Monday, 13 November 2017

Lead In to Multiplication Inquiry

To begin our new unit inquiring into multiplication, I wanted to find a way where I could gain an informal glimpse of where each child was already at with their conceptual understanding and at the same time give them an opportunity to rethink what they already know. 

So, I posed this question:

The children wrote their ideas on a shared paper (so that they could be perhaps be inspired by other ideas being generated in their group). 

To help encourage some diverse thinking, we were reminded how visualising in maths is a key element, so how could we visually show what multiplication looks like.

This served as a very useful pre-assessment to help gain an insight of where each child was at with their conceptual understanding of multiplication.

After some time, we then chose two ideas we had and shared those with our group. This generated some interesting discussions and helped with some misconceptions a few of us were harbouring.

We then swapped our paper to the next group. They read through the ideas and then drew a smiley face beside one of the ideas they found interesting.

The children found it interesting to see what their classmate had found interesting about their understandings and found out orally why they thought so.

Our collective understandings:

We then discussed as a class what the 'big ideas' were that we understood about multiplication.  We had a good understanding that multiplication is repeated addition and some shared the connection with division.  When one student theorised that multiplication sums are the same, giving the example of 3 x 7 = 7 x 3, another student questioned that. 

To help with this wondering, I drew the following on the board:

Which does this represent?   3 x 7    or   7 x 3?

Most of us thought it represented 3 x 7 and a few of us thought   7  x 3

Some children were asked to share their reasoning and eventually, as a class we concluded it must represent   7 x 3 because 'the times symbol represents groups of'.  With this situation we are looking at 7 groups of 3, so it must represent 7 x 3. 

We then sketched what  3 x 7 would look like on our paper to help us solidify this understanding.

As a provocation to help raise curiosity and spark wonderings to explore in our unit, the following was posed: 

We used the 'think-pair-share' routine.  We spent about 10 minutes thinking of different possible strategies and were encouraged to try to also create our own. The strategies didn't need to be effective, we were more importantly trying to find as many different strategies as we could. 

We then shared and discussed these with our group. Lots of great discussions took place especially with the more creative strategies they made. 

Our groups then decided which of these strategies worked and if so, they published them and added them to their group poster.

When we completed our posters, we passed them around to see other strategies others in our class came up with and we discussed a few of these together as a whole class.  

For our reflection, we had some time reflecting our learning in our maths diaries.( Link to Maths Reflection Diaries )  

Using our reflection thoughts, we shared these with our group and then as a whole class we came up with the following big ideas:

This has also sparked some interesting wonderings which we will use in the unit to find out about:

Creating provocations to being number units can be a bit challenging to design. It needs to be able to cater to a broad range of different understandings and to also spark lots of wonderings which will form the inquiries.  Looking at our initial wonderings, I think this provocation was quite successful. The children were really engaged and enjoyed the creativity aspect of creating their own strategies. 

Once we have begun exploring different strategies for multiplication and begun evaluating them, I'm sure they will enjoy this creative challenge I did last year with my class: 

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