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

3.6 · Part II

Supported Application · Guided Entry to Today's Problem

Convert Measurements within the Same System · Conversion factor

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 3.6 · Part II
1Converting Measurements (Same System)
2Strategy Model — step by step
  1. Identify the conversion factor (e.g. 1 ft = 12 in, 1 km = 1,000 m)
  2. Larger to smaller unit: Multiply by the conversion factor
  3. Smaller to larger unit: Divide by the conversion factor
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.
  1. 1 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
📐 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 3-6-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.6 · Part II

On-Level Application · Standard Rigor

Convert Measurements within the Same System · Conversion factor

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 3.6 · Part II
1Converting Measurements (Same System)
2The Structural Procedure
  1. Identify the conversion factor (e.g. 1 ft = 12 in, 1 km = 1,000 m)
  2. Larger to smaller unit: Multiply by the conversion factor
  3. Smaller to larger unit: Divide by the conversion factor
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 DRAG SORT

    Sort each conversion by what happens to the NUMBER.

    Target Categories: The number gets bigger The number gets smaller
    • 7 feet → inches
    • 84 inches → feet
    • 2 liters → milliliters
    • 5,000 milliliters → liters
    • 3 pounds → ounces
    • 64 ounces → pounds
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 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. 3 MULTIPLE CHOICE

    How many inches are in 2 feet?

    1. A24
    2. B14
    3. C10
    4. D12
    ✏️ 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 3-6-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.6 · Part II

Extension & Non-Routine Application

Convert Measurements within the Same System · Conversion factor

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 3.6 · Part II
1Converting Measurements (Same System)
2The Structural Procedure
  1. Identify the conversion factor (e.g. 1 ft = 12 in, 1 km = 1,000 m)
  2. Larger to smaller unit: Multiply by the conversion factor
  3. Smaller to larger unit: Divide by the conversion factor
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

    A rope measures 7 feet. Using 1 foot = 12 inches, how long is the rope in inches?

    1. A84 inches
    2. B19 inches
    3. C7 inches
    4. D0.58 inches
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    A tap fills 250 milliliters every 10 seconds. Will it fill a 3-liter jug in under 2 minutes?

    1. AYes — it delivers 3,000 mL in 120 seconds, exactly filling the jug at the 2-minute mark
    2. BNo — 250 mL in 10 seconds is far too slow for 3 liters
    3. CYes — 3 liters is only 300 mL, so it takes 12 seconds
    4. DThere is not enough information to tell
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 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
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