Area Perimeter Showcase

Overview

Students apply their understanding of area, perimeter, multiplication, fractions, and measurement to design, model, solve, and explain a rectangle-based challenge. As the final lesson in “Build, Model, Solve,” students collaborate on a performance task, present their reasoning, and reflect on strategies used across the unit.

Learning intentions

Students will be able to:

• Use square units and formulas to find the area of rectangles.
• Find the perimeter of rectangles and explain how it differs from area.
• Build, represent, and solve a multi-step measurement problem.
• Present a mathematical model and justify their solution using equations and words.

Success criteria

• I can tile or draw a rectangle and label its dimensions in units.
• I can use multiplication to find area and addition or a formula to find perimeter.
• I can solve a multi-step problem and show my work clearly.
• I can explain how my model proves that my answer makes sense.

Curriculum links

• Measurement and Data — apply area and perimeter formulas for rectangles using standard units.
• Operations and Algebraic Thinking — solve multi-step and multiplicative comparison problems with equations and an unknown.
• Number and Operations in Base Ten — use place value, multiplication, division, and computation strategies accurately.
• Number and Operations—Fractions — represent fractional parts of a whole and use equivalent fractions where appropriate.

Lesson structure (60 minutes)

1. 0–7 min · Hook and retrieval. Teacher opens the introduction and retrieval slides and displays two rectangles with the same perimeter but different areas. Ask, “Can shapes have the same perimeter but different areas?” Students estimate, turn and talk, then recall the meaning and units of area and perimeter. Invite two students to share contrasting ideas.

2. 7–17 min · Model the mathematics. Teacher uses the slides and a rectangle made from square tiles to model area as the number of square units inside a shape and perimeter as the distance around it. Record (A = l \times w) and (P = l + w + l + w), then connect this to (P = 2l + 2w). Students build a 4-by-6 rectangle, label its dimensions, calculate its area and perimeter, and explain why the answers use different units.

3. 17–25 min · Guided investigation. Teacher distributes the Build, Model, Solve performance-task recording sheet and provides geoboards and bands. Use the slides to present the challenge: “Design a rectangle with an area of 24 square units. Find its perimeter. Then design a different rectangle with the same area and compare the perimeters.” Students work with a partner to build at least two rectangles, record dimensions, and use equations to verify both answers.

4. 25–43 min · Collaborative performance task. Teacher forms groups of four, assigns roles using the group role cards, and displays the task directions on the investigation and showcase instruction slides. Each group completes one design challenge: create a small park or garden represented by a rectangle, with a total area between 24 and 48 square units; include a path or section described as a fraction of the whole; calculate the area and perimeter; and solve one additional multi-step question such as the cost of fencing or the number of equal rows of tiles. Students build or draw the model, label all measurements, write equations, check computations, and prepare a one-minute explanation. Encourage students to use multiplication, division, and fraction representations accurately.

5. 43–54 min · Math showcase. Teacher organizes a gallery walk or three-minute presentation rotation. Groups display their models and explain their dimensions, area, perimeter, fraction section, and multi-step solution while classmates use the slides’ prompts: “What does this number represent?” and “How do you know the model and equation agree?” Students present, ask one clarifying question, and record one strategy or representation they noticed from another group.

6. 54–60 min · Reflection and exit assessment. Teacher displays the reflection and exit slides and posts the reflection prompts poster. Students complete the final section of the worksheet: find the area and perimeter of a 7-by-3 rectangle, explain the difference between the two measurements, and describe one strategy that helped their group solve the task. Collect responses and invite a few students to share.

Resources

• the Build, Model, Solve lesson deck
• the Build, Model, Solve performance-task recording sheet
• Geoboards and rubber bands
• Square tiles or grid paper
• Pencils, colored pencils, rulers, and chart paper
• Calculators for selected students who need computation support
• the group role cards
• the reflection prompts poster

Assessment

• During modeling, check whether students distinguish the inside measurement of area from the distance around a shape and use correct square and linear units.
• During group work, question students about how their dimensions, model, equations, fraction section, and multi-step solution connect. Use the recording sheet to assess accuracy and reasoning.
• Use the final rectangle problem and written reflection as an individual exit check. Look for correct formulas, labeled units, a valid explanation, and evidence that the student can distinguish area from perimeter.

Differentiation

• Support students with pre-drawn grids, square tiles, a formula reference, color-coding for length and width, and sentence starters such as “The area is ___ because…” and “The perimeter is different because…”
• Provide rectangles with one dimension given for students who need a reduced entry point; allow students to explain orally before recording written reasoning.
• Pair multilingual learners with supportive peers and explicitly model terms such as inside, around, length, width, square units, and equivalent. Use gestures and labeled visuals during directions.
• Extend ready students by asking them to find all rectangles with an area of 36 square units, compare their perimeters, or create two different designs with equal perimeter but different areas. Encourage them to justify whether their design is most efficient and why.