Problem
Recover the original number from a wrong product
A number should have been multiplied by 7, but instead 7 was subtracted, giving 409. Find what the correct answer (number times 7) should be.
Operations
Your answer
Watch out Don't stop at the original number, 416 -- you still need to multiply it by 7 to get the correct answer.
How to solve
Strategy Work Backwards — We know the result of the wrong operation (subtract 7 gives 409). Undo the subtraction by adding 7 to recover the original number, then do the correct operation (multiply by 7).
1STEP 1
Undo the wrong operation
The mistake subtracted 7 to get 409. To find the original number, add 7 back.
409 + 7 = 416
Adding undoes subtracting, so we work backward to the start.
3.OA.A.4Work BackwardsAdding 7 to the wrong result 409 gives back the original starting number.
Why?
The 409 is what was left after 7 was taken away from the original number.
Why?
To reach the original number again, you put back the same 7 that was taken away.
Why?
Adding back exactly what was subtracted cancels the subtraction and returns to the starting number.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
2STEP 2
Do the correct operation
The number should have been multiplied by 7. Multiply 416 by 7.
416 × 7 = 2800 + 70 + 42 = 2912
Break 416 into 400 + 10 + 6, multiply each by 7, then add.
3.OA.C.7Identify SubproblemsAnswer
2912
416 × 7 = 2912
The original number 416 is a bit over 400, and 400 x 7 = 2800, so the correct answer should be near 2900; 2912 fits, and checking: 416 - 7 = 409 matches the wrong result.
Takeaway
Undo the mistake first, then do it right -- working backwards is a Grade 3 superpower!
- Undo the wrong operation
- Do the correct operation
Where next?
Another one like thissuggested
Step back and solidifysuggested