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Lesson plan Grade 3 Math

Redstone Creek's Rain Garden Border: A Perimeter Lesson

A grade 3 math lesson where students find the perimeter of a rain garden that catches roof runoff, then compare two garden shapes that share a perimeter.

Objectives

  1. Students will calculate the perimeter of a rectangular rain garden given its side lengths.
  2. Students will find a missing side length when given the perimeter and the other three sides.
  3. Students will compare two rain garden designs that share the same perimeter but enclose different areas.

Vocabulary

Key words: perimeter, rectangle, side length, runoff

Teacher overview

The fictional Redstone Creek Elementary is building a rain garden next to the cafeteria to catch water running off the roof before it reaches the storm drain. The garden bed needs a stone edging border around its outside, and the school wants to know how many one-foot edging stones to order. A common misconception in this lesson is that students count only two sides of a rectangle instead of all four, or forget that opposite sides of a rectangle are equal length when a side measurement is missing; the guided practice is built to surface and correct that error directly.

Procedure

Hook (5 min): Show the chart-paper diagram of Redstone Creek's planned rain garden: a rectangle 8 feet long and 5 feet wide. Ask students to estimate, without calculating, about how many one-foot edging stones would go all the way around it.

Direct instruction (10 min): Model finding the perimeter by tracing all four sides on the diagram: 8 + 5 + 8 + 5 = 26 feet, so the school needs 26 one-foot edging stones. Show a second rain garden design, 10 feet long and 3 feet wide, and find its perimeter the same way: 10 + 3 + 10 + 3 = 26 feet. Ask: both gardens need the same number of edging stones, so are they the same size? Guide students to see that the first garden's area (8 × 5 = 40 square feet) is larger than the second garden's area (10 × 3 = 30 square feet), even though the perimeters match.

Guided practice (15 min): In pairs, students work with a rain garden design that has a total perimeter of 24 feet. Two of its sides are already labeled 7 feet each. Students find the length of the two missing (equal) sides: 24 − 7 − 7 = 10, and 10 ÷ 2 = 5 feet each. Pairs then compare this garden's area (7 × 5 = 35 square feet) to a square garden with a side length of 6 feet (perimeter 24 feet, area 36 square feet), confirming again that equal perimeters do not mean equal areas.

Independent practice (10 min): Each student solves two problems on the handout: (1) find the perimeter and area of a square rain garden with a side length of 6 feet, and (2) find the perimeter of a rectangular garden that is 9 feet long and 4 feet wide, then compare its area to the square garden's area from problem 1.

Closure / exit ticket (5 min): Students answer one problem on an index card: a small rectangular rain garden needs 20 feet of edging in total, and one side already measures 6 feet. What is the length of the side next to it? Collect the cards and check whether students correctly divided the remaining perimeter by 2 for the two unknown equal sides.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

  1. Answer: 24 feet perimeter, 36 square feet area.
    A square with side length 6 feet has perimeter 6 + 6 + 6 + 6 = 24 feet and area 6 × 6 = 36 square feet.

  2. Answer: 26 feet perimeter.
    A 9-foot by 4-foot rectangle has perimeter 9 + 4 + 9 + 4 = 26 feet. Its area, 9 × 4 = 36 square feet, is the same as the square garden's area even though its perimeter (26 feet) is larger than the square's perimeter (24 feet), which shows the same area can come with a different perimeter.

  3. Exit ticket answer: 4 feet.
    The total perimeter is 20 feet and one known side is 6 feet. Since a rectangle has two pairs of equal sides, 20 − 6 − 6 = 8 feet remains for the two unknown equal sides, so each one is 8 ÷ 2 = 4 feet.

Differentiation

Support (below grade level)

Provide a diagram with all four sides of each rectangle already labeled with tick marks, and let students find the perimeter by counting tick marks and adding, rather than working from only two given side lengths. Allow a calculator for the division step in the guided practice.

Extension (above grade level)

Ask students to design their own rain garden rectangle with a perimeter of exactly 28 feet, then find its area. Have them compare their design's area to a classmate's different rectangle that also has a 28-foot perimeter, and write one sentence explaining which shape (closer to a square or closer to a long strip) tends to enclose more area.

ELL supports

Pre-teach "perimeter," "side," and "border" using a physical string or yarn model: lay string around the outside of a taped rectangle on the floor or a desk, cut it to length, and measure the string afterward. Allow students to label diagrams with numbers and tick marks instead of writing full sentences for the guided-practice comparison.

Extensions

Have students measure the perimeter of an actual garden bed, sandbox, or planter on the school grounds using a tape measure, then calculate how many one-foot edging stones or bricks it would take to border it, connecting the classroom math to a real measurement task.