Saturday, 26 April 2014

Pie charts and percentages with Smarties

This was a nice easy and fun way to explore percentages and pie charts - plus it was edible! It came from an image on Twitter:

What a great way of doing pie charts! No arithmetic involved! Normally there is just a little too much involved in achieving a pie chart. How about we combine that with a circle divided into one hundred - then we simply have to count around that circle for the percentage! The paper was there on printablepaper.net.

So we handed out the boxes of Smarties.

We each had a packet, and sorted them into colours. Then we arranged them in a circle. That was the tricky bit. Sometimes we had to jiggle the circle quite a bit so all the Smarties would fit, and so it was fairly circular. We marked off the different colours on the outside circle divided into a hundred.

Then we coloured in the circle with the right colour, and added on some pie cuts:

Here are more photos:

And the finished pie charts look like this:

Wednesday, 23 April 2014

Five Rectangles

In Year 4 we've been looking at a puzzle, taken from Gary Antonick's 'Numberplay' in the New York Times:
Create a set of five rectangles that have sides of length 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 units.
The really quick and easy way to explore this is with Cuisenaire rods:

After we'd found five rectangles with those side lengths, we recorded them using the Cuisenaire Environment:

Here are more pictures:

Then we started looking at the area the rectangles covered.

We got total areas of
120, 121, 123, 125, 130, 154, 161 and 184.

Next question: what is the biggest possible area?

Alicia answered this - use the biggest side lengths on the same rectangles:

 Area = 190
Can you see why this is the maximum?

And then, what is the smallest possible area?

Mimi answered this one - use biggest and smallest lengths on the same rectangle:
 Area = 110
Can you see why this is the minimum?

This is a great investigation - manageable, easy to understand, and susceptible to taking off in many directions. We didn't try to see how many possible ways of making the rectangles there are - that was a step too far.

But just seeing some of the ways was worthwhile. It works well because the rods and the numbers 1 to 10 are easy to grasp. And the maths it takes us into is worth it - length, area, 2 X 3 = 3 X 2, multiplication facts, addition of five numbers... And then a bit of more abstract thinking - what would the maximum and minimum be, and why.

It may be the first time a class has tackled this particular puzzle. We can certainly recommend it to other classes!

We rounded this investigation off with a small puzzle:
Make these rectangles, and then see if you can make a square by putting them together:
1x6 4x7 5x8 3x9 2x10
3x6 4x7 2x8 1x9 5x10
1x2 4x5 3x8 7x9 6x10
1x2 4x6 3x7 8x9 5x10