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

3.6 Small Group · Group 1

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

Convert Measurements within the Same System · Conversion factor · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — Converting inside one measurement system
1Write the conversion factor as a unit ratio (12 inches : 1 foot), then multiply to go to the smaller unit and divide to go to the larger one. The amount never changes — only the unit does.
  • Two measurements can only be compared when they are written in the same unit. Converting uses a special ratio — a unit ratio — that says how much of the smaller unit fits into exactly 1 of the larger unit. 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 check the ride height rule
  1. A ride requires riders to be at or above 44 inches tall. A child is 4 feet tall. The two measurements use different units, so I cannot compare them yet.
  2. Both units belong to the customary system, and there are 12 inches in one foot. That relationship is the conversion factor. As a ratio it is 12 : 1 — a unit ratio, because it compares an amount to exactly 1 foot.
  3. Inches are smaller than feet, so there will be MORE of them: I multiply. 4 × 12 = 48.
  4. The child is 48 inches tall. Now the comparison is fair: 48 inches is greater than 44 inches, so the child can go on the ride.
3Mathematical Word Bank
  • Convert Measurements within the Same System (Convertir medidas dentro del mismo sistema) — Rewriting a measurement in a different unit of the SAME system, such as feet into inches or liters into milliliters.
  • Conversion factor (Factor de conversión) — The ratio that links two units in the same measurement system, such as 12 inches to 1 foot. Within one system it is exact.
  • Unit ratio (Razón unitaria) — A ratio that compares an amount to exactly 1 unit of another quantity, like 12 inches to 1 foot.
  • Convert (Convertir) — To change a measurement from one unit to another without changing how much it is.
  • Measurement system (Sistema de medidas) — A family of units that go together — customary units like inches and feet, or metric units like milliliters and liters.
  • Double number line (Recta numérica doble) — Two number lines lined up so matching tick marks show two units for the same amount.
4Watch out
  • A common mistake when converting within a measurement system is choosing the operation by habit instead of by unit size — multiplying every time. Converting 36 inches to feet by multiplying gives 36 × 12 = 432 feet, taller than a 40-story building. Ask first which unit is smaller: it takes MORE small units to make the same amount, so going to a smaller unit multiplies, and going to a larger unit divides.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Diamond needs 4 liters of water. Her bottle holds 500 milliliters. How many times must she fill it?

    1. A8 times
    2. B4 times
    3. C2 times
    4. D40 times
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    How many inches are in 2 feet?

    1. A24
    2. B14
    3. C10
    4. D12
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    How many liters is 2,000 milliliters?

    1. A2 L
    2. B2,000 L
    3. C200 L
    4. D20 L
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    Which pair belongs to the SAME measurement system?

    1. ACups and quarts
    2. BInches and centimeters
    3. CPounds and grams
    4. DLiters and gallons
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Find the error

    1. 1Setup:Convert 5 feet to inches.
    2. 2Step 1:There are 12 inches in 1 foot.
    3. 3Step 2:5 ÷ 12 = 0.42
    4. 4Step 3:So 5 feet is about 0.42 inches.

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 OPEN RESPONSE

    Michael's mother is setting four fence posts. Each post needs 250 ounces of concrete mix, one bag holds 80 ounces, and each bag needs 1 quart of water. How many bags and how many cups of water does she need? Show your conversions.

    ✏️ 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