We have been fascinated by the idea of mathematical thinking requires creativity and visualising.

To help us explore this further, and to gain some key number sense terminologies and number talk beginning as mathematicians, today we explored the number 12.

The children had a few minutes to jot down anything they knew about the properties of 12. This in itself, proved to be a very informative informal assessment as I noticed those who had the language and understandings to discuss numbers and those that haven't yet.

We used the think-pair-share strategy so after sharing with their table partners what they knew, we shared as a whole class:

Collectively, we knew quite a lot. As children shared what they knew about 12, we paused and discussed what each means. Our understanding of what makes a number even was a bit shaky, but together we were able to find a deeper understanding rather than a number that ends with the digit 0, 2, 4, 6, 8. This in itself helped us to think about how this year in maths learning, we should really focus on the WHYS of maths rather than just the WAHATS or HOWS. We discussed how deep understanding and more interesting wonderings develop when we think of the WHYS.

To help us investigate further how mathematical thinking is about visualising and creativity, table groups were given counters and explored different ways we can visually represent the number 12.

Some interesting investigations took place:

This student explained how she thought of the factors of 12.

You have to love this type of thinking:

After groups had time to explore, we did a gallery walk to see what others had thought about. During the gallery walk, the children shared their thinking and were encouraged to share their successes but equally things they had tried, but hadn't worked out as planned. It is important that children see the value in attempts in maths as equal to successes.

What ideas could inspire us to take our thinking further?

Being inspired, the table partners returned to their counters and explored further.

We then had cuisenaire rods to help us creativity represent the number 12. It was apparent that for most of the children, they hadn't used these for a long time. But, it made the learning richer as they slowly began discovering for themselves that each rod could be given a numerical value. Once they were discovering these, their thinking really took off!

Some samples of the number 12:

During our next gallery walk of sharing and seeking inspiration, we appreciated the thinking of those who thought in 3D and also the group below who created these addition combinations below:

After sharing, we shared some wonderings that this learning experience invoked that we would like to explore:

° How can visualising numbers help our learning in maths?

° How many possible ways could exist using the counters?

° Which numbers would be easy or challenging to visually represent?

° Could we find just as many ways with an odd number?

and one of my favourites:

° Can we do this again tomorrow?!?!?

beautiful representations by students: this is empowering students!!Great work.

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