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
What is your answer?
Geomaths 