5.MD.C.5 Lesson 1-4-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

1.4 · Part II

Supported Application · Guided Entry to Today's Problem

argument · conjecture

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 1.4 · Part II
1Math Practices: Mathematical Arguments & Justification
2Strategy Model — step by step
  1. State a clear claim or conjecture supported by calculations
  2. Use accurate units and vocabulary (e.g. cubic units for volume)
  3. Test with counterexamples to verify that the rule holds true every time
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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 2 OPEN RESPONSE

    Yuzuki can buy three large boxes or two jumbo boxes for the same price. Give ONE reason in words (no equations) for either choice.

    💬 Sentence Starter: I recommend ___ because ___ .<br>A reason that is not about volume is ___ .
    ✏️ Mathematical Justification & Response
  2. 3 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
📐 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
5.MD.C.5 Lesson 1-4-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

1.4 · Part II

On-Level Application · Standard Rigor

argument · conjecture

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 1.4 · Part II
1Math Practices: Mathematical Arguments & Justification
2The Structural Procedure
  1. State a clear claim or conjecture supported by calculations
  2. Use accurate units and vocabulary (e.g. cubic units for volume)
  3. Test with counterexamples to verify that the rule holds true every time
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.
  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
📐 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
5.MD.C.5 Lesson 1-4-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

1.4 · Part II

Extension &amp; Non-Routine Application

argument · conjecture

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 1.4 · Part II
1Math Practices: Mathematical Arguments & Justification
2The Structural Procedure
  1. State a clear claim or conjecture supported by calculations
  2. Use accurate units and vocabulary (e.g. cubic units for volume)
  3. Test with counterexamples to verify that the rule holds true every time
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

    A student claims: “Greater box volume ALWAYS means more cereal inside.” Which is the best counterexample?

    1. AA jumbo box with more volume that is sold half-filled with air
    2. BA large box that costs more than a jumbo box
    3. CTwo jumbo boxes that are easier to store than three large boxes
    4. DA box of a different cereal brand
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    The garden needs 48 cubic feet of soil. One decomposition used two prisms of 24 cubic feet each. Which of these is ANOTHER decomposition of the same garden volume?

    1. AA 4 × 4 × 2 prism and a 4 × 2 × 2 prism
    2. BA 4 × 4 × 2 prism and a 4 × 4 × 2 prism
    3. CA 3 × 3 × 3 prism and a 3 × 3 × 2 prism
    4. DA 6 × 4 × 2 prism and a 2 × 2 × 2 prism
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 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
📐 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