Heads and Legs, Guess and Check

In short: Guess and check means making a guess, checking it, and using what you learn to make a better one. For heads-and-legs problems, pretend all the animals are one kind, see how far off the total is, then swap some to fix it.

Before you start

• Multiplying and dividing whole numbers.
• Money: 100 cents $=1$ dollar.
• Simple equations can help, but they are not needed here.

Method 1: guess, check, improve

Make a sensible guess. Check it. Use what went wrong to make a better guess.

Method 2: pretend they are all one kind

Sum and difference

"Two numbers add to 67 and their difference is 11."

Quick summary

• Guess, check, improve: use a table to steer your guesses.
• Pretend everything is one kind, find how far off you are, then divide by how much each swap changes the total.
• When one kind adds and the other takes away, each swap changes the total by both amounts together.
• Sum and difference: smaller $=$ (sum $-$ difference) $÷2$.
• Always check your answer in the original story.

Quiz