Problem
If all were chickens, that's 20 legs — 12 short of 32.
Counting all legs as 2 each is an easy starting guess, and the shortfall tells how many extra legs are needed.
Guess And Check3.OA.A.3Multiplication FactsEach chicken-to-cow swap adds 2 legs — 12 ÷ 2 = 6 swaps means 6 cows.
Every cow adds exactly 2 legs over a chicken, so dividing the missing 12 by 2 gives the number of cows.
Guess And Check3.OA.D.8Turning 6 chickens into cows supplies exactly the 12 missing legs, so 6 of the animals are cows.
Turning one chicken into a cow adds exactly 2 legs to the total.
A cow's 4 legs are the chicken's 2 legs plus 2 more, so the swap keeps 2 legs and adds only 2 new ones.
Filling the missing 12 legs at 2 legs per swap needs 6 swaps, because 12 splits into 6 groups of 2.
Sharing 12 into equal groups of 2 gives 6 groups, since 6 groups of 2 build back up to 12.
Six swaps make 6 cows, because each swap turns exactly one chicken into exactly one cow.
6 cows, 4 chickens → 6×4+4×2=32 checks out — cows exceed chickens by 2.
Verifying the legs confirms the guess, and subtracting gives how many more cows there are.
Systematic List3.OA.D.8Guess all chickens, then swap in cows two legs at a time until the totals check out.