Math Game: What Two Numbers?

Here’s a simple, conversational game you can play anywhere — no equipment necessary. It’s great for helping your children develop number fluency and algebraic thinking.

Excerpted from my upcoming book, Prealgebra & Geometry: Math Games for Middle School, scheduled for publication in early 2021. Sign up for my newsletter to get updates.

What Two Numbers?

Math Concepts: addition, multiplication, inverse operations, positive and negative numbers.

Players: two or more.

Equipment: no equipment needed.

How to Play

The leader chooses any two numbers and mentally figures their product and sum. Then the leader asks, “What two numbers multiply to make ___ and add up to ___?”

The leader may choose any two operations to ask. For example:

What two numbers add up to 15 and multiply to make 50? (5 and 10)
What two numbers have a difference of 2 and a sum of zero? (−1 and 1)
What two numbers have a product of 1/6 and also have a difference of 1/6? (−1/3 and −1/2) or (1/3 and 1/2)

The other players race to find the numbers. The first player to name them correctly gets to lead the next round. Or with two players, just take turns trying to stump each other.

Remember to consider both positive and negative numbers when creating your puzzle. Or make it extra tricky with fractions or decimal numbers.

Words to Know

In case you need a reminder of the answer words: The sum is what you get when you add two numbers. The difference is when you subtract. You multiply to find the product, and divide to get the quotient.

History

An anonymous teacher left this game in a comment on my blog and added, “I love playing math games in the car with a ‘captive audience.’”

The What Two Numbers? game was designed to prepare students for factoring quadratic equations, where one knows a sum and product and must deduce the original numbers. When we offer players a wider choice of operation clues, it becomes a more creative problem-solving game.