This lesson is designed to further students’ concept of area and measurement skills. One of the goals is to recognize that all measurement is approximate. As they compare their results with others there will be differences. This would be a good time to talk about errors inherent in measurement. Students will also combine data and calculate mean and median.

#### Objectives

- We will be able to measure accurately in centimeters.
- We will be able to calculate and compare areas.
- We will be able to compare areas using fractions.

#### Assessment

- Participation in class discussions
- Step worksheet
- Area of a Square worksheet
- Students’ use of rulers
- Ability to fill out a table

#### Time Required

1 hour

## Materials/Resources Needed

- Document camera/projector
- Art images (linked below in the activities)
- Activity pages (1–3)
- Centimeter rulers
- Paper
- Pencil

## North Carolina Curriculum Alignment

## Activity One: Step

**NOTE:** *All pages referenced below are linked above in Materials/Resources Needed as “Activity pages.”*

- Project
*Step*by Kenneth Nolan and hand out the Step worksheet (activity page 1). Before discussing, ask students to list what they see in the artwork (types of colors, lines, shapes, etc.) and how they interpret the artwork (what the artist is trying to communicate to the viewer, how it was made, etc.) - Share ideas as a class and discuss the artwork further. If students don’t suggest it on their own, ask if they can see the artwork as five squares placed on top of each other diagonally from smallest (bottom right) to largest (top left). Have students write down any ideas that classmates share that they didn’t already write down themselves. Collect papers.

## Activity Two: Area of a Square

**NOTE:** *All pages referenced below are linked above in Materials/Resources Needed as “Activity pages.”*

- Provide students with Area of a Square worksheet and a reproduction of Kenneth Nolan’s
*Step*(activity pages 2–3). Ask students to look at*Step*closely. Ask students to think of the image as five squares placed on top of each other (as you discussed in Activity One). Then, students will measure the length of sides of the five squares that are layered on top of each other and record their findings in the table on activity page 2. They should measure to the nearest tenth of a centimeter. - Students will then calculate the area of each square and record this information in their table.
- Once they have measurements, students will calculate the percentage of the largest square covered by the smallest square. Repeat this with each of the other three squares. Data should be recorded in their table.
- As a class, compare students’ results. Have a whole class discussion about the results obtained. One question that might arise is why the area increases so much faster than the length of side.
- Students will then find the mean and median area for each square. Median works better than average (mean) since a score that is way off could result in less representative numbers.
- Students will complete the exercise by calculating the ratio of the lengths of sides and the areas of the darkest colored square to the largest square. Discuss with the students any patterns they discover when comparing these calculations.