## Thursday, 31 March 2016

### Kids Create Own Ratio / Proportions to Investigate & Visualise

It's important that children are given opportunities to visualise ratios & proportions to gain deep understandings of their concept.

We are privileged to have 1 to 1 laptops in our class and so using google docs is a great tool to help visualise by copy-n-pasting images.

We began by brainstorming as a class different types of ratio / proportion investigations we could create and solve.

Two of these ideas are shown below:

Visualising Ratios & Proportions

The ratio of time I am asleep compared to being awake.

= 1 hour asleep   = 1 hour awake

In one average day my ratio is:

 Asleep Awake

In an average day, my ratio of being asleep to being awake is  8 : 16

I can simplify this is 4 : 8  or even further to 2 : 4 or 1 : 2.

This means that for every 1 hour I am asleep, I am asleep for 2 hours.

In an average day, my ratio being asleep to the whole day is 8 : 24.
I can simplify this to    4 : 12     or      2 : 6     or     1 : 3.
This means that for every 3 hours, I am asleep for 1 hour.

In an average day, my ratio of being awake to the whole day is 16 : 24.

I can simplify this to   8 : 12  or   4 : 6   or   2  : 3.
This means that for every 3 hours, I am awake for 2 hours.

My proportion challenge question:

How many hours do I sleep for in 1 week?

 Asleep Awake

To solve this, I multiplied the ratio 8 : 16 by 7.

Another group created and investigated selling cupcakes (below):

I sold cupcakes to raise money for Oxfam.

I sold three flavours:  vanilla, strawberry and chocolate at this ratio-

2 vanilla      :   3 strawberry     :  1 chocolate

My proportion challenge question is:

If I sold 42 cupcakes, how many of each flavour should I bake for tomorrow
If I expect to sell double the amount?

 Vanilla 28 Strawberry 42 Chocolate 14

To solve my question; I first calculated how much of
each cupcake I sold. I divided 42 by 6 because the total
of the ratio was 6. To find out how much I should bake to
Sell double the amount, I multiplied each ratio number by
14 because that is double 7.

Given children the opportunity to create and solve their own questions helps them to deepen what they are learning and thinking about. To be able to create a challenging investigation, we need to have a solid understanding of ratio and proportions as a concept. Some groups discussed how their initial questions were too easy to solve and they then used these findings to create more challenging questions to investigate (like the selling double amount of cupcakes above). Other pairs and groups (like the asleep / awake above) remained at a simpler investigation because they felt that was as challenging as they could go with that type of data.

When the children shared with each other their investigations, they asked if others could think of a way to make the investigation even more challenging. They recorded ideas they liked and will use these peer challenge questions to investigate tomorrow.

What I liked about this learning experience was that the children were very engaged and that's because they were creating their own investigations. Seeking suggestions of how to take their learning even further was a great strategy as it generated interesting discussions about the types of data we handle and their limitations or levels of depth they could go to.

When reflecting as a whole class, students shared strategies they used - both the successful and unsuccessful. We talked more about the 'unsuccessful' because, as we often discuss, it is mistakes that really help us to deepen our learning and to take our learning further.