Most children will begin
this problem through trial and improvement. The calculator
allows them to try lots and lots of calculations without getting
stuck in the mechanics, which in turn frees them to concentrate on
logical thinking.

This activity would work well with a small group, perhaps
those who have been working on addition and subtraction and need a
challenge whilst others in the class are consolidating their
understanding.

Prepare your own calculator first by entering 9+ secretly.
Perform the first 'trick' - enter 12, then tell the children that
this calculator turns numbers round. Enter = and confirm that 21 is
the reverse of 12. Magic! Let them have a go on their
own calculators and they will find that pressing 12= does not
produce 21!

How did you do it? Perform trick two, this time
telling the children that you needed to prepare the calculator
first, so that they now understand that there was a prior
operation. Do this without them seeing what number you put in, talk
about the results and ask the children if they have any ideas what
you did. Give them a little time to explore before showing them the
pre-numbers for both tricks. Let them replicate the tricks until
they are sure they work. Offer another low number in which the
units digit is higher than the tens - can they reverse 13 to make
it 31?

When they have done this and perhaps a few other smaller
numbers successfully, offer the 141414 challenge.

There will be some who will see the addition/subtraction
connection. You may wish to suggest that the children keep a note
of what they have inputted so that they can see when they are
getting closer. Most children will succeed through successive
approximations but they will soon realise that this only gives them
the answer for a particular question, not a general rule for what
to do. The latter is much more powerful.

Is the first number bigger or smaller than the second?

What might you do to the first number to get the second? Try
it.

What order of key presses could you try?

Those who have found a rule will be able to reverse any two
digit number where the units digit is bigger than the tens. Can
they do the same where the units digit is smaller? Or reverse a
three digit number?

Those who find this unproblematic could see how many different
numbers and operations they can find to pre-input in order to
reverse any one number. For example, to get from 12 to 21 you can
add 9, or multiply by 1.75 ...

Prepare this activity by making some 'magic' cards. Help the
children to choose a magic number (say 12) and to put numbers which
add up to 12 on each side - 1 and 11, 2 and 10, etc. The children
then tell you what's on the each side of each card. Repeat with
other magic numbers to consolidate the connection between addition
and subtraction. Then introduce the activity.