6.AT.3 Lesson 3-5-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.5 Small Group · Group 1

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

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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Store A sells 3 mangoes for $6. Store B sells 5 mangoes for $9. Which store offers a better price per mango?

    1. AStore B
    2. BStore A
    3. CSame price
    4. DCannot determine
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Chef Academy's snack bar sells 3 mini quiches for $6 or 5 mini quiches for $8. Which is the better deal per quiche?

    1. A5 quiches for $8
    2. B3 quiches for $6
    3. CThey cost the same
    4. DCannot determine
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Two soup recipes use salt. Recipe A uses 4 tsp salt for 10 cups of broth. Recipe B uses 3 tsp salt for 8 cups of broth. Which soup is saltier per cup?

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

    Chef Mara's lemon glaze uses 6 oz of lemon juice for 9 cupcakes. Chef Devi's uses 4 oz for 7 cupcakes. Whose glaze has more lemon per cupcake?

    1. AChef Mara
    2. BChef Devi
    3. CSame amount
    4. DCannot determine
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Read the problem:Chef Priya makes hot chocolate with 2 tbsp cocoa for 4 oz milk. Chef Owen makes hot chocolate with 3 tbsp cocoa for 8 oz milk. Whose hot chocolate is more chocolatey?
    2. 2Compare the cocoa:Chef Owen has 3 tbsp cocoa. Chef Priya has 2 tbsp cocoa.
    3. 3Draw a conclusion:Since 3 is greater than 2, Chef Owen's hot chocolate must be more chocolatey.
    4. 4Conclusion:Chef Owen's hot chocolate is more chocolatey.

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Level 2 Extension — Chef Omar's Glaze Comparison

    1. 1Read the problem:Chef Omar compares two glazes: 3 oz syrup for 8 oz water and 5 oz syrup for 16 oz water. Which is sweeter per ounce of water?
    2. 2Look at the syrup:Glaze 1 has 3 oz syrup. Glaze 2 has 5 oz syrup.
    3. 3Compare the syrup amounts:Since 5 > 3, Glaze 2 must have more syrup per ounce of water.
    4. 4Conclusion:Glaze 2 is sweeter per ounce of water.

    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