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Welcome to GO Talent Problem Solvers - Middle

Welcome to GO Talent - Problem Solvers - Middle!

This is our sample lesson. This session is likely to take around an hour to complete, and each week we have an online meeting. Sessions can be completed anywhere, anytime, and most work can be completed using our online portfolio. 

Let's begin...

Another Classic Roman Frame by j4p4n

In this session our focus is on Classic Maths Problems. Classic maths problems are those that have been given to us throughout history and have stood the test of time as fascinating puzzles. 

Today we're going to explore prime numbers.

First meet this chap... his name was Eratosthenes. He was an ancient Greek, who lived around 200BC. You can read more about him here

Image credit: Public domain

Apart from being an all round groovy Greek, he invented a great system for finding all the prime numbers to 100, which we know as the Sieve of Eratosthenes.

Wait, what? 
strainer - lineart by frankes



A sieve... I thought this was a sieve... Yep that's a sieve alright. So is Eratosthenes' system - it's a way of filtering some things out (non-primes) and catching other things (primes).

Let's have a go!

First download and print a hundreds chart (like this one), then follow these instructions:

How to sieve, Eratosthenes style!
- circle the 2, then cross out all the numbers that are multiples of 2 (every number that can be evenly divided by 2)
- circle the next number that is not crossed out, then every multiple of THAT number
- continue until every number is either CIRCLED or CROSSED OUT.

So now... which numbers do you think are the PRIME numbers and which are non-primes. Check here to see if you were right!

Did you know, the correct word for a number that is not a prime is a composite number?

Do you think this would this work for numbers over 100? Try a 1000 grid maybe!

Now, try out this riddle which uses the same kind of thinking:

Do you think you could make up a puzzle like this one?
Could you invent a different way of sieving numbers?
Publish your thinking in your Problem Solver's Blog (here a link is usually given to a short tutorial about how to do this)

Today in Developing your problem-solving skills find out a little more about some other ancient mathematicians... you might start with this:

Share what you have found out!

Unless specified otherwise, all images on this page are from openclipart.org, licensed for unlimited commercial use