6.AT.2 Lesson 3-2-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.2 Small Group · Group 1

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

Rates and Unit Rates · Rate · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What is a unit rate, and how does it help me find the better buy?
1To find a unit rate, divide the total cost by the number of items. A unit rate that gives a cost is called a unit price, and the lower unit price is the better buy.
  • A rate compares two amounts with different units. A unit rate tells you the amount for just 1 of something, like the cost for 1 game. 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
  1. Booth A charges $3 for 5 games. I want the cost for just 1 game.
  2. I divide the cost by the games: $3 ÷ 5 = $0.60.
  3. So Booth A costs $0.60 per game. That is the unit rate.
  4. Because this unit rate is money for one item, it has its own name: it is the unit price.
  5. Now I can compare this booth's unit price fairly with any other booth's.
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

    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
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  4. 4 MULTIPLE CHOICE

    Nova: 78 points in 6 min. Pulse: 75 points in 5 min. Which scores faster (more points per minute)?

    1. APulse, at 15 points per minute
    2. BNova, at 13 points per minute
    3. CThey score at the same rate
    4. DThere is not enough information
    ✏️ Workspace & Solution Steps
  5. 5 MULTIPLE CHOICE

    Machine A: 150 coins for 5 plays. Machine B: 168 coins for 8 plays. Which is the better value (fewer coins per play)?

    1. AMachine B, at 21 coins per play
    2. BMachine A, at 30 coins per play
    3. CThey are the same value
    4. DMachine A, because it costs fewer coins total
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Read the problem:A booth charges $6.00 for 4 games. Find the unit rate (cost per game).
    2. 2Set up the division:$6.00 ÷ 4 = $1.50, but the student writes $1.05 per game.
    3. 3State the unit rate:The student says each game costs $1.05.

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

    ✏️ Corrected Mathematical Work & Explanation
📐 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