I'm tired of how textbooks treat area and perimeter. For one thing, it's very formula-based, and I believe that strips away some of the thought processes when trying to understand these concepts. Take a look at this example on finding the area of a rectangle:

Now, I understand why you might give a formula for the area or volume of some shapes, but why on Earth would you give one for perimeter? You've just taken an idea that is really easy to understand and apply, and have made it much more difficult and subject to error. Students also lose the meaning of perimeter because they're not connecting the idea with the sum of the sides. They're just looking for the formula that begins with a P and cranking out an answer.

On top of that, textbooks and worksheets always conveniently give students the measurements.

I have two problems with this. For one, if I get an answer for area, I don't really have a way to check it. So my answer is 288 square meters. How do I know if I'm right...or even close? Is that answer reasonable? How would I know?

Second, people always complain that students are terrible at measurement. Then we give them tasks that are devoid of measuring. Why would we do that? It doesn't make sense. If there's an opportunity for your students to measure something in class, make them do it. How else do you expect them to get any good at it?

If you must use a worksheet, I would suggest it look more like this:

It's not terribly exciting, but it accomplishes a couple of things.

1. There are no measurements listed. Students have to find their own measurements. They also have to think about which measurements are necessary...especially for area.

2. I print this out so that figure A is 1 square inch. With that, I can make guesses about the area of every other figure. I can check to make sure that my answer makes sense.

3. I can make comparisons between shapes. I can rank them in order of biggest to smallest. I can check to see that the sum of the areas of the shapes total the same area as the entire worksheet.

4. Students can compare answers, and once seeing that not everyone has the exact same answer, talk about error in measurement.

If you try this, let me know how it goes.

Here's an area question that doesn't focus on formulas:

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I love the five triangles website. Thanks!

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