Mathematics · Year 5 · The Value of Math: Money and Time · Term 4

Calculating Change and Making Purchases

Practicing calculating change from purchases and making decisions about spending money.

• ACARA Content Descriptions
• AC9M5N08

About This Topic

Time is a unique measurement system because it isn't base-ten; it's a mix of 60s and 24s. In Year 5, students move beyond telling time to calculating 'elapsed time', the duration between two events. They also learn to navigate the 24-hour clock and interpret complex timetables for transport and events. This topic is part of the ACARA Measurement and Space strand, focusing on the practical application of time in a globalized world.

In Australia, understanding 24-hour time is essential for travel and emergency services. Students learn that 13:00 is just 1:00 PM, and that 'crossing the hour' (e.g., from 10:45 to 11:15) requires a different strategy than standard subtraction. This topic comes alive when students can use real-world schedules. By planning a 'trip across Sydney' using train timetables or calculating the length of a movie marathon, they see that time math is a daily necessity. Students grasp this concept faster through collaborative investigations where they must solve 'time-travel' problems involving different time zones or schedules.

Key Questions

1. Explain different strategies for calculating change accurately.
2. Design a shopping list within a specific budget and calculate the total cost and change.
3. Analyze the importance of checking change received after a purchase.

Learning Objectives

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

Before You Start

Addition and Subtraction of Whole Numbers

Why: Students need a solid foundation in basic addition and subtraction to perform calculations involving money.

Introduction to Decimals (Tenths and Hundredths)

Why: Understanding decimal place value is crucial for representing and calculating monetary values accurately.

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.

Watch Out for These Misconceptions

Common Misconception

Students often try to use standard column subtraction for time (e.g., 2:15 minus 1:45 = 1:70).

What to Teach Instead

This happens because they treat 100 minutes as an hour. Use an 'Empty Number Line' strategy where students 'jump' to the next hour (e.g., jump 15 mins to get to 2:00, then 15 more to get to 2:15). Peer modeling of these 'jumps' makes the base-60 system visible.

Common Misconception

Thinking that 12:00 PM is midnight and 12:00 AM is midday.

What to Teach Instead

This is a very common confusion. Use the 24-hour clock to clarify: 12:00 is midday (the sun is up), and 00:00 is the start of the new day (midnight). A 'Daylight/Darkness' chart helps anchor these terms.

Active Learning Ideas

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.

50 min·Small Groups

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.

25 min·Pairs

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.

40 min·Small Groups

Real-World Connections

• Cashiers at supermarkets like Coles or Woolworths use these skills daily to accurately provide change to customers, ensuring customer satisfaction and preventing financial errors.
• Consumers planning a birthday party can use these skills to create a shopping list for decorations and food within a set budget, ensuring they don't overspend at stores like Kmart or Target.
• Small business owners, such as a local bakery or a market stall vendor, must be proficient in calculating change to manage their daily earnings and track their profits effectively.

Assessment Ideas

Quick Check

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.

Exit Ticket

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.

Discussion Prompt

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.

Frequently Asked Questions

Why do we use the 24-hour clock?

The 24-hour clock removes the confusion between AM and PM. It's used globally by pilots, doctors, and the military to ensure there are no mistakes in timing. In Year 5, learning this system helps students prepare for international travel and more advanced science and technology topics.

What is the best strategy for calculating elapsed time?

The 'Mountains, Hills, and Rocks' method is excellent. Use a number line: 'Mountains' are 1-hour jumps, 'Hills' are 10-minute jumps, and 'Rocks' are 1-minute jumps. This visual tool prevents the common errors that happen when trying to use standard subtraction.

How can active learning help students understand timetables?

Timetables are overwhelming on paper. Active learning, like the 'Amazing Race' simulation, gives students a 'mission.' When they have to find a specific connection to 'win' the race, they learn to scan for information and calculate durations with a level of focus and purpose that a worksheet can't provide.

How do time zones work in Australia?

Australia has three main time zones (and more during Daylight Savings!). This is a great extension for Year 5. You can ask: 'If it's 3:00 PM in Sydney, what time is it for a student in Perth?' This adds a layer of complexity to their elapsed time calculations.