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K–12 teaching and learning · from the UNC School of Education

Discovering perimeters

By using string, students will discover a formula for finding the perimeter of a rectangle.

A lesson plan for grades 6–12 Mathematics

By Jenny Crumpler

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Learning outcomes

Students will perform and analyze measuring exercises to develop the formula for finding the perimeter of any given rectangle.

Teacher planning

Time required for lesson

1.5 hours

Materials/resources

  • String for each student
  • Scissors
  • Rulers
  • Overhead chart for students to record data

Technology resources

  • overhead projector
  • calculators at the discretion of the teacher

Pre-activities

Geometric definitions appropriate to students’ prior learning for the following terms:

  • rectangle
  • square
  • perimeter

Activities

  1. Give each student a 20″ string. Have them tie it in a circle.
  2. Have students make rectangles of various sizes: 2×8, 3×7, 4×6, etc. Point out all are 20″ in. perimeter.
  3. Give each student a ball of yarn and let them cut their own strings to whatever length they desire. Let each student make various rectangles with their string—recording length, width, and perimeter on the chart provided.
  4. Have each student answer the questions provided, sharing their answers in groups at the teacher’s discretion. Questions can be altered or adjusted for younger students. Help students condense w+w+l+l=perimeter to 2w+2l=perimeter to 2(w+l)=perimeter

Assessment

Give students a worksheet with pre-drawn rectangles so they can compute perimeter, give dimensions only and have students compute perimeter from the formula, and give the perimeter and one side and have students find the remaining side.

Supplemental information

Comments

My main inspiration came from the fact that some of my students knew about perimeters but could not find the value of perimeters when given dimensions.

North Carolina curriculum alignment

Mathematics (2004)

Grade 6

  • Goal 2: Measurement - The learner will select and use appropriate tools to measure two- and three-dimensional figures.
    • Objective 2.01: Estimate and measure length, perimeter, area, angles, weight, and mass of two- and three-dimensional figures, using appropriate tools.

Grade 8

  • Goal 2: Measurement - The learner will understand and use measurement concepts.
    • Objective 2.01: Determine the effect on perimeter, area or volume when one or more dimensions of two- and three-dimensional figures are changed.

Grade 9–12 — Geometry

  • Goal 2: Geometry and Measurement - The learner will use geometric and algebraic properties of figures to solve problems and write proofs.
    • Objective 2.03: Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs:
      • Triangles.
      • Quadrilaterals.
      • Other polygons.
      • Circles

Grade 9–12 — Integrated Mathematics 1

  • Goal 1: Number and Operations - The learner will perform operations with numbers and expressions to solve problems.
    • Objective 1.02: Use algebraic expressions, including iterative and recursive forms, to model and solve problems.
  • Goal 2: Geometry and Measurement - The learner will use properties of geometric figures to solve problems.
    • Objective 2.01: Use the length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

Grade 9–12 — Introductory Mathematics

  • Goal 2: Geometry and Measurement - The learner will use properties and relationships in geometry and measurement concepts to solve problems.
    • Objective 2.01: Determine the effect on perimeter, area or volume when one or more dimensions of two- and three-dimensional figures are changed.

Grade 9–12 — Technical Mathematics 1

  • Goal 2: Geometry and Measurement - The learner will measure and apply geometric concepts to solve problems.
    • Objective 2.03: Use the length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

  • Common Core State Standards

    • Mathematics (2010)

      • Grade 6

        • Expressions & Equations
          • 6.EE.7Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

        • Grade 7

          • 7.EE.4Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x...