Mathematics · Year 5

Active learning ideas

Division by 10, 100, 1000

Active learning works for this topic because students often confuse shifting digits for division with the movement for multiplication. Hands-on, movement-based tasks let them physically move digits on place value charts or with money, creating lasting mental models of why values decrease when dividing by powers of ten.

• National Curriculum Attainment Targets
• KS2: Mathematics - Multiplication and Division

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Carousel Brainstorm
• 25 min · Pairs

Place Value Shift Relay: Division Dash

Prepare large place value charts. In pairs, one student calls a number and divisor (10, 100, or 1000), the other shifts digits right on the chart. Switch roles after five problems, then pairs justify one shift to the class.

Compare the effect of multiplying by 100 with dividing by 100 on a number.

Facilitation Tip

During Place Value Shift Relay: Division Dash, circulate and listen for students to say 'each division by 10 moves digits one place to the right' without teacher prompting.

What to look for

Present students with three problems: 780 ÷ 10, 4.5 ÷ 100, and 12,300 ÷ 1000. Ask them to write the answer and draw an arrow on a place value chart to show the digit movement for each calculation.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 02

• Carousel Brainstorm
• 40 min · Small Groups

Money Division Stations: Budget Challenges

Set up stations with scenarios like dividing £500 by 100 for per-person shares. Small groups use play money to model divisions, record results, and create their own problems. Rotate stations and share one insight per group.

Justify why dividing by 10 moves digits one place to the right.

Facilitation Tip

In Money Division Stations: Budget Challenges, challenge groups to explain why 450 pence divided by 100 equals 4.5 pounds, not 45 pounds.

What to look for

Ask students: 'If you divide a number by 100, what happens to the digits? Now, what happens if you multiply the same number by 100? How are these actions related?' Encourage them to use examples to explain their reasoning.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 03

• Carousel Brainstorm
• 30 min · Pairs

Decimal Roll and Divide: Game Boards

Students roll dice for decimals (e.g., 4.2) and divide by 10, 100, or 1000 cards drawn. In pairs, they plot answers on number lines, discuss patterns, and race to fill boards first while checking work.

Construct an example where dividing a decimal by 100 results in a smaller decimal.

Facilitation Tip

For Decimal Roll and Divide: Game Boards, require students to record their decimal shifts on mini whiteboards before moving to the next station to reinforce precision.

What to look for

Give each student a card with a decimal, for example, 6.7. Ask them to write two division problems using this number: one dividing by 10 and one dividing by 100. They should then write the answers and explain how the decimal point moved in each case.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 04

• Carousel Brainstorm
• 20 min · Whole Class

Whole Class Pattern Hunt: Multiples Match

Project numbers. Whole class chorally divides by 10s, tracking digit shifts on personal whiteboards. Vote on predictions for decimals, then reveal and discuss why shifts work the same way.

Compare the effect of multiplying by 100 with dividing by 100 on a number.

Facilitation Tip

In Whole Class Pattern Hunt: Multiples Match, pause after each match to ask, 'How does this pattern show the inverse relationship between multiplying and dividing by 100?'

What to look for

Present students with three problems: 780 ÷ 10, 4.5 ÷ 100, and 12,300 ÷ 1000. Ask them to write the answer and draw an arrow on a place value chart to show the digit movement for each calculation.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Start with concrete manipulatives like base-10 blocks or place value charts to model the shift. Then move to semi-concrete representations like arrow cards or digit cards that students physically move. Finally, transition to abstract recording with place value language. Avoid rushing to the abstract; students need time to internalise the shift through repeated, varied practice. Research shows that students who physically manipulate digits develop stronger place value understanding than those who only write or say the steps.

Successful learning looks like students confidently shifting digits right for division by 10, 100, or 1000 without prompts, explaining the shift with place value language, and accurately solving both whole number and decimal division problems. They should also articulate the inverse relationship between division and multiplication by powers of ten.

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Watch Out for These Misconceptions

• During Place Value Shift Relay: Division Dash, watch for students who move digits left when dividing, mimicking multiplication.

  During Place Value Shift Relay: Division Dash, hand each pair a place value chart and ask them to model 420 ÷ 10 by moving digits right one place. Circulate and ask, 'Why did the digits move right?' to prompt place value reasoning.

• During Money Division Stations: Budget Challenges, watch for students who convert 5.5 pounds divided by 100 into a whole number like 55 pounds.

  During Money Division Stations: Budget Challenges, provide each group with real or play money in pounds and pence. Ask them to divide 5.50 pounds by 100 and explain why the result is 0.055 pounds, not 55 pounds.

• During Place Value Shift Relay: Division Dash, watch for students who believe dividing large numbers by 1000 always rounds up the result.

  During Place Value Shift Relay: Division Dash, give students base-10 blocks to model 12,300 ÷ 1000. Ask them to regroup the thousands into hundreds, tens, and ones to see the exact shift without rounding.

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Methods used in this brief

• Carousel Brainstorm