6.AT.3 Lesson 3-7-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.7 · Part II

Supported Application · Guided Entry to Today's Problem

Convert Measurements Between Systems · Conversion factor

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 3.7 · Part II
1Converting Measurements Between Systems
2Strategy Model — step by step
  1. Identify the conversion ratio connecting systems (e.g. 1 in ≈ 2.54 cm, 1 kg ≈ 2.2 lbs)
  2. Set up a ratio table or proportion aligning customary and metric units
  3. Multiply or divide by the conversion factor to compute the equivalent measurement
3Mathematical Word Bank
  • Convert Measurements Between Systems (Convertir medidas entre sistemas) — Rewriting a customary measurement as a metric one, or the reverse, so two amounts can be compared.
  • Conversion factor (Factor de conversión) — The ratio that links a unit in one system to a unit in the other, such as 1 mile to about 1.609 kilometers.
  • Customary system (Sistema usual) — The measurement system used in the United States: inches, feet, miles, ounces, pounds, cups, quarts, gallons.
  • Metric system (Sistema métrico) — The measurement system used in most of the world, built on tens: centimeters, meters, kilometers, grams, kilograms, liters.
  • Approximately (Aproximadamente) — Close to, but not exactly equal. Conversions between systems are almost always approximate, so they use the ≈ sign.
  • Ratio table (Tabla de razones) — A table of equal ratios used to scale a conversion factor up to the amount you actually need.
4Watch out
  • A common mistake converting between systems is comparing the bare numbers without converting at all — deciding that 5 kilometers and 5 miles are the same distance because both say 5. They are not: 5 kilometers ≈ 3 miles. A second mistake is writing = instead of ≈. Conversion factors between systems are rounded (1 mile is about 1.609344 kilometers), so the result is approximate no matter how carefully you multiply.
  1. 1 MULTIPLE CHOICE

    A sign in Mexico gives a distance of 80 kilometers. Using 1 km ≈ 0.6 mi, about how far is that in miles?

    1. AAbout 48 miles
    2. BAbout 80 miles
    3. CAbout 133 miles
    4. DAbout 8 miles
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    (Lesson 3.5) Chef A uses 2 cups of cheese for every 8 crackers. Chef B uses 3 cups of cheese for every 9 crackers. Who uses more cheese per cracker?

    1. AChef B
    2. BChef A
    3. CThey use the same amount
    4. DCannot determine
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    (Lesson 3.5) Which ratio is greater: 3:4 or 5:8?

    1. A3:4
    2. B5:8
    3. CThey are equal
    4. DCannot determine
    ✏️ 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
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
6.AT.3 Lesson 3-7-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.7 · Part II

On-Level Application · Standard Rigor

Convert Measurements Between Systems · Conversion factor

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 3.7 · Part II
1Converting Measurements Between Systems
2The Structural Procedure
  1. Identify the conversion ratio connecting systems (e.g. 1 in ≈ 2.54 cm, 1 kg ≈ 2.2 lbs)
  2. Set up a ratio table or proportion aligning customary and metric units
  3. Multiply or divide by the conversion factor to compute the equivalent measurement
3Mathematical Word Bank
  • Convert Measurements Between Systems (Convertir medidas entre sistemas) — Rewriting a customary measurement as a metric one, or the reverse, so two amounts can be compared.
  • Conversion factor (Factor de conversión) — The ratio that links a unit in one system to a unit in the other, such as 1 mile to about 1.609 kilometers.
  • Customary system (Sistema usual) — The measurement system used in the United States: inches, feet, miles, ounces, pounds, cups, quarts, gallons.
  • Metric system (Sistema métrico) — The measurement system used in most of the world, built on tens: centimeters, meters, kilometers, grams, kilograms, liters.
  • Approximately (Aproximadamente) — Close to, but not exactly equal. Conversions between systems are almost always approximate, so they use the ≈ sign.
  • Ratio table (Tabla de razones) — A table of equal ratios used to scale a conversion factor up to the amount you actually need.
4Watch out
  • A common mistake converting between systems is comparing the bare numbers without converting at all — deciding that 5 kilometers and 5 miles are the same distance because both say 5. They are not: 5 kilometers ≈ 3 miles. A second mistake is writing = instead of ≈. Conversion factors between systems are rounded (1 mile is about 1.609344 kilometers), so the result is approximate no matter how carefully you multiply.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Converting between systems: sort each conversion by what happens to the number.

    Target Categories: The number gets smaller The number gets bigger
    • Kilometers → miles
    • Miles → kilometers
    • Pounds → kilograms
    • Kilograms → pounds
    • Inches → centimeters
    • Centimeters → inches
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    A dog weighs 31 pounds. Flea medicine comes in packages for 4–10 kg, 10–25 kg, and 25–40 kg. Which package is correct?

    1. AThe 10–25 kg package
    2. BThe 4–10 kg package
    3. CThe 25–40 kg package
    4. DNone — 31 is above every range
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    1 inch ≈ 2.54 cm. About how many centimeters is 4 inches?

    1. A10.16 cm
    2. B6.54 cm
    3. C1.57 cm
    4. D254 cm
    ✏️ 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
6.AT.3 Lesson 3-7-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.7 · Part II

Extension & Non-Routine Application

Convert Measurements Between Systems · Conversion factor

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 3.7 · Part II
1Converting Measurements Between Systems
2The Structural Procedure
  1. Identify the conversion ratio connecting systems (e.g. 1 in ≈ 2.54 cm, 1 kg ≈ 2.2 lbs)
  2. Set up a ratio table or proportion aligning customary and metric units
  3. Multiply or divide by the conversion factor to compute the equivalent measurement
3Mathematical Word Bank
  • Convert Measurements Between Systems (Convertir medidas entre sistemas) — Rewriting a customary measurement as a metric one, or the reverse, so two amounts can be compared.
  • Conversion factor (Factor de conversión) — The ratio that links a unit in one system to a unit in the other, such as 1 mile to about 1.609 kilometers.
  • Customary system (Sistema usual) — The measurement system used in the United States: inches, feet, miles, ounces, pounds, cups, quarts, gallons.
  • Metric system (Sistema métrico) — The measurement system used in most of the world, built on tens: centimeters, meters, kilometers, grams, kilograms, liters.
  • Approximately (Aproximadamente) — Close to, but not exactly equal. Conversions between systems are almost always approximate, so they use the ≈ sign.
  • Ratio table (Tabla de razones) — A table of equal ratios used to scale a conversion factor up to the amount you actually need.
4Watch out
  • A common mistake converting between systems is comparing the bare numbers without converting at all — deciding that 5 kilometers and 5 miles are the same distance because both say 5. They are not: 5 kilometers ≈ 3 miles. A second mistake is writing = instead of ≈. Conversion factors between systems are rounded (1 mile is about 1.609344 kilometers), so the result is approximate no matter how carefully you multiply.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A backpack weighs 5 kilograms. Using 1 kilogram ≈ 2.2 pounds, about how much does it weigh in pounds?

    1. A11 pounds
    2. B2.27 pounds
    3. C7.2 pounds
    4. D10 pounds
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Rosa runs a 5-kilometer race. Her cousin runs 3.5 miles. Using 1 km ≈ 0.6 mi, who ran farther?

    1. AThe cousin — 5 km is about 3 miles, and 3.5 miles is farther than that
    2. BRosa — 5 is greater than 3.5
    3. CThey tie exactly
    4. DYou cannot compare kilometers with miles
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 OPEN RESPONSE

    The Golden Gate Bridge can hold about 35,924,000 pounds. An average midsize car weighs about 1,524 kilograms. Using 1 kilogram ≈ 2.2 pounds, about how many midsize cars could be on the bridge at one time? Explain each step, and say why your answer is an estimate.

    ✏️ 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