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

5.4 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each composite figure by whether you ADD or SUBTRACT the areas to find the total.

    Target Categories: Add the areas Subtract the areas
    • 2 FILL TABLE

      Solve the mathematical problem. Show all of your work and reasoning.

      FigureShape 1 AreaShape 2 AreaOperationTotal Area
      L-shaped deck
      Floor with alcove
      Wall with window cutout
      Courtyard with fountain cutout
      ✏️ Scratchpad / Reasoning
    SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
    1. 3 MULTIPLE CHOICE

      An L-shaped room is made of two rectangles: 10 ft × 6 ft and 4 ft × 3 ft. What is the total area?

      1. A72 sq ft
      2. B60 sq ft
      3. C12 sq ft
      4. D72 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. 4 MULTIPLE CHOICE

      A rectangular patio is 15 ft × 10 ft with a 5 ft × 4 ft rectangular flower bed cut out. What is the remaining area?

      1. A130 sq ft
      2. B150 sq ft
      3. C20 sq ft
      4. D170 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. 5 MULTIPLE CHOICE

      Find the area of an L-shape made of a 5×3 rectangle and a 2×4 rectangle.

      1. A23 sq units
      2. B15 sq units
      3. C8 sq units
      4. D20 sq units
      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?
    4. 6 MULTIPLE CHOICE

      When should you subtract areas instead of adding them to find the area of a composite figure?

      1. AWhen a piece is cut out or removed from a larger shape
      2. BWhen the shapes overlap
      3. CWhen one shape is larger than the other
      4. DAlways subtract — never add
      ✏️ Workspace & Solution Steps
    🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

    Group Discussion Prompt: How does your visual model justify your mathematical solution?

    🗣️ Partner A:
    Partner A: "I modeled this by identifying the relationship and..."
    👂 Partner B:
    Partner B: "I agree with your step because the standard mathematical rule states..."
    ✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

    Complete each sentence stem to demonstrate precise mathematical reasoning:

    BECAUSE The mathematical model proves the solution because each step preserves quantitative equivalence.
    BUT An estimate provides a quick benchmark, but an exact proof is required for precision.
    SO The quantities follow the standard rule, so the final result is verified with certainty.
    📐 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