CCSS 6.G.A.1

Area Architect — Area of Polygons

What to do: Build a shape and find areas of polygons. Type each answer in the box. Then press Check My Work at the bottom.

Learning Target

Standard: CCSS 6.G.A.1 Estimated time: 30–40 min Materials: This activity, pencil/scratch paper
Teacher Notes & Pacing

Pacing

  • Whole class (5 min): Review the vocab box and the four area formulas together. Model Q2 (rectangle) as a think-aloud.
  • Partner or independent work (20–25 min): Students complete Q1–Q6. Circulate and prompt with "Which formula matches this shape?"
  • Debrief (5–10 min): Share Q5 (trapezoid) and Q6 (composite) strategies. Discuss why the height must be perpendicular.

Grouping

  • Works well as partner activity for Q1 (build a rectangle together, then each student answers Q2–Q6 independently).
  • For whole-class: display the build grid on a projector; call on students to click squares.

Differentiation — Support

  • Provide a printed formula reference card (b×h, ½bh, ½(b1+b2)h).
  • Allow students to draw the split lines on Q6 before calculating.
  • Pre-fill the first step: for Q4 ask "8 × 5 = ?" then "now take half."

Differentiation — Challenge

  • Ask students to create their own composite figure with a given total area (e.g., 48 units²).
  • Have students verify Q1 by proving the filled area is rectangular (equal rows & columns).
  • Extend Q6: "What if you removed a 2×2 square from a corner — what is the new area?"

ESOL / Language Supports

  • Key vocabulary is defined in the vocab box; point to it explicitly.
  • "Perpendicular height" — demonstrate with a right-angle corner; avoid "straight-up" if confusing.
  • Allow students to label diagrams in their home language before writing the numeric answer.
  • Pair sentence frames: "The base is ___ and the height is ___, so I multiply ___ × ___ = ___."
Area = number of square units inside a shape (units²).   Rectangle / Parallelogram: base × height.   Triangle: ½ × base × height.   Trapezoid: ½ × (base₁ + base₂) × height.
Progress: 0 of 6 answered

Build a rectangle with area 24 square units

Click squares to fill them. Build a rectangle that has exactly 24 filled squares. The counter shows your area.

Filled squares (your area): 0 units²

Find the area of the rectangle

Multiply base × height. Each grid square is 1 unit.

base = 9 height = 4
units²

Find the area of the parallelogram

Area = base × height. Use the straight-up height, not the slanted side.

base = 10 height = 6
units²

Find the area of the triangle

Area = ½ × base × height. Multiply, then take half.

base = 8 height = 5
units²

Find the area of the trapezoid

Area = ½ × (base₁ + base₂) × height. Add the two bases first.

base₁ = 6 base₂ = 10 height = 4
units²

Find the area of the L-shaped floor

Break the L into 2 rectangles. Find each area, then add them. Each square is 1 unit.

8 3 3 4

Top rectangle is 8 × 3. Bottom-left rectangle is 4 × 3. Add the two areas.

units²

Performance Rubric — Area of Polygons (6.G.A.1)

Score Level Descriptor
4 — Exceeds Expert Correctly applies all four area formulas (rectangle/parallelogram, triangle, trapezoid) and accurately decomposes the composite figure. Can explain the strategy used in Q6 and justify why the height must be perpendicular.
3 — Meets Proficient Correctly answers 5–6 of 6 problems. Applies the correct formula for each shape with at most one arithmetic error. Reflection shows understanding of the "break-apart" strategy for composite figures.
2 — Approaching Developing Correctly answers 3–4 of 6 problems. May confuse base × height with ½ × base × height, or incorrectly add the bases on the trapezoid. Q1 rectangle may not be a true rectangle (random cells filled).
1 — Beginning Emerging Answers 0–2 problems correctly. May not apply the correct formula, or may measure the slanted side instead of the perpendicular height. Needs direct instruction on area formulas and grid models.
Teacher Answer Key

Correct Answers

  1. Q1 — Build rectangle: Any true rectangle with exactly 24 filled cells. Accepted arrangements: 4×6, 6×4, 3×8, 8×3. Cells must form a solid rectangle (no gaps, no extra cells).
  2. Q2 — Rectangle: 9 × 4 = 36 units²
  3. Q3 — Parallelogram: 10 × 6 = 60 units² (use perpendicular height 6, not the slant side)
  4. Q4 — Triangle: ½ × 8 × 5 = ½ × 40 = 20 units²
  5. Q5 — Trapezoid: ½ × (6 + 10) × 4 = ½ × 16 × 4 = ½ × 64 = 32 units²
  6. Q6 — L-shape (composite): Top rectangle: 8 × 3 = 24. Bottom-left rectangle: 4 × 3 = 12. Total: 24 + 12 = 36 units²

Common Errors to Watch For

  • Q3: Students may multiply 10 × slant side. Ask them which measurement goes straight up.
  • Q4: Students may forget to take half (answer 40). Remind them ½ means divide by 2.
  • Q5: Students may forget to add the two bases before multiplying (e.g., ½ × 6 × 4 + 10 = 22). Emphasize the parentheses: add first.
  • Q6: Students may multiply the full bounding box 8×6=48 without subtracting the missing corner (48 − 12 = 36 also gives correct answer via subtraction method).
Deliverable: Complete all 6 problems and the reflection above, then press Check My Work. When your results appear, use Save as PDF or Save as DOC to submit your completed activity to your teacher.