What is Area?

## Teacher Lesson Plan

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This activity is aligned to NCTM Standards - Grades 6-8: Geometry, Measurement, Problem Solving, Communication, Reasoning and Proof and to California Mathematics Standards Grade 7: Measurement and Geometry #2.1 and Mathematical Reasoning #1.1, 1.2, 1.3, 2.1.

### Objectives:

1. To understand that area is measured in square units.
2. To learn that the area of a rectangle can be found by counting the number of squares.
3. To understand that perimeter is measured in linear units.
4. To learn that the perimeter of a rectangle can be found by counting the units around the outside of the figure.

### Materials:

(for each group of four students)

1. one bucket of 1 inch square tiles
2. one sheet of grid paper - 1 inch size
3. four sheets of grid paper - 1 centimeter size
4. four pencils
5. (optional) colored pencils/pens/crayons
6. Hands-On Math software by Ventura Educational Systems

### Procedure

I modeled the first problem and told them they were to do the same thing for the others. I asked them to build a rectangle with an area of 4 square units. Next using my overhead 1 inch squares I showed them on the overhead the three possibilities: 2x2, 4x1 and 1x4. Then I showed them what I wanted on their individual graph paper: draw the model (I used the 2x2 size) and then put

A = 4 sq. units
P = 8 units

Then I wrote 9 more problems, giving them just the area. Each group was to model it (the students in each group took turns being the person to make the rectangle using the squares) and then each student was to draw the answer and label A(rea) and P(erimeter).

They were talking and comparing and sharing - it was SUPER. Some kids who started out without a clue were saying, "OH, I get it!"

Near the end of the period I had them stop, and on the overhead I drew a 4x4 and a 3x1. I asked them what the area and the perimeter were for each. They could do it. Then I said, "Remember how you all said that area equaled length times width?" I heard a chorus of "Yeeeees," so I asked, "Is there a rule to find perimeter or do you always have to count?" "Hmmmmm."

Then it was time to move to the lab. I had them open a software program called Hands-On Math by Ventura Educational Systems which has geoboards in it. Along with the geoboards, which you can make shapes on, there is a side window with length, perimeter, and area noted as you draw the rectangle. I again posed the question about a rule for finding perimeter.

They all worked for a while and pretty soon a student raised his hand. I went over to him and he whispered, "If you have a square all you have to do is find the length of the side and then multiply by 4." I asked him if he would give that speech to the class.

I had all the students sit on the carpet in the middle of the room and the student gave his speech! Lately I have been giving out pencils when I have a question in the lab or task that I want to reward, and I heard someone say, "He will probably get a pencil for this." Instead of getting out a pencil, though, I went to my "prize bucket" where I had some notebook calculators (they are 3-hole punched so that you can put them in your notebook) and I rewarded him with one of those!

Now, I said, everyone has to go figure a rule for rectangles other than the special case of squares. After a while a pair of students said, "Well, don't you add the length and the width and then multiply by 2?" and I said, "can you give a speech?" And they said, "Yes."

After I called the kids back to the carpet and the pair of students gave their speech I gave them calculators too. They were quite pleased - and so was I!

### Evaluation:

1. Teacher observation during the group activity.
2. Each student turns in the centimeter grid paper with a sketch, area, and perimeter for each of the 10 rectangles.
3. Teacher observation during the computer activity.