Clever keys
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Age
7 to 11
Challenge level
Problem
On a calculator, make $15$ by using only the $2$ key and any of the operations keys ($+$, $-$, $\times$, $\div$).
How many ways can you find to do it?
Getting Started
$15$ is what kind of number?
Using a calculator to check out your ideas might help.
Using a calculator to check out your ideas might help.
Student Solutions
Joshua from Brooklands Primary, Suffolk says:
I found that $2$ divided $2$ was $1$ (which gave me an odd number).Hence $2\div2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 15$
Josh from Ampthill, Bedfordshire also got that answer, as well as:
$2 \times2 \times2 \times2 \times2 = 32$, then $32-2 = 30$,
then divided by $2$ gives $15$
and
$2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 30$
divided by $2$ to give $15$.Luke and William from Essex sent very similar solutions to Joshua.
Teachers' Resources
Why do this problem?
This short challenge presents children with the opportunity of
exploring number operations and practising mental arithmetic in a
motivating context.
Key questions
What kind of number is $15$?
How will you remember what you have pressed?
What have you tried so far?
Possible extension
You could challenge children to explain how they would work
out, say $24 \times 37$ if a particular number on the calculator
was broken. How would they do it if the $2$ was broken? What about
if the $1$ and $2$ were broken etc.?
Possible support
Having calculators to hand will allow learners to check their
ideas and they may need to be reminded to record the process in
some way.