Teacher's Tricks

If you are a maths teacher for Secondary or Higher Secondary Classes
you can use the following trick to amuse your students.

Ask each of the student to take a fresh page and write 2 small numbers 1 below the other. Ask him to right get the third number by adding the first 2. Then a fourth number by adding the second one and the third one. Thus he lengthens the list by appending the sum of the last 2 to the list. E.g. 4,3,7,10,17....

When he has 10 numbers in the list, ask him to show you the list. You casually glance the list and tell him (or write on the sheet) a number. Ask him add all the 10 ten numbers in his list. It is the same as what you have told (written).

How do you get the sum without actually adding all?


Answer.

Take 2 variables (e.g. a,b) and work out on a sheet all the numbers in the lsit of the student. (a,b,a+b,a+2b,2a+3b......). Also find the sum of alll these 10 numbers. If you look at the numbers in the list, you will find the sum to be a simple multiple of one of the numbers in the list. Take further explanation as an excercise.

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