Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.2

Lesson 5.105.4–5.10 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 5.4–5.10 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Area of Composite FiguresSpanish: 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). Total area = area of rectangle 1 + area of rectangle 2.
Composite FigureSpanish: Figura compuesta A shape made by putting two or more simple shapes together. An L-shaped room = a 12×8 rectangle joined to a 6×5 rectangle; total area = 96 + 30 = 126 sq ft
DecomposeSpanish: Descomponer To break a shape into smaller, simpler shapes. Draw a dashed line across the L-shape to split it into two rectangles — now you can find each area separately
AddSpanish: Sumar Add up the areas of the smaller shapes to get the total. T-shaped hallway: top rectangle = 30 sq ft, bottom rectangle = 28 sq ft → total = 30 + 28 = 58 sq ft
SubtractSpanish: Restar Take away the area of a missing piece from a bigger shape. A 14×10 pool with a 6×4 cutout: 140 − 24 = 116 sq ft of water surface
FormulaSpanish: Fórmula A math rule written with symbols. Rectangle: A = l × w; Triangle: A = ½ × b × h; use the right formula for each piece of a composite figure

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Lesson 5.4 — Apply Area Concepts to Solve Problems: Break the figure into simple shapes. ADD the areas when shapes are joined; SUBTRACT when a piece is cut out.

  1. Lesson 5.5 — Determine the Volume of Rectangular Prisms: To find the volume of a box, multiply all three edges: V = length × width × height.
  2. Lesson 5.6 — Represent Three-Dimensional Figures in Two Dimensions: A box has 3 pairs of matching faces, so add up all 6 faces to get the surface area.
  3. Lesson 5.7 — Determine Surface Area of Prisms: No matter the prism, find the area of every face and add them all together.
  4. Lesson 5.8 — Determine Surface Area of Pyramids: Surface area of a pyramid = base area + the area of all the triangular lateral faces.
  5. Lesson 5.9 — Area of Regular Polygons: A regular polygon splits into the same number of triangles as it has sides, so total area = (one triangle's area) × (number of sides).
  6. Lesson 5.10 — Volume of Rectangular Prisms: A fractional edge does not change the rule: still multiply length × width × height.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

From 5.4: Now an L-shape made of a 5 ft by 4 ft rectangle and a 3 ft by 2 ft rectangle.

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • Capsules A and B both have V = because × × = × × . I'd choose because .

Word bank Area of Composite FiguresComposite FigureDecomposeAddSubtractFormula3volumesamedifferentdimensionsshape

Watch outA common mistake

A common mistake in Volume of Rectangular Prisms is rounding a fractional edge length to the nearest whole number before multiplying, instead of using the exact fraction or decimal. For a box that is 2 ft × 1.5 ft × 1 ft, a student might round 1.5 down to 1 and compute 2 × 1 × 1 = 2 ft³, but the correct volume uses the exact edge length: 2 × 1.5 × 1 = 3 ft³ — a full cubic foot larger. Before you submit, ask: 'Did I multiply using the exact fractional or decimal edge length, or did I round it off first?'

Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.2

Lesson 5.105.4–5.10 Catch-Up

Catch-UpSkill bridge

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can show I am caught up on Lessons 5.4–5.10 by using each lesson's big idea in mixed practice.

  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 5.4) An L-shaped room is made of two rectangles: 10 ft × 6 ft and 4 ft × 3 ft. What is the total area?

    1. A12 sq ft
    2. B60 sq ft
    3. C72 sq ft
    4. D72 ft

    Hint The L-shape is already split into two rectangles for you: 10 × 6 and 4 × 3.

    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. 2Circle the letter of the best answer. Show how you know.

    (Lesson 5.4) 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. A20 sq ft
    2. B130 sq ft
    3. C150 sq ft
    4. D170 sq ft

    Hint The flower bed is CUT OUT of the patio — that phrase tells you which operation to use.

    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. 3Circle the letter of the best answer. Show how you know.

    (Lesson 5.5) What is the volume of a rectangular prism with l = 7 in, w = 3 in, h = 4 in?

    1. A14 in³
    2. B42 in³
    3. C84 in³
    4. D84 in²

    Hint Notice the three edge lengths: l = 7 in, w = 3 in, h = 4 in. Volume asks how much space fills the whole box.

    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. 4Circle the letter of the best answer. Show how you know.

    (Lesson 5.5) A time capsule box has a volume of 120 cm³. Its length is 10 cm and width is 4 cm. What is its height?

    1. A3 cm
    2. B4 cm
    3. C6 cm
    4. D12 cm

    Hint You already know the volume (120 cm³) and two edges (10 cm and 4 cm). The height is the missing piece.

    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?
  5. 5Circle the letter of the best answer. Show how you know.

    (Lesson 5.6) A rectangular prism has l = 6 in, w = 4 in, h = 2 in. What is its surface area?

    1. A44 in²
    2. B48 in²
    3. C88 in²
    4. D88 in³

    Hint Surface area covers all 6 faces of the 6 × 4 × 2 box — it's not the same as the space inside.

    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?

Explain your thinkingCapsules A and B have the same volume (3 ft³) but different dimensions. Why? Which design would you choose and why?

Sentence starter Capsules A and B both have V = ___ because ___ × ___ × ___ = ___ × ___ × ___. I'd choose ___ because ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help