6.GR.1 Lesson 5-4-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.4 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
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.
3Second Model — Try it together — then prove it
  1. Now an L-shape made of a 5 ft by 4 ft rectangle and a 3 ft by 2 ft rectangle.
  2. First rectangle: 5 × 4 = 20 square feet.
  3. Second rectangle: 3 × 2 = 6 square feet.
  4. Are they joined or cut out? Joined, so we add: 20 + 6 = 26 square feet.
  5. Now prove it: say why that move had to work at all — not just that it did.
  6. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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 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
  2. 2 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem: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.
    2. 2A classmate at our table answered:192 sq ft

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 4 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Identify the shapes:A 16 ft × 9 ft floor has a 4 ft × 5 ft supply closet cut out of one corner. Find the usable floor area.
    2. 2Find the large rectangle area:A = 16 × 9 = 144 sq ft.
    3. 3Find the cutout area:A = 4 × 5 = 20 sq ft.
    4. 4Find the usable area:Usable area = 144 + 20 = 164 sq ft.

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 5 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
  4. 6 OPEN RESPONSE

    A T-shaped room can be decomposed in two different ways. Show both ways and prove they give the same total area. Use a T-shape where the top is 14 ft × 4 ft and the stem is 6 ft × 10 ft.

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

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

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It