Opening up with Provocations / Open-Ended Tasks

Each maths learning time for our unit exploring volume and capacity, I give the children an open-ended task or provocation to think about before we split off into our hands on group investigations.

I know from our pre-assessment and from other activities we have been doing that about half haven't learnt yet the formula for measuring the volume of cuboids and rectangular prisms, so I thought this prompt would help some of them to start their understanding of that.


We sat in a circle with the box in the middle:

I explained:
- We continue to discover this year how maths thinking is about creative thinking.   Examine the box.  How many different strategies can you create to find how much space it is taking up?  In other words, its volume.   The strategies don't need to be effective or the fastest.  This is about thinking creatively.

We used the think-pair-share strategy.

When it came time to share with their partner their strategies, we were reminded how ideas often help spark other ideas, so as we listen to other partner see if their ideas help you to spark new ideas.


When it was time to share as a class, a few of us discussed how listening to their partner helped them expand on their idea to create a new one. 


I think that is a useful way to use the think-pair-share strategy because often in the 'pair' time, children can sometimes think it is about passive listening, when really it is an important thinking time.


Some of our creative ideas to measure the volume of the box included:

° fill it with water and then measure the amount

° use a base 10 cube to help estimate how many of those it equals

° use a ruler to measure its length, height and width and multiply them

° fill with cushions and use them as an informal unit

° build an identical shape beside it using cubic centimetres

° put the hoover back inside the box, fill the remaining space inside with foam. Then take them both out and measure their volume

° Find another box that fits perfectly inside that box. Measure its volume and then add the volume amount of the first box's cardboard volume.





To reflect, I asked:  Why do you think you were asked to think of as many strategies as you can rather than create one strategy?


We shared our ideas and as hoped, someone felt that it is important to not only think of one strategy and then use it because it might not be the most effective. If we think of different ways to solve a problem, we can then evaluate which is the most effective and which isn't and why.



These type of short whole class provocations can be really useful to extend and challenge thinking.  I'm hoping they also help us deepen our understanding of what mathematical thinking is about.