## Tuesday, 11 March 2014

### The Laws of Maths - The Associative Law with Multiplication

We're getting close to the end of our time looking at the Laws of Maths (and the kids will be glad to move on to something new).

So, we brought the multiplication process into the Associative spotlight.

Now we were getting into some interesting territory.

Having spent the last two weeks:
1. learning about the Commutative and Associative Laws
and..
2. experimenting with using arrays

...we were now in a place where we could start thinking for ourselves and the teacher could take a bit more of a backseat.

So once again we pulled out the counters and started thinking about the provocation.

A nice looking display - at the top we have 5 groups of 4 x 2
and underneath we can see 2 groups of 4 x 5

So when we put them together we can see that the two groups
are the same. Nice proof.

This one was a bit confusing to me. We've got 4 x 5 at the top
and 2 lots of 2 x 5 at the bottom. Not quite the same as the provocation at the top.

So we reorganised things a bit and had a chat about what we were looking for.
I find these little chats that follow moments of confusion really significant -
helps me to assess and diagnose.

And just when I thought everything was going so smoothly, I came across this
example of someone trying to model the symbolic notation using blocks
rather than making an array.
Time to reflect on my tuning in process for this inquiry.

Having come this far, we are going to finish with the Distributive Law later in the week.

Can't do it tomorrow because we have "Gruffalo Day"

...but that is another story!