6.AT.3 Lesson 3-9-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.9 Small Group · Group 1

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

Equivalent Ratios · Ratio · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What are equivalent ratios?
1Multiply or divide both numbers by the same amount to make an equivalent ratio.
  • Equivalent ratios are ratios that mean the same thing. You make one by multiplying or dividing BOTH numbers by the same amount. 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 Montoya's soup serves 8 people, but she needs to serve 32.
  2. I find the scale factor: 32 divided by 8 = 4.
  3. The recipe uses 3 cups of tomatoes to 2 cups of broth, a 3:2 ratio.
  4. I multiply both by 4: 3 x 4 = 12 cups of tomatoes, and 2 x 4 = 8 cups of broth.
  5. So 3:2 and 12:8 are equivalent ratios, and the flavor stays the same.
3Mathematical Word Bank
  • Equivalent Ratios (Razones equivalentes) — Ratios that compare quantities in the same relationship.
  • Ratio (Razón) — A way to compare two amounts, like 3 to 2.
  • Rate (Tasa) — A ratio comparing two amounts with different units, like miles per hour.
  • Proportion (Proporción) — A math sentence saying two ratios are 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.
  • Ratio table (Tabla de razones) — A table of equal ratios that shows a pattern.
4Watch out
  • A common mistake in Equivalent Ratios is ADDING the scale factor to one part instead of MULTIPLYING both parts by it. For example, scaling 2:5 by a factor of 4 should give 8:20 (2×4 and 5×4) — not 6:9 (2+4 and 5+4). Adding changes the taste of the recipe (and the value of the ratio); only multiplying or dividing both numbers by the same amount keeps it equivalent.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Marcus earns $45 for every 3 hours of work. How much does he earn in 8 hours?

    1. A$120
    2. B$90
    3. C$135
    4. D$105
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Chef Montoya's dressing uses 3 spoons of oil to 4 spoons of vinegar (3:4). Which recipe card shows an EQUIVALENT ratio?

    1. A9:12
    2. B4:3
    3. C3:8
    4. D6:7
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    The lemonade station mixes 5 cups of lemon juice to 2 cups of sugar (5:2). Which batch keeps the SAME taste?

    1. A15:6
    2. B10:6
    3. C5:4
    4. D7:4
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Spot the Common Mistake — Lemonade Ratio

    1. 1Set up the ratio:2 cups lemon : 5 cups water = 6 cups lemon : ? cups water
    2. 2Find the multiplier:6 ÷ 2 = 3
    3. 3Apply to the water:5 + 3 = 8
    4. 4Answer:6 cups lemon : 8 cups water

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Spot the Common Mistake — Simplifying a Ratio

    1. 1Set up the ratio:A student wants to write 12:18 in simplest form.
    2. 2Find the common factor:Both 12 and 18 can be divided by 6.
    3. 3Divide each part:12 ÷ 6 = 2 and 18 ÷ 3 = 6, so they wrote 2:6.
    4. 4Answer:12:18 simplifies to 2:6

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Level 2 Extension — The Scaled-Up Pancake Batter

    1. 1Set up the ratio:3 cups flour : 8 cups water = ? : 24 cups water
    2. 2Find the multiplier:24 ÷ 8 = 3
    3. 3Apply to the flour:3 + 3 = 6
    4. 4Answer:6 cups flour : 24 cups 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