6.AT.3 Lesson 3-9-part2 Apply Day · Practice
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3.9 · Part II

Application Practice for Today's Problem

Equivalent Ratios · Ratio

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 3.9 · Part II
1Proportions & Equivalent Ratios
2Strategy Model — step by step
  1. Two ratios are equivalent if their simplified forms or cross products are equal
  2. Find the scale factor between corresponding terms
  3. Multiply or divide to solve for the missing term in the proportion
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

    What is the simplest form of the ratio 15:25?

    1. A3:5
    2. B5:3
    3. C1:5
    4. D15:25
    ✏️ Workspace & Solution Steps
  2. 2 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
  3. 3 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
  4. 4 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. 5 OPEN RESPONSE

    A store sells 3 pens for $2. Another store sells 9 pens for $6. Are these equivalent ratios? If so, prove it using at least two different methods (simplifying, scaling, or cross-multiplying).

    ✏️ Mathematical Justification & Response
📐 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