Receipt Detectives: Find the Two Mistakes

In this guide

Four lines on a receipt. Two amounts are wrong. Can your class find both mistakes, explain each repair and work out the change without trusting the printed numbers? Turn a fictional classroom purchase into a short investigation in multiplication, addition and subtraction.

Download the pupil receipt and teacher key (PDF). Page 1 is for pupils; keep page 2 with the teacher. You can also copy the receipt onto the board.

Make checking the mathematical job

Use this after pupils have practised multiplying a two-digit number by a one-digit number and adding and subtracting within 200. Start with equal groups if they need to rebuild that meaning. The aim is more than spotting an odd-looking number: pupils should show why an amount is wrong and check the repaired result another way.

Delhi’s official 2026–27 Class IV Mathematics programme, page 3 includes whole-number operations and simple money transactions, with “Equal Groups” in the October–December sequence. This original receipt connects those ideas; it is not a prescribed textbook exercise. The reference describes Delhi’s programme, so match the methods and timing to your school’s current teaching. The official Class 4 Math-Mela resource listing provides a route to the book and its resources.

Introduce the fictional receipt

Tell pupils: “Our imaginary classroom needs these supplies. The quantities and prices are correct. Exactly two printed line amounts are wrong. Your job is to investigate the calculations, not accuse a person.” All prices below are invented for this task; they are not market-price advice.

Item	Quantity	Price each	Printed line amount
Notebooks	3	Rs 24	Rs 62
Pencils	4	Rs 7	Rs 28
Erasers	2	Rs 9	Rs 16
Ruler	1	Rs 15	Rs 15

Total: __________   Paid: Rs 200   Change: __________

The total and change spaces are deliberately blank. They are not the two mistakes. Each line amount can be checked on its own, so finding one error does not require finding the other. Do not add a printed subtotal: that would create an extra, consequential number for pupils to untangle.

Lesson 1: uncover both errors – 35 minutes

Minutes	Teaching and pupil activity
0–5	Read the challenge. Cover the printed-amount column and ask pairs to estimate whether the whole purchase is likely to cost less than Rs 200. Do not ask for an exact total yet.
5–11	Model the structure with a separate example: 2 folders at Rs 12 each cost Rs 24. Draw two groups of 12, then connect 12 + 12 with 2 × 12. Do not solve a faulty receipt line for the class.
11–21	Pairs check all four lines. One partner calculates while the other asks how the quantity and unit price were used; swap roles after two rows. Keep the first method visible.
21–29	Pairs mark the two wrong printed entries and write a calculation beside each correction. Invite two different methods for one line. Ask what evidence protects a correct line from being changed.
29–35	Individually, pupils explain one correction and one line they would leave unchanged. Keep the marked receipt for lesson 2. If only one error is found, direct attention to an unchecked line rather than revealing the answer.

A pupil who adds 3 + 24 may be treating the two numbers as unrelated amounts. Ask, “How many notebooks? What does each one cost?” Draw three equal groups of 24 or split each 24 into 20 and 4. A pupil who changes every line because the title promises errors needs a different prompt: “Which calculation proves this line already works?”

Pupil challenge: repair, total and check

Keep this task visible while pairs work. Pupils may explain instead of writing full sentences, but each proposed correction needs mathematical evidence.

Task	Evidence to produce
1. Check each printed line amount. Circle exactly two wrong amounts.	Show quantity × price or an equivalent repeated-addition or place-value method.
2. Write the two corrected line amounts.	For each, explain what the printed amount should be. Do not change the quantity or price.
3. Add the four corrected line amounts.	Record the total and show how the amounts were combined.
4. Find the change from Rs 200.	Show a subtraction or a count-up method.
5. Check the change another way.	Show that corrected total + change equals the amount paid.

Lesson 2: make the repaired receipt trustworthy – 35 minutes

Minutes	Teaching and pupil activity
0–5	Revisit the two repairs. Ask pupils to explain the difference between one item’s price and a line amount for several items.
5–13	Pairs total the four corrected line amounts. Invite a useful grouping or column method. Keep the corrected amounts beside the calculation so that an old printed value is not carried forward.
13–22	Find change from Rs 200. Compare subtraction with counting up from the corrected total. Ask why both should describe the same difference.
22–29	Swap repaired receipts with another pair. Check the line calculations, total and the inverse check. The checker gives one specific reason for agreement or one question about a calculation.
29–35	Complete the individual exit task below. Use responses to decide who needs equal-group support, addition practice or help connecting subtraction and counting up.

Worked answers and complete checking key

Open the two-error key, corrected total and change

The two independent errors are the notebooks and erasers line amounts. Notebooks: 3 × 24 = 3 × 20 + 3 × 4 = 60 + 12 = Rs 72, not Rs 62. Erasers: 2 × 9 = 9 + 9 = Rs 18, not Rs 16. These are separate wrong products; neither is a subtotal copied from another line.

Keep these lines: pencils, 4 × 7 = Rs 28; ruler, 1 × 15 = Rs 15. The corrected total is 72 + 28 + 18 + 15. One useful grouping is 72 + 28 = 100 and 18 + 15 = 33, so the total is Rs 133.

Change: 200 − 133 = Rs 67. A count-up check is 133 + 7 = 140, then + 60 = 200; the steps add to 67. The inverse check is 133 + 67 = 200. If a pupil finds Rs 79 change, check whether the incorrect printed amounts were added: 62 + 28 + 16 + 15 = 121, and 200 − 121 = 79. That subtraction is consistent with an unrepaired receipt, so the pupil must return to the products.

Sample explanation: “Three notebooks means three groups of 24. I split 24 into 20 and 4. That makes 60 and 12, so the line needs 72.” Repeated addition, an accurate grouping drawing or a conventional algorithm can justify the same repair. Do not require this exact wording or one preferred written method.

Exit task key: 2 cards at Rs 18 cost Rs 36. Paying Rs 50 gives Rs 14 change. Check 36 + 14 = 50. These are fresh numbers, so success is more informative than copying the investigation’s answer.

Notice the reason behind the answer

Observe	Useful evidence	Next teaching move
Uses equal groups	Connects 3 notebooks to 3 × 24, with a drawing, words or calculation	Practise a similar product with different numbers.
Checks rather than guesses	Corrects the two faulty products and defends at least one correct line	Compare two methods for the same line.
Carries the repairs forward	Uses all four corrected line amounts to find the total	Keep the corrected column visible during addition.
Connects total and change	Explains how total plus change equals the amount paid, or counts up accurately	Use an open number line before another subtraction.

Individual exit task: A different fictional stall sells cards at Rs 18 each. You buy 2 and pay Rs 50. What is the cost, what is the change, and what addition checks your change? Accept a short spoken explanation or a supported drawing as well as written calculations. Record which part the pupil completed independently.

Choose a useful next investigation

Repeat with a smaller whole-rupee receipt if equal groups are still uncertain. For pupils ready to extend, let them create a new four-line receipt with exactly one wrong product and blank total and change spaces. A partner must justify the repair; the maker checks that the other three products are genuinely correct.

For a different Class 4 reasoning task, try Same Perimeter, Different Gardens. The tens-and-ones game offers an earlier-stage grouping model to adapt when a learner needs concrete support. Today’s next step is small: keep one marked line and its explanation, then use that evidence to choose the next calculation.

AI assistance was used to finalize this contribution. The views expressed are personal views of the author; official statements are identified through linked official sources.