Mathematics · Primary 3

Active learning ideas

Dividing by 6, 7, 8, and 9

Active learning helps students build fluency and confidence with division by 6, 7, 8, and 9. Moving beyond abstract numbers, hands-on activities make the inverse relationship between multiplication and division visible and concrete for young learners.

• MOE Syllabus Outcomes
• MOE: Numbers and Algebra - P3
• MOE: Multiplication and Division - P3

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

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

Manipulative Sharing: Counter Division

Give each small group 36 to 72 counters and division cards (e.g., 48 ÷ 6). Students share counters equally into the given number of groups, record the quotient, and check by multiplying back. Discuss any remainders using drawings.

How does knowing a multiplication fact help you solve a related division problem?

Facilitation Tip

During Manipulative Sharing: Counter Division, circulate and ask each pair to verbalize how their counters represent the division equation.

What to look for

Present students with a division problem, such as 63 ÷ 7. Ask them to write down the related multiplication fact and then state the answer to the division problem. Observe if they correctly link the two operations.

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

Activity 02

• Think-Pair-Share
• 25 min · Pairs

Grouping Relay: Object Sets

In pairs, students receive a total of items like 56 buttons and form as many equal groups of 7, 8, or 9 as possible. They race to record the division fact, then verify with multiplication. Switch roles for multiple rounds.

What is the difference between sharing equally and making equal groups?

Facilitation Tip

For Grouping Relay: Object Sets, ensure the relay moves quickly but allow students to pause and record their equation before the next team runs.

What to look for

Give each student a card with a division problem (e.g., 49 ÷ 7). Ask them to write two sentences: one explaining how they solved it using multiplication, and one describing if it represents sharing equally or making equal groups.

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

Activity 03

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

Fact Family Match: Card Game

Prepare cards with multiplication (e.g., 6 × 7 = 42) and division facts (42 ÷ 6 = 7). In small groups, students match related facts, solve missing numbers, and explain connections. Play multiple rounds with timers.

How can you check a division answer using multiplication?

Facilitation Tip

In Fact Family Match: Card Game, monitor pairs to make sure they discuss each match aloud before placing it on the table.

What to look for

Pose the question: 'If you have 40 apples and want to put them into bags of 8, how many bags do you need? How would you check your answer?' Facilitate a brief class discussion where students explain their strategies and use multiplication to verify.

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

Activity 04

• Think-Pair-Share
• 35 min · Whole Class

Whole Class Check: Division Bingo

Distribute bingo cards with division problems by 6-9. Call out answers; students solve and mark. First to complete a line shares workings, including multiplication checks. Adapt for remainders in advanced rounds.

How does knowing a multiplication fact help you solve a related division problem?

What to look for

Present students with a division problem, such as 63 ÷ 7. Ask them to write down the related multiplication fact and then state the answer to the division problem. Observe if they correctly link the two operations.

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

A few notes on teaching this unit

Teach division by connecting it directly to multiplication facts students already know. Use consistent language like 'share equally' and 'groups of' to reinforce both interpretations of division. Avoid rushing to symbols; let students build meaning through repeated hands-on experiences before moving to written work.

Students will confidently use multiplication facts to solve division problems with 6, 7, 8, and 9. They will explain their thinking using both sharing and grouping models and correctly handle remainders when they occur.

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Watch Out for These Misconceptions

• During Manipulative Sharing: Counter Division, watch for students who only model sharing and never form groups of a specific size.

  Prompt students to switch between the two models with the same set of counters. Ask, 'Can you show the same number of counters grouped in a different way?' Have them explain how both models represent the same division equation.

• During Grouping Relay: Object Sets, watch for students who ignore or discard leftovers when grouping objects.

  Stop the relay at each station and ask, 'How many counters are left over? What does that mean about your answer?' Have students write the remainder as part of their equation before continuing.

• During Fact Family Match: Card Game, watch for students who match cards without noticing the inverse relationship between multiplication and division.

  Before starting the game, model thinking aloud: 'I see 8 × 6 = 48, so 48 ÷ 6 = 8 must also be true because division is the opposite of multiplication.' Require students to state the link out loud with each match.

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Methods used in this brief

• Think-Pair-Share