Measuring Area

Est. Class Sessions: 1–2

Developing the Lesson

Describe and Measure Area. Start this lesson by reviewing the concept of area and ways to measure area of irregular shapes. Display the polygon you have already drawn on the Centimeter Grid Paper Master.

Ask:

What is the area of this figure?
What unit are you counting? (square centimeters)

Use a clear plastic ruler to measure each side of a square. Point out that the length of each side is one centimeter, so the area of the square is one square centimeter. When we measure area, we are measuring the amount of space that is covered by a shape.

Ask a student volunteer to count the area of the polygon in square centimeters. Emphasize how parts of square centimeters can be put together. See Figure 1 for a counting example.

Display one square-inch tile and measure each side of the square in inches. Remind students that each tile covers one square inch.

Ask:

About how many square-inch tiles will cover this polygon? (A rough estimate is appropriate. For the example in Figure 1, it will take about three square-inch tiles to cover the polygon.)
Did the area of the polygon change? (No, just the size of the unit. The number of square-inch tiles needed to cover the area of the polygon should be less than the number of square-centimeter tiles.)
Who would like to show the class how to find the area of the shape in square inches? Tell us what you are doing. (Cover the shape with square-inch tiles and count, putting fractional pieces together to equal one square inch.)

Ask students to look at the floor in the classroom.

Ask:

How can I find the area of the classroom floor? (Possible responses: Count the square tiles; lay square-inch tiles on the floor and count them; lay square pieces of paper on the floor and count them.)
What is the unit of measure? (Possible responses: tiles, square inches, squares)

Ask a small group of students to find the area of the classroom floor while the rest of the class listens as they work. Other students may help this small group with counting or keep track of partial floor tiles.

Ask:

How many floor tiles does it take to cover the floor in our classroom?
What did you do when you found pieces of tiles rather than whole tiles? (Put pieces together or find mates that add up to a whole when put together.)
What would it be like to count square-inch tiles to find the area of the classroom floor? (Possible response: It would take a long time because the unit is so small.)
Would the area of the floor change? (No, the area of the floor would not change. It would take a lot more square-inch tiles to cover the floor than floor tiles but the area would not change.)
Which unit of measure do you think is best to use when finding the area of the floor, square inches or floor tiles? (Floor tiles is more appropriate because we can make better sense of that number and it is easier to count.)

Refer students to the polygon you drew on Centimeter Grid Paper Master.

Ask:

Would floor tiles be a good unit to use for finding the area of this shape? (No, because the unit is larger than the shape. Square inches or square centimeters are more appropriate units of measure.)

Stress that even if the unit of measure changes, the area—the amount of surface to be covered—stays the same.

Find the Area of Professor Peabody's Living Room and Hall. Have students read the introduction to area on the Measuring Area pages in the Student Guide. Display and direct their attention to the picture and diagram that shows Professor Peabody laying tile on the floor of his living room and hall. Ask students to answer Check-In: Questions 1–6 as you circulate and observe students working.

Use Check-In: Questions 1–6 in the Student Guide to assess students' ability to find the area of shapes with straight or curvy sides by counting square units [E3]. Use these questions to guide your student observations:

Do students understand that area is the amount of surface to be covered?
Can students put pieces together to make whole units?
Are students starting to seek or use more efficient strategies (e.g., breaking up shapes into smaller shapes)?
Do students know to add the areas of each piece together to find the area of the entire floor?

Organize centers or choose one or two of the following activities to provide targeted practice:

Prepare the Putting Pieces Together Masters to provide practice with matching pieces of a square unit to approximate a whole.
Prepare the Make Your Own Shape Masters to provide practice with finding the area of shapes with curvy sides.
For students ready to find more efficient ways of finding area, ask them to revisit the Area of Five Shapes page from the Student Activity Book. Ask students to find shortcuts or more efficient ways to find the area.

In Question 2, students should see that Professor Peabody counted halves of tiles by “piecing” them together to make whole squares; thus, two squares can each be numbered with the same number to show that two halves together are one whole. Figure 2 shows how area can be counted this way.

In Question 3, students must help the professor calculate how many tiles he will need to cover the entire living room floor, the octagonal portion of the diagram. As shown in Figure 2, the area of the tiled portion of the living room floor is 32 tiles. Since the tiled and untiled portions are symmetrical, Professor Peabody will need an additional 32 tiles to finish the room. In Question 4, students are asked to find the area of the living room and hall.

Students may need assistance with piecing together the half squares in Shape B in Question 5. Ask a student to demonstrate their strategies for counting and keep tracking of putting pieces together using a display of Question 5.

Professor Peabody shows how he estimated the area of a shape with curved sides in Question 6. The procedure for finding the area of this shape is similar to that used in counting the area of polygons. See Figure 3. However, it will not be as easy to find appropriate matches to piece together into wholes. Emphasize that students will only be able to estimate the area of the curved shapes.

Student Guide: 99 100

Answers