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zero from the other four numbers? One way is 2 [(4 + 3) – 7] = 0. The solution be- comes 5 + 2 [(4 + 3) – 7] = 5 or 5 + 0 = 5. Is it always possible to find a solution using all five numbers to get the objective? It is rare, but sometimes there is no solution. Here are the only two examples I have encountered in the 45 years I have been playing the game. 3, 23, 13, 16, 1 Objective = 20 9, 9, 7, 16, 4 Objective = 25 If you search the internet for a “Krypto solver” you will find some sites that will check your hand for you. If it is solvable, they do it for you. If not, they will tell you it is unsolvable. Whenever we hit a tough hand in a classroom that no one seems to be able to solve, I write it on the corner of the board. By the next day, it always seems to be solved by someone! As a challenge for middle school students who seem adept at this game, I give five numbers but no objective. They write the five numbers at the top of a piece of lined notebook paper. They write the numbers 1-25 down the margin on the left. This gives them 25 possible objectives. An example is given in the next column. This activity can be done by individuals or groups. It is an excellent setting to motivate the use of order of operations notation. The game of Krypto can also be used as a classroom management activity. I use it to fill the last minute or two before dismissal. I tell students to cross their arms when they are ready to leave. I quickly write the numbers on the board and ask them to solve the hand using only mental arithme- tic. They stay focused and quiet while thinking. If it is solved before the bell, I generate a new hand. This strategy helps make every minute count in math class! References Lach, T. and Sakshaug, L. (2005). Let’s do math: Wanna play? Mathematics Teaching in the Middle School , 11 (4), 172-176. May, L. (1995). Motivating activities, Teaching PreK-8 , 26 (1), 26-27.

Way, J. (2011). Learning mathematics through games. Series 1: Why games? Retrieved from http://nrich.maths.org/2489.

Use these five numbers to get each of the objectives listed on the left. Use correct Order of Operations symbols! Two of them are done for you. 3 6 8 25 22

1 =

2 =

(25 – 22) ÷ 3 x (8 – 6)

3 =

4 =

22 ÷ (25 – 14) + 8 – 6

5 =

6 =

7 =

8 =

9 =

10 =

. . .

23 =

24 =

25 =

Dana T. Johnson Retired Faculty College of William and Mary dtjohn@wm.edu

Virginia Mathematics Teacher vol. 44, no. 1

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