Mathematics · Year 2

Active learning ideas

Division by 2, 5, and 10

Active learning turns division facts into lived experience, not just memorised symbols. When pupils move counters, build arrays, and tell stories with real objects, they connect abstract numbers to concrete actions. This builds fluency and confidence faster than worksheets alone.

• National Curriculum Attainment Targets
• KS1: Mathematics - Multiplication and Division

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

Activity 01

• Think-Pair-Share
• 25 min · Pairs

Pairs: Counter Sharing

Provide pairs with 20 to 60 counters and division cards (÷2, ÷5, ÷10). Pupils share into equal groups, record quotients, and explain using multiplication. Pairs then swap cards to check.

Explain how division is the inverse of multiplication.

Facilitation Tip

During Counter Sharing, circulate and ask each pair to explain their sharing method aloud while you watch their counters move.

What to look for

Give each student a card with a division problem (e.g., 30 ÷ 10 = ?). Ask them to write the answer and then write the related multiplication fact that proves their answer.

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

Activity 02

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

Small Groups: Array Builders

Groups receive interlocking cubes or drawings to make arrays for multiples of 2, 5, 10. They divide arrays and label facts. Rotate roles: builder, recorder, checker.

Predict the quotient when dividing by 2, 5, or 10.

Facilitation Tip

When groups build arrays, remind them to place a sticky note with the division sentence on each completed array for later sharing.

What to look for

Ask students to hold up fingers to show the answer to rapid-fire division questions (e.g., 'What is 12 divided by 2?'). Then, ask a few students to explain their answer using the inverse multiplication fact.

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

Activity 03

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

Whole Class: Fact Family Chains

Display a multiplication fact like 4 × 5 = 20. Class calls out divisions: 20 ÷ 5 = 4, 20 ÷ 4 = 5. Chain to next fact, using fingers or whiteboards to track.

Construct a real-world problem that requires division by 5 to solve.

Facilitation Tip

In Fact Family Chains, pause after each round to highlight one family and ask students to predict the next possible chain before continuing.

What to look for

Pose the question: 'Imagine you have 25 sweets and want to share them equally among 5 friends. How many sweets does each friend get? How do you know?' Encourage students to explain their reasoning using division and multiplication.

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

Activity 04

• Think-Pair-Share
• 15 min · Individual

Individual: Story Problems

Pupils draw pictures and write one ÷2, ÷5, ÷10 problem from daily life, like halving a pizza. Swap with a partner to solve and verify with drawings.

Explain how division is the inverse of multiplication.

What to look for

Give each student a card with a division problem (e.g., 30 ÷ 10 = ?). Ask them to write the answer and then write the related multiplication fact that proves their answer.

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

A few notes on teaching this unit

Build fluency by alternating between concrete, pictorial, and abstract representations. Avoid rushing straight to symbols; instead, let pupils manipulate materials to internalise the inverse link between multiplication and division. Research shows that pupils who physically separate and group objects develop stronger mental models than those who only write equations.

By the end of these activities, pupils will recall division facts for 2, 5, and 10 with speed and accuracy. They will explain division as the inverse of multiplication using clear language, and use sharing and grouping to solve real-world problems independently.

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Watch Out for These Misconceptions

• During Counter Sharing, watch for pupils who think 40 ÷ 10 means 'add a zero to make 400'.

  Give each pair base-10 rods and ask them to remove groups of 10 rods from 40, counting aloud as they go. Remind them to notice how the total count gets smaller each time a group is removed.

• During Array Builders, watch for pupils who reverse the operation and write 20 ÷ 5 = 100.

  Ask the group to count the total dots in their array first, then point to each row while counting 5, 10, 15, 20. Write the division sentence together and underline the connection to 4 × 5 = 20 on the board.

• During Array Builders, watch for pupils who believe division only means sharing, not grouping.

  Provide a second set of counters and ask the same group to arrange 20 counters into groups of 5 without sharing one by one. Compare the two arrangements and discuss how both models show division.

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Methods used in this brief

• Think-Pair-Share