Illuminations: Exploring Krypto

Exploring Krypto

 The rules of Krypto are amazingly simple — combine five numbers using the standard arithmetic operations to create a target number. Finding a solution to one of the more than 3 million possible combinations can be quite a challenge, but students love it. And you’ll love that the game helps to develop number sense, computational skill, and an understanding of the order of operations.

Learning Objectives

 By the end of this lesson, students will: Investigate the game of Krypto and develop strategies for finding solutions efficiently. Explore the order of operations using Krypto challenges.

Materials

 Computer with Internet connection Deck of Krypto cards (optional) Krypto Rules & Strategies Order of Operations Activity Sheet Scientific calculator

Questions for Students

 What are some strategies that can be used to find a solution in Krypto? [If one of the 5 cards is equal to the target number, try to get 0 or 1 with the other four cards. Then, you can multiply by 1 or add 0 to find the solution. More generally, both 0 and 1 are good intermediate results to obtain, because of the additive identity property and multiplicative identity property.] Why is the order of operations important? [It ensures that the values of expressions are always computed in the same way. For instance, the value of 3 + 4 × 5 would be 35 if calculations were done left-to-right, but its value is 23 if the order of operations is used. There is less likelihood of confusion if everyone uses one consistent method for evaluating expressions.]

Assessment Options

 The Order of Operations activity sheet can be used for assessment. Review the sheet with the class, or collect it to review each student's work. It is probably unfair to evaluate students based on their ability to solve a Krypto challenge. However, evaluating their ability to turn a verbal description into a mathematical expression is reasonable. You may want to choose one Krypto challenge with multiple solutions and present it to the entire class. Students will likely find different solutions, but you can evaluate students based on their ability to form a correct expression. You could have students enter their expressions into a calculator to check themselves.

Teacher Reflection

 Were students excited about this lesson? How can you help to engage those students who were not enthused about this lesson? What modifications would you make if you were to teach this lesson again? How did you challenge the high achievers while still providing adequate support to struggling students? How did students demonstrate that they understood the mathematics of the lesson? That is, how did you ensure that they were learning something instead of just playing a game?

NCTM Standards and Expectations

 Algebra 3-5Identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers. Number & Operations 3-5Understand and use properties of operations, such as the distributivity of multiplication over addition. Understand the effects of multiplying and dividing whole numbers. Develop fluency in adding, subtracting, multiplying, and dividing whole numbers; Number & Operations 6-8Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers. Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation. Develop meaning for integers and represent and compare quantities with them.
 This lesson prepared by Samuel E. Zordak.

1 period

Activities

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