Mathematical games are an enjoyable way to reinforce basic math skills and learn to apply those skills in practical but novel ways. Logic games help students develop their ability to reason. The games can usually be adjusted to accommodate beginners and experts. Mathematical games involving arithmetic, algebra, geometry and probability -- and games of logic that involve code breaking -- all come in varying levels of difficulty.

One popular arithmetic game requires that players use a prescribed set of digits and a fixed set of operations to generate all the numbers in a specified range. For example, players might have to use four fours and the operations +, -, x and / to generate all the numbers from one to 20. Solutions for one to three include: 44/44 = 1, (4 x 4)/(4 + 4) = 2, and (4 + 4 + 4)/4 = 3. The first person to generate all the possibilities in the designated range wins. Choose a new set of digits and a new set of operations to create a fresh game for students who have already mastered four fours.

Guess the Starting Number is an algebra game in which two students take turns describing a sequence of operations on a chosen but unspecified number. One student selects the number but does not reveal it, then describes the sequence of operations carried out on the number, and the result. The goal is for the other student to find the original number. For example, one student might say, "My number is doubled and then three is added to it. The result is 15. What is the number?" More advanced students might include more complex operations such as cubes and factorials.

In geometry, dissection is the process of cutting a shape into pieces that can be reassembled to create another shape. This process can be turned into a game by choosing a beginning and an ending shape and then letting the contestants race to do the dissection. For beginning students, you might assign a well-documented dissection, and then let them search for a solution online.

Games involving probability are easy to find. This category includes most card and dice games. Classic games can be made more interesting by tweaking the rules. For example, the game of blackjack, also known as 21, becomes a new game if the goal is 25 instead of 21. Dice games look very different when five dice are used instead of the traditional two.

Code-breaking games involve creating and deciphering messages written in a secret language. An easy code involves shifting each letter in the original message to the next letter in the alphabet: A becomes B, B becomes C, and so on until Z becomes A. The phrase "here we go" becomes "ífsf xf hp." A more difficult code involves doubling the number of letters from the preceding shift. To code the word "here" for example, change H to I (a shift of one letter), E to G (a shift of two letters), R to V (a shift of four letters), and the final E to M (a shift of eight letters). Using the doubling algorithm, "here" becomes "igvm." Breaking codes requires discovering what algorithm was used to create the code, a discovery that requires knowledge of both logic and English.

#### References

#### Resources

- Education.com: High School Math Worksheets and Printables
- The New York Times: Daily Lesson Plan – Practical Math
- College Degrees: Online Education -- Math Logic and Math Problems
- SuperKids: SuperKids Games of Logic and Reasoning
- Institute for Mathematics and Computer Science: Logic Games for Active Brains

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