Determine the educational purpose of the game. If using this game as a teacher, consider the age group the game is created for and the mathematical concepts you want them to learn through the game. Base the game on the skills you want your students to acquire.
Define the objective. Determine how you win the game and the rules one must follow to get the desired results. For example, if the objective is to make the numbers 1 through 20 using only 4s, are students allowed to use all of the operations on the calculator, such as the plus, minus, multiplication and other mathematical functions?
Play the game yourself. Make sure it is possible to win the game with the set of rules you've defined and then, if applicable, search for different ways to win. Try to gauge how long it takes to play the game and what age level it will be appropriate for.
Revise the game as needed. Fine-tune the rules or objective to make it easier or more challenging, as necessary. You can make different sets of rules for different age groups that will be playing.
Test the game on children of appropriate ages. This is the best way to see how effective the game is in teaching the mathematical concepts and how interesting the students find it. If the game appears to be ineffective in either case, you may have to go back to the drawing board. If not, you've created a unique and useful tool for your students.