AMC 8 · 2015 · #9
Grade 3 arithmeticpatternPick an answer.
AMC 8 2015 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The daily sales 1, 3, 5, 7, … are the odd numbers, so this is really a question about the sum of the first 20 odd numbers. Tool #9 (Easier Problem) computes the running totals for small day counts (n = 1, 2, 3, 4). Tool #5 (Look for a Pattern) then spots that each running total is a perfect square (1, 4, 9, 16 = n²), so the answer for n = 20 is 20² — no long addition needed. Tool #3 (Eliminate) is a quick sanity check against the five answer choices.
Start easy — add up the first few days to get the running totals 1, 4, 9, 16.
Adding the first few odd numbers is just Grade 2 addition within 20 — small, safe, and it gives us real data to look at.
2.OA.B.2Solve An Easier Related ProblemThose totals are the perfect squares — the running total after n days equals n².
Spotting a numerical pattern in the running totals is the Grade 3 "identify arithmetic patterns" standard in action.
3.OA.D.9Look For A PatternTest one more case — day 5 adds 9 widgets, giving 25 = 5², so the pattern holds.
A pattern from 4 cases can still fool you — testing one more case is the cheap insurance the toolkit asks for.
3.OA.D.9Look For A PatternApply the pattern to n = 20 — the total after 20 days is 20².
Squaring a multiple of 10 is a Grade 3 single-digit multiplication fact (2 × 2 = 4) with two extra zeros tacked on.
3.OA.C.7Look For A PatternMatch to the choices — 400 is option (D), and no other choice is 20 squared.
Eliminating answer choices is the standard AMC multiple-choice safety check.
3.OA.C.7Eliminate PossibilitiesThis AMC 8 problem only needs the Grade 3 fact that the sum of the first n odd numbers is n² — which you can discover yourself with Grade 2 addition!