6.AT.2 Lesson 3-2-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.2 · Part II

Supported Application · Guided Entry to Today's Problem

Rates and Unit Rates · Rate

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 3.2 · Part II
1Rates & Unit Rates
2Strategy Model — step by step
  1. Rate: A ratio comparing two quantities with different units (e.g. $12 for 3 lbs)
  2. Unit Rate: A rate simplified to a denominator of 1 unit ($4 per 1 lb)
  3. Divide numerator by denominator to compute the per-one amount
3Mathematical Word Bank
  • Rates and Unit Rates (Tasas y tasas unitarias) — A rate compares different units; a unit rate compares a quantity to 1 unit.
  • Rate (Tasa) — A ratio comparing two amounts with different units, like miles per hour.
  • Unit Rate (Tasa unitaria) — A rate for just 1 of something, like cost for 1 item.
  • Per (Por) — For each one. Example: 5 dollars per book.
  • Ratio (Razón) — A way to compare two amounts, like 3 to 2.
  • Unit price (Precio unitario) — A unit rate that gives the cost of exactly 1 item, like $0.60 per game.
4Watch out
  • A common mistake in Rates and Unit Rates is comparing total costs instead of unit rates: a student sees Pack X at $4.00 for 10 tokens and Pack Y at $6.00 for 16 tokens and picks Pack X just because $4.00 is the smaller number, without dividing to find the cost per token ($0.40 for Pack X vs. $0.375 for Pack Y — Pack Y is actually the better buy). A second common mistake is dividing backwards — finding tokens ÷ cost instead of cost ÷ tokens — which turns 'dollars per token' into 'tokens per dollar' and gives an answer that looks reasonable but answers the wrong question. Always divide the total cost by the number of items, and check that your unit rate answers 'the cost for ONE item,' not the reverse.
  1. 1 MULTIPLE CHOICE

    Which is a unit rate?

    1. A12 miles per 1 hour
    2. B24 miles in 2 hours
    3. C36 miles for 3 gallons
    4. D100 points in 5 games
    ✏️ 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.2 Lesson 3-2-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.2 · Part II

On-Level Application · Standard Rigor

Rates and Unit Rates · Rate

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 3.2 · Part II
1Rates & Unit Rates
2The Structural Procedure
  1. Rate: A ratio comparing two quantities with different units (e.g. $12 for 3 lbs)
  2. Unit Rate: A rate simplified to a denominator of 1 unit ($4 per 1 lb)
  3. Divide numerator by denominator to compute the per-one amount
3Mathematical Word Bank
  • Rates and Unit Rates (Tasas y tasas unitarias) — A rate compares different units; a unit rate compares a quantity to 1 unit.
  • Rate (Tasa) — A ratio comparing two amounts with different units, like miles per hour.
  • Unit Rate (Tasa unitaria) — A rate for just 1 of something, like cost for 1 item.
  • Per (Por) — For each one. Example: 5 dollars per book.
  • Ratio (Razón) — A way to compare two amounts, like 3 to 2.
  • Unit price (Precio unitario) — A unit rate that gives the cost of exactly 1 item, like $0.60 per game.
4Watch out
  • A common mistake in Rates and Unit Rates is comparing total costs instead of unit rates: a student sees Pack X at $4.00 for 10 tokens and Pack Y at $6.00 for 16 tokens and picks Pack X just because $4.00 is the smaller number, without dividing to find the cost per token ($0.40 for Pack X vs. $0.375 for Pack Y — Pack Y is actually the better buy). A second common mistake is dividing backwards — finding tokens ÷ cost instead of cost ÷ tokens — which turns 'dollars per token' into 'tokens per dollar' and gives an answer that looks reasonable but answers the wrong question. Always divide the total cost by the number of items, and check that your unit rate answers 'the cost for ONE item,' not the reverse.
  1. 1 MULTIPLE CHOICE

    Token packs: Pack A is 20 tokens for $5.00, Pack B is 35 tokens for $7.00, and Pack C is 50 tokens for $12.50. Which pack is the best deal per token?

    1. APack A
    2. BPack B
    3. CPack C
    4. DThey are all the same
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Runner A completes 4 laps in 12 minutes. Runner B completes 5 laps in 14 minutes. Who runs more laps per minute?

    1. ARunner B
    2. BRunner A
    3. CSame rate
    4. DCannot determine
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    The Star Blaster cabinet scored 90 points in 3 games. What is the unit rate in points per game?

    1. A30 points per game
    2. B270 points per game
    3. C3 points per game
    4. D93 points per game
    per 1
📐 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.2 Lesson 3-2-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.2 · Part II

Extension & Non-Routine Application

Rates and Unit Rates · Rate

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 3.2 · Part II
1Rates & Unit Rates
2The Structural Procedure
  1. Rate: A ratio comparing two quantities with different units (e.g. $12 for 3 lbs)
  2. Unit Rate: A rate simplified to a denominator of 1 unit ($4 per 1 lb)
  3. Divide numerator by denominator to compute the per-one amount
3Mathematical Word Bank
  • Rates and Unit Rates (Tasas y tasas unitarias) — A rate compares different units; a unit rate compares a quantity to 1 unit.
  • Rate (Tasa) — A ratio comparing two amounts with different units, like miles per hour.
  • Unit Rate (Tasa unitaria) — A rate for just 1 of something, like cost for 1 item.
  • Per (Por) — For each one. Example: 5 dollars per book.
  • Ratio (Razón) — A way to compare two amounts, like 3 to 2.
  • Unit price (Precio unitario) — A unit rate that gives the cost of exactly 1 item, like $0.60 per game.
4Watch out
  • A common mistake in Rates and Unit Rates is comparing total costs instead of unit rates: a student sees Pack X at $4.00 for 10 tokens and Pack Y at $6.00 for 16 tokens and picks Pack X just because $4.00 is the smaller number, without dividing to find the cost per token ($0.40 for Pack X vs. $0.375 for Pack Y — Pack Y is actually the better buy). A second common mistake is dividing backwards — finding tokens ÷ cost instead of cost ÷ tokens — which turns 'dollars per token' into 'tokens per dollar' and gives an answer that looks reasonable but answers the wrong question. Always divide the total cost by the number of items, and check that your unit rate answers 'the cost for ONE item,' not the reverse.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Booth A charges $3 for 5 games. What is the unit rate in dollars per game?

    1. A$0.60 per game
    2. B$1.67 per game
    3. C$15.00 per game
    4. D$0.30 per game
    per 1
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 2 OPEN RESPONSE

    An arcade sells tokens in three packs: 25 tokens for $5, 60 tokens for $10.80, and 100 tokens for $19. A student says the 100-token pack is always the best deal because you get the most tokens. Is the student correct? Find all three unit rates and explain.

    ✏️ 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