Mathematics · Year 3

Active learning ideas

Dividing by 10 and 100

Active learning helps Year 3 students grasp place value shifts during division by 10 and 100. Concrete experiences with manipulatives and movement build mental images that abstract symbols alone cannot. Watching digits move in real time makes the invisible visible.

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

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

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

Manipulative Challenge: Base-10 Division

Provide base-10 blocks and place value mats. Students build numbers like 240, then divide into 10 groups of 24 or 100 groups of 2.4, recording digit shifts each time. Discuss patterns as a group.

Explain what happens to the digits of a number when it is divided by 10.

Facilitation Tip

During Manipulative Challenge, circulate and ask each pair to verbalize the shift they see happening with the base-10 blocks.

What to look for

Present students with a number, for example, 750. Ask them to write down the answer to 750 divided by 10. Then, ask them to write down the answer to 750 divided by 100. Observe their written answers for accuracy and understanding of place value shifts.

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

Activity 02

• Think-Pair-Share
• 25 min · Pairs

Partner Race: Predict and Check

Pairs draw cards with numbers like 630. One predicts the quotient for division by 10 or 100, the other checks with counters or calculators. Switch roles and score correct predictions.

Compare dividing by 10 to dividing by 100.

What to look for

Pose the question: 'Imagine you have 500 building blocks. How would you explain to a friend what happens to the number of blocks each person gets if you share them among 10 people versus sharing them among 100 people?' Listen for explanations that clearly describe the place value changes.

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

Activity 03

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

Whole Class: Scaling Station Relay

Set up stations with measuring tapes, beakers, and recipes. Teams relay to scale items by dividing lengths or volumes by 10 or 100, then report back to the class.

Predict the quotient of any number divided by 100.

What to look for

Give each student a card with a number like 340. Ask them to complete two calculations: 340 ÷ 10 = ? and 340 ÷ 100 = ?. On the back, ask them to draw an arrow showing where the digit '3' moves when dividing by 10 and by 100.

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

Activity 04

• Think-Pair-Share
• 20 min · Individual

Individual Chart: Digit Shift Creator

Students create personal place value charts with movable digits. They input numbers, slide digits for /10 and /100, and write explanations of changes.

Explain what happens to the digits of a number when it is divided by 10.

What to look for

Present students with a number, for example, 750. Ask them to write down the answer to 750 divided by 10. Then, ask them to write down the answer to 750 divided by 100. Observe their written answers for accuracy and understanding of place value shifts.

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

A few notes on teaching this unit

Experienced teachers anchor this concept in place value language rather than mnemonic devices. They emphasize the physical movement of digits and use consistent phrasing like ‘shifts one place to the right’ across all activities. Avoid phrases like ‘move the decimal point’; instead, focus on the value each digit represents after the shift.

Students will confidently explain that dividing by 10 shifts digits one place right and dividing by 100 shifts two places right. They will predict quotients for numbers like 450 divided by 100 equals 4.5 without relying on tricks or shortcuts.

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Watch Out for These Misconceptions

• During Partner Race: Predict and Check, watch for students who subtract 10 instead of dividing by 10.

  Pause the race and have partners model 50 beads split into 10 equal groups using counters or base-10 blocks. Ask them to count the beads in each group and compare it to their subtraction answer.

• During Manipulative Challenge, watch for students who believe dividing by 100 simply removes the last two digits.

  Have students rebuild 500 with base-10 blocks, then physically divide them into 100 equal groups. Ask them to count the value in one group to see it is 5, not 0.

• During Scaling Station Relay, watch for students who think dividing by 10 and 100 has the same effect.

  Set up a mini whiteboard at the station showing 450 divided by 10 equals 45 and 450 divided by 100 equals 4.5. Ask each runner to compare the two results and explain the difference in digit movement.

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Methods used in this brief

• Think-Pair-Share