AMC 10 · 2012 · #1
Grade 4 arithmeticPick an answer.
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 the students come to 72.
Same amount in each room means one multiplication does the work of adding four times.
The same number in every room means one multiplication does the work of adding four times.
▸ Why?
Equal groups repeated is exactly what multiplying records.
▸ Why?
The whole school is exactly its four rooms put together, so the counts simply add.
Count all the rabbits
All the rabbits come to 8.
The rabbits scale up by the same factor of 4 as the students do.
4.NBT.B.5Identify SubproblemsSubtract to find how many more
Subtracting gives 64, choice (C).
"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