AMC 8 · 2024 · #9
Grade 4 arithmeticPick an answer.
AMC 8 2024 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Once you notice G must be even, the most natural move is Tool #6 (Guess and Check): try the smallest even green counts G = 2, 4, 6, 8, … and just build the collection. After a few tries, Tool #5 (Look for a Pattern) reveals the totals are 7, 14, 21, 28, … — multiples of 7. Since the problem is multiple choice, Tool #3 (Eliminate Possibilities) finishes the job by keeping only the choice that is a multiple of 7. This avoids algebra entirely; we ‘build’ the answer with concrete numbers.
Red is half of green, so green must be even; the smallest even case G = 2 gives R = 1, B = 4.
‘Half as many’ and ‘twice as many’ are multiplicative comparison phrases, which are introduced in the Grade 4 multiplicative-comparison standard.
4.OA.A.1Guess And CheckAdding the three counts gives the smallest total: 1 + 2 + 4 = 7.
Adding three small whole numbers to get a single total is the Grade 1 three-addend addition skill.
1.OA.A.2Guess And CheckTrying G = 4, 6, 8 gives totals 14, 21, 28 — they rise by 7 each time, so every total is a multiple of 7.
Generating a number pattern from a rule (each new even G adds 7 to the total) is the Grade 4 ‘generate a pattern from a rule’ standard.
4.OA.C.5Look For A PatternAmong the choices, only 28 = 7 × 4 is a multiple of 7, and (R,G,B) = (4,8,16) confirms it works.
Recognizing which whole numbers are multiples of 7 is exactly the Grade 4 ‘factors and multiples’ standard.
4.OA.B.4Eliminate PossibilitiesThis AMC 8 problem only needs Grade 4 multiplicative comparison and multiples of 7 you already know!