Wednesday, 23 March 2016

Using Ratios to Comprehend our World

Having a Peter's Projection world map is the best to display in our classrooms I think.  

World maps are politicised. Countries making their continent look disproportionately larger than they really are. 

It's strange, but true. 

The Peter's Projection map are accurate. The area of each country, ocean etc is a true ratio scale. 

Children (and adults) are often shocked when they see a Peter's Projection because for the first time they see the relative size of countries etc. 

A Peter's Projection map:

Yesterday in our discussion of ways we use ratios in real life, a student pointed to our world map and thought that we use them to compare sizes of countries.

Indeed we do use scale ratios for maps.

Early in the year, we had created ratio perimeters of our countries.

I thought now would be a good opportunity to extend our understanding of ratios more by using them to compare the ratio scale comparison sizes of the continents. 

The group and I began with Switzerland where we live.

We found the area and decided to round it down to 41 000 to make it an easy number to play with.

We looked at an MAB flat and thought about ways we could use it as a ratio scale.

Different ideas were suggested and tried.

Our most successful, we felt, was making 1 flat equivalent to 1 000 sq km.

By using that as our ratio scale, we could easily create a scaled map of Switzerland:

Our next challenge was to then create a world map.

We rounded the area of each continent up or down to the nearest million to make them easy numbers to play with.

We then thought of different ratio scales 1 flat could equal and eventually decided we would try    1 flat :  1 000 000

With that scale, we could easily calculate how many flats we would need to make each continent (below).

Having done the mathematical calculations, it was now time for some creativity.

How could we use the scaled ratio flats to create the shape of each continent?

It took quite a lot of collaborative skills and decision making to make it happen:

We then shared with the rest of the class the strategies, challenges and feelings of success we felt.

Their peers asked them some great questions about how and why they used the strategies they did.

Looking at our scaled world map, we particularly were surprised to notice how large Antarctica is relatively to other continents. We felt we never really get that sense because Antarctica is often shown 'cut off' at the bottom of the map all stretched out.  

Amongst some of the questions that classmates asked, one was, " How did this help deepen your understanding of ratios?"

A participant replied, " It made me realise that there are even more ways that we can use ratios then we have already discovered. It also made me see how rounding numbers is a helpful strategy and that we can use ratios with all different sorts of things - even area."

We liked that reflection and appreciated being able to tackle a pretty big mathematical project like this.

I'm so glad I'm not a worksheet maths teacher; the children and I would be missing out on this creative ways to engage in maths.

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