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

3.2 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Find the unit rate for each arcade deal.

    DealTotal CostNumber of GamesUnit Rate
    Deal A
    Deal B
    Deal C
    ✏️ Scratchpad / Reasoning
  2. 2 FILL TABLE

    Complete the table to find unit rates and determine the best deal.

    DealQuantityCostUnit Rate
    Tokens Pack A
    Tokens Pack B
    Tokens Pack C
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 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
    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?
  2. 4 MULTIPLE CHOICE

    A car travels 180 miles using 6 gallons of gas. What is the unit rate in miles per gallon?

    1. A30 miles per gallon
    2. B6 miles per gallon
    3. C180 miles per gallon
    4. D36 miles per gallon
    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?
  3. 5 MULTIPLE CHOICE

    A pack of 8 markers costs $6.00. What is the cost per marker?

    1. A$0.75
    2. B$0.80
    3. C$1.33
    4. D$0.60
    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. 6 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
🗣️ 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
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