Repair a receipt and verify the change

model. 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.

1. 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.
2. 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.
3. Subtract the corrected subtotal from the $3.00 payment to obtain $0.95 change. Updating only the subtotal would leave the receipt inconsistent.
4. 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.

Worked example: 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.

p1. Three erasers cost $0.35 each. Enter the correct line total in dollars.

Answer: 1.05

Teacher response: Three copies of 35 cents make 105 cents.

p2. One item costs $1.60 and another costs $0.75. Enter their subtotal in dollars.

Answer: 2.35

Teacher response: Align dollars, tenths and hundredths before adding.

p3. The correct subtotal is $2.35 and the payment is $5.00. Enter the change in dollars.

Answer: 2.65

Teacher response: The change and subtotal must add back to the five-dollar payment.

e1. A notebook costs $2.20 and two clips cost $0.45 each. You pay $4.00. Enter the correct change in dollars and write the item subtotal.

Answer: 0.90

Look for:

• Includes each quantity before adding prices.
• Verifies change against the corrected subtotal rather than the printed incorrect subtotal.

Teacher response: Both clips cost $0.90, so the subtotal is $3.10 and the change is $0.90.

transfer. 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.

Answer: 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.

teach-1. 3 minutes: Show the incorrect receipt and ask which checks would reveal a missing item.

teach-2. 4 minutes: Repair the quantity, subtotal and change in order; verify both the items and the payment equation.

teach-3. 5 minutes: Complete the practice receipts. Partners identify which quantity each arithmetic expression represents.

teach-4. 3 minutes: Complete the independent receipt and write a two-part check: item coverage and payment balance.

misconception. The subtotal plus the stated change equals the payment, so the entire receipt must be correct.

Teacher response: That equation checks internal balance, not whether every item was included. Compare the receipt with the item quantities before accepting the change calculation.

support. Rewrite prices as whole cents and use one row per item before returning to decimal dollars.

extend. Create an incorrect receipt whose subtotal and change balance but omit an item, then have a partner detect it using the item list.