Practice 1
Answer and teaching response
1.05 · Three copies of 35 cents make 105 cents.
Repair a receipt and verify the change
Trace a subtotal error through a payment record, correct it and use the payment equation to verify the change.
Get the student and teacher materialsPrepare the group
Learning goal: Produce a corrected receipt with line totals, subtotal and change, accompanied by an explanation of the omitted item and a check using place-value units.
You will need: Paper and pencil. Prices are invented classroom amounts in dollars; ignore tax and discounts. No purchasing or personal information is involved.
Start with this question
A receipt lists a notebook at $1.25 and two pencils at $0.40 each, then claims a $1.65 subtotal and $1.35 change from $3.00. Repair it.
The pencils cost $0.80 together. The correct subtotal is $2.05, and the correct change is $0.95. The incorrect receipt counted only one pencil.
- Read quantity and price separately. The notebook is one item at $1.25, while two pencils each cost $0.40; the pencil line must include two equal prices.
- Calculate the line totals, then add equal place-value units: $1.25 + $0.80 = $2.05. Keep the cents column aligned even when a price is written with one decimal digit.
- Subtract the corrected subtotal from the $3.00 payment to obtain $0.95 change. Updating only the subtotal would leave the receipt inconsistent.
- Check both the arithmetic and the item record. $2.05 + $0.95 = $3.00, and the subtotal includes all three items. A payment check alone cannot reveal an omitted item if subtotal and change share the same error.
Run the 15-minute workshop
- 3 minutes. Show the incorrect receipt and ask which checks would reveal a missing item.
- 4 minutes. Repair the quantity, subtotal and change in order; verify both the items and the payment equation.
- 5 minutes. Complete the practice receipts. Partners identify which quantity each arithmetic expression represents.
- 3 minutes. Complete the independent receipt and write a two-part check: item coverage and payment balance.
A useful error to discuss
A learner might say: The subtotal plus the stated change equals the payment, so the entire receipt must be correct.
That equation checks internal balance, not whether every item was included. Compare the receipt with the item quantities before accepting the change calculation.
Practise, then check independently
Try the first three tasks with the worked model. Try the final task without help. Enter a number, fraction or mixed number, such as 3/4 or 1 1/4. The number check does not assess your drawing or explanation.
Practice 2
Answer and teaching response
2.35 · Align dollars, tenths and hundredths before adding.
Practice 3
Answer and teaching response
2.65 · The change and subtotal must add back to the five-dollar payment.
Independent check
Answer and teaching response
0.90 · Both clips cost $0.90, so the subtotal is $3.10 and the change is $0.90.
Transfer the idea
A second receipt lists one $0.60 item and one $0.25 item as a total of $0.31. Explain a likely place-value error and state the correct subtotal.
Discuss a possible response
The six tenths may have been treated as six hundredths: 6 + 25 = 31 hundredths. Six tenths is sixty hundredths, so the correct subtotal is $0.85.
Choose the next teaching step
Look for:
- Includes each quantity before adding prices.
- Verifies change against the corrected subtotal rather than the printed incorrect subtotal.
If the idea is not secure: Rewrite prices as whole cents and use one row per item before returning to decimal dollars.
If the learner is ready: Create an incorrect receipt whose subtotal and change balance but omit an item, then have a partner detect it using the item list.
Materials for your group
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