Building Equations: Free Math Game - Play Discover Learn 24/7

Building Equations: Free Math Game

A FREE math game is always a winner, and getting students building  their own equations is sure to be the most necessary test for mathematical comprehension. Yet, there are few games or exercises that really allow you to check this comprehension.

In Gattegno’s Textbook 1,  by the end of the literal work, the student is well equipped to provide notations for certain structures built with the Cuisenaire Rod.  In conjunction with these exercises, I had been reading Goutard’s book, Mathematics and Children, which offers interesting insights into the pedagogy behind teaching notations.


While reading Goutards book, Mathematics and Children, I was overwhelmed by her point to overemphasize the fact that students shouldn’t be given a notation unless they had need for it.  Of course, she didn’t specific yet how to cultivate this need, but I assume that the exercises provided in Textbook 1 were sufficient for creating need.

Yet, I felt she was pointing to an even stronger need.  I was getting impatient for her to get to the point even though I do enjoy her philosophical presentations.  I put the book down to think to myself.  How could one cultivate such a need?

So I began to play with the idea.  Without mathematical notation, a child can easily create a variety of designs using rods.  For what cause would they need to know notation?

What cause do we have to learn to write at all except as an alternative form of communication when oral simply won’t do.  We often begin learning to write because we are told to but occasionally, a child will begin to see the purpose of writing out of their own desire.

A variety of desires include to make mommy smile with a love note, to make a Christmas list so Mommy doesn’t forget and so on.  For what purpose motivates a child to put forth a mathematical idea in the form of notation?  So I began to think how to create an environment that encouraged children to communicate in written mathematical notation.


Every day, we use math to exchange goods and services. What if the student had a need for a specific rod that another student had?  Could this cultivate an environment where the student had a need to build an equation to equal the desired rod?  This is how the game “The Exchange” came about.

Number of Players

2-5 players


  • Number Building Play Mats or Staircase Template or Design Template of your choice
  • Scrap paper to write down equations.
  • 1-2 Small Group Sets of Cuisenaire Rods
  • Score sheet


Each student uses Cuisenaire Rods to build a specific template design like a staircase or to fill up a Number Building Play Mat. To encourage students to be more creative in the creation of their equations, use the score sheet.   Some may finish before others, but this does not necessarily mean the end of the game.  Instead let everyone complete their template.  Once everyone completes the template, tally up the points. The ones who have the most points wins.


Each child needs a bank of at least two different color rods.  One color should be odd.  One color should be even.  Depending on the objective, disperse the rest of the rod colors as you choose evenly to the students.  For rods that cannot be dispersed evenly, I would just give all students that rod to put on their objective template design.

Each student take turns requesting a rod from another student’s bank that they need to complete their template design.  The student makes the request using mathematical notations that they write on a scrap paper.

The student must only use the rods in their own bank to create the equation.   For example, the student has only red and black rods in their bank and needs a purple rod.  The student could build and write the following equations: 2r =p or r + r = p or 6/7 of k – 2/7 of k = p.    The student could also ask for 2 purple rods if their template design calls for it, too.

They must hand the rods needed to build the equation with the written mathematical notation to the banker with the desire rod.  The banker must build the notation to verify the request is valid and equals the desired rod.  If the equation is not valid, then the student does not receive the desired rod and the next player goes.  This teaches the importance of writing correct notations.

As the student learns and practices notations, their notations will become more sophisticated.   The score sheet is designed to encourage more sophisticated notations by rewarding them with more points for using fractions, parentheses, multiplication and so on in their equations.


We played this game a few times these last couple of weeks.  I added the score sheet most recently after talking to a friend about this game.  I really wanted to encourage my children to push beyond their comfort zone.  It is easy for a child to stick with just addition and subtraction, and I found all of them except my oldest would do this.

The score sheet worked wonders in providing just the right incentive to create more complicated notations  My children took more time to carefully craft their notations, and it was fun to see them working so hard trying to get the most points in a single notation.

I was also able to see what they were really comfortable doing and what they were still struggling with.   For the most part, they avoided fractions.  I took note of that and decided to spend the rest of the week practicing on building fractions and writing notations with fractions.

For making it this far in the post,  you get a free download!  Yay for a FREE MATH GAME! This download includes the rules, a sheet to create your own template design and a score sheet.

Aren’t you excited to see your children makes some crazy fun equations!  Share the fun and tweet, instagram, or Facebook your children’s equations! I want to see so hash tag those pics with #cuisenairerods or tag me!

Lacy | Play Discover Learn 24/7

Knowing the best kind of learning comes from a highly motivated internal drive, Lacy Coker cultivates tools and resources that help to make learning for young children playful and self-directed.

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