Eco-Friendly City Metrics

Overview

In this first lesson of a two-day unit, students begin to understand area and perimeter using rectangles and grids connected to building an eco-friendly city. They will practice finding perimeter by counting lengths and finding area by counting unit squares, laying groundwork for later real-world problems.

Learning intentions

• Students will be able to use a coordinate plane to locate points in the first quadrant to plan positions for building features.
• Students will be able to describe the difference between area and perimeter in context.
• Students will be able to calculate perimeter of right rectangular shapes with whole-number side lengths.
• Students will be able to calculate area of right rectangular shapes by counting or using multiplication with whole-number side lengths.

Success criteria

• I can explain that perimeter is the distance around a shape.
• I can find the perimeter of a rectangle by adding side lengths.
• I can find the area of a rectangle by counting unit squares or using a multiplication fact.
• I can interpret points on a coordinate plane as locations tied to a city-planning scenario.

Curriculum links

• Geometry: Use a coordinate system with axes and ordered pairs.
• Geometry: Graph points in the first quadrant and interpret coordinate values in context.
• Geometry: Understand relationships within a category of 2D figures (rectangles and squares) to connect side lengths and right angles.
• Measurement: Connect area/perimeter to real-world problem solving by using right rectangular prism volume formulas as a later extension reference for “length × width × height” thinking (CCSS.MATH.CONTENT.5.MD.C.5b).

Lesson structure (30 minutes)

1. 0–5 min · Hook (City Design Prompt). Teacher shows a simple “city block” rectangle on a grid and asks: “If we walk around the outside of this block, what are we measuring?” Students think-pair-share and write one sentence: “Perimeter is…” and one sentence: “Area is…”

2. 5–10 min · Mini-direct teach: Perimeter vs. Area. Teacher draws a rectangle with labeled side lengths (whole numbers) and highlights the “walk around” path in one color and the “cover the surface” region in another. Students repeat and complete a quick template: “Perimeter measures ____. Area measures ____.”

3. 10–16 min · Guided practice: Perimeter on grids. Teacher presents three rectangles on grid paper (or on a slide): e.g., 2×5, 3×4, 1×6 (side lengths are whole numbers). Students, for each rectangle, calculate perimeter by adding side lengths (4 sides), and they check by verifying the top+bottom equals left+right.

4. 16–21 min · Coordinate plane quick connection (placing buildings). Teacher draws coordinate axes with the origin labeled at 0 and reminds: “First number tells how far from the origin along the x-axis; second number tells along the y-axis.” Students locate 2–3 points given as ordered pairs in the first quadrant (for example, (2,3), (4,1), (1,5)) on a blank grid and place small “buildings” at those locations.

5. 21–27 min · Guided practice: Area for right rectangles. Teacher displays one rectangle from earlier (choose 3×4 for clarity). Students count unit squares and then express area as a multiplication sentence: area = length × width. Students compute area for the remaining rectangles from step 3 and record answers as “___ square units” (or “square units” with a consistent unit label).

6. 27–30 min · Exit check and wrap. Teacher hands out or displays one final rectangle (e.g., 2×7). Students answer two prompts: “Perimeter =?” and “Area =?” Teacher collects or reviews quickly and previews that tomorrow students will apply these ideas to multi-step city design tasks.

Resources

• Grid paper and pencils
• Colored pencils or markers (one color for perimeter path, one for area region)
• Small printed rectangles with whole-number side lengths (or slide deck images)
• Coordinate plane worksheet (first quadrant only)
• Exit ticket (one rectangle with labeled dimensions)
• Optional: sticky notes for placing “buildings” at coordinates

Assessment

• Teacher observes in steps 3 and 5: Are students adding the correct sides for perimeter? Are they counting unit squares correctly or using correct multiplication?
• Listen for misconceptions during step 2 (students confusing area and perimeter) and address immediately.
• Exit ticket: check both perimeter and area accuracy for one right rectangle.

Differentiation

• Support: Provide a perimeter sentence frame (“Perimeter = __ + __ + __ + __”) and an area sentence frame (“Area = __ × __ = __ square units”).
• Support: Offer a partially completed coordinate plane grid with the origin and axes already drawn.
• Extension: If students finish early, challenge them to create their own rectangle with whole-number sides, then compute perimeter and area and label it with at least one coordinate point inside the first quadrant.
• EAL/SEN: Use consistent visuals and keep vocabulary tight: “around = perimeter,” “cover = area,” and “x first, then y.”