5.MD.C.5 Lesson 1-4-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

1.4 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

argument · conjecture · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — 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.
  • Getting an answer is only half the work. The other half is explaining it so clearly — with conjectures, examples, and counterexamples — that someone else can decide whether your argument is convincing. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
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.
3Mathematical 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.
4Watch 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

    Which unit should the garden group use when reporting how much soil fills the beds?

    1. ACubic feet
    2. BFeet
    3. CSquare feet
    4. DDegrees
    ✏️ Workspace & Solution Steps
  2. 2 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
  3. 3 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
  4. 4 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. 5 OPEN RESPONSE

    Why does it help to explain your thinking to others instead of just giving the answer?

    💬 Sentence Starter: Explaining helps because ___ .<br>When someone hears my reasons, they can ___ .
    ✏️ Mathematical Justification & Response
  2. 6 OPEN RESPONSE

    A student recommends the three large boxes because the cereal stays fresher — each box is open for less time. Is this argument convincing? Explain.

    💬 Sentence Starter: I find this argument ___ because ___ .<br>It would be stronger if ___ .
    ✏️ Mathematical Justification & Response
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It