Math Game Monday: Krypto Insanity

“Krypto Insanity” is free on this website for one week only. It’s an excerpt from Prealgebra & Geometry: Math Games for Middle School, available as an ebook at my bookstore (Thank you for cutting out the middleman!) and in ebook or paperback through many online retailers. Read more about my playful math books here.

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.

This game will push each player’s mental math skills to the limit. Calculators optional.

Krypto Insanity

Math Concepts: addition, subtraction, multiplication, division, order of operations, fractions, decimals, integers, absolute value, powers and roots, factorials.

Players: any number.

Equipment: one deck of playing cards (or two decks for a large group), pencil and paper for each player and for keeping score. Calculator optional.


Agree on which color represents negative numbers. Agree on the value of face cards — for example, jack = eleven, queen = twelve, king = thirteen. Or maybe you want all face cards to equal ten, while the ace can be worth the player’s choice of either one or eleven.

Decide whether to set limits on the math operations allowed in your game.

How to Play

Deal ten hands — sets of five cards each, face down on the table. Turn up one of the two remaining cards as the first target number. Set the final card under it, to use later.

Play three rounds:

  1. Current face-up target number
  2. Final card as target number
  3. Target number is zero

Everyone plays at once. Pick up any of the face-down hands. Try to make the target number with those five cards.

You may add, subtract, multiply, or divide the numbers, and you can use a card as an exponent, but you cannot put two cards together to make a two-digit number. You must use all five cards. Each card may be used only once in the calculation.

Calculations may include:

  • The arithmetic operations +, −, ×, ÷
  • Decimal points, so that 5 could become 0.5 (The zero before a decimal point doesn’t count as making a two-digit number. But you cannot add zeros after the decimal point to make something like 0.05.)
  • Absolute values
  • Square roots
  • Exponents — take one card to the power of another
  • Factorials
  • Parentheses, brackets, or other grouping symbols
  • The overhead-bar (vinculum) to mark a repeating decimal

You may combine these calculations in creative ways. For example, if one of the cards is −1, you could use a decimal point and a vinculum to make the repeating decimal equivalent to −1/9. Then use the absolute value, if a positive fraction is more useful in reaching the target number. And the square root can turn that positive fraction into 1/3, if you wish.

If you cannot see a solution, turn that hand face down and pick up another. You may choose a different hand as many times as you like.

When you (or any player) call “Krypto,” everyone else stops working to listen. Show your cards and explain the calculation. If all players agree it’s a valid expression, set that hand of cards in your scoring pile. Then grab another hand and keep going. If your expression isn’t valid, return that hand to the table and try a different set of cards.

Keep the hands in your scoring pile separate by turning each set of cards at a right angle to the set below it. That makes it easy to count points and keeps the hands ready for the next round.

If there are no hands left on the table, players can share with anyone who still has cards. On a shared hand, the first player to call Krypto scores the point.

After all the other cards are claimed, the player who has the last hand spreads it face up on the table. Everyone races for the final Krypto.

If all players agree it’s impossible to make the target number with any hand, put those cards aside while you count score. Players score one point per hand in their scoring piles. Then return all ten sets of cards to the table, face down, to play the next round.

The player with the highest final score wins the game.

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