Mathematics · Year 6

Active learning ideas

Mastering Decimal Multiplication and Division

Students learn decimal multiplication and division most effectively when they manipulate physical models and discuss their reasoning. Moving digits on place value sliders or handling real currency makes the abstract shift of digits visible and memorable. These concrete experiences help students replace vague rules with clear ideas about how multiplication and division transform numbers.

• ACARA Content Descriptions
• AC9M6N06

• 15–45 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Stations Rotation
• 40 min · Small Groups

Stations Rotation: Place Value Sliders

Students use physical 'sliders' to move digits across a place value chart as they multiply or divide by powers of ten. They record the 'before' and 'after' positions of the decimal point.

What happens to the value of a digit when we multiply a decimal by ten?

Facilitation Tip

During Place Value Sliders, circulate and ask each group to verbalize the digit shift before they record the result.

What to look for

Present students with the calculation 3.45 x 10. Ask them to write the answer and explain in one sentence what happened to the digits. Then, ask them to write 12.68 ÷ 100 and explain the digit movement.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: The Estimation Check

Before solving a decimal multiplication problem, students must estimate the answer. They share their estimation strategy with a partner (e.g., rounding 4.9 to 5) to predict where the decimal point should go.

How can estimation help us check the placement of a decimal point in a product?

Facilitation Tip

For The Estimation Check, require students to write their estimate first, then compare it to the exact answer to build number sense.

What to look for

Give students two problems: 1. Calculate 4.8 x 3. Ask them to show their work and then estimate to check their answer. 2. Calculate 15.75 ÷ 5. Ask them to write the quotient and circle the digit in the tenths place.

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

Activity 03

• Inquiry Circle
• 45 min · Small Groups

Inquiry Circle: Currency Converter

Groups are given 'exchange rates' for different Pacific currencies. They must multiply and divide decimals to convert Australian dollars into other currencies for a hypothetical travel trip.

Why does dividing by a number less than one result in a larger quotient?

Facilitation Tip

During Currency Converter, ask each pair to present one conversion and explain how the decimal moved in terms of dollars and cents.

What to look for

Pose the question: 'Why does multiplying 0.5 by 10 give you 5, but dividing 5 by 0.1 also gives you 50?' Facilitate a discussion where students explain the inverse relationship and the impact of multiplying/dividing by numbers greater or less than one, focusing on decimal place value.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

A few notes on teaching this unit

Experienced teachers start with place value tools before introducing algorithms. They avoid phrases like 'move the decimal' and instead focus on the digits shifting through columns. Teachers model the inverse relationship between multiplication and division by using the same starting number in both operations. They also connect these ideas to metric conversions and money to give the work authentic meaning.

By the end of these activities, students should confidently explain why multiplying by 10 moves digits left, while dividing by 100 moves them right. They should also justify why multiplying a number by 0.5 makes it smaller. Look for clear verbal explanations and accurate calculations on exit tickets and quick-checks.

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Watch Out for These Misconceptions

• During Place Value Sliders, watch for students who think multiplying always increases the number. Redirect them by showing that sliding digits left increases the value only when the multiplier is greater than one.

  Pause the activity and ask students to slide their digits three places to the right for 0.5 x 10. They will see the number become 5, demonstrating that multiplying by a number larger than one changes the value, but multiplying by a decimal less than one would shrink it.

• During The Estimation Check, watch for students who rely on shifting the decimal point without understanding digit movement. Redirect them using the place value mats from the previous activity.

  Have students lay out 3.45 on a place value mat and physically move the digits one column to the left as they multiply by 10, keeping the decimal point fixed. They will see the digits shift while the decimal stays in place.

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Methods used in this brief

• Stations Rotation
• Think-Pair-Share
• Inquiry Circle