reinforcing that 1 is always a factor.

• During Multiples Skip Count, watch for students to skip even multiples when counting odd numbers.

  Have the class count aloud while you write multiples on the board, pausing to ask, 'How do we know 15 is a multiple of 5?' to redirect any errors in rhythm or pattern.

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Methods used in this brief

• Stations Rotation