Think of a number, but how does it work?

This is a nice development of the classic “Think of a Number” problems that are a good way of introducing algebraic equations.  Nrich covers this introductory activity with Your Number Is… and other linked activities.

This one takes it a stage further.  Proving algebraically why this works would be a nice extension activity. Note that with the numbers below, this will only work in 2015.  I’ll leave you to work out what you need to change for subsequent years!

Work this out as you read.

Be sure you don’t read to the bottom until you’ve worked it out.

First, pick a number 1 to 7

Multiply this number by 2.

Add 5.

Multiply it by 50.  (Come on, you can do that without a calculator).

If you have already had your birthday this year, add 1765

If you haven’t, add 1764

Now, subtract the four digit year that you were born.  e.g. 1984

You should have a 3 digit number:

The first digit of this was your original number.

The next two numbers are your age.

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