Additional Math Pages & Resources

Tuesday, May 3, 2011

Grand Complications, Part II

This blog talks about using elementary math. Yesterday I coined the term Grand Complication Math (which is often tediously called higher-order thinking skills).

I use this term because I am a watch collector, and we call a watch with multiple complex functions a Grand Complication. Here's one from Jaeger-LeCoultre. It's called the Hybris Mechanica Grande Sonnerie, and it makes music as well as containing a perpetual calendar and many other functions.

In our Excel Math curriculum, we help kids prepare for adult life by giving them opportunities to solve grand complex problems. Here's an example that will be familiar to anyone who's had to move house. It comes from our Fifth Grade curriculum.

The Romero family is moving. The children, Julio and Marisa, threw away lots of stuff, but they have plenty left to move. Mr. Romero asked Julio to look at all the furniture and decide what geometric shape each piece resembled, so he could calculate the size of the moving truck they would need to rent. Here are some of the pieces.


The drawing above shows how the geometric shapes could be used to estimate the size of the load. The table below shows the answers to the first question asked in this Grand Complication problem:


Having accomplished the first task, Julio then had to compare the size of their load to the capacity of the trucks for rent. Since the price of the truck is based on its capacity, plus the difficulty of maneuvering a large vehicle, Mr. Romero didn't want to get one too large.

However, as anyone of us can attest who has rented too small a truck, there's also a price to be paid for unloading it (when it's proven to be inadequate) and moving everything to a larger truck. Or making two trips.

Here are the truck dimensions. We multiply the length x width x height of the truck body to get total volume.


Our 5th grade students generally say that Mr. Romero could rent the smallest truck. But they haven't accounted for all the other items in a house! Here's a list of items I found on moving sites:
  • BOOK CARTON = 1.5 CU FT
  • LINEN CARTON = 3.0 CU FT
  • LARGE CARTON = 4.5 CU FT
  • EX.LARGE CARTON = 6.0 CU FT
  • CLOTHING WARDROBE = 10-20 CU FT
  • DISH PACK = 5.2 CU FT
  • PICTURE CARTON = 3-5 CU FT
NOTE: Don't forget to subtract about 60 cu ft to allow for  the roll-up door!

So far this isn't rocket science.
  1. Inventory the furniture, calculate the volume of each piece, get the sum of all the volumes and set aside. 
  2. Inventory the trucks, calculate all the volumes, and compare those volumes to the sum you already have. 
  3. Choose a truck.
What next?

As any truck driver knows, trucks have capacity limits for WEIGHT as well as CUBE (cubic volume). A truck full of feathers is always within limits, but a truck full of math books is not. The current federal limit is 80,000 lbs for an 18-wheeler tractor-trailer. Smaller trucks have lower limits. Our Excel Math delivery truck cannot be filled to the brim, or it would be squashed flat to the ground by the weight of our curriculum.

How do you calculate the weight load of the truck without having to fill it up, go to a scale, weigh the truck, and then off-load any excess?

Come back tomorrow for Part III of Grand Complication Math.