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.

• Year 5
• Mathematics
• 3 activities
• 25 min–50 min

Learning Objectives

1. Calculate the exact change received from a purchase using subtraction strategies.
2. Design a shopping list for a specific budget, accurately calculating the total cost and remaining funds.
3. Compare different methods for calculating change and identify the most efficient strategy.
4. Analyze the impact of sales tax on the total cost of items and the final change received.
5. Evaluate the reasonableness of change received after a transaction, identifying potential errors.

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.

Prepare & details

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.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

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

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.

Prepare & details

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.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

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.

Prepare & details

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.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After The Amazing Race, display a new train departure problem on the board (e.g., 14:47 minus 14:12). Ask students to record the elapsed time on mini-whiteboards and hold them up for a quick visual check.

Exit Ticket

After The Movie Marathon, give each student a ticket with a film’s start and end time (e.g., 15:30–17:15). Ask them to calculate the duration and write one sentence explaining how they arrived at their answer.

Discussion Prompt

During The 24-Hour Translator, pose the prompt: ‘Why might a 24-hour clock reduce mistakes at airports?’ Facilitate a short class discussion and note which students connect clarity to fewer mix-ups between AM and PM.

Extensions & Scaffolding

• Challenge: Provide a multi-leg train timetable across two time zones and ask students to calculate the total journey time including a 30-minute layover.
• Scaffolding: Give students a partially completed empty number line with the hour jumps pre-marked to support their subtraction of minutes.
• Deeper exploration: Have students create their own bus schedule for a field trip, converting all departure times to 24-hour notation and calculating the intervals between stops.

Key Vocabulary

Purchase	The act of buying something, involving an exchange of money for goods or services.
Change	The money returned to a customer when the amount paid is more than the cost of the purchase.
Budget	A plan for how to spend a limited amount of money over a specific period or for a particular purpose.
Total Cost	The combined price of all items purchased, including any applicable taxes or fees.
Transaction	An instance of buying or selling something; a business deal.