6.AT.3 Lesson 3-7-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.7 Small Group · Group 1

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

Convert Measurements Between Systems · Conversion factor · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — Comparing across two measurement systems
1Write the conversion factor as a ratio (1 km ≈ 0.6 mi), then scale it with a ratio table until it reaches your amount. Between systems the result is approximate, so write ≈, not =.
  • Kilometers and miles both measure distance, but they come from different measurement systems, so the numbers cannot be compared directly. A conversion factor links the two systems, and a ratio table scales it up to the amount you need. 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 compare two speed limits
  1. Evelyn sees a Canadian highway sign reading 100 kilometers per hour and wonders whether that is faster or slower than 100 miles per hour.
  2. Kilometers are metric and miles are customary, so 100 and 100 cannot be compared as they stand. Both measure distance, so a conversion factor links them: 1 kilometer ≈ 0.6 mile, or the ratio 1 : 0.6.
  3. I build a ratio table from that unit ratio. Kilometers 1, 10, 100 pair with miles 0.6, 6, 60 — each column multiplies both numbers by the same factor.
  4. So 100 kilometers ≈ 60 miles, which means 100 kilometers per hour ≈ 60 miles per hour.
  5. Now the comparison is fair: 100 miles per hour is faster, because in one hour you would travel 100 miles instead of only about 60.
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 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. 2 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
  3. 3 MULTIPLE CHOICE

    Which unit is metric?

    1. ALiter
    2. BQuart
    3. CGallon
    4. DPint
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    Why do conversions between systems use the ≈ symbol?

    1. AThe conversion factors are rounded, so results are approximate
    2. BBecause the two amounts are actually different
    3. CBecause metric units are always larger
    4. DBecause you are allowed to guess
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Find the error

    1. 1Setup:1 kilometer ≈ 0.6 mile. About how many miles is 20 kilometers?
    2. 2Step 1:The ratio is 1 : 0.6.
    3. 3Step 2:20 ÷ 0.6 = 33.3
    4. 4Step 3:20 kilometers ≈ 33.3 miles.

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 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
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