3rd Grade Two Numbers from Sum and Difference Worksheet: 3 Puzzles

Two secret numbers can be found from just two clues. This 3rd grade two numbers from sum and difference worksheet has three puzzles, numbered 1 to 3. Each puzzle gives the sum of two numbers, a and b, and their difference. For example, in puzzle 1, the difference is 5 and the sum is 27. Your child finds both numbers. Each puzzle leaves a large grid space for working. A small chicken hangs from a string on the right. Page two solves each puzzle with two equations, so it reads like a worked example for an older child.

Three pairs of numbers

The answers are a = 16 and b = 11, then a = 8 and b = 1, then a = 29 and b = 11. In puzzle 1, the key adds the two equations, a − b = 5 and a + b = 27, to get 2a = 32. This gives a = 16, and then b = 27 − 16 = 11. The key always takes a as the larger number, although the page never says so.

This method uses a system of equations, which is middle school algebra. So, for a third grader, a guess-and-check approach works better. Every answer in the key is right, and your child can check it: 16 + 11 = 27 and 16 − 11 = 5.

At the table: guess, check, adjust

For puzzle 2, ask your child to list pairs that add to 9: 8 and 1, 7 and 2, 6 and 3. Then they find the pair with a difference of 7, which is 8 and 1. For larger sums, a shortcut helps: take the difference away from the sum and halve it. For example, (27 − 5) ÷ 2 = 11 gives the smaller number.

The key has slips. In puzzle 1, it says "equation 1 above" but uses a + b = 27, which is equation 2. It also writes "2a + 0 = 32", where the "+ 0" is not needed. Finally, "a two variable equation" should read "two equations".

After the page: the two hands

Hide 12 buttons in two hands, with 2 more in one hand than the other. Say: "There are 12 in all, and one hand has 2 more. How many are in each hand?" Your child tries pairs until 7 and 5 works. Then swap roles. In the end, check the three puzzles with the answer key on page two.