## Tuesday, 6 June 2017

### Creative Volume Problem Solving

Giving children opportunities to problem solve creatively is a key element of mathematical thinking we need to be constantly valuing in our classrooms rather than 'getting answers'.

To help with this, partners were given a thesaurus and an atlas to examine and were asked:

Which do we estimate takes up the most amount of space?

(I didn't want to use the term 'volume' just yet to allow the children to gain a better understanding of what volume actually is and I had chosen two books which looked like they had a pretty similar volume)

Without using any resources, rich discussions took place as partners discussed and created estimating strategies.  They then individually recorded their thoughts using the sentence starter:

I estimate that the thesaurus / atlas takes up more space because.......

Giving children sentence starters like this, I think, helps them develop stronger communication skills and also gives them an opportunity to deepen their own thinking without being influenced by others.

After they wrote their thoughts, we discussed together.

Firstly, we showed hands how many of us thought the thesaurus took up more space (4), the atlas (11) and the same amount (5).

Students were invited to share why they thought so and some very creative thinking and strategies emerged.

We first heard from those we thought the thesaurus takes up more space:

- I visualised smooshing the book down as if it was playdough and I could see it taking up more space than the atlas.

- I can see the thesaurus is much thicker so I can sense it takes up more space.

- I visualised taking out all the pages of both books and lining those pages up side by side. I could see that the pages of the thesaurus would be much longer so that makes me think it takes up more space.

We then heard from some students who thought the atlas takes up more space:

- I imagined cutting the atlas in half and stacking both halves on top of each other. By doing that I could visualise it being thicker and so taking up more space.

- I drew a dot at the halfway mark of pages on the side of the thesaurus. I then placed the atlas beside it and imagined doubling it. By doing that I could visualise it taking up more space.

- I opened the thesaurus up at exactly halfway and placed it spread out on top of the atlas.  I then looked at them at table level and could see clearly that the atlas took up more space.

- When I placed the thesaurauas on top of the atlas, I could see it is almost half the area size of it. So, I visualised doubling that and then tried to estimate the thickness of both to see which might take more space. I'm not exactly sure, but I think I can see the atlas taking up more space.

We then heard from those who thought they took up an equal amount of space.
They had used similar estimating strategies and some had thought about estimating the width and length to mentally calculate which took up more space. That was interesting to me because up till then no one had suggested the books being rectangular prisms nor formulas for measuring the volume of those shapes.

I then asked, what mathematical concept are we using when we measure how much space an object takes up?

A few of us shared how it is volume.

What things in our room have volume?

- chairs, tables, our bodies etc were shared.

What about the air in our room? Does it have volume?

That question raised a lot of different opinions. When asked why we thought so, someone shared how a balloon gives us evidence that air has volume.

Another shared how fire 'breathes in' oxygen and when there is no oxygen left in a room a fire goes out so that must prove air has volume because when there is no more of it, it has an impact on fire. Amazing thinking! :)

Another wondered, but what about in space? There is no oxygen there so does space have no volume?

We then began investigating:

How many different strategies can you create to measure the volume of each book?

The 'how many' part of investigations really opens up possibilities for children to stretch their minds.  We are not valuing an answer; instead we are are valuing creative thinking.

We discussed how creative thinking is a key element in maths and that it doesn't matter in this learning experience if the strategy is effective or not. What we are doing is thinking creatively.

Partners were given string, MAB units, longs and flats as well as being able to use rulers or any other object in our room to explore the measuring.

Loads of very impressive creative strategies emerged.....

Some students counted the number of pages inside both books and did calculations to try to find out which had the most number of pages and then doubled / halved the number to see if it would help them measure their volumes.

One student found a connection between numbers and others were discussing the difference in volume they felt they had measured between the two books.

Some cut the string to use as a measuring tool when comparing.

This student thought about whether if he rolled a bottle once, then placed the measurement using a pencil and then rolled it again to measure whether it would help him measure the volume of both books or not.  He wasn't sure if it would help, but his idea intrigued many of his classmates and me.

Lots of very rich mathematical theories, reasonings and knowledge were being shared whilst partners created different strategies.

We did a gallery walk hearing the different strategies and were amazed that the incredibly creative ideas that emerged.

I think this was a pretty successful investigation and introduction to volume which we will expand upon in further learning experiences.