6.GR.2 Lesson 5-10-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.10 Small Group · Group 2

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

Visual Models · Volume of Rectangular Prisms · Volume · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do we find volume when an edge is a fraction?
1A fractional edge does not change the rule: still multiply 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 capsule is 2 ft long, 1.5 ft wide, and 1 ft tall. I write V = length × width × height.
  2. I put in the numbers: V = 2 × 1.5 × 1.
  3. First I multiply 2 × 1.5 = 3.
  4. Then 3 × 1 = 3.
  5. So the volume is 3 ft³. A fractional edge like 1.5 did not change my steps at all.
3Second Model — Try it together — then prove it
  1. Now try a box that is 4 long, 2 wide, and 0.5 tall. Let's do it the base-area way. What is the base, 4 × 2?
  2. The base area is B = 8. Picture that base sitting on the table — that is one layer.
  3. Now stack the base up the height: V = B × h = 8 × 0.5 (that means half of 8). What is the volume?
  4. Yes, V = 4 cubic units. Check it the other way: 4 × 2 × 0.5 = 4. Same answer, because B × h already used the length and width.
  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 of Rectangular Prisms (Volumen de prismas rectangulares) — The space inside a rectangular prism. Formula: V = Bh = 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.
  • Dimensions (Dimensiones) — How long, how wide, and how tall a shape is.
  • Base area (Área de la base) — The area of the bottom of a solid. Volume = base area × height.
5Watch out
  • 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?'
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A time-capsule box measures 6 in long, 4 in wide, and 3 in tall. What is its volume?

    1. A72 cubic in
    2. B13 cubic in
    3. C24 cubic in
    4. D72 square in
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  2. 2 MULTIPLE CHOICE

    Two storage boxes are ready to pack. Box A is 5 × 5 × 2 inches and Box B is 4 × 4 × 3 inches. Which box holds more?

    1. ABox A, because 50 cubic in is more than 48 cubic in
    2. BBox B, because 48 cubic in is more than 50 cubic in
    3. CThey hold the same amount
    4. DBox B, because it is taller
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Two boxes: Box A is 10 × 5 × 4 inches. Box B is 8 × 6 × 5 inches. Which has more volume and by how much?

    1. ABox B by 40 in³
    2. BBox A by 40 in³
    3. CBox B by 60 in³
    4. DThey're equal
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A cube has an edge length of 5 cm. What is its volume?
    2. 2A classmate at our table answered:25 cm³

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 OPEN RESPONSE

    A box has a volume of 24 cm³. Give THREE different sets of whole-number edge lengths that work. Then explain why doubling just ONE edge doubles the volume, but doubling ALL THREE multiplies it by 8 — not by 6.

    ✏️ Mathematical Justification & Response
  3. 6 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Dimensions:A box is 6 in long, 4 in wide, and 1/2 in tall.
    2. 2Formula:V = length × width × height
    3. 3Calculate:V = 6 × 4 × 1/2, and the student dropped the 1/2: V = 6 × 4 = 24 cubic in
    4. 4Answer:Volume = 24 cubic in

    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