Mathematics · Year 5

Active learning ideas

Perimeter of Rectilinear Shapes

Active learning works for perimeter of rectilinear shapes because students must visualize and trace outer edges rather than rely on abstract rules. Physical manipulation of shapes and materials helps them see how internal lines do not contribute to perimeter, making the concept concrete before moving to abstract calculations.

• National Curriculum Attainment Targets
• KS2: Mathematics - Measurement

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Perimeter Challenges

Prepare four stations with rectilinear shapes on grid paper: simple rectangles, L-shapes, shapes with missing lengths, and composite figures. Students measure sides, calculate perimeters, and explain missing values using station worksheets. Groups rotate every 10 minutes, then share one key insight as a class.

Explain how to find the perimeter of a shape with missing side lengths.

Facilitation Tip

During Station Rotation, place a timer at each station and circulate with a clipboard to listen for students’ strategies, noting who uses addition efficiently and who still traces edges with fingers.

What to look for

Provide students with a worksheet featuring several rectilinear composite shapes, some with missing side lengths. Ask them to calculate the perimeter for each shape, showing their working. Check for accurate addition and correct identification of missing lengths.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Gallery Walk
• 30 min · Pairs

Design Challenge: Fixed Perimeter Builds

Provide multilink cubes or straws and ask pairs to build rectilinear shapes with exactly 24 units perimeter. They sketch designs, measure to verify, and label side lengths. Pairs present one shape and justify how they achieved the target.

Design a rectilinear shape with a perimeter of 24 cm.

Facilitation Tip

For the Design Challenge, provide grid paper and rulers, and explicitly remind students that internal edges do not count toward perimeter before they begin building.

What to look for

Present students with a square and a rectangle that have the same area (e.g., a 4x4 square and an 8x2 rectangle, both area 16). Ask: 'Which shape has the larger perimeter? How do you know?' Facilitate a discussion comparing their findings and reasoning.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 03

• Gallery Walk
• 25 min · Pairs

Puzzle Pairs: Missing Lengths

Give pairs cards with rectilinear shapes showing some lengths and totals. They deduce missing sides by adding known parts or using opposites equal. Switch puzzles midway and discuss strategies whole class.

Compare the perimeter of a square with a rectangle that has the same area.

Facilitation Tip

In Puzzle Pairs, give each pair two identical composite shapes cut from paper so they can physically overlap them to find missing lengths before calculating.

What to look for

Give each student a card with the instruction: 'Design a rectilinear shape with a perimeter of 20 cm. Draw it and label all side lengths.' Collect the drawings to assess their ability to create a shape meeting the specified perimeter.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 04

• Gallery Walk
• 35 min · Whole Class

Compare and Sort: Whole Class Relay

Display rectangles and squares with same areas on board. Teams race to calculate perimeters, sort shapes by perimeter size, and explain why the square has the smallest. Debrief patterns observed.

Explain how to find the perimeter of a shape with missing side lengths.

What to look for

Provide students with a worksheet featuring several rectilinear composite shapes, some with missing side lengths. Ask them to calculate the perimeter for each shape, showing their working. Check for accurate addition and correct identification of missing lengths.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Teaching perimeter of rectilinear shapes benefits from a progression from physical to visual to symbolic. Start with hands-on building using grid paper or straws to trace perimeters, then move to drawn shapes with labeled sides. Avoid rushing to formulas; instead, encourage students to verbalize their steps to uncover gaps in understanding. Research shows that students who explain their process aloud catch errors earlier and retain strategies longer.

Students will confidently identify outer edges, break down composite shapes into rectangles, and calculate perimeters accurately. They will explain their reasoning using terms like equal opposite sides and missing lengths, showing clear work for both simple and complex figures.

---

Watch Out for These Misconceptions

• During Station Rotation: Perimeter Challenges, watch for students who add all sides, including internal edges, when measuring composite shapes.

  Direct students to use a colored pencil to trace only the outer path on their shape templates, then count the edges they colored to highlight that internal lines do not count.

• During Puzzle Pairs: Missing Lengths, watch for students who assume all opposite sides are equal without checking parallel alignment.

  Have pairs physically overlap their two identical puzzle shapes, then slide one to verify side equality before labeling; prompt them to explain why some matches work and others don’t.

• During Compare and Sort: Whole Class Relay, watch for students who believe rectangles with the same area must have the same perimeter.

  After sorting physical models, ask students to measure each shape’s perimeter and record data on a class chart, then lead a discussion on why longer, thinner rectangles have larger perimeters.

---

Methods used in this brief

• Stations Rotation
• Gallery Walk