Math Game Monday: Digit Disguises

This game requires students to make logical deductions about number relationships.

Many parents remember struggling to learn math. We hope to provide a better experience for our children. And one of the best ways for children to enjoy learning is through hands-on play.

So what are you waiting for? Let’s play some math!

Digit Disguises

Math Concepts: addition, subtraction, multiplication, division, algebraic reasoning.

Players: two players or two teams. Best with teams.

Equipment: printed gameboards (optional), pencils and paper, or whiteboard and markers.

Set-Up

The FREE 68-page printable (pdf) Prealgebra & Geometry Printables file features hundred charts, coordinate grids, assorted graph paper, and all the game boards for the Math You Can Play: Prealgebra & Geometry book.

Each player or team needs a separate gameboard.

If you’re not using printed gameboards, each player or team makes a chart with two columns labeled Mine and Theirs. List the letters A–J in each column. Next to each letter in your own column, write one of the whole numbers 0–9 in any mixed-up order. Fold your paper to keep that column hidden from your opponent. Slip a paperclip over the fold for greater security.

How to Play

On your turn, ask for the result of a basic arithmetic calculation involving two different letters. For example, you might ask:

• A + B = ?
• C − D = ?
• E × F = ?
• G ÷ H = ?

But you may not ask for something like “I − I” or “J ÷ J.”

The other player/team figures out the answer to your question, using their values for each letter, but they do not tell you the number. If the answer is on their chart, they tell you the letter for that value. Or they tell you that the result is not one of their letters.

Players never say a number in response to a question. They only say a letter or “Not a letter.”

Write notes to help you remember each clue. You’ll need these to deduce your opponent’s number code.

Then it is their turn to ask you for a clue about your secret code.

When one player/team claims to have broken the opponent’s number code, the game is over. They read aloud the number values they have figured out. If they’re entirely correct, they win the game. But if any of the answers are wrong, the opponent wins.

Variations

Don’t end the game after the first code is guessed. Whether the guessing team won or lost, the other team keeps asking questions until they also break the code. If both teams fail, the game is a tie.

For Beginners: Start with only four unknown numbers, and allow players to give number answers in response to each question.

Keeper of the Code: (Mastermind-style) One player makes the code, and the other players try to crack it. Players take turns asking for clues, but they may discuss the answers and plan a strategy together. This variation is good for younger players, if you let them be the Keeper while older students or adults are guessing.

History

Math lecturer David Butler created this game and writes:

“I was struck by how quickly the logic got complicated, and then how quickly it all cascaded into finding everything when I finally got a few different numbers.”

Butler also shared a printable gameboard that can fold to stand on the table Battleship-style, hiding your secret code.