3.10 Small Group · Group 2

Tier 1 Extension · Non-Routine Synthesis · Misconception Traps · Rigorous CER Proofs

Convert Measurement Units · Conversion Factor · Procedural Fluency · Reasoning & Critique

Name: Date: Period: Learning Goal:

■ ADVANCED CONCEPT ANCHOR: Push further — How do I change one measurement unit into another?

1Multiply when changing to a smaller unit, and divide when changing to a bigger unit — and you can say why it is true, and where it would stop being true.

You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.

2Worked Example — Watch me

The cabinet is 5 feet tall. I want to know how many inches that is.
My conversion factor is 1 foot = 12 inches.
Inches are smaller than feet, so I multiply: 5 × 12 = 60.
So 5 feet = 60 inches.

3Second Model — Try it together — then prove it

A wire is 4 yards long. The factor is 1 yard = 3 feet.
Feet are smaller than yards, so do we multiply or divide? (Multiply)
What is 4 × 3 feet? (12 feet)
Now a metric example: a power cable is 3 meters long. The factor is 1 meter = 100 centimeters.
Centimeters are smaller than meters, so we multiply: 3 × 100 = 300 centimeters.
Now prove it: say why that move had to work at all — not just that it did.
Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."

4Mathematical Word Bank

Convert Measurement Units (Convertir unidades de medida) — Rename a measurement in a different unit without changing its amount.
Conversion Factor (Factor de conversión) — A ratio that helps you change one unit into another.
Unit (Unidad) — A standard amount used to measure, like an inch or a liter.
Equivalent (Equivalente) — Having the same value, just in different units.
Ratio (Razón) — A way to compare two amounts, like 3 to 2.
Customary units (Unidades usuales (sistema inglés)) — The U.S. way of measuring, like inches, feet, and pounds.

5Watch out

A common mistake in Convert Measurement Units is applying the conversion factor in the wrong direction — for example, converting 4 feet to inches by dividing (4 ÷ 12 = 0.33 inches) instead of multiplying (4 × 12 = 48 inches), or converting 80 ounces to pounds by multiplying (80 × 16 = 1,280 pounds) instead of dividing (80 ÷ 16 = 5 pounds). Before you answer, ask: am I changing to a SMALLER unit (there will be MORE of them, so multiply) or a BIGGER unit (there will be FEWER of them, so divide)?

SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]

1 MATCHING GAME
Match each measurement to its equivalent value.
1. 3 yards
2. 4 feet
3. 5 pounds
4. 2 yards
5. 36 inches
6. 3 pounds
- A9 feet
- B48 inches
- C80 ounces
- D72 inches
- E3 feet
- F48 ounces
2 FILL TABLE

An arcade cabinet has parts measured in different units. Convert each to the target unit.

Part Measurement Target Unit Converted
Power cord
Top panel
Weight
Side rail

✏️ Scratchpad / Reasoning

SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]

3 MULTIPLE CHOICE
Leg 1: The joystick rod is 3 feet long, but the parts catalog lists it in inches. How many inches is that? (1 ft = 12 in)
1. A36 inches
2. B15 inches
3. C30 inches
4. D33 inches
✏️ Workspace & Solution Steps
4 MULTIPLE CHOICE
Leg 2: A power cable on the cabinet plan measures 2.5 kilometers across the whole arcade network. How many meters is that? (1 km = 1,000 m)
1. A2,500 meters
2. B250 meters
3. C25 meters
4. D25,000 meters
✏️ Workspace & Solution Steps
5 MULTIPLE CHOICE
Leg 3: The coin box weighs 5 pounds, but the shipping label needs the weight in ounces. How many ounces is that? (1 lb = 16 oz)
1. A80 ounces
2. B21 ounces
3. C75 ounces
4. D16 ounces
✏️ Workspace & Solution Steps

SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]

6 ERROR ANALYSIS
Level 2 Extension — Multiply or Divide?
1. 1Convert 4 feet of side panel to inches:4 feet → inches
2. 2Use the conversion factor:1 foot = 12 inches
3. 3Operate:4 ÷ 12 = 0.33 inches
4. 4Final answer:4 feet ≈ 0.33 inches
Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

✏️ Corrected Mathematical Work & Explanation

🗣️ 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

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.

✍️ AUTHOR YOUR OWN EXTENSION CHALLENGE

Create an original multi-step word problem aligned to this standard. Include constraints, and write the complete step-by-step mathematical proof below.

✏️ Author Workspace & Complete Solution Key

Student Mastery Self-Assessment:

1 · Need More Support

2 · Getting Closer

3 · Got It / Solid

4 · Master / Can Teach It

Part	Measurement	Target Unit	Converted
Power cord
Top panel
Weight
Side rail