LESSON PLAN

Perimeter of Complex Shapes

Apothem Team

Grade 6 · Measurement

LESSON AT A GLANCE

Warm-up

5 min

Explore

15 min

Formalize

10 min

Practice

12 min

Exit ticket

3 min

Warm-up

Give a simple L-shape with 4 sides labeled. Students add them up quickly.

Explore

Students work with L-shapes and T-shapes on grid paper. Some sides are labeled; others must be deduced. Try both methods: counting all sides, and decomposing into rectangles.

Formalize

Record the key idea: When a side isn't labeled, use the fact that opposite sides of a rectangle are equal. For an L-shape, the missing sides can be found by subtraction or by recognizing rectangle properties.

Perimeter of Complex Shapes = Sum of all outer edges. Use decomposition to find missing side lengths.

Show the two approaches side by side. Both work; choose what feels natural for the shape.

Practice

Students find perimeter of 4–6 complex shapes on grid paper. Exit ticket: one L-shaped or T-shaped figure with missing labels.

Exit ticket

Students find perimeter of 4–6 complex shapes on grid paper. Exit ticket: one L-shaped or T-shaped figure with missing labels.

TIP Emphasize decomposition early. Many students find it easier than trying to count all the sides at once.

WORKED EXAMPLES

An L-shape has outer dimensions 8 cm by 5 cm, with an inner cutout of 3 cm by 2 cm. Find the perimeter.

Trace around the outside: 8 + 2 + 3 + 2 + 5 + 3 = 23 cm (or decompose into two rectangles and add their outer edges).

MATERIALS

•Grid paper

•Rulers

•Colored pencils

•L-shaped or T-shaped templates

WATCH FOR

!Forgetting that missing side lengths can be deduced from the shape's structure.

!Confusing perimeter (distance around) with area (space inside).

!Counting an inner edge when only the outer perimeter is needed.