 Breakdown! Years 2 - 8

### Summary

In these problems the calculator is being used to stimulate thought about alternative ways of creating given numbers, or alternative ways of achieving an operation. Class discussions based on the students' suggestions contribute naturally to growth in number sense. There are many forms of these problems and teachers frequently find that they result in the children doing many more 'arithmetic' problems than would be achieved in the same time using a text or worksheet.

A further development of this activity can be found in the Members section as Broken Calculator Problems. It shows that the activity can be adapted to younger children simply by limiting the operations and the size of the numbers. ### Procedure

The photo above shows plugs being used to represent...
8 + 9 = 17
• How do you know this is correct?
• Can you check it another way?
Discuss and record all the suggestions and encourage the using a calculator as one way. Mathematicians can choose to use this tool if they wish. So can children.
• What happens if the 9 button on your calculator is broken?
That means there is no use pressing 9 because it won't work.
(If you are using the MathMaster calculator, demonstrate that you really can make the 9 button stop working.)
• Can you still check your work with a calculator?

### 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
Discuss all the ways the children can think of to add nine without actually pressing the 9 button. There will be several suggestion, but if it doesn't come up, you could ask:

There are many variations on this activity, each of which presents a new challenge in the familiar 'broken calculator' context. That is why the activity can be threaded. Here are some examples.

#### Example 1:

The 7, 8 & 9 keys are broken. They do not work when pressed, so there is no point pressing them.
• How could these problems be worked out on the calculator?
625 + 292 ... 138 + 80 ... 89 x 19 ... 875 - 125
• Is there only one answer in each case?
• Which way uses the fewest keystrokes?

#### Example 2:

Suppose the only working keys are:

3 ... 8 ... x ... - ... =
• Show how you can still get all the answers from 1 to 10.
• What is the least number of key strokes (button presses) it takes to get each one?
• Which of your solutions can you demonstrate using Poly Plug? Calculating Changes ... is a division of ... Mathematics Centre