AMC 8 · 2022 · #11
Grade 4 arithmeticlogicPick an answer.
AMC 8 2022 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The end state (how many pieces and how much pasta is left) is given, and we want the start state (original length). That is the textbook trigger for Tool #11 (Work Backwards): replay each bite in reverse to put back what was eaten. Before we can do that, we need Tool #5 (Look for a Pattern) to notice a clean rule about how the piece count changes with each bite — every bite turns one piece into two, so the number of pieces grows by exactly 1 per bite. That single pattern tells us how many bites happened, which is what unlocks the work-backwards calculation.
Each bite removes a middle and leaves two ends, turning 1 piece into 2 — so after n bites there are 1 + n pieces.
Each bite removes a middle and leaves two ends, so the rule "one bite, one extra piece" is a clean number pattern.
4.OA.C.5Look For A PatternThe final pile has 10 pieces, so 1 + n = 10, meaning 9 bites.
Filling in the missing number in 1 + □ = 10 is a Grade 1 unknown-addend question.
1.OA.D.8Look For A PatternEach of the 9 bites ate 3 inches, so the total eaten is 9 × 3 = 27 inches.
Equal-groups multiplication (9 groups of 3 inches) is the Grade 3 way to total identical bites.
3.OA.A.3Work BackwardsWork backwards — add the eaten pasta back to the 17 inches still on the table: 17 + 27 = 44 inches.
Putting back what was removed is exactly the work-backwards move, and the final sum is a basic Grade 2 addition within 100.
2.NBT.B.5Work BackwardsThis AMC 8 problem only needs the Grade 4 idea of "find the pattern, then work backwards" you already know!
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