6.AT.3c Lesson 3-10-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.10 Small Group · Group 2

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

Convert Measurement Units · Conversion Factor · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do I change one measurement unit into another?
1Multiply when changing to a smaller unit, and divide when changing to a bigger unit — 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. The cabinet is 5 feet tall. I want to know how many inches that is.
  2. My conversion factor is 1 foot = 12 inches.
  3. Inches are smaller than feet, so I multiply: 5 × 12 = 60.
  4. So 5 feet = 60 inches.
3Second Model — Try it together — then prove it
  1. A wire is 4 yards long. The factor is 1 yard = 3 feet.
  2. Feet are smaller than yards, so do we multiply or divide? (Multiply)
  3. What is 4 × 3 feet? (12 feet)
  4. Now a metric example: a power cable is 3 meters long. The factor is 1 meter = 100 centimeters.
  5. Centimeters are smaller than meters, so we multiply: 3 × 100 = 300 centimeters.
  6. Now prove it: say why that move had to work at all — not just that it did.
  7. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • Convert Measurement Units (Convertir unidades de medida) — Rename a measurement in a different unit without changing its amount.
  • Conversion Factor (Factor de conversión) — A ratio that helps you change one unit into another.
  • Unit (Unidad) — A standard amount used to measure, like an inch or a liter.
  • Equivalent (Equivalente) — Having the same value, just in different units.
  • Ratio (Razón) — A way to compare two amounts, like 3 to 2.
  • Customary units (Unidades usuales (sistema inglés)) — The U.S. way of measuring, like inches, feet, and pounds.
5Watch out
  • A common mistake in Convert Measurement Units is applying the conversion factor in the wrong direction — for example, converting 4 feet to inches by dividing (4 ÷ 12 = 0.33 inches) instead of multiplying (4 × 12 = 48 inches), or converting 80 ounces to pounds by multiplying (80 × 16 = 1,280 pounds) instead of dividing (80 ÷ 16 = 5 pounds). Before you answer, ask: am I changing to a SMALLER unit (there will be MORE of them, so multiply) or a BIGGER unit (there will be FEWER of them, so divide)?
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Final Leg: The finished cabinet ships in a crate holding 8 quarts of packing gel, but the supplier sells gel by the gallon. How many gallons is that? (4 qt = 1 gal)

    1. A2 gallons
    2. B32 gallons
    3. C4 gallons
    4. D12 gallons
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    How many inches are in 7 feet?

    1. A84 inches
    2. B72 inches
    3. C70 inches
    4. D96 inches
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    A shelf is 30 inches long. How many feet and inches is that?

    1. A2 feet 6 inches
    2. B3 feet 0 inches
    3. C2 feet 8 inches
    4. D1 foot 18 inches
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Leg 3: The coin box weighs 5 pounds, but the shipping label needs the weight in ounces. How many ounces is that? (1 lb = 16 oz)
    2. 2A classmate at our table answered:16 ounces

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Convert 80 ounces of bolts to pounds:80 ounces → pounds
    2. 2Use the conversion factor:1 pound = 16 ounces
    3. 3Operate:80 × 16 = 1,280 pounds
    4. 4Final answer:80 ounces = 1,280 pounds

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find the Conversion Error

    1. 1Convert 6 feet to yards:6 feet → yards
    2. 2Use conversion factor:1 yard = 3 feet
    3. 3Multiply:6 × 3 = 18 yards
    4. 4Final answer:6 feet = 18 yards

    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