Math Is Fun Forum

Here's something weird that I found out whilst doing some coursework: if one of the sides is one unit less than the hypotenuse, the other side has a length equal to the square root of the other two sides' sum.

e.g. 3²+4²=5² --> 3²=4+5

There are two jazzes? (What is the plural of jaz?)

Polly, you have the wrong board.

Because it is interesting, challenging and is useful in so many ways. Why else?

I have 3 ideas.

One is Piaget's capacity idea - you know - short fat holds the same as long thin. Use glasses of different widths/heights and coloured water.Get the kids to estimate before you pour. (Young kids often assume the tall will hold more - it is so funny when they stare in amazement as you keep pouring from tall to short and it doesn't overflow!) But older kids can do things like use measuring cups and  pens to mark things out.

Another idea is to have rocks, pebbles sand and water. Get a large glass container and fill it with rocks. Then add pebbles, and they fit (around the rocks - give it a shake)! Then add sand, and it fits! Then add water and it fits! You can show how this works by emptying then filling with water, then show the water spilling out when you add rocks, pebbles, sand.

My third idea: give them a challenge with one of these measuring puzzles