What Price Land Regeneration?

I recently spotted this remarkable opportunity on the back of a Robinsons Fruit Shoot drink.

The concept is called Transform Your Patch, and the Robinsons website informs me that “Every drink represents a 1 square centimetre patch of real land that needs regenerating. To help transform a patch all you need to do is buy a participating soft drink.”

That got me thinking mathematically. Square centimetres are not the first unit of choice when measuring land, so I wondered how the figures would actually rack up in real life. This, I also thought would be a useful, real-life use of mathematics for a group of Y5 children; provoking a number of interesting investigative questions.

I set my Y5 children the challenge of using the data to determine how much it would cost them to help Robinsons transform different areas of land.

We start the maths work

The Transform Your Patch website indicates that all Robinsons drinks are included in the project. But, to keep things simple I chose to stick to the original bottle of Fruit Shoot that piqued my interest.

Fruit Shoot is sold in packs of 8 for around £2.00 – That’s 50p per bottle. So we imagined that it would cost us (the buyer) 50p per square centimetre. That’s interesting, but we didn’t know many people who would be happy playing in such a small space. So we moved on to slightly bigger things.

A4 paper is abundant in the classroom and has an area that someone could usefully use – even if they were only standing still!

The children measured the A4 paper, used a calculator to calculate the area and found the following:

21.0 cm x 29.7 cm = 623.7 sq cm = £311.75

Now that put it in perspective for the children (and for me). We found that we would need to buy over £300 worth of fruit drink to transform a piece of land the size of an A4 sheet of paper.

Big areas

We decided to look at a more standard measure: 1 sq metre.

My class were able to tell me that  1 sq metre = 100 cm x 100 cm. And from this we could see that we were really talking about 10 000 sq cm. Comprehending the enormityy of these figures is sometimes tricky. It seems illogical that something the size of a square metre should contain that many square centimetres, so I used an image to help the children see that 1 sq cm was really a very tiny fraction of a square metre.

Click on the image to see a larger version – there is a single green square (representing 1 sq cm) and 9 999 white squares.

We had now found that to transform an area equal to 1 sq metre we would need to buy 10 000 bottles of juice. The cost to us then, of helping Robinsons to ‘transform’ 1 sq metre of earth = 50p x 10 000 or £5000!

Bigger areas

My class then went on to choose many varied different land areas, the most thought provoking though was the common football pitch. We first had to agree on the size of a football pitch and found that there isn’t any specific regulations regarding this. However, most sources suggested that the smallest pitch size for an international adult match would be 100 metres x 65 metres. The children liked this size because of the easy calculations it offered!

100 m x 65 m = 65 000 sq metres

= 65 000 000 sq cm

Yes, that made the class pause for a moment. That really is 65 million. And the cost to transform this space (at 50p per bottle), £32.5 million!

At this point someone said that “Everyone in the country would need to buy a bottle of Fruit Shoot.” A comment that proved startlingly close to the truth. A quick check on the Internet told us that the UK population is currently at 61.9 million. We were able to conclude that:

If everyone in the country bought a bottle of Fruit Shoot we still wouldn’t have enough to transform a single piece of land the size of a football pitch.

As you can probably guess, we had an enjoyable lesson and the children worked out some amazing facts. Facts which I know they were eager to share with their parents. They also cheerfully worked through many quite complex calculations. And learnt to be grateful for seeing mathematical opportunities everywhere, and the undeniable value of linking maths investigations to things that are both relevant, and ‘real’.