Broken Calculator Problems Years 1 - 6

Summary The concept of the broken calculator - one or more keys not working - is used to encourage children to find alternative forms of the 'broken' number or operation. The activity is a practical example of the mathematician's question Can I check this another way?. Broken Calculator Problems can be used with any calculator, but it is especially sweet with the MathMaster because that machine has a Key Eliminator function. If you press and hold a particular key for a few seconds a dot will appear on the left hand side of the screen. This indicates that the key you held no longer works. MathMaster also calculates according to the convention of order of operations. Suitable for threading. This activity is a partner to Breakdown! in the Free Tour section. Materials One Poly Plug per pair One MathMaster or other calculator per pair

Procedure Use this activity with a whole class in a 'fishbowl' situation to introduce it, or work with small groups or pairs. Begin by asking the children to make an addition such as: 8 + 9 = 17 with their Poly Plug as in the photo above. Ask them to check with their calculator using the mathematician's question Can I check it another way?. What happens if the 9 button on your calculator is broken? That means there is no use pressing 9 because it won't work. Can you still check your work with a calculator? If you are using the MathMaster, demonstrate that you really can make the 9 button stop working. Use this problem to help the children explore equivalents for nine such as:

Content addition facts beyond 10 addition facts to 10 conservation of number equations: creating/solving multiplication operations - whole number order of operations pattern recognition problem solving recording - calculator recording - written subtraction using brackets visual and kinaesthetic representation of number

8 + 5 + 4 = 17

or 8 + 3 + 3 + 3 = 17 which, on the MathMaster, would also work as 8 + 3 x 3 = 17 [Other four function calculators would give the answer 33 to buttons pressed in this order.]

or even 8 + 10 - 1 = 17

Each time the children make an alternative with the plugs they check it on the calculator. Of course it is okay to find a calculator solution first then show it with the plugs.

Also, each time you use the activity ask the children to record (drawings, numbers, words?) five different ways to solve the broken calculator problem of the day. Thread the activity through your curriculum by using a new problem each day for, say, 10 minutes each day, three days a week for a term.

Extensions

1. How many ways can you find to solve the problem?
2. Can you arrange your solutions to make a pattern?
3. What happens if two (or more) numbers are broken today?
4. What happens if the + key (or other operation key) is broken today?

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