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.

• Primary 3
• Mathematics
• 4 activities
• 20 min–35 min

Learning Objectives

1. Calculate the quotient and remainder when dividing numbers up to 72 by 6, 7, 8, or 9.
2. Explain the relationship between multiplication facts and division problems involving divisors 6, 7, 8, and 9.
3. Compare and contrast the concepts of 'sharing equally' and 'making equal groups' in division scenarios.
4. Verify division answers by applying the inverse operation of multiplication.

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.

Prepare & details

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.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

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.

Prepare & details

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.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

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.

Prepare & details

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.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

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.

Prepare & details

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

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Manipulative Sharing: Counter Division, present 63 ÷ 7. Ask students to write the related multiplication fact and the division answer, then turn and tell a partner how they connected the two.

Exit Ticket

After Grouping Relay: Object Sets, give each student a card with 49 ÷ 7. Ask them to write two sentences: one explaining how they used multiplication to solve it and one describing whether it was sharing equally or making equal groups.

Discussion Prompt

During Whole Class Check: Division Bingo, pose: '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?' Let several students explain their strategies, then verify answers together using multiplication.

Extensions & Scaffolding

• Challenge early finishers to create their own division word problems using numbers they choose, then trade with a partner to solve.
• For students who struggle, provide pre-partitioned counters or dot paper grids so they can focus on the equation without the extra step of arranging objects.
• Deeper exploration: Invite students to investigate patterns in remainders when dividing by 6 through 9, then present their findings to the class using charts or drawings.

Key Vocabulary

Quotient	The answer to a division problem. For example, in 48 ÷ 6 = 8, the quotient is 8.
Remainder	The amount left over after dividing a number by another number when it cannot be divided equally. For example, in 50 ÷ 6, the remainder is 2.
Sharing Equally	Distributing a total number of items into a specific number of groups so that each group has the same amount.
Making Equal Groups	Forming sets of a specific size from a total number of items, determining how many sets can be made.