## Tuesday, 23 January 2018

### FInding the Fraction of a Quantity Investigation

Today we started exploring how to find the fraction of a quantity which is a key way we use fractions in everyday life.

To find out strategies the children already knew and to give them an opportunity to create their own strategies, we looked at the following situation:

Developing number sense requires children to constantly estimate and get a feeling for numbers, so before we started working it out, the children were asked to identify their 'gut instinct' of which they feel might be cheaper and to write a star beside it to test later.

We then had time either using strategies we already knew or trying to create strategies to help find out.

For those children who could find a successful strategy easily, their challenge was to try to create another strategy that might also work. I think that giving children opportunities like this helps develop their creative thinking whilst also helping them to delve deeper into mathematical understandings.

As they were creating strategies, this was a great opportunity to discuss with children their thinking and to find a few interesting startegies that could be shared with the class.

I found the following, wrote them up and then those children shared their strategy with the class who then gave feedback on what they thought of it:

After discussing these strategies, we then needed to discuss which t-shirt was actually cheaper since we had different ideas.

Some children hadn't realised they needed to subtract the fraction from the original price so listening to others explain why helped them to see the mathematical thinking needed:

Looking at the various thinking that took place can greatly help create a picture of where each child is at, whether they prefer visualising or not and any misconceptions they might be harbouring such as the last sample where the child is thinking a third equates to 25%.

We then extended this understanding with our next situation:

Again, to help develop their number sense, before applying any strategies, the children drew a star next to their estimate or 'gut feeling' for which was greater.

This question helped identify misconceptions some children were harbouring and we used some of those ideas to help deepen learning of everyone in our discussion.

We are constantly reminding oursleves that mistakes are great when we take the time to think why they are mistakes and how sharing mistakes can help deepen everyone else's understandings.

This was a great example:

Quite a few children had explored this as a strategy. Others were able to explain how we either need to 'stretch out' the fifths or 'shrink' the tenths so they are the same sized whole.

Some thought of comparing the two fractions to a half as a strategy which we thought was an interesting idea:

Students were then invited to share stratgeies of how we can find the fraction of the amount that helped us to determine which was more.

We really loved this classmates' visual strategy:

We thought this was an interesting strategy too:

Lots of questions were asked when a student shared this strategy:

Finally, this student's strategy was chosen to be shared:

We then practised a few 'fractions of an amount' questions and reflected in our Maths Reflection Diary: