AMC 10 · 2012 · #1
Grade 4 arithmeticPick an answer.
AMC 10 2012 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The question bundles two counts (students and rabbits) over 4 rooms, so Tool #7 (Identify Subproblems) splits it into clean pieces: total students, total rabbits, then their difference. Tool #3 (Eliminate Possibilities) catches the classic trap of stopping at 72 (the student total, choice (D)) instead of subtracting the rabbits.
Count all the students
All 4 rooms hold 18 students each, so multiply: 18 × 4 = 72 students in the grade.
Same amount in each room means one multiplication does the work of adding four times.
The same amount in every room means one multiplication does the work of adding four times.
▸ Why?
Multiplying is exactly counting equal groups, so the total falls out at once.
▸ Why?
The four rooms together make the whole school, so nothing sits outside the total.
Count all the rabbits
The rabbits scale the same way: 2 per room × 4 rooms = 8 rabbits in all.
The rabbits scale up by the same factor of 4 as the students do.
4.NBT.B.5Identify SubproblemsSubtract to find how many more
"How many more" means subtract: 72 - 8 = 64, so (C) — leaving 72 is the trap (D).
"How many more" always means take away the smaller count from the larger one.
3.NBT.A.2Eliminate PossibilitiesScale each count up to all the rooms first, then subtract — "how many more" always means take the smaller total away from the bigger one.
- Count all the students
- Count all the rabbits
- Subtract to find how many more