Mathematics · Year 5

Active learning ideas

Calculating Change and Making Purchases

Active learning works for time calculations because students often struggle to transfer base-ten thinking to the base-sixty system of time. Hands-on activities let them visualize the jumps between minutes and hours, turning abstract differences like 2:15 minus 1:45 into something they can physically move through. Real-world contexts, such as catching a train or buying lunch, make the need for accuracy immediate and meaningful.

• ACARA Content Descriptions
• AC9M5N08

• 25–50 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Simulation Game
• 50 min · Small Groups

Simulation Game: The Amazing Race (Timetable Edition)

Groups are given a 'starting point' and a 'destination' with a series of bus and train timetables. They must find the fastest route, accounting for 'transfer times' between stops, and calculate their total travel duration in hours and minutes.

Explain different strategies for calculating change accurately.

Facilitation Tip

During The Amazing Race, circulate with a stopwatch and time each team’s stage to model precise start and end points for elapsed-time practice.

What to look for

Present students with a scenario: 'You bought a toy for $7.50 and paid with a $10 note. How much change should you receive?' Ask students to show their calculation on a mini-whiteboard and hold it up.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 02

• Think-Pair-Share
• 25 min · Pairs

Think-Pair-Share: The 24-Hour Translator

Students are given a list of 'digital times' (e.g., 17:30, 04:15, 22:00). They think about what they would be doing at that time, pair up to 'translate' them to AM/PM time, and share their 'Day in the Life' schedule with the class.

Design a shopping list within a specific budget and calculate the total cost and change.

Facilitation Tip

For The 24-Hour Translator, provide dual clocks—one analog, one digital—so students physically move the hour hand to match the 24-hour notation.

What to look for

Give each student a slip of paper with a shopping list and a budget. For example: 'Budget: $20. Items: Apple ($1.50), Banana ($0.75), Orange ($1.25), Milk ($3.00).' Ask them to calculate the total cost, the change received, and write one sentence about how they checked their answer.

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

Activity 03

• Inquiry Circle
• 40 min · Small Groups

Inquiry Circle: The Movie Marathon

Students are given the run-times of three movies (e.g., 105 mins, 92 mins, 118 mins). They must calculate the total duration, convert it to hours and minutes, and determine what time the marathon will end if it starts at 14:00.

Analyze the importance of checking change received after a purchase.

Facilitation Tip

In The Movie Marathon, give groups a printed film schedule with overlapping start times so they must sequence events and calculate gaps between them.

What to look for

Pose the question: 'Why is it important to count your change before leaving the shop?' Facilitate a class discussion, encouraging students to share personal experiences or potential problems that could arise from not checking change.

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

A few notes on teaching this unit

Teach elapsed time by moving from concrete to abstract: start with physical clocks, then empty number lines, then mental math. Avoid teaching algorithms that rely on borrowing; base-sixty subtraction works best when students break time into chunks. Research shows that students grasp 24-hour time faster when they link it to daylight and darkness—anchor lessons in daily routines like sunrise and bedtime.

Successful learning looks like students confidently converting between 12-hour and 24-hour clocks, calculating elapsed time without borrowing across 60, and checking change totals against a budget. They should explain their steps aloud and catch common errors like treating 100 minutes as an hour. Peer discussions and written explanations confirm understanding beyond correct answers.

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Watch Out for These Misconceptions

• During The Amazing Race, watch for students who try to subtract 1:45 from 2:15 using column subtraction and arrive at 1:70.

  Pause the race and have peers model an empty number line: jump 15 minutes to reach 2:00, then another 15 to land at 2:15. Write ‘1 hour 30 minutes’ on the board so the group sees the correct result.

• During The 24-Hour Translator, watch for students who label 12:00 PM as midnight and 12:00 AM as midday.

  Show the 24-hour chart and ask students to color-code daylight hours in yellow and darkness hours in blue. Point to 12:00 as midday and 00:00 as midnight to anchor the new terms.

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Methods used in this brief

• Simulation Game
• Think-Pair-Share
• Inquiry Circle