Thursday, 5 May 2016

Divergent Thinking: How many ways can we measure the volume of the odd shape?

Maths often requires creative thinking.

Giving divergent thinking opportunities where we try to generate creative ideas by exploring many possible solutions is a useful way to show children how maths is about thinking creatively.  It also takes anxiety away from some children who harbour misconceptions that maths is all about being 'right / wrong' that they may have been taught previously.

To help us with divergent thinking (and to solidify our new understanding that 1 millilitre = 1 cubic centimetre), I made this odd-looking 3D shape by connecting boxes:

How many different ways can we measure the volume of the shape in litres?

The group explored the shape and came up with these amazing ideas:

° measure the volume of each box in cubic centimetres, add together and convert to litres

° create different prisms that connect part of two or three boxes to measure then add together

° fill a bathtub with water.  Submerge the shape in it.  Measure how much water overflowed from the bath and that will tell the volume.

° fill the shape up with water and then measure how much water was used

° make the same shape with base 10 /MAB blocks and then calculate how many cubic centimetres it is. Then convert to litres.

° use a Hoover to suck out all the air in the shape. Then blow the air into a balloon. Put the balloon into a container of water and measure how much the water rose.

After generating these possibilities, we then evaluated each and discussed which we thought would be the easiest and the most complex by arranging them in order.

In our oral reflection together we discussed what we gained from this learning experience and how it helps us with other areas of maths.

A student explained how in maths there are usually many different strategies to solve problems. We should try to find different strategies and then evaluate which are better to use for those situations. Such a great connection!

The children also shared how they enjoyed the learning experience because they liked how they could think of 'mad' ideas and they were deemed good.