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Unit 5 · HyperDoc

Area of Polygons

Standard 6.G.A.1 — Find the area of rectangles, triangles, and shapes you can break apart. Work through each step. Type your name in the box before you start.

📌 Learning Target

I can…

  • Find the area of a rectangle using base × height.
  • Find the area of a triangle using (base × height) ÷ 2.
  • Break apart a composite figure into rectangles and/or triangles and add their areas.
📐 Standard: 6.G.A.1 ⏱ Est. time: 45–55 min 📦 Materials: pencil, calculator (optional)
Teacher Notes — Unit 5 (click to expand)

Pacing

Engage 5 min · Explore 10 min · Explain 8 min · Apply 15 min · Reflect 8 min. Total ≈ 46 min. Can be split across two 25-min sessions.

Grouping

Explore in pairs (shared device). Apply and Reflect independently. Share reflections with a partner before submitting.

Differentiation — Support

  • Provide a formula card (base × height; ÷ 2 for triangles).
  • Allow graph-paper sketches for Q4 (composite figure).
  • Read questions aloud for students who need it.

Differentiation — Challenge

  • Ask: Can you find the area of a parallelogram? A trapezoid? How?
  • Extension: Design your own composite figure and compute its area.

ESOL / Language Supports

  • Key vocabulary is pre-taught in the Explain section with visuals.
  • Sentence frames for Reflect: "To find the area I… first I…, then I…"
  • Allow L1 drafts of reflections, then translate.
  • Highlight cognates: area → área, rectangle → rectángulo.
Step 1 · Engage

Think First

You are an Area Architect. You must cover a gold floor with tiles. No gaps. No tiles on top of each other.

Big question: How many square tiles fit inside a shape? That number is the area.

Area is measured in square units, like square meters (m²).

Step 2 · Explore

Play and Look

Open these. Build, watch, and read about area.

Step 3 · Explain

How It Works

Area — the space inside a flat shape. Use square units.
Base (b) — the bottom side you measure.
Height (h) — how tall the shape is, straight up.
Composite — a shape made of smaller shapes joined together.

Rectangle: Area = base × height

A rug is 6 m long and 4 m wide. Area = 6 × 4 = 24 m².

Triangle: Area = (base × height) ÷ 2

A flag has base 8 m and height 5 m. Area = (8 × 5) ÷ 2 = 40 ÷ 2 = 20 m².

Composite (break it apart):

Cut an L-shape into two rectangles. Find each area, then add them together.

Step 4 · Apply

Your Turn — Solve

Answer all 6. Type numbers only (no units). Then press Check My Work at the bottom.

Quick Check — check yourself before the big submit:

SC1. A rectangle has base 5 m and height 4 m. What is its area?

SC2. A triangle has base 6 m and height 4 m. What is its area?

SC3. An L-shape is cut into two rectangles: 3 m × 2 m and 4 m × 5 m. What is the total area?

1. A rectangle has base 7 m and height 3 m. What is the area?

Area = base × height. Type the number of square meters.

2. A square tile floor is 9 m on each side. What is the area?

A square has equal sides. Area = side × side.

3. A triangle has base 10 m and height 6 m. What is the area?

Area = (base × height) ÷ 2.

4. An L-shape is made of two rectangles. One is 5 m × 4 m. The other is 3 m × 2 m. What is the total area?

Find each rectangle's area, then add them.

5. Which formula finds the area of a triangle?

6. A garden is 12 m by 5 m. You cover it with 1 m × 1 m square tiles. How many tiles do you need?

Number of unit squares = area. Type the number.

📊 Rubric

Level Score What it looks like
4 — Exceeds 6/6 All areas and composite figures correct. Reflections show deep understanding of the process and explain why formulas work.
3 — Meets 4–5/6 Most areas correct. May make a minor arithmetic slip. Composite figure method is sound. Reflections are complete.
2 — Approaching 2–3/6 Can find area of rectangles but struggles with triangles or composites. Reflections are brief or incomplete.
1 — Beginning 0–1/6 Confuses perimeter with area, or applies formulas incorrectly. Needs re-teaching of core concepts.
Answer Key (teacher only)
  1. Q1: 7 × 3 = 21 m²
  2. Q2: 9 × 9 = 81 m²
  3. Q3: (10 × 6) ÷ 2 = 60 ÷ 2 = 30 m²
  4. Q4: (5 × 4) + (3 × 2) = 20 + 6 = 26 m²
  5. Q5: (base × height) ÷ 2 (option c)
  6. Q6: 12 × 5 = 60 tiles
  7. SC1: c — 20 m²
  8. SC2: b — 12 m²
  9. SC3: a — 26 m²
Step 5 · Reflect

Think About It

Write 2–4 sentences for each prompt below. Use math vocabulary (area, base, height, composite). Your reflections are saved in your PDF/DOC and count toward your grade.

Deliverable: Complete both reflections, then press Check My Work above and submit your PDF or DOC to the class folder.

When you are done: scroll up to the name bar and press Save as PDF or Save as DOC to turn in your HyperDoc.