24 - Make the Order of Operations Fun!

Players: 1 or more
Ages: 8 and up
Math Ideas: Order of operations, writing expressions
Are there any other ways you can get to 24?
What other numbers can you get to using this card?

This week I'm sharing a game that is a mainstay in math classrooms all across the country.

The reasons are obvious: the game gets kids to use their knowledge of operations to solve problems, but in a way that feels much more like a creative exercise or a puzzle than most classroom activities.

While it's perfect for the elementary or middle school classroom, it's also a fun brain teaser to play with your kids.  As long as they are decent with their multiplication facts, they're old enough to play!

The game is called 24.

How to Play

To play 24, you don't really need any supplies! Pencil and paper can help, but this is a game you can play in the car, as long as you can keep track of a few numbers at once.

Of course, there is a set of playing cards that is organized by difficulty, so you may want to get those in case you're worried about accidentally starting with a very challenging set of numbers.

Pick a card and look at the four numbers listed on it. The goal of the game is to add, subtract, multiply, or divide these numbers to get to 24.

So let's do one together! See that white dot in each corner? That means this is an easy card. Harder cards are designated with more dots.

Let's see... 5*5 is 25, which is close! And 4 - 3 is 1. Then we can do 25 - 1 to get 24!

Of course, there are more ways to get to 24, which we will discuss below. But the basic game is just to find a way to get to 24.

Where's the Math?

The point of 24 is to get kids thinking flexibly about the operations. It's almost like a worksheet, except your kids are generating each problem themselves.

Let's return to the problem from above. When I first tried to solve it, I focused on the 4. I know that 4*6 is 24, so I tried to figure out a way to get the other three numbers to equal 6. I wasn't able to do so, so I tried to get the 4, 5, and 5 to equal 8 so that I could finish by multiplying 8*3.

That also turned out to be a dead end (at least for me). So then I started multiplying the numbers to see how close I could get to 24. 5*5 got me very close, and then I realized that 4 and 3 could subtract to 1, which led me to my answer.

But once you've found one method, don't be satisfied! Can you find other ways? I saw that 5*3 is equal to 15, and then  4 + 5 + 15 equals 24.

If you and your child are playing with paper, I suggest an additional level of depth: Can you write out your solution as a single expression?

Now we get into the world of order of operations, which is a vitally important set of skills that middle schoolers need to succeed.

Think about the first solution from earlier:

5*5 is 25, and 4 - 3 is 1. Then we can do 25 - 1 to get 24

But if I write 5*5 - 4 - 3, I don't get 24! Instead I get 18, which is way off.

In order to write a correct expression, I need to communicate that the subtraction problem 4 -3 comes before 25 - 1. How do I do that? With parentheses! Now your child might see the usefulness of parentheses in this sort of problem:  5*5 - (4 - 3) does, in fact, equal 24.

I already gave away the best question to ask while playing 24: "Can you find a different way to get 24?"

This question is interesting because you can get into all sorts of interesting discussions about what counts as a "different way" to get 24.

Let's say you have the numbers 3, 6, 7, and 8. Perhaps your child finds that 3 + 6 + 7 + 8 works as a solution. You ask them to find a different way, and they come up with 8 + 7 + 6 + 3.

Does this count as different? Maybe, maybe not! In some sense this solution is clearly different. The numbers are listed in a different order, so it's not literally the same. But the way that they are combined through addition remains the same. Maybe there is some sort of mathematical property that proves that these two methods are always equivalent (brainstorm which property it is on your commute today...).

I bet you and your child can agree that the solution 8 * 3 * (7 - 6) is moredifferent. Buy why? Deciding on what makes a solution count as "different" is a wonderful little path for your mathematical conversation to take.

If you're tired of finding 24, you can reverse the problem: "We already used these four numbers to make 24. What other numbers can we make?"

This question is a feast! You may be shocked at how many numbers you can get to, simply by adding, subtracting, multiplying or dividing four numbers. Older kids could even add in different operations (exponents, square roots, factorials, whatever!)

If you've got the time, you could even make a chart with all the numbers from 0 to, say, 50. Which ones can you fill in simply using the numbers 3, 6, 7, and 8?  You could even give your kids a reward for finding five, ten, fifteen, or twenty different numbers using the four numbers provided.

Like I said, you don't need the cards to play. All you need is a set of four numbers. But if you like having some sets of numbers that have been vetted for difficulty, you can pick up the cards at the link below. Enjoy!