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

5.5 Small Group · Group 2

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

Visual Models · Volume with Whole-Number Edges · Volume · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do we find the volume of a box?
1To find the volume of a box, multiply all three edges: V = length × width × height — 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 time capsule box is 6 long, 4 wide, and 3 tall. I write the formula: V = length × width × height.
  2. I put in the numbers: V = 6 × 4 × 3.
  3. First I multiply two of them: 6 × 4 = 24.
  4. Then I multiply by the last one: 24 × 3 = 72.
  5. So the volume is 72 cubic units. I use cubic units because volume fills space in 3 directions.
3Second Model — Try it together — then prove it
  1. Now a smaller box: 5 long, 2 wide, 2 tall. What formula do we use?
  2. Let's put in the numbers: V = 5 × 2 × 2. What is 5 × 2?
  3. We got 10. Now multiply 10 × 2. What is the volume?
  4. Yes, V = 20 cubic units. Don't forget the cubic units!
  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
  • Volume with Whole-Number Edges (Volumen con aristas de números enteros) — The number of unit cubes inside a rectangular prism. Formula: V = l × w × h.
  • Volume (Volumen) — How much space is inside a solid shape.
  • Rectangular prism (Prisma rectangular) — A solid box shape with six flat rectangle sides.
  • Cubic units (Unidades cúbicas) — The units used to measure space inside, like cubic inches.
  • Length, width, height (Largo, ancho, altura) — How long, how wide, and how tall a box is.
  • Net (Plantilla (desarrollo plano)) — A flat shape that folds up into a solid.
5Watch out
  • A common mistake in Volume with Whole Number Edges is multiplying only two of the three edges and stopping there — for example, seeing a box that is 6 in long, 4 in wide, and 3 in tall, multiplying just 6 × 4 = 24, and calling that the volume, when 24 is only the area of the bottom face (in square inches), not the volume of the whole box. The height must also be multiplied in: V = 6 × 4 × 3 = 72 cubic inches. A second common mistake is adding the three edges instead of multiplying them (6 + 4 + 3 = 13 instead of 6 × 4 × 3 = 72 cubic inches). Volume always MULTIPLIES all three edges, and the answer is always labeled in cubic units (in³), never square units (in²) or plain units (in).
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A time capsule box is 5 units long, 3 units wide, and 2 units tall. How many unit cubes fill it?

    1. A30 cubic units
    2. B10 cubic units
    3. C15 cubic units
    4. D25 cubic units
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    You stack unit cubes in a capsule: each layer has 6 cubes, and there are 4 layers. What is the volume?

    1. A24 cubic units
    2. B10 cubic units
    3. C12 cubic units
    4. D18 cubic units
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  3. 3 MULTIPLE CHOICE

    Two storage bins: Bin A is 8 × 6 × 5 inches. Bin B is 9 × 4 × 7 inches. Which holds more and by how much?

    1. ABin B by 12 in³
    2. BBin A by 12 in³
    3. CBin B by 24 in³
    4. DThey hold the same
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    A rectangular prism has length 8 cm, width 5 cm, and height 4 cm. What is its volume?

    1. A17 cm³
    2. B160 cm³
    3. C80 cm³
    4. D120 cm³
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A rectangular prism has length 8 cm, width 5 cm, and height 4 cm. What is its volume?
    2. 2A classmate at our table answered:17 cm³

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Added the Last Edge

    1. 1Dimensions:A capsule is 6 long, 5 wide, and 3 tall
    2. 2Formula:V = length × width × height
    3. 3Calculate:V = 6 × 5 + 3 = 33 cubic units
    4. 4Answer:Volume = 33 cubic units

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

    ✏️ Corrected Mathematical Work & Explanation
📐 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