6.AT.3 Lesson 3-5-part2 Apply Day · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.5 · Part II

Second Practice Form · Independent Application and Spiral Review

Compare Ratios · Unit rate

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 3.5 · Part II
1Comparing Ratio Relationships
2The Structural Procedure
  1. Convert each ratio to a unit rate (e.g. price per item or miles per gallon)
  2. Alternatively, scale both ratios to a common term (like a common denominator)
  3. Compare the resulting unit rates to identify the better buy or faster rate
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

    Car A travels 180 miles on 6 gallons. Car B travels 225 miles on 9 gallons. Which car gets better gas mileage?

    1. ACar A, at 30 miles per gallon
    2. BCar B, at 25 miles per gallon
    3. CCar B, because it traveled farther
    4. DThey are equal
    ✏️ Workspace & Solution Steps
  2. 2 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
  3. 3 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
  4. 4 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 OPEN RESPONSE

    Store A sells 5 notebooks for $12. Store B sells 8 notebooks for $20. Without calculating, a student says Store B must be cheaper because you get more notebooks. Is the student's reasoning valid? Find the unit rates to prove your answer.

    ✏️ 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
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It