## Monday, November 22, 2010

### Backbreaking Math

I have a case study to examine today. Can we solve the problems with the elementary school math we teach to kids in our Excel Math curriculum? (Yes!)

Chris is building a planting bed in his back yard. It will keep soil from washing down from the neighbor's yard (a bit higher), and give him a place to grow vegetables. Take a look:

He bought these metal baskets called gabions, and will fill those with soil. How does he know how much soil to buy? Can he buy soil in bags from the garden center, or does he need a truck?

Chris has to fill these 8 containers:

5 large gabions = 1m x 1m x .5m = .5 cubic meters x 5 = 2.5 cubic meters
3 small gabions = 1m x .5m x .5m = .25 cubic meters x 3 = .75 cubic meters

He needs 3.25 about cubic meters of soil.

We'll estimate that Chris needs 3.5 cubic meters of soil since some will leak out the holes and wash away, or be lost in the grass. However, he has to buy soil by the cubic yard (plastic bags) or ton (determined by weighing the delivery truck), so now we need to convert from cubic meters to yards or tons.

A cubic yard of soil weighs 2000-3000 pounds or 1.0-1.5 tons.

A cubic meter = 1.3 cubic yards; a cubic yard = .76 cubic meters

3.25 cubic meters x 1.3 = 4.225 cubic yards

So we need about 4.25-4.5 cubic yards of soil.

You need 54 40-lb. bags of soil per yard, so Chris could buy 4.25 x 54 = 230 bags of soil from the garden center
OR
4.25 x 1.0 to 1.5 tons of soil = 4.25-6.35 tons delivered by a truck

After looking at the weight and his available vehicles, Chris didn't bother with any more math, such as calculating the number of trips it would take to pick up 230 bags.

He called the soil delivery man instead. Here's the the pile of dirt which is just arriving in his back yard: