Creating Strategies for Ratio Proportions

A small group and I continued to explore our central idea:

We use ratios and proportions to help see the relationship between values in real life situations.

We began by discussing what we had already discovered about our central idea and what we were still curious about.

One of our wonderings was if there are different strategies we can use and so this tied in well with what we were about to do.

We looked at the following scenario:

A farmer had a free-range egg farm.

  

       Free-range Eggs                                  Caged Eggs

In each section of her farm, she wanted to keep the ratio of hens to roosters as 8 : 2

Use the table strategy to work out possible proportions of hens to roosters:

Hens	8	4	16		32
Roosters	2			10
Total	10

Use the images to show the proportions in each section of her farm:

= hen         = rooster

Section 1 had 10 chickens in total:	Section 2 had 5 chickens in total:
Section 3 had 30 chickens in total:	Section 4 had 20 chickens in total:

Using Google docs is a great tool to help children see what ratios and proportions look like.  

After using the table strategy to find different proportions, the children could then copy and paste the hens and roosters to visualise the proportions like so:

Section 1 had 10 chickens in total:	Section 2 had 5 chickens in total:
Section 3 had 30 chickens in total:	Section 4 had 20 chickens in total:

We looked at the proportions created and one student commented on how she could see the reason why we might want to simplify ratios.  When we simplify a ratio, it makes more sense to us! - Exactly!

I then presented the following question and in partners or alone they tried to create more than one strategy to solve it:

On Monday, she had collected 150 eggs, 25 of which were brown. The rest were white.  

What is the ratio of white to brown eggs?

1.   1 to 3
2.   1 to 4
3.   1 to 5
4.   1 to 6
5.   2 to 5

Create a similar word problem based upon the number of eggs (any amount) for others to solve using the same strategy. Ensure you have the answer.

Both and I and the children like it when we try to create more than one strategy. It helps us to realise that maths isn't about getting the answer compared to creating effective strategies to help get an answer.

After some time, we shared and discussed strategies we had created:

This student wanted to share what she was thinking about and asked us why she was getting stuck. This is exactly the type of great shared learning we want to generate. We talked about the beginning of this strategy and why it wasn't really helping us to make sense of the ratio proportion and so that's why it came to a dead end. Mistakes are wonderful ways to stretch our minds another student reminded us and so we appreciated this sharing because it helped stretch all of our minds whilst think about it:

We did the same learning activity of creating different strategies to solve this:

The farmer looks at all the eggs in her barn.

There is a white to brown ratio of 8 : 11.

If there are 88 white eggs, what is the total number of eggs?

1.  121
2.  128
3.   152
4.   176
5.   209

Again, we explored all the different strategies shared and reflected on those we felt made more sense, those we felt were the quickest and those we felt best helped to visualise the question.

We didn't reflect on who got the correct answer or even gave that much thought to what the correct answer was and that is what we should hope to instill in mathematical learning. Maths is about creativity and by creating different strategies rather than focusing on getting answer, we are broadening our maths understanding and creating a learning environment where mistakes are valued.