Using the State Curriculum: Mathematics, Grade 3

light-colored string and dark marker
1-inch grid paper
8.5 × 11 student grid paper (for recording)

Provide pairs of students with a one inch grid and a loop of light-colored string 24 inches long. Mark each inch with a dark marker. In pairs, students should determine what different-sized rectangles can be made with the 24 inch perimeter. Students may record their rectangles on a separate sheet of grid paper and compare with other pairs of students (sample responses below).

Ask:

• Why is it possible to make many different rectangles with the same perimeter? [The perimeter will stay the same because the loop of string does not change size, so the distance around the rectangle never changes.]
• Was the area inside each rectangle the same? [No]
• Why not? [The area inside the rectangle can change, even if the perimeter does not, depending on the length and width of the rectangle. The longer you make two parallel sides, the narrower the shape becomes and the shorter the other two sides become, making the area inside the rectangle smaller. The more regular or equal the sides, the more equal the height and width of the shape making the interior, or area, larger.]
• Which has the smallest area? [The rectangle that is 1 × 11 has an area of 11 sq. inches.]
• Which has the largest area? [The square that is 6 × 6 has an area of 36 sq. inches.]

Students may independently determine three classroom objects that they estimate will have a perimeter of 24-inches, such as a textbook, computer monitor, or chair seat. Record their predictions.

Using the same piece of string, ask students to measure the actual objects.

Ask: Were their estimations correct? If not, is the actual perimeter larger or smaller than estimated? How can you tell?

Sample Response: The textbook cover was actually smaller than I predicted. I know it is smaller because when I measured using the loop of string, which represented a perimeter of 24-inches, the string was larger than the cover of the textbook.

Ask students to use a tape measure to determine the actual perimeter of the classroom object they used.

To extend this activity, provide students with a string of another length and repeat the activity.

Adapted from: Van de Walle, J.A. & Lovin, L.H. (2006). Teaching Student-Centered Mathematics, Grades 3-5 (Vol. 2). New York: Pearson Education