The 24 Game

If you are looking for a math activity that is easy, fun and effective, I've got just the thing.  I didn't invent the 24 Game but I elevated it to an art form.  It was my secret weapon. With it, I could teach numerous operations, principles and strategies all at once while scaling it to fit all math levels simultaneously. Not only that, the students loved it as long as I didn't tell them we were practicing number theory and algebraic principles. I used 24 circles for warm ups, bonuses, challenge activities and dead time fillers in addition to being a mainstay of classroom teaching. Sound too good to be true?  Read on...





The basic premise behind the 24 Game is to combine a given set of four numbers in three sequential equations so the final answer is always 24. I presented the problem by drawing this diagram, called a 24 Circle,  on the board.




Then plug in the numbers and operations you want them to use.  Each number can only be used once and they have to use them all.  The operations can be used in any combination and they don't have to use them all.  If you want to zero in on a particular skill set, you can eliminate one or more operations.  When I did that, I wouldn't tell them right away.  That way, they had to observe and size up the problem first. 

Here's what it looks like.

They do the rest.  There are usually multiple solution sets, such as...


                      3 x 4 = 12

                      1x2 = 2

                      2 x 12 = 24


                      2 x 3 = 6

                      4 x 6 = 24

                      24 x 1 = 24


                      1 2 = 1/2

                      3 x 4 = 12

                      12 1/2 = 24


My students volunteered like crazy to go up to the board and write their solutions. Of course, I'm making learning points as we go, such as the use of 1 in the second solution as the Multiplicative Identity.  Along the way, I would issue challenges, such as see if you can create a fraction and work it into the solution.

The key to using these as an interactive teaching tool is to keep up a constant commentary as you cruise the room.  What are we looking at? What is it asking us to do? What do we have to work with?  Is there a pattern? How do we manipulate negative numbers to get a positive answer?  Have we seen this kind before?  What is the minus sign telling us? Is it subtraction or a negative number?  It can go either way but it can't do both at the same time.  You have to be fast on your feet and prepared to modify a circle or bring out learning points as "teachable moments" appear - and with this system, they will.

So you can see that this one simple problem can be used to exercise a wide range of skills at multiple levels.  Inclusion and differentiation are built right into the program.  The possibilities are endless and limited only by your imagination and creativity.  Here are some variations.

Negative numbers.                            

Possible solutions...


                -6 + (-6) = -12

                3 x 4 = 12

                12 - (-12) = 24


                -6 x -6 = 36

                3 x 4 = 12

                36 - 12 = 24








Here's another negative number exercise.  The first impression of most students is "It can't be done."  No, what can't be done is turn four positive 6's into a -24.  This point/counterpoint tactic is simple to do and very effective. Change the sign of one or more of the numbers and see if it's still possible.  Do it enough and patterns will start to emerge. Pattern recognition is the key to success in mathematics. The best part is, the students will discover them. It's a great way to teach number properties.


              Anyway, here's this one...


              -6 x -6 = 36

              -6 + -6 = -12

              36 + (-12) = 24













Fractions anyone?


The concept of dividing a whole number by a fraction to get a bigger number is difficult to grasp for some students.  I purposely engineered it into this one so they would have to use it.  The circles are great for that. You can pick a single idea and create a circle to guide them to it.         


              -3 x -4 = 12

              1 1/2 = 2

              2 x 12 = 24


              -4 1/2 = -8

              -3 x 1 = -3

              -3 x -8 = 24







How about variables?  Substitute and solve where N = 5.





Here they have to correctly substitute to get the four numbers first.  The circles can be as simple or complex as you want to make them. N could be a -5 or an exponential number or a reciprocal.  You could also start out with an equation where they have to solve for N and then plug it in.













Here's the last example and probably my favorite type.



This one has vocabulary and unit conversion in it.  You can also put in basic facts from any other subject such as how many continents, the number of lines in a limerick or notes in an octave.  Sometimes for fun, I'd throw in something like the number of dwarfs in "Snow White" or bears in "Goldilocks".  You'd be amazed  at the number of students who didn't know them.  I think part of it was they were shocked to see them in math class, which one of the reasons I did it.  I had students ask me occasionally "Is there anything you can't turn into a math problem?" No I don't think so.  Math is everywhere.  Be careful not to spend too much time on the first part - getting the numbers. Otherwise, the natives get restless.





There is a commercial version of the 24 Game.  You can find it at The 24 Game.  We purchased it one year and then budget cuts got the best of us.  It's not that terribly expensive but you know how it is these days.  I continued to freelance with it and developed some variations that you won't find in the paid version.  Some of them I've demonstrated here. In whatever manner you use it, this is a great program.  I hope this page has given you some ideas you can use.  Try it.  You won't be disappointed.