6.GR.1 Lesson 5-4-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.4 · Part II

Supported Application · Guided Entry to Today's Problem

Area of Composite Figures · Composite Figure

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 5.4 · Part II
1Area of Composite Figures
2Strategy Model — step by step
  1. Decompose: Split the irregular shape into basic figures (rectangles, triangles, trapezoids)
  2. Calculate: Find the area of each individual sub-figure
  3. Combine: Add the areas together (or subtract if a piece is removed/cut out)
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).
  1. 1 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
  2. 2 MULTIPLE CHOICE

    (Lesson 5.9) A regular hexagon is divided into 6 equal triangles from the center. Each triangle has a base of 6 ft and a height of 5.2 ft. What is the area of one triangle?

    1. A15.6 sq ft
    2. B31.2 sq ft
    3. C11.2 sq ft
    4. D15.6 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

    (Lesson 5.9) Using the triangle from the previous question, what is the total area of the hexagonal skylight?

    1. A93.6 sq ft
    2. B15.6 sq ft
    3. C187.2 sq ft
    4. D62.4 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?
📐 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
6.GR.1 Lesson 5-4-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.4 · Part II

On-Level Application · Standard Rigor

Area of Composite Figures · Composite Figure

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 5.4 · Part II
1Area of Composite Figures
2The Structural Procedure
  1. Decompose: Split the irregular shape into basic figures (rectangles, triangles, trapezoids)
  2. Calculate: Find the area of each individual sub-figure
  3. Combine: Add the areas together (or subtract if a piece is removed/cut out)
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).
  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
  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
  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
📐 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
6.GR.1 Lesson 5-4-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.4 · Part II

Extension & Non-Routine Application

Area of Composite Figures · Composite Figure

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 5.4 · Part II
1Area of Composite Figures
2The Structural Procedure
  1. Decompose: Split the irregular shape into basic figures (rectangles, triangles, trapezoids)
  2. Calculate: Find the area of each individual sub-figure
  3. Combine: Add the areas together (or subtract if a piece is removed/cut out)
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).
  1. 1 MULTIPLE CHOICE

    An L-shaped room splits into two rectangles: one is 12 feet by 8 feet, the other is 6 feet by 5 feet. What is the total floor area?

    1. A126 square feet
    2. B96 square feet
    3. C30 square feet
    4. D62 square feet
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
📐 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