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Unit 10 · CCSS 6.G.A.2

Volume Vault: Volume of Prisms

Find how much space fits inside a box. You will pack unit cubes, use a formula, and solve real problems — including prisms with fractional edge lengths.

Learning Target

📋Standard: CCSS 6.G.A.2
⏱Estimated time: 50 – 60 minutes
📦Materials: This page, calculator (optional)
🎯Unit: Geometry — Unit 10
Teacher Notes — Pacing, Grouping & Differentiation

Pacing Guide

  • Engage (5 min) — Think-Pair-Share: "How many unit cubes fill the box?" No writing yet.
  • Explore (10–15 min) — Students open the 3D Volume Vault game in a new tab; circulate and prompt: "What happens to volume when you double the height?"
  • Explain (10 min) — Class reads vocab and formula together; teacher models the fractional-edge worked example on a whiteboard.
  • Apply (15–20 min) — Self-check items first (individual), then NTKit graded set; encourage showing arithmetic work on scratch paper.
  • Reflect (5–8 min) — Individual typed responses; collect PDF or DOC.

Grouping Suggestions

  • Self-Check: individual, then compare answers with a partner after all three are done.
  • NTKit graded questions: individual work; discuss after submission.
  • Reflect: individual only.

Differentiation — Support

  • Provide physical or virtual unit cube manipulatives for Q1 and Q3.
  • Allow calculators for all fractional-edge questions.
  • Offer a formula reference card: V = l × w × h and V = B × h.
  • Reduce Apply to Q1–Q4 and offer Q5–Q6 (fractional edges) as challenge.

Differentiation — Challenge

  • Ask: "A prism has volume 60 cm³ and base area 12 cm². What is the height? Write an equation."
  • Extend: "Design a box with volume exactly 1/2 ft³ using fractional dimensions. Show your work."

ESOL / Language Supports

  • Display anchor chart with labeled 3D prism diagram showing l, w, h in the student's home language.
  • Sentence frame: "The volume is ___ cm³ because I multiplied ___ × ___ × ___."
  • Pair newcomers with bilingual partners during Explore game.
  • Allow labeled diagrams as evidence in the Reflect instead of prose.

Your Name

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Engage

How much fits inside?

Imagine a treasure box shaped like a rectangle (a rectangular prism). You want to know how many small cubes fill it all the way up.

Think: If the box is 4 cubes long, 3 cubes wide, and 2 cubes tall, how many cubes fit inside? That number is the volume.

Discuss with a partner: Would a box that is 2 × 6 × 2 hold more, less, or the same amount as the 4 × 3 × 2 box? Why?
Explore

Play and explore

Open these to see volume in action. Come back here after.

Play: Volume Vault (3D game) Math Hub Math Graphic Novels
Do this: In the game, pack the prism with unit cubes. Watch the cubes add up to the volume. Try a prism with a fractional side length — what changes?
Explain

What is volume?

Volume is the amount of space inside a 3D solid. We measure it in cubic units (like cm³ or in³). Each unit is one small cube.

Key words

The formula

Volume = length × width × height
V = l × w × h

You can also write it as V = B × h, where B is the area of the base (B = l × w).

Worked example — whole numbers

A box is 5 cm long, 3 cm wide, and 2 cm tall. Find the volume.

Step 1: Multiply length × width 5 × 3 = 15
Step 2: Multiply by height 15 × 2 = 30
Answer 30 cm³

Worked example — fractional edge lengths (6.G.A.2)

A box is 1½ ft long, ⅔ ft wide, and 2 ft tall. Find the volume. (Convert mixed numbers to fractions first.)

Convert 1½ to fraction 1½ = 3/2
Multiply l × w 3/2 × 2/3 = 6/6 = 1
Multiply by height 1 × 2 = 2
Answer 2 ft³

Key idea: The formula V = l × w × h still works when edges are fractions. Multiply the fractions just like any fraction multiplication.

Apply

Your turn — solve the problems

Quick Self-Check — try these first!

Choose an answer, then press Check to see instant feedback.

SC 1. A box is 3 m long, 4 m wide, and 5 m tall. What is its volume?

SC 2. The base area of a prism is 8 cm² and the height is 6 cm. What is the volume?

SC 3. A prism has edges ½ in × ½ in × 4 in. What is its volume?

Graded Practice — submit with NTKit

Type each answer. Write only the number (no units). Then press Check My Work.

Teacher Answer Key

Self-Check answers:

  1. SC 1: 60 m³ — V = 3 × 4 × 5 = 60. Multiplying all three edges gives volume.
  2. SC 2: 48 cm³ — V = B × h = 8 × 6 = 48. Base area replaces l × w.
  3. SC 3: 1 in³ — V = ½ × ½ × 4 = ¼ × 4 = 1. Fractional edges multiply normally.

Graded practice answers:

  1. Q1: 24 — 2 × 3 × 4 = 24 cm³
  2. Q2: 125 — 5 × 5 × 5 = 125 in³
  3. Q3: 36 — 6 × 2 × 3 = 36 unit cubes
  4. Q4: 200 — 10 × 4 × 5 = 200 cm³
  5. Q5: 36 — B × h = 12 × 3 = 36 cm³
  6. Q6: 2.25 — ¾ × ¾ × 4 = 9/16 × 4 = 36/16 = 9/4 = 2.25 ft³

Note on Q6: Accept "9/4" or "2.25" or "2 1/4".

Rubric

How your work is scored

Level Score Description
Mastery 5 – 6 / 6 All or nearly all graded questions correct, including the fractional-edge problem (Q6). Self-check completed. Reflect responses explain V = l × w × h in own words and connect to a real context.
Proficient 4 / 6 Most whole-number volume questions correct. Minor errors in Q5 (V = B × h) or Q6 (fractional edges). Reflect addresses both prompts with volume vocabulary (volume, cubic unit, prism).
Developing 2 – 3 / 6 Frequently adds instead of multiplies, or multiplies only two of three dimensions. Reflect responses are short or missing key terms. Needs targeted reteach with unit-cube models.
Beginning 0 – 1 / 6 Most questions blank or incorrect. Cannot apply V = l × w × h independently. Reflect not attempted. Requires one-on-one re-teaching of the volume formula before independent work.
Reflect

Think about your learning

Use complete sentences. Try to use at least one math word from the Explain section (volume, cubic unit, prism, base area, formula).

Deliverable: Type your responses below, then save your finished HyperDoc as a PDF or DOC using the Save buttons at the top. Submit the saved file to your teacher's Google Drive folder or as directed by your teacher.