6.AT.3 Lesson 3-6-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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3.6 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    There are 4 cups in 1 quart. Complete the conversion table.

    QuartsCups
    1
    3
    6
    ✏️ Scratchpad / Reasoning
  2. 2 FILL TABLE

    There are 1,000 milliliters in 1 liter. Complete the double number line as a table.

    LitersMilliliters
    1
    2
    4
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    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. 4 MULTIPLE CHOICE

    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. 5 MULTIPLE CHOICE

    There are 16 ounces in 1 pound. How many pounds is 48 ounces?

    1. A3 pounds
    2. B64 pounds
    3. C768 pounds
    4. D32 pounds
    ✏️ Workspace & Solution Steps
  4. 6 MULTIPLE CHOICE

    A child is 4 feet tall. A ride requires 44 inches. Can the child ride?

    1. AYes, because 4 feet = 48 inches, which is more than 44
    2. BNo, because 4 is less than 44
    3. CYes, because 4 feet = 44 inches exactly
    4. DYou cannot compare feet and inches
    ✏️ Workspace & Solution Steps
🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."
👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The ratio remains equivalent because both quantities are scaled by the exact same multiplicative factor.
BUT Two ratios may look similar, but inverting the order of terms fundamentally changes the comparison.
SO The recipe requires 3 parts flour to 2 parts water, so the unit rate is 1.5 cups of flour per cup of water.
📐 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