Mathematics · Grade 3

Active learning ideas

Making Change

Active learning works for making change because students transfer abstract calculations into hands-on, realistic experiences. When they handle coins and bills in role-play or games, they see why counting up reduces errors and speeds up decision-making.

• Ontario Curriculum Expectations
• 2.MD.C.8

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

Activity 01

• Hot Seat
• 45 min · Pairs

Role-Play: Classroom Market Stall

Label tables as market stalls with priced items using play money. Students pair up: one as vendor, one as buyer paying with a bill. Vendor counts up change aloud and hands it over; partners switch roles and record on charts. Debrief strategy use as a class.

Explain different strategies for making change.

Facilitation Tip

During the Classroom Market Stall role-play, circulate with a small basket of coins to model efficient counting up strategies for students who are stuck.

What to look for

Present students with a purchase price (e.g., $4.75) and an amount paid (e.g., $10.00). Ask them to write down the steps they would use to calculate the change using the 'counting up' strategy and then solve it.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 02

• Hot Seat
• 50 min · Small Groups

Small Groups: Change Challenge Circuits

Set up four stations with purchase cards and payments. Groups rotate every 10 minutes, solving by counting up on whiteboards, then verifying with subtraction. Include one station for creating custom problems. Share solutions in plenary.

Analyze why counting up is an effective strategy for making change.

Facilitation Tip

In Change Challenge Circuits, place a timer at each station to encourage speed and accuracy, but remind groups to discuss their reasoning before moving on.

What to look for

Pose the following: 'Imagine you bought an item for $1.35 and paid with a $5 bill. Explain to a classmate why counting up from $1.35 to $5.00 might be faster than subtracting $1.35 from $5.00.' Facilitate a brief class discussion on their reasoning.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 03

• Hot Seat
• 30 min · Whole Class

Whole Class: Money Line-Up Game

Call out purchase and payment amounts. Students line up coins/bills physically to demonstrate counting up from cost to payment. Discuss efficient groupings, then have volunteers model for the class.

Design a scenario where making change is necessary and solve it.

Facilitation Tip

For the Money Line-Up Game, use a whiteboard to record each group’s change calculations so students can compare their strategies after each round.

What to look for

Give each student a card with a scenario: 'You bought a toy for $8.50 and gave the cashier a $20 bill.' Ask them to write the amount of change they should receive and list the specific coins and bills they would count up to get there.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

Activity 04

• Hot Seat
• 25 min · Individual

Individual: Scenario Design Centers

Provide templates for students to draw items, assign prices, and choose payments. Solve using preferred strategy, then trade with a partner for verification and strategy comparison.

Explain different strategies for making change.

Facilitation Tip

At Scenario Design Centers, provide real receipts or price tags so students create problems that reflect actual shopping experiences.

What to look for

Present students with a purchase price (e.g., $4.75) and an amount paid (e.g., $10.00). Ask them to write down the steps they would use to calculate the change using the 'counting up' strategy and then solve it.

• Apply
• Analyze
• Evaluate
• Social Awareness
• Self-Awareness

A few notes on teaching this unit

Teach making change by starting with physical coins and bills, not just numbers on paper. Use counting up as the primary strategy because research shows it reduces errors when students group coins to the next dollar first. Avoid rushing students to subtraction; instead, let them explore why counting up feels more natural for many scenarios. Encourage peer teaching as students explain their steps aloud, which reinforces their own understanding.

By the end of these activities, students will confidently determine change using counting up, explain their strategies, and adapt to different payment types. They will also justify why counting up can be more efficient than subtraction in some cases.

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Watch Out for These Misconceptions

• During the Classroom Market Stall role-play, watch for students who immediately subtract payment minus cost without counting coins. Redirect them by asking, 'Show me how you would give back each coin step-by-step to the customer.'

  During Change Challenge Circuits, if students ignore efficient coin combinations, prompt them to compare their change with a partner and ask, 'Could you use fewer coins? What would that look like?'

• During Change Challenge Circuits, watch for students who insist on using only quarters for every amount. Redirect them by asking, 'What larger coin could you use to cover most of the amount first?'

  During the Money Line-Up Game, if students struggle with mixed payments, provide a sample calculation on the board showing how counting up works from any starting point, even partial bills.

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Methods used in this brief

• Hot Seat