OLD Resources. The resources on this page have NOT yet been updated to align with the revised elementary mathematics TEKS. These revised TEKS were adopted by the Texas State Board of Education in 2005, with full implementation scheduled for 2006–07. These resources align with the original TEKS that were adopted in 1998 and should be used as a starting point only.

Clarifying Lessons

Grade 3: What Can I Make with 30 Centimeters?

Lesson Overview

Students compare shapes with perimeters of 30 centimeters by categorizing them and looking for patterns.

Mathematics Overview

Students create polygons with perimeters of 30 centimeters, use the centimeter grid paper to determine the area of each shape, and organize the shapes to make generalizations from the patterns they see.

Set-up (to set the stage and motivate the students to participate)

  1. Give students square tiles and have them build a flat shape. Have students discuss the perimeter and area of their shapes. (3.11A, B, C)
  2. Challenge students to build a flat shape with a perimeter of 16 units (where a unit is equal to the length of the side of one of the square tiles). Discuss the areas of the different shapes made. Bring students to the conclusions that different shapes can have the same perimeter, and shapes with the same perimeters can have different areas. (3.11A, B, C; 3.17A)
  3. Pass out centimeter grid paper and ask students to find as many shapes as possible that have perimeters of 30 units. Discuss the need to follow the lines on the grid paper in making the figures in order to be able to measure the perimeter easily. (3.11B, 3.13, 3.15D)
  4. Have students post their shapes in a display area. (3.15B, D)
  5. Have the class organize the displayed shapes in various ways, such as from least area to greatest area, and discuss patterns they see. (3.11A, B, C; 3.15B, D; 3.17A)

Teacher Notes (to personalize the lesson for your classroom)

Guiding Questions (to engage students in mathematical thinking during the lesson)

  • How do you know the perimeter of this shape is 30 units? (3.11A, B)
  • Are you using the same number of squares (same area) each time to make a shape with a perimeter of 30 units? (3.11C)
  • What strategies are you using to find your shapes? (3.13; 3.15B, D)
  • What patterns have you found in the shapes? (3.17A)

Teacher Notes (to personalize the lesson for your classroom)

Summary Questions (to direct students' attention to the key mathematics in the lesson)

  • How is perimeter measured? (3.11A, B)
  • How is area measured? (3.11C)
  • What techniques could you use to change a shape to increase its area while keeping the perimeter the same? (3.13; 3.15B, D)
  • What techniques could you use to decrease a shape's area while keeping the perimeter the same? (3.13; 3.15B, D)
  • Do all the shapes with perimeters of 30 centimeters have the same area? (3.11A, B, C; 3.13; 3.17A)
  • Do some of them have the same area? (3.11A, B, C; 3.13; 3.17A)
  • What is similar about the shapes with the smallest area compared to the shapes with the largest area? (3.13, 3.17A)
  • What statements could you make about using a certain perimeter to enclose the smallest area? The largest area? (3.13, 3.17A)
  • What strategies did you use to find shapes with perimeters of 30 centimeters? (3.13; 3.15B, D)
  • Did looking for patterns help you solve the problem? If so, how? (3.17)

Teacher Notes (to personalize the lesson for your classroom)

Assessment Task(s) (to identify the mathematics students have learned in the lesson)

  • Have students record their summary statements in a journal.
  • Have students write a description of the activity and what they learned from it.
  • Have students make a shape on the grid paper that has a perimeter of 42 centimeters and encloses the most (or least) area. Students should justify their choice of shape.

Teacher Notes (to personalize the lesson for your classroom)

Extension(s) (to lead students to connect the mathematics learned to other situations, both within and outside the classroom)

Students can investigate questions such as: Can you make your initials with a 30-centimeter perimeter? On the grid paper? What if you had a piece of string 30 centimeters long? If you had a piece of string 30 centimeters long, how could you use it to find shapes with 30-centimeter perimeters? Would you still have to follow the lines on the grid paper? Find some other shapes using the string.

Teacher Notes (to personalize the lesson for your classroom)