6.AT.2 Lesson 3-8-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.8 Small Group · Group 2

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

Unit Rate Problem Solving · Unit Rate · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do I use unit rates to find the better buy?
1Divide the price by the number of items to get the cost per unit. The lower cost per unit 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. Fun Supply Co. sells 500 tokens for $60. I want the cost for 1 token.
  2. I divide the price by the tokens: $60 ÷ 500 = $0.12.
  3. So this deal is $0.12 per token. That is the unit rate.
  4. Now I can compare it fairly to a deal with a different number of tokens.
3Second Model — Try it together — then prove it
  1. Arcade Depot sells 350 tokens for $38.50. What do we divide?
  2. We divide price by tokens: $38.50 ÷ 350 = ?
  3. What is the cost per token, and is it lower than $0.12? ($0.11 — yes, the better buy.)
  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
  • Unit Rate Problem Solving (Resolución de problemas con tasas unitarias) — Find an amount per 1 unit and use it to compare choices or solve a problem.
  • Unit Rate (Tasa unitaria) — A rate for just 1 of something, like cost for 1 item.
  • Better Buy (Mejor compra) — The choice that costs less for each item.
  • Comparison (Comparación) — Looking at two or more amounts to see how they are related.
  • Per Unit (Por unidad) — For each single item.
  • Rate (Tasa) — A ratio comparing two amounts with different units, like miles per hour.
5Watch out
  • A common mistake in Solve Problems with Unit Rates is comparing the total prices instead of the cost per item — the deal with the smaller total can still cost more per unit. Always reduce each option to its unit rate before you decide, then pick the lower one.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Which is the better buy: 6 bouncy balls for $4.50 or 10 bouncy balls for $8.00?

    1. A6 for $4.50 — $0.75 each
    2. B10 for $8.00 — $0.80 each
    3. CThey cost the same per ball
    4. DNot enough information
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    A machine dispenses 24 tokens in 3 minutes. At this rate, how many tokens does it dispense in 10 minutes?

    1. A80 tokens
    2. B60 tokens
    3. C72 tokens
    4. D240 tokens
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    A factory produces 360 widgets in 8 hours. At the same rate, how many widgets are produced in a 12-hour shift?

    1. A540 widgets
    2. B480 widgets
    3. C360 widgets
    4. D720 widgets
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Level 2 Extension — Which Water Deal Wins?

    1. 1Which is the better buy: 4 bottles for $5.00 or 6 bottles for $7.20?:Compare two water deals for the snack bar
    2. 2Compare the deals:$5.00 is less than $7.20, so the 4-bottle deal is the better buy.
    3. 3Conclusion:Buy the 4 bottles for $5.00.

    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:The ticket counter sells redemption tickets two ways: 8 tickets for $2.00 or 15 tickets for $3.00. Which costs less per ticket?
    2. 2A classmate at our table answered:Cannot determine

    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:A vending machine dispenses 24 tokens in 3 minutes. How many tokens per minute is that?
    2. 2Attempt:A student writes: 3 ÷ 24 = 0.125, so the machine dispenses 0.125 tokens per minute.
    3. 3Check:The student divided minutes by tokens, which gives minutes per token, not tokens per minute.

    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