1. Multiplying and dividing recap
[N1.1 Support Starter]
Pick a whole number between 1 and 9.
Use your number as the input to this function machine.
Repeat using some other whole numbers between 1 and 9 as inputs.
What do you notice about the output?
Find the function machine that produces this output from the input provided:
What do you notice about the functions in this machine compared to the first?
Check that is works for the inputs and outputs that you found in the first part.
Preamble
A simple investigation using a calculator, hopefully the rather surprising result will add some interest in finding the inverse function in the reverse function machine. This activity revises some of the terms connected with function machines such as input/output and inverse function. Pupils, once they have “discovered” how to reverse the function machine should be encouraged to investigate if the number pattern is always observed. Depending on the calculator rounding may well result in a output for the reverse machines of – a useful discussion point.
Possible content
Using number machines, using the fact that multiplication and division are inverse functions.
Resources
Calculators.
Solution/Notes
The input number forms a nine digit number made up of itself. For example: an input of 3 gives an output of
The reverse of the original function machine is ÷ , then ÷ 9 (but see above for possible calculator rounding artefact).
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010