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Reverse Trick

Stage: 2 Challenge Level: Challenge Level:1

Why do this problem?

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.

Possible approach

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.

Key questions

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?

Possible extension

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 ...

Possible support

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.