AMC 10 · 2012 · #5
Grade 3 arithmeticPick an answer.
AMC 10 2012 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The total is built from a chain of smaller counts: females, then litters, then kittens, then the grand total. Solving each small count in order and keeping cats and kittens as separate groups avoids the classic slip of reporting only the kittens.
Count the female cats
Half of the 100 adult cats are female, so 100 ÷ 2 = 50 female cats.
"Half of" a group just means split it into two equal parts and take one.
3.OA.A.3Identify SubproblemsCount the litters
Half of the 50 females each came with a litter, so 50 ÷ 2 = 25 litters.
One litter per female that had kittens, so the number of litters equals that half.
3.OA.A.3Identify SubproblemsCount the kittens
Each of the 25 litters averages 4 kittens, so 25 × 4 = 100 kittens.
Equal-sized groups repeated means multiply the number of groups by the group size.
Equal-sized groups repeated means multiplying the number of groups by the group size.
▸ Why?
Multiplying is exactly counting equal groups, so the total falls out at once.
▸ Why?
Each litter belongs to exactly one mother, so the number of litters matches the number of mothers.
Add cats and kittens
Both groups count, so 100 adults + 100 kittens = 200 in all, choice (B).
The question asks for everything received, so the adults and the new kittens both belong in the sum.
3.NBT.A.2Analyze The UnitsBreak a word problem into small counts, solve them in order, and add every group the question asks about.
- Count the female cats
- Count the litters
- Count the kittens
- Add cats and kittens