## Framed

### Cindy Jacobs

#### Description

This lesson allows students to experiment with and calculate perimeter and area of given shapes.

#### Objectives

The student uses concrete and graphic models to develop procedures for solving problems related to measurement including length, weight, time, temperature, perimeter, area, volume, and angles.

#### Materials

- Grid Transparency Sheets for Overhead
- Grid Paper (One Per Child)
- One Inch Square Overhead Tiles

#### Preparations

2. Find or make overhead grid transparencies.
4. Gather enough grid paper for each of your students.

#### Procedures

This lesson only teaches and assesses perimeter and area.

1. Draw a large rectangle on one-inch unit grid transparency sheet on the overhead projector. (The rectangle's area will take up 20 square inch units with four or five rows.)

2. Tell students that this shape is a picture frame, and their help is needed to calculate the distance around the frame to determine its size. State to students that the distance around the frame is the perimeter. Write the definition of perimeter for the students to see.

3. Demonstrate by counting aloud with students the number of units to calculate the perimeter. Write this as a number sentence for the students to see.
Example: 4 + 5 + 4 + 5 = 18 inches

4. Ask students if there is a quicker way to calculate the perimeter of the rectangle without counting each side. Help students realize that if a side has a side of equal length, it is not necessary to have to count each individual unit. They can automatically calculate the length based on the calculation of the equal side. In this case, two sides have sides of equal length.
Example: 4 + 4 + 5 + 5 = 18 inches

5. Repeat above steps several times using rectangles and squares of different sizes. Allow students to assist with demonstrations.

6. Using the original transparency (rectangular model that has an area of 20 square inch units and has four rows and five rows), tell students that you are going to use this frame to frame a lovely tile picture. The students will pretend that each square unit inside the perimeter represents a tile. Cover each square unit with an overhead tile or shade with a colored overhead pen to emphasize. State that the number of tiles or shaded units (if using an overhead pen) inside the frame that covers that portion of the transparency makes up the area. Write the definition of area for students to see.

7. Figure the area by counting the number of tiles with the students.

8. Ask students the following questions:
A. How many rows of tiles are there? (Answer: 5 rows or 4 rows.)
B. How many tiles are in each row? (Answer: 4 tiles or 5 tiles.)
C. Is there an easier way to calculate area without having to count each individual tile?
Help students realize that they can create a multiplication sentence to calculate area.
Example: 4 x 5 = 20 square units

9. Do several more examples on the overhead to calculate area. Allow students to assist with demonstrations.

10. Review perimeter and area. Ask students to explain the difference between perimeter and area. Answer: Perimeter measures the distance around the outside of a shape. Area measures the square units that cover a particular figure.

11. Give each student a sheet of grid paper with one-inch square units.

12. Tell each student to draw two shapes on the grid paper. Each draws a large rectangle and square on the grid paper without looking at the shapes other students are drawing.

13. When finished, students will exchange papers with partners. Students calculate the perimeter and area of each other’s shapes, write a number sentence for the perimeter and area of each shape, and share their findings with their partners.

#### Assessments

NOTE: This lesson only teaches and assesses perimeter and area.
Completed grid sheets can be assessed on a mastery or non-mastery basis according to whether or not each student calculates the correct perimeter and calculates the correct area. Mastery and non-mastery can be informally based on observation of student participation and feedback while demonstrating examples, observing partners, and through the use of questioning techniques. Students who are having difficulty should receive feedback and additional monitored practice.

#### Extensions

1. Use paper clips to measure the perimeter of a figure, such as a book, paper, and desk.
2. Use color tiles or cubes to create shapes on grid paper, and then calculate the perimeter and area of these shapes.
3. Make a large rectangle or square on the floor using masking tape. Students estimate the number of sheets of paper needed to cover each shape. Discover and explore ways to test their predictions.