6.GR.1 Lesson 5-4-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.4 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Area of Composite Figures · Composite Figure · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do we find the area of a composite figure?
1Break the figure into simple shapes. ADD the areas when shapes are joined; SUBTRACT when a piece is cut out.
  • A composite figure is a shape made of two or more simple shapes joined together. We decompose it into basic shapes, find each area, then add or subtract. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me
  1. My L-shaped room splits into two rectangles: one is 12 ft by 8 ft, the other is 6 ft by 5 ft.
  2. First rectangle: A = length × width = 12 × 8 = 96 square feet.
  3. Second rectangle: A = 6 × 5 = 30 square feet.
  4. The pieces are joined, so I add: 96 + 30 = 126.
  5. So the total area is 126 square feet.
3Mathematical Word Bank
  • Area of Composite Figures (Área de figuras compuestas) — The total space inside a figure made of basic shapes. Formula: A = A₁ + A₂ — add the parts (or subtract a missing piece).
  • Composite Figure (Figura compuesta) — A shape made by putting two or more simple shapes together.
  • Decompose (Descomponer) — To break a shape into smaller, simpler shapes.
  • Add (Sumar) — Add up the areas of the smaller shapes to get the total.
  • Subtract (Restar) — Take away the area of a missing piece from a bigger shape.
  • Formula (Fórmula) — A math rule written with symbols.
4Watch out
  • A common mistake in Area of Composite Figures is adding every piece even when a piece has been cut out of the figure. For a 10 ft by 8 ft rectangle with a 3 ft by 2 ft rectangular notch cut from one corner, students compute the full rectangle 10 × 8 = 80 sq ft and stop, or they add the notch instead of removing it (80 + 6 = 86 sq ft) instead of subtracting it: 80 − (3 × 2) = 80 − 6 = 74 sq ft. Before submitting, check whether each piece is part of the figure (add it) or missing from the figure (subtract it).
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A 7 ft by 5 ft rectangle has a triangle (base 7 ft, height 4 ft) on top. Add the two areas. What is the total area?

    1. A49 sq ft
    2. B35 sq ft
    3. C14 sq ft
    4. D63 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  2. 2 MULTIPLE CHOICE

    Plan 2 — L-shaped lobby: decompose the L into two rectangles, one 9 ft by 6 ft and one 7 ft by 3 ft, then ADD. What is the total floor area?

    1. A75 sq ft
    2. B63 sq ft
    3. C54 sq ft
    4. D21 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  3. 3 MULTIPLE CHOICE

    Plan 4 — Design studio: the floor is a 16 ft by 12 ft rectangle, but a 5 ft by 4 ft storage closet is cut out of one corner. Find the usable floor area.

    1. A172 sq ft
    2. B192 sq ft
    3. C212 sq ft
    4. D20 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Identify the shapes:An L-shaped room is made of two joined rectangles: 8 ft × 5 ft and 4 ft × 3 ft.
    2. 2Find each area:First rectangle = 8 × 5 = 40 sq ft. Second rectangle = 4 × 3 = 12 sq ft.
    3. 3Combine the areas:Total = 40 × 12 = 480 sq ft.

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Level 2 Extension — Catch the Architect's Area Mistake

    1. 1Identify the shapes:A clubhouse wall is a 18 ft by 11 ft rectangle with a triangular gable (base 18 ft, height 6 ft) joined on top.
    2. 2Find the rectangle area:A = 18 x 11 = 198 sq ft
    3. 3Find the triangle area:A = 1/2 x 18 x 6 = 54 sq ft
    4. 4Add the areas for the total:Total = 198 + 198 + 54 = 450 sq ft

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find the Area Error

    1. 1Identify the shapes:Rectangle: 16 ft × 10 ft, with a 4 ft × 6 ft piece cut from the corner
    2. 2Find the large rectangle area:A = 16 × 10 = 160 sq ft
    3. 3Find the cutout area:A = 4 × 6 = 24 sq ft
    4. 4Find total area:Total = 160 + 24 = 184 sq ft

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It