 Constant Function Years 1 - 8

### Summary

Children are always fascinated by the Constant Function of a calculator which constantly repeats the last operation it was asked to do if the [=] button is constantly pressed.
• We can make use of this interest to encourage a little thinking.
• The way the constant function is accessed could be different to the examples given here.
• If unsure, check the instructions - or ask the children!

This activity is related to Predict A Count.

### Materials

• One calculator per person or pair
If you would like to know more about the calculator shown see Preferred Materials. Closer inspection shows it has features that other simple four function machines don't have and the pricing and ordering process seems economic and efficient. However for some Calculating Changes activities you would have mask the first line of the display. For example, the answer to my multiplication is 2,628. What could the multiplication be? ### Procedure

Press [+] then a number. eg:

[+] then  followed by [=] gives 4 on the screen.

The reason is that when you turn on the calculator, there is a zero on the screen. When you press [+]  the calculator needs to add the 4 to something. It has been programmed to add it to the screen number. Pressing [=] has been programmed to mean [repeat the previous operation].

Now press [=] again. The calculator will repeat the previous operation ... [+]  ... to give an answer of 8. With each on-going press of [=] another [+]  will occur until the operation is changed, or cleared.
• Can you predict the next number? Guess then check.
• How many times will you press [=] to reach 40? Guess then check.
(Be careful, you have already pressed the four once.)
Discuss and record the patterns noticed.

### Content

Listed alphabetically.
Primary content in bold.
• addition facts beyond 10
• counting
• decimal calculations
• decimal interpretation
• estimating/predicting number
• group counting
• operations - whole number
• pattern interpretation
• pattern recognition
• place value
• problem solving
• recording - calculator
• recording - written
• subtraction

#### 1. Subtraction using the constant function

    [-]   [=]
990
[=]
980
[=]
970 ...

#### 2. Doubling

 [x]  [=]
6
[=]
12 ...
Notice how the multiplication works. The operator is 2x, not x3 as you might expect from the way the other three operators work. Consider the array model for multiplication. The language we use for 2 x 3 is 'two rows of three' not 'two in three rows' which would look like:
X X
X X
X X
and in array language would be 'three rows of two' or 3 x 2.

#### 3. Halving

    [÷]  [=]
500 ...
• The numbers get smaller and smaller. Do they become negative?
• What would it look like if you graphed the number of presses against the screen number?
The first pairs on the graph would be (0, 1000) ... (1, 500) ... (2, 250) ...
• What happens if you keep on pressing the equals button?
Why does this happen?

#### 4. Close Your Eyes Counting

• An example is to start with zero on the screen and teach the calculator to count forward by 7 (say) by pressing [+] .
• Now, close your eyes and press [=] until you think the screen will show 84 (say).
• Open your eyes. Were you correct?
• Try counting backwards. Calculating Changes ... is a division of ... Mathematics Centre