CCSS 6.G.A.2 · Volume of Prisms

Volume Architect — Pack the Prism

You are the architect of the Volume Vault. Pack each box with unit cubes, then use V = length × width × height to find the volume.

Learning Targets

Standard: 6.G.A.2 Est. time: 35–45 min Materials: This page, optional physical unit cubes Format: Individual or pair work
📋 Teacher Notes

Pacing

Allow 5–7 min for Q1 (cube builder), 3–4 min each for Q2–Q4, 5 min for Q5 (fractions), and 5 min for Q6 (inverse). Reserve 5 min for the reflection.

Grouping

Works well as individual practice. For pairs, one student designs the box in Q3 and the partner verifies the volume. For whole-class launch, project Q1 and ask: "How many cubes does one row hold? How many rows?"

Differentiation — Support

  • Provide physical unit cubes so students can build the models for Q1–Q3 before typing.
  • For Q5, write out 1.5 as 3/2 and multiply step-by-step: 3 × 2 = 6, then 6 × 1.5 = 9.
  • For Q6, provide a graphic organizer: write the formula, substitute the known values, then solve for the missing variable.

Differentiation — Challenge

  • Ask: if you double the height of the box in Q4, what happens to the volume? What if you double all three dimensions?
  • Challenge Q3: can you find two different boxes with the same volume but different dimensions?
  • Extension: if the box in Q6 needs to hold 96 cubic units, what possible integer dimensions would work?

ESOL / Language Supports

  • Key vocabulary with visuals: rectangular prism, volume, length, width, height, unit cube, layer, edge, dimension.
  • Sentence frame for Q2: "There are ___ cubes in one layer. There are ___ layers. The total is ___ × ___ = ___."
  • Sentence frame for Q6: "I know V = ___, l = ___, and w = ___. I solve h = V ÷ (l × w) = ___."
  • Post the formula V = l × w × h visually in the room. Allow native-language glossaries.

Scoring Rubric

Level Score Descriptor
Mastery 6 / 6 Correctly packs the cube layer; uses V = l × w × h without error for all word problems; correctly handles the fractional edge; algebraically solves for the missing dimension.
Proficient 4–5 / 6 Mostly correct with at most one arithmetic error; packs the layer correctly; applies the formula consistently; may make a minor error with the fractional edge or the inverse problem.
Developing 2–3 / 6 Can pack the cube layer and state the formula but makes errors applying it; confuses area with volume; struggles with fractional edges or working backwards from volume.
Beginning 0–1 / 6 Cannot consistently pack the layer to the target; does not recall V = l × w × h; needs direct re-teaching of the relationship between layers and volume.

Step 0 of 6 done

1. Build one layer

Skill: Cubes in one layer

Click cubes to fill the floor. Make a layer with 12 cubes (length 4, width 3).

Bottom layer (top view)

Cubes placed: 0

2. Stack the layers

Skill: Layers × height

One layer has 12 cubes. The box is 5 layers tall. How many unit cubes fill the box? Type the total.

3. Design your own box

Skill: V = l × w × h

Pick length, width, and height. The cube count updates. Type the volume in cubic units.

One layer (length × width)

Cubes per layer: 6 · Layers: 4

4. Find the volume

Skill: V = l × w × h

A storage box is 7 cm long, 4 cm wide, and 5 cm tall. Type the volume in cubic centimeters (cm³).

5. A half-unit edge

Skill: Fractional edge lengths

A box is 3 units long, 2 units wide, and 1½ (1.5) units tall. Type the volume in cubic units. You may type 9 or 9.0.

6. Find the missing edge

Skill: Solve for an edge

A box has volume 48 cubic units. It is 4 units long and 2 units wide. How tall is it? Type the height in units.

Reflection

Think about what you learned in this activity:

Deliverable: When you finish all 6 problems and the reflection, press Check my work below, then use Save as PDF or Save as DOC to submit your Volume Architect activity to your teacher.

Your score and a per-skill report appear at the top. Use Save as PDF or Save as DOC to turn it in.

🔑 Answer Key (Teacher Only)

Q1: Build one layer (4 × 3)

Answer: 12 cubes. The grid is 4 columns × 3 rows = 12 cells. All 12 cubes should be filled (pressed).

Q2: Stack the layers (12 cubes/layer, 5 layers)

Answer: 60. 12 × 5 = 60. This models V = (area of base) × height = 12 × 5.

Q3: Design your own box

Answer: varies based on student's chosen dimensions. The correct volume equals l × w × h for the values selected. The default (l=3, w=2, h=4) gives 3 × 2 × 4 = 24. The grader accepts whatever V = L × W × H computes for the chosen values.

Q4: Storage box 7 cm × 4 cm × 5 cm

Answer: 140 cm³. V = 7 × 4 × 5 = 28 × 5 = 140.

Q5: Box 3 × 2 × 1.5

Answer: 9 cubic units. V = 3 × 2 × 1.5 = 6 × 1.5 = 9. You can also think of it as 3 × 2 × (3/2) = 18/2 = 9.

Q6: Find the missing height (V=48, l=4, w=2)

Answer: 6 units. V = l × w × h ⇒ 48 = 4 × 2 × h = 8h ⇒ h = 48 ÷ 8 = 6.