6.AT.2 Lesson 3-2-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.2 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — 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
  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.
3Second Model — Try it together — then prove it
  1. A booth charges $4 for 8 games. What do we divide?
  2. We divide cost by games: $4 ÷ 8 = ?
  3. What is the unit price, the cost for just 1 game? ($0.50 per game.)
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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

    A booth charges $4.50 for 9 games. What is the unit rate?

    1. A$0.50 per game
    2. B$0.45 per game
    3. C$2.00 per game
    4. D$4.50 per game
    per 1
  2. 2 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
  3. 3 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Level 2 Extension — Inverted Unit Rate: Points per Minute

    1. 1Find the scoring rate in points per minute: 96 points in 6 minutes:96 points in 6 minutes
    2. 2Set up the division:6 ÷ 96 = 0.0625
    3. 3Write the unit rate:The unit rate is 0.0625 points per minute

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem: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?
    2. 2A classmate at our table answered:Pack A

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Read the problem:Pack X is 10 tokens for $4.00. Pack Y is 16 tokens for $6.00. Which is the better buy (lower cost per token)?
    2. 2Compare the deals:Pack X costs $4.00 and Pack Y costs $6.00. The student says Pack X is the better buy because $4.00 is the lower total price.
    3. 3State the answer:The student chooses Pack X.

    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
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