Problem
If all were chickens, that's 20 legs — 12 short of 32.
Counting every leg as 2 gives an easy starting guess. Subtracting that (20) from the real total (32) leaves a shortfall (12) that tells us exactly how much needs to shift toward cows.
Guess And Check3.OA.A.3Multiplication FactsEach chicken-to-cow swap adds 2 legs — 12 ÷ 2 = 6 swaps means 6 cows.
Swapping one chicken for a cow keeps 2 legs and adds only 2 new ones (a cow's 4 legs = a chicken's 2 plus 2 more). So filling the missing 12 legs, 2 at a time, takes 12 ÷ 2 = 6 swaps — and each swap turns exactly one chicken into one cow, so there are 6 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.
Recomputing the legs and getting 32 confirms the guess was right. Once both conditions hold, subtracting the two counts directly gives how many more cows there are than chickens.
Systematic List3.OA.D.8Guess all chickens, then swap in cows two legs at a time until the totals check out.