5.MD.C.5 Lesson 1-4-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

1.4 Small Group · Group 2

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

argument · conjecture · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — When we do math, we develop arguments to defend our thinking
1We can defend a recommendation using equations, drawings, or words — and volume in cubic units gives the equations something exact to say — 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 argue with equations
  1. Suppose each large box is 8 inches long, 3 inches wide, and 10 inches tall. Its volume is 8 × 3 × 10 = 240 cubic inches, so three large boxes hold 240 × 3 = 720 cubic inches.
  2. Suppose each jumbo box is 10 inches long, 4 inches wide, and 10 inches tall. Its volume is 10 × 4 × 10 = 400 cubic inches, so two jumbo boxes hold 400 × 2 = 800 cubic inches.
  3. I recommend buying two jumbo boxes because 800 cubic inches is greater than 720 cubic inches — the total volume is greater, so there is more cereal for the same price.
3Second Model — Try it together — then prove it
  1. Not every good reason is an equation. Finish this argument: “I recommend buying two jumbo boxes because …”
  2. The book offers two word-based reasons: there is less packaging with two boxes, and two boxes are easier to store than three boxes.
  3. Now listen to the other side. One student recommends the three large boxes because the cereal will stay fresher — each box is open for less time — and because greater volume does not always mean more cereal inside.
  4. How convincing is each argument? That judgment is math too.
  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
  • argument (argumento) — A chain of reasons — equations, drawings, or words — used to defend your thinking.
  • conjecture (conjetura) — A mathematical statement you believe is true but have not yet proven.
  • counterexample (contraejemplo) — A single example that shows a statement is not always true.
  • volume (volumen) — The amount of space a solid figure takes up, measured in cubic units.
  • cubic unit (unidad cúbica) — A cube with edges 1 unit long — the unit used to measure volume.
5Watch out
  • Reporting volume without cubic units — saying the garden needs '48 feet' of soil, which is a length, or '48 square feet', which is an area.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Three large boxes hold 240 cubic inches each. Two jumbo boxes hold 400 cubic inches each. Which is the correct volume comparison?

    1. A720 cubic inches vs. 800 cubic inches — the jumbo option holds more
    2. B720 cubic inches vs. 800 cubic inches — the large option holds more
    3. C240 cubic inches vs. 400 cubic inches — the jumbo option holds more
    4. D480 cubic inches vs. 800 cubic inches — the jumbo option holds more
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    One garden bed is 4 ft long, 3 ft wide, and 2 ft deep. A second bed is 6 ft long, 2 ft wide, and 2 ft deep. How much soil fills BOTH beds?

    1. A48 cubic feet
    2. B24 cubic feet
    3. C19 cubic feet
    4. D96 cubic feet
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    The group found the volume by decomposing the garden into prisms and adding. Why would they compute it a SECOND, different way?

    1. AIf both ways give the same answer, the solution is accurate
    2. BBecause the first way is always wrong
    3. CTo get a bigger number for the soil order
    4. DBecause volume changes each time you measure it
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 OPEN RESPONSE

    Another garden bed design is also being considered. What information would you need to compare the two designs, and how would you argue for the one you recommend?

    ✏️ Mathematical Justification & Response
  2. 5 OPEN RESPONSE

    Write TWO arguments for the same recommendation about Yuzuki's cereal — one using equations, one using only words. Then say which you think would convince a classmate more, and why.

    ✏️ Mathematical Justification & Response
  3. 6 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:One garden bed is 4 ft long, 3 ft wide, and 2 ft deep. A second bed is 6 ft long, 2 ft wide, and 2 ft deep. How much soil fills BOTH beds?
    2. 2A classmate at our table answered:96 cubic feet

    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