Reinforcement mathematics thinking of 10 years old child by teaching "patterns"

Question

As Lynn Steen in The Science of Patterns says, I think Mathematics is the science of pattern too.

I have a 10 years old student which is weak in mathematics. It seems he can do arithmetic(addition, multiplication, ...) but cannot understand the meaning of problems and their relation to real word. I want to help him to rebuild foundation of his mathematics and promote his creativity and attention to real world. Now with respect to the role of patterns in mathematics, I want to start with them.

Do you know free (probably online) resources like PDF files which have much exercises in various flavors or have ideas for me to make them? I know I can build exercises by paying attention to the world, but the time is important for me and it is better to use ideas of other peoples. Also my approach is to hold enjoyment and so, games have advantage.

Answer 1

This article on the Fibonacci numbers could provide you with rich material. But you would have to develop an approach suitable for your 10-yr old.

George Dvorsky. "15 Uncanny Examples of the Golden Ratio in Nature." (gizmodo.com link.)

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You might explore this wartgames.com site, which has some possibly useful links on the Fibonacci numbers for children (which I didn't explore carefully).

Answer 2

Most elementary students enjoy finding all the patterns in Pascal's triangle. This link at mathisfun covers many different patterns including the Fibonacci numbers (yes, they are in Pascal's triangle) and the Hockey Stick pattern. The page also explains the connection between Pascal's Triangle and The Sierpinski Triangle. You can also see the connection in this YouTube video. Have fun.