Mathematics · Grade 3 · Financial Literacy: Money Matters · Term 4

Making Change

Students calculate change from a purchase using various strategies.

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

About This Topic

Making change builds students' ability to determine the amount returned after a purchase by comparing payment to cost, using strategies like counting up from the purchase price or direct subtraction. Grade 3 students handle Canadian coins and bills: pennies, nickels, dimes, quarters, loonies, and toonies. They explain multiple approaches, justify why counting up reduces steps and errors by grouping to the next dollar first, and create their own realistic scenarios to solve.

Aligned with Ontario's Mathematics Curriculum in the Number strand and Financial Literacy expectations, this topic reinforces addition and subtraction within 1000, promotes mental math flexibility, and connects to real-world money management. Students develop reasoning skills as they analyze strategy efficiency and communicate solutions clearly.

Active learning excels for making change because play money and price tags turn calculations into engaging transactions. When students rotate through cashier and customer roles in small groups, they apply strategies repeatedly, discuss choices with peers, and self-correct through immediate feedback, making the process concrete and memorable.

Key Questions

1. Explain different strategies for making change.
2. Analyze why counting up is an effective strategy for making change.
3. Design a scenario where making change is necessary and solve it.

Learning Objectives

• Calculate the correct change from a purchase using Canadian currency up to $20.
• Compare the efficiency of counting up versus direct subtraction for making change.
• Explain at least two different strategies for calculating change.
• Design a realistic shopping scenario and accurately determine the change required.
• Analyze the steps involved in a given change-making problem and justify the chosen strategy.

Before You Start

Addition and Subtraction within 100

Why: Students need a solid foundation in basic addition and subtraction facts to perform the calculations required for making change.

Identifying Canadian Coins and Bills

Why: Students must be able to recognize the value of different Canadian coins (penny, nickel, dime, quarter, loonie, toonie) and bills to work with them.

Key Vocabulary

Purchase Price	The amount of money a customer pays for an item or service.
Amount Paid	The total money a customer gives to the cashier for their purchase.
Change	The money returned to a customer when the amount paid is more than the purchase price.
Counting Up	A strategy for making change where you start from the purchase price and count up to the amount paid, using the fewest coins and bills possible.
Direct Subtraction	A strategy for making change where you subtract the purchase price from the amount paid to find the difference.

Watch Out for These Misconceptions

Common Misconception

Change requires subtracting payment minus cost, leading to coin-counting errors.

What to Teach Instead

Counting up from cost to payment groups coins logically and avoids large subtractions. Partner verification activities let students compare methods side-by-side, revealing fewer mistakes with counting up through guided discussions.

Common Misconception

All coins must be used equally, ignoring efficient combinations like using loonies over many quarters.

What to Teach Instead

Effective change prioritizes largest coins first in counting up. Role-play stations encourage trial and error, where peers suggest better combinations, helping students internalize efficiency during collaborative play.

Common Misconception

Counting up only works from exact bills, not mixed payments.

What to Teach Instead

The strategy adapts to any payment by incrementing to the next unit. Circuit rotations expose varied scenarios, building flexibility as groups articulate steps and refine approaches together.

Active Learning Ideas

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.

45 min·Pairs

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.

50 min·Small Groups

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.

30 min·Whole Class

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.

25 min·Individual

Real-World Connections

• Cashiers at grocery stores like Loblaws or Sobeys use making change skills constantly to process customer transactions accurately, ensuring both the store and customer receive the correct amounts.
• Customers at a local farmers' market, like St. Lawrence Market in Toronto, often need to calculate change themselves when paying with cash, especially for smaller purchases where exact change might not be available.
• Small business owners, such as a baker running a local bakery, must be proficient in making change to manage daily sales and ensure their till balances correctly at the end of the day.

Assessment Ideas

Quick Check

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.

Discussion Prompt

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.

Exit Ticket

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.

Frequently Asked Questions

What is the counting up strategy for making change?

Counting up starts at the purchase amount and adds coin values up to the payment: for $3.47 from $5, add 53 cents (3 nickels and 8 pennies, or 2 quarters and 3 pennies). This minimizes mental steps compared to subtraction and highlights coin combinations. Practice with visuals like number lines reinforces the path from cost to payment, building confidence in real transactions.

How do you teach making change with Canadian coins in Grade 3?

Introduce coin values through sorting and matching games, then model counting up with purchase cards. Use play money for repeated practice in store simulations. Emphasize jumping to the next dollar first (e.g., 53 cents to $5), then align with curriculum by having students explain strategies and design problems, ensuring mastery of expectations like 3.MD.B.4 equivalents.

What active learning activities help with making change?

Role-play markets or circuit stations engage students kinesthetically: handling coins while counting up aloud in pairs builds fluency and peer teaching. Line-up games visualize increments class-wide, while designing scenarios individually promotes ownership. These approaches make abstract math tangible, reduce anxiety through play, and foster discussion of strategy strengths, leading to 20-30% better retention per studies on embodied learning.

Why is counting up more effective than subtraction for change?

Counting up uses smaller, sequential additions familiar from skip-counting, reducing cognitive load and errors in coin selection. For $7.82 from $10, add 18 cents versus subtracting 2.18, which risks borrowing issues. Classroom challenges show students self-discover this through timed comparisons, aligning with Ontario's focus on efficient mental math strategies.