Squares,Cubes,Roots,Triangular numbers

Why we like this activity....
The excitement of number theory is the surprise in discovering the many and diverse family ties between the many "tribes" of numbers. Can you identify the different tribes and show how they unite to form the army of integers (what is an integer?) ?

How this activity can be used....
It's about tenacity and determination. Anything worth discovering isn't going to be immediately obvious. Do you think Sir Edmund Hilary (who is Sir Edmund Hilary?) or Christopher Columbus (?) would be so famous if what they had discovered was obvious and required little thought and effort . . . ?

What to expect when using this activity, from our experience...
You'll probably need a recap of what "squaring" and "powers" notation means / is asking you to do! You'll also probably need a few example solutions of making other numbers using squares, roots etc. to get the idea of what exactly it is this pesky problem is prodding you to produce some possibilities for! But once you're clear on the land to be explored, there's plenty of surprises, strategies and short cuts to lighten the load and get that tingly feeling of discovery!

Extra notes

Oliver Bowles 20.09.09

Investigating Squares, Roots, Cubes and Triangles square numbers cubes roots powers triangular numbers
	Description/Aim
		Why are they called square numbers? Cubed numbers? Triangular numbers? Can't we make lots of different triangles? What on earth does "square root" mean? Welcome to Mathematics, the language of the universe we inhabit such a tiny corner of . . . . . What numbers, from 1 to 36 can and can't be made using square numbers?

	Teachers Notes - Why? How? What?
	Why we like this activity.... The excitement of number theory is the surprise in discovering the many and diverse family ties between the many "tribes" of numbers. Can you identify the different tribes and show how they unite to form the army of integers (what is an integer?) ? How this activity can be used.... It's about tenacity and determination. Anything worth discovering isn't going to be immediately obvious. Do you think Sir Edmund Hilary (who is Sir Edmund Hilary?) or Christopher Columbus (?) would be so famous if what they had discovered was obvious and required little thought and effort . . . ? What to expect when using this activity, from our experience... You'll probably need a recap of what "squaring" and "powers" notation means / is asking you to do! You'll also probably need a few example solutions of making other numbers using squares, roots etc. to get the idea of what exactly it is this pesky problem is prodding you to produce some possibilities for! But once you're clear on the land to be explored, there's plenty of surprises, strategies and short cuts to lighten the load and get that tingly feeling of discovery! Extra notes Oliver Bowles 20.09.09
	www.thinkmathematics.com


	Great ideas and resources for teaching engaging mathematics lessons

Great ideas and resources for teaching engaging mathematics lessons

Investigating Squares, Roots, Cubes and Triangles