Here are some tasks I have been using with my Year 7 class which bring together some of the recent algebra work we’ve been studying, and a mild element of surprise. The students like them and the tricks are a good vehicle for them to start seeing the point of algebra. I chose the tricks below because the algebra which explains them are appropriate for their current level of understanding. I’ve avoided ones which need solving of equations and concentrated instead on examples which exemplify like terms, simplifying algebraic fractions, linear factorising, and place value.

Of course there are other classics like 1089 and a grey elephant from Denmark that I haven’t included here. None of the below are my inventions, they’ve all been borrowed from elsewhere. I’ve added the instructions, a numerical example and an algebraic proof of each. If they work well, or if you have any other mathematical magic tricks I’d love to hear from you; I’m @geomathsblog

Trick 1

Choose a number

Double it

Add 12

Subtract your original number

Subtract 5

Subtract your original number

What number do you have?

Trick 2

Choose a whole number

Add to it the number which is one more than than your number

Add 9

Divide by 2

Subtract the original number

What number do you have?

Trick 3

Choose any 3 digit number where all the digits are the same

Divide your number by the sum of the digits

The answer will be 37

Trick 4

Choose any three digit number

Write it twice so that you have a 6 digit number

Divide it by 7 then 11 then 13

The answer is your original number

Trick 5

Choose any 3 different integers less than 10

Make all the possible 2 digit numbers with them (there will be 6)

Add all the 2 digit numbers together

Divide the total by the sum of your original three numbers