Area: teacher workshop activity (written in 2003 by Don Yost)
Teacher notes follow, for a student lab
Each group will need 24 one cm by one cm squares.
Make a large flat figure : 6 squares by 4 squares.
If you wanted to tell someone how large the figure was, you could count the number of squares.
1. How many squares are there?
You should have counted 24 squares . Each square is called a square centimeter. The number
of these squares in the figure is the “area”. Therefore the area of the big figure is 24 square
centimeters.
2. If each edge of the squares is one centimeter (cm) long, how long are each
of the edges of the big square?
You should have answered 6 cm. by 4 cm.
3. What is 6 X 4?
Now arrange the squares in a large shape 2 wide by 12 long.
4. How many squares are in this large shape?
5. What is 2 X 12
6. What is the area of this large shape?
Now arrange the squares in a large shape 3 wide by 8 long.
7. How many squares are in this large shape?
8. What is 3X8?
9. What is the area of this large figure?
You should notice that there are several ways to find the area of a surface:
a. You can count the number of one cm. squares showing.
b. You can multiply the width by the length.
10. What is the area of a figure, 3 squares by 4 squares?
11. What is the area of a 2 square by 6 square figure?
12 What is the area of a one square by 12 square figure?
Note: 1 cm squares are available from math catalogues through Nasco. An alternative would be
to use clear plastic ruled cm by cm sheets. Probably available through a math catalog. Use
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overhead pens to mark the areas. Graph paper could also be used if you could find or make one
using cm scales.
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AREA MEASURING & MODELING: teacher notes
(written in 2008 by Don Yost)
Apparatus
24 flat 1cm x 1cm squares
4 squares drawn on paper or 4 cutouts: 2cm x 12 cm, 4 cm x 6 cm, 3 cm x 8 cm, 1 cm x 12 cm.
Different colors might make identification easier.
Optional: square cm. graph paper
A leaf or leaf cut out
1 inch cube
Pre-activity discussion
Area is a measure of the amount of “cover” something has. A basketball court covers a lot, so it
has a large area. The head of a pin has a very small area. Students will use small squares to
cover something. How could you find how many squares would cover an object? Give out some
flat rectangles. Cover one of the rectangles completely with cardboard squares. Count the
number of cardboard squares it took to cover the rectangle. Make a data table showing your
results. In order to tell the rectangles apart, call them by the length of each side from a corner. (If
the square is 3 cems by 8 cems, call it the 3 X 8 rectangle.) Graph paper has cem squares marked
on it. How could you use graph paper to find larger areas?
Performance notes
Students should interpret area as the number of unit areas which will cover an object.
Lab Activity:
Take three more different rectangles and cover and count as before. List all your data on a data
table.
Post–activity discussion
The number of cems it takes to cover a rectangle is called the area. Since students are no longer
measuring in just one direction, they can’t measure area in “cems.” As they are going in two
directions, label the area covered in “cem cems” or “square cems”.
There is a shortcut to counting the number of squares covering a rectangle. Have you figured out
what that short cut is? What is it? (Hint: look what you called the rectangle)
Deployment
Measure the area of a “leaf.” Students will have to estimate partial squares
Using 1cc graph paper, determine the area of an object.
Measure the surface area of a 1” cube.
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