## Thursday, 1 February 2018

### Multiplying Decimals

As part of our Unit of Inquiry exploring forces, today we were going to find out how much we would weigh on different planets- the kids love it!

Part of that requires multiplying their body mass with decimals.

So, to better understand what we will be doing with the numbers, we began with this lead in:

We used the think-pair-share strategy.  Firstly the children jotted down different ways. They then shared with their table group and then we discussed and shared ideas as whole class.  Some of the key understandings included:

We have done this a few times over the year and each time additionally unique perceptions are shared which I find really interesting. I can see how some children's conceptual understandings and abilities to express have expanded and deepened.

The whole class sharing raised some interesting discussions such as a child sharing how decimal numbers are like negative numbers.

- Are they? What do we think about that?

Some of us agreed, some disagreed and many were unsure.

Another asked: Can we have negative decimals?

- Can we?

We thought of having a temperature of   - 1 . 5 ° C

Does this prove we can have negative decimals?

Does this mean a decimal is a negative number?

A student shared a theory that:

This really got us wondering: Can a demoninator be zero?

We chatted about what this might mean- Can we have zero whole parts?  Could this represent a decimal as a negative number?

It was a very interesting thought and I explained that we will definitely come back to this in a few weeks when we explore negative numbers.

Some of us still weren't 100% sure about decimals being negative numbers or not and that is ok. I think it's good to keep wonderings floating in our minds to think more about later.

Having tuned our minds back into what a decimal is, we then looked at the following:

I posed this question to help build number sense and to also value creating theories which we are always doing.

We showed with thumps up, down or sideways what we our theory was.

There was a mixed initial thought to this.

To help each of us find out for ourselves, the following was posed:

Asking 'How many different ways......' is a great way to encourage deeper thinking and creativity.

If we ask children to think of one way / one answer, we are limiting their potential to discover different ways of thinking.

Again, we used the think-pair-share routine.
It was interesting to be able to walk around and chat / observe the different ways the children were trying to visualise it.

One children shared a great hypothesis:

When we multiply numbers, the answer is bigger so my theory is that the answer to 5 x 0 . 5 will be bigger.

This completely makes sense and I love how she has drawing upon prior conceptual knowledge to create and test a theory.

After a while, the children shared with ther table partners their visual ways. Each table group were asked to select one of the visualisations that they thought the whole class would benefit from seeing.

Together we discussed the following shared:

We appreciated all the different ways we could visualise the numbers.

We then repeated with a larger decimal:

Again, we first estimated and then tested by visually drawing what it looks like in different ways.

Some of the table sharing included:

We really loved the creative story behind the one below. He explained how there were 5 whole people at the airport and each carried a bag that was 0 . 25 of their body mass:

Valuing creativity and visualising in maths can greatly help children to make stronger number sense like these examples show.

Lastly, the children created and visually showed their own number sums. Afterwards, they shared and discussed these with their table partners:

Some wanted to challenge themselves further by multiplying a decimal with a decimal to see what it looks like:

And this student found it very interesting to discover how small the number would be when multiplying 5 by 0 . 0000002. We giggled about it being about half the size of a ladybird's poo :P

Before moving on to multiplying the gravitational force of our mass to see how much we would weigh on different planets, I asked if we had some wonderings we wanted to explore next week and so we have the folllowing to find out about:

I think this has helped us launch into some really interesting wonderings to explore that will further help develop our number sense with decimals and fractions.

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