## Friday, August 13, 2010

### Teaching Estimation!

I had decided sometime last year that as one of my focuses (foci?) for Geometry, I would push their estimation abilities this year. We would estimate before measuring everything.

Today was Content Day 1 of Geometry, and I gave them a list of questions to answer as the Do-Now. Kids had NO IDEA how to answer some of these questions, which was my intention. We ended up with a really great discussion about how you would go about estimating some of these. (We ran out of time today, but I plan on returning to these very quantities on Monday and have them actively measure some of these, to check their own accuracies in estimation. Estimate-measure-estimate-measure-estimate-measure!)

• What is the height of this classroom in centimeters? In meters?

• What is the length of your foot in centimeters? In millimeters?

• What is the length of your hair in meters?

• What is the distance of your house from the school in kilometers? In meters?

• How many hours are you in school a week? How many minutes?

• How many kilograms does your textbook weigh? How many grams?

• How fast can you run in m/s?

It was great! (And funny that even when they know how big a meter is, they still can't estimate how fast they can run in m/s.) Some kids said really awesome things like, "I am about 160cm tall, and the classroom is about twice my height," or "Our new principal* is about 200 centimeters, and he is about a meter away from the ceiling." I followed this Do-Now/discussion by teaching them the mnemonic device for remembering how to convert between metric units. (Kangaroos Hopping Down Stairs Drinking Chocolate Milk).

The big concept (often overlooked) that I always try to teach for unit conversions is that when the unit gets larger in size, the number needs to get smaller. ie. 1 kg = 1000 grams. Otherwise the right-hand side of the equation either shrinks too much (if both the unit and number are getting smaller) or expands too large (if both the unit and number are getting larger) to remain equal to your original quantity! I say this even during metrics conversion, because if the kids get this concept down, it's a lot easier for them to figure out that 78 cm = ______ inches should have an answer that is smaller than 78, even though the numbers are messier.)

We used the Kangaroo Stairs to figure out how many decimals you move. (ie. Number of steps you take on the stairs = number of places you move the decimal.) Again, once the kids can reason through whether the number needs to get bigger or smaller, they can usually figure out the rest with a small bit of practice. Moving the decimal isn't the hard part; knowing which way to move it is the crux of those problems.

It was lovely.

*Yes, our new principal is a giant. :)

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My Precalculus class was also awesome today! We had to teach vectors as part of the support for their Physics classes, so I adopted Kate's activity of pushing desks around to show how vectors add differently when they point in same/different/perpendicular directions, and I also drew arrows (vectors) on transparencies and moved them around a large projected grid, to demonstrate how you would add vectors graphically. The kids figured out quickly as a class that you can find the magnitude of a vector with simple Pythagorean Theorem. Yesss!

It was really cool. I think I've got some difficult kids in there (or so I hear), but my plan is to kill them with kindness for now, so that three weeks in, they'll feel bad to act up in my class. So far, so good.