Five Games: A Manual for Mathematical Practice
The Games Manual gives you five simple pencil-and-paper games for exploring mathematics through play.
The games help students learn to substitute, generalize, organize, transform, strategize, and evaluate mathematical relationships. They begin simply, but they don't stay simple: the same games can be played with elementary arithmetic, fractions, algebra, geometry, and other mathematical structures.
See the Games Played
The manual includes two videos of real kids playing the games so you can see what this kind of mathematical play actually looks like.
These are not polished demonstrations with rehearsed students. You'll see normal kids thinking, responding, making moves, getting stuck, changing direction, and figuring things out as they play.
A demonstration of From Here to There will be added fall of 2026.
The Five Games
The Substitution Game
Practice renaming quantities while preserving equality and begin seeing how one mathematical relationship can take many forms.
Exhausting the Relationships
Take a mathematical structure and find as many relationships within it as possible. Students begin looking beyond a single answer toward generalization and structure.
Number Webs
Organize mathematical relationships into connected families and look for the patterns that hold them together.
From Here to There
Begin with one mathematical expression and find a path to another. Students plan, choose moves, revise their strategy, and discover that there may be many legitimate ways to reach the same destination.
Is It True?
Examine mathematical statements, decide whether they are true, and transform false statements into true ones in one or two thoughtful moves.
What You Need
Paper and pencils.
Whiteboards also work.
Freezer paper and markers could be a great choice.
You can play these games with one child, siblings, partners, small groups, or the whole family. The manual also includes variations for extending the games into different domains as your child's understanding grows.
Where to Begin
The Substution Game. Watch the accompanying demonstration. Then play.
Pay attention to what your child does. Notice the moves they make, the relationships they see, where they hesitate, and what surprises both of you.