6.AT.3 Lesson 3-5-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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3.5 Small Group · Group 1

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

Compare Ratios · Unit rate · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do we compare two ratios?
1Compare ratios fairly by making one part equal or by finding the unit rate.
  • To compare ratios fairly, make one amount the same in both, or find the unit rate (the amount for just 1). Then you can see which ratio is bigger. 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. Chef Reyes uses 3 tbsp cocoa for 5 oz milk (3:5). Chef Tran uses 4 tbsp for 7 oz milk (4:7).
  2. I cannot compare yet because the milk amounts are different.
  3. I scale both to 35 oz of milk. For Reyes: 5 x 7 = 35, so 3 x 7 = 21 tbsp, giving 21:35.
  4. For Tran: 7 x 5 = 35, so 4 x 5 = 20 tbsp, giving 20:35.
  5. Now the milk is equal, so I compare cocoa: 21 > 20, so Chef Reyes's cocoa is more chocolatey.
3Mathematical Word Bank
  • Compare Ratios (Comparar razones) — Decide which ratio is greater, less, or equal by using equivalent ratios or unit rates.
  • Unit rate (Tasa unitaria) — A rate for just 1 of something, like cost for 1 item.
  • Equivalent ratio (Razón equivalente) — Two ratios that mean the same thing.
  • Compare (Comparar) — To look at ratios and see which is bigger, smaller, or equal.
  • Simplify (Simplificar) — To write a ratio with smaller numbers that still compares the same way. 6:8 and 3:4 are the same ratio.
  • Common denominator (Denominador común) — A bottom number that two fractions can share so you can compare them.
4Watch out
  • A common mistake in Compare Ratios is thinking the ratio with the bigger raw number automatically wins — like assuming Chef Tran's 8 tablespoons of cocoa must be more chocolatey than Chef Reyes's 6 tablespoons, without checking that the milk amounts (14 oz vs. 10 oz) are different. Never compare the raw numbers alone — always scale both ratios to the same amount or find each unit rate first.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Find the unit rate for each option to compare them.

    OptionRatioUnit Rate
    Juice A
    Juice B
    Juice C
    ✏️ Scratchpad / Reasoning
  2. 2 DRAG SORT

    Match each scenario to the correct answer: Which ratio is greater?

    Target Categories: Correct Comparison Incorrect Comparison
    SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
    1. 3 MULTIPLE CHOICE

      Chef A uses 2 cups of cheese for every 8 crackers. Chef B uses 3 cups of cheese for every 9 crackers. Who uses more cheese per cracker?

      1. AChef B
      2. BChef A
      3. CThey use the same amount
      4. DCannot determine
      ✏️ Workspace & Solution Steps
    2. 4 MULTIPLE CHOICE

      Which ratio is greater: 3:4 or 5:8?

      1. A3:4
      2. B5:8
      3. CThey are equal
      4. DCannot determine
      ✏️ Workspace & Solution Steps
    3. 5 MULTIPLE CHOICE

      Which lemonade recipe is more lemony? Recipe A: 2 lemons for 6 cups of water. Recipe B: 3 lemons for 7 cups of water.

      1. ARecipe B
      2. BRecipe A
      3. CThey are the same
      4. DCannot determine
      ✏️ Workspace & Solution Steps
    4. 6 MULTIPLE CHOICE

      Which is the better deal: 4 apples for $3 or 6 apples for $5?

      1. A4 apples for $3
      2. B6 apples for $5
      3. CThey cost the same
      4. DCannot determine
      ✏️ 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