Mathematics · Primary 4

Active learning ideas

Multiples and Number Sequences

Active learning builds deep number sense with multiples and sequences. When students manipulate objects, draw models, and collaborate, they move from memorizing steps to understanding why patterns repeat. This hands-on work turns abstract rules into concrete discoveries that stick.

• MOE Syllabus Outcomes
• Singapore MOE Mathematics Syllabus (2021): Primary 4, Number and Algebra, Whole Numbers: Determine if a 1-digit number is a factor of a given number.
• Singapore MOE Mathematics Syllabus (2021): Primary 4, Number and Algebra, Whole Numbers: List the first 12 multiples of a given 1-digit number.
• Singapore MOE Mathematics Syllabus (2021): Primary 4, Number and Algebra, Number Patterns: Recognise and complete number patterns.

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Gallery Walk
• 30 min · Small Groups

Small Groups: Multiples Tower Challenge

Provide counters or linking cubes to small groups. Instruct students to build towers for multiples of a given number, such as levels of 4, 8, 12 cubes. Have them label heights, extend to 5 terms, and share growth rules with the class.

How do you list the multiples of a number, and what pattern do they follow?

Facilitation Tip

During Multiples Tower Challenge, circulate and ask groups to predict the next block before they build, reinforcing the fixed increment rule.

What to look for

Present students with a list of numbers (e.g., 7, 14, 21, 28, 35). Ask: 'What is the rule for this number sequence?' and 'What is the next number in the sequence?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Gallery Walk
• 25 min · Pairs

Pairs: LCM Path Game

Pairs draw number lines for two numbers like 6 and 8. They mark multiples of each, shade common ones, and circle the lowest common multiple. Discuss why it is smallest and solve a related word problem on schedules.

What are common multiples, and how do you find the lowest common multiple of two numbers?

Facilitation Tip

For the LCM Path Game, set a timer so pairs must move quickly, forcing them to rely on multiples rather than trial and error.

What to look for

Give students two numbers, such as 5 and 8. Ask them to list the first five multiples of each number and then identify the lowest common multiple (LCM).

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 03

• Gallery Walk
• 20 min · Whole Class

Whole Class: Pattern Parade

Students line up in class formation representing a sequence, such as multiples of 3 with claps or steps. Extend the pattern by adding participants. Record the sequence on board and describe the rule as a group.

Can you use multiples to solve a word problem about events that repeat at regular intervals?

Facilitation Tip

In Pattern Parade, assign each student a unique starting number so the whole class sees how different sequences align or miss each other.

What to look for

Pose this problem: 'A baker makes cookies in batches of 6 and muffins in batches of 4. What is the smallest number of cookies and muffins the baker can make so that there are equal numbers of each item?' Facilitate a discussion on how they found their answer.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 04

• Gallery Walk
• 15 min · Individual

Individual: Shape Sequence Sketch

Each student sketches geometric shapes growing by multiples, like triangles with 2, 4, 6 dots. Label the sequence, predict the 6th term, and write the rule. Share one with a partner for feedback.

How do you list the multiples of a number, and what pattern do they follow?

Facilitation Tip

For Shape Sequence Sketch, provide tracing paper so students can overlay shapes to verify consistent spacing before drawing.

What to look for

Present students with a list of numbers (e.g., 7, 14, 21, 28, 35). Ask: 'What is the rule for this number sequence?' and 'What is the next number in the sequence?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Teach multiples as repeated groupings first, then as number sequences, so students see both the count and the pattern. Avoid rushing to the algorithm for LCM; let students list and compare multiples until they notice the shared jump. Use language like 'every third block' or 'one more set of five' to anchor the concept in concrete actions. Research shows that students who generate their own examples before formal rules develop stronger number flexibility.

By the end of these activities, students will confidently list multiples, spot patterns in sequences, and find lowest common multiples without guessing. They will explain their reasoning using clear language and visual evidence from their work. Collaboration will reveal misconceptions through peer feedback and shared problem-solving.

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Watch Out for These Misconceptions

• During the LCM Path Game, watch for students who multiply the two numbers immediately without listing multiples first.

  Have pairs pause their game and list the first five multiples of each number on their game board side-by-side, then circle the first match to redirect their thinking.

• During Multiples Tower Challenge, some students may stop building after a few blocks, assuming the pattern changes.

  Ask groups to add three more blocks and explain how they know the next one fits, reinforcing the fixed increment through physical extension.

• During the LCM Path Game, students may confuse common multiples with averages, like thinking 4 and 6 share 5.

  Use the game’s Venn diagram spaces to sort exact multiples only; prompt pairs to test 'Is 5 a multiple of 4? Is it a multiple of 6?' to correct the error.

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Methods used in this brief

• Gallery Walk