Depth · one concept from first principles · step 2 of 4
The mistake subtracted 7 to get 409. To find the original number, add 7 back.
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.
The 409 is what was left after 7 was taken away from the original number.
To reach the original number again, you put back the same 7 that was taken away.
Adding back exactly what was subtracted cancels the subtraction and returns to the starting number.
The number should have been multiplied by 7. Multiply 416 by 7.
Break 416 into 400 + 10 + 6, multiply each by 7, then add.
3.OA.C.7Identify SubproblemsUndo the mistake first, then do it right -- working backwards is a Grade 3 superpower!
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The same shape shows up later on the AMC, as Arithmetic Expression Decomposition, Branching State Enumeration, Multiplicative Ratio with Integrality Constraints. Why the shapes repeat →