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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

Give each student a 20″ string. Have them tie it in a circle. Have students make rectangles of various sizes: 2×8, 3×7, 4×6, etc. Point out all are 20″ in. perimeter. 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. 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

None

Related websites

N/A

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.
    • Objective 2.02: Solve problems involving perimeter/circumference and area of plane figures.

Grade 7

  • Goal 5: Algebra - The learner will demonstrate an understanding of linear relations and fundamental algebraic concepts.
    • Objective 5.04: Develop fluency in the use of formulas to solve problems.

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.
  • Goal 3: Geometry - The learner will understand and use properties and relationships in geometry.
    • Objective 3.02: Apply geometric properties and relationships, including the Pythagorean theorem, to solve problems.