6.AT.3 Lesson 3-7-part2 Apply Day · Set B
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3.7 · Part II

Second Practice Form · Independent Application and Spiral Review

Convert Measurements Between Systems · Conversion factor

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■ 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.
  1. 1 MULTIPLE CHOICE

    (Lesson 3.6) There are 12 inches in 1 foot. How many inches are in 5 feet?

    1. A60 inches
    2. B17 inches
    3. C7 inches
    4. D50 inches
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    (Lesson 3.6) There are 1,000 milliliters in 1 liter. How many milliliters are in 3 liters?

    1. A3,000 mL
    2. B1,003 mL
    3. C300 mL
    4. D30 mL
    ✏️ 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
  5. 5 MULTIPLE CHOICE

    1 kilometer ≈ 0.6 mile. About how many miles is 5 kilometers?

    1. A3 miles
    2. B5.6 miles
    3. C8 miles
    4. D30 miles
    ✏️ Workspace & Solution Steps
  6. 6 MULTIPLE CHOICE

    1 pound ≈ 0.45 kilogram. About how many kilograms is 10 pounds?

    1. A4.5 kg
    2. B10.45 kg
    3. C22 kg
    4. D45 kg
    ✏️ Workspace & Solution Steps
  7. 7 MULTIPLE CHOICE

    Which pair of units comes from two DIFFERENT measurement systems?

    1. AMiles and kilometers
    2. BInches and feet
    3. CCups and quarts
    4. DGrams and kilograms
    ✏️ 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