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

3.1 Small Group · Group 1

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

Understand 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 is a ratio?
1A ratio compares two quantities, and the order you write them in matters. You can write a ratio in words or with a colon, and you can draw it with a tape diagram or a double number line.
  • A ratio compares two amounts. It tells how much of one thing there is for another thing. 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 cups of apple juice for every 2 cups of sparkling water.
  2. I am comparing two amounts: apple juice and sparkling water.
  3. I write apple juice to sparkling water, in that order, as 3 to 2, or 3:2.
  4. I can also draw the ratio. On a tape diagram I give apple juice 3 equal parts and sparkling water 2 equal parts, so one batch is 5 parts in all.
  5. Those same 5 parts show a second ratio: apple juice to the whole fruit drink is 3 to 5.
  6. On a double number line I line the two amounts up: 5 cups of fruit drink pairs with 3 cups of apple juice, and 10 cups of fruit drink pairs with 6 cups of apple juice.
3Mathematical Word Bank
  • Understand Ratios (Comprender razones) — Use a ratio to compare two quantities by division.
  • Ratio (Razón) — A way to compare two amounts, like 3 to 2.
  • Comparison (Comparación) — Looking at two or more amounts to see how they are related.
  • Part-to-part (Parte a parte) — A ratio comparing one part of a group to another part.
  • Part-to-whole (Parte a todo) — A ratio comparing one part to the whole group.
  • Colon notation (Notación con dos puntos) — Writing a ratio with two dots between the numbers, like 3:2.
4Watch out
  • A common mistake in Understand Ratios is writing the ratio in the wrong order: when asked for the ratio of apple juice to sparkling water in a recipe that uses 3 cups of apple juice for every 2 cups of sparkling water, some students write 2:3 (sparkling water to apple juice) because they list the ingredients in whatever order comes to mind rather than the order the question asks for. The two ratios describe different drinks — 3:2 means 3 cups of juice for every 2 cups of water, while 2:3 would mean only 2 cups of juice for every 3 cups of water. Always match the order of your ratio to the order named in the question: "apple juice to sparkling water" means the apple juice number comes first, giving 3:2.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A fruit salad has 5 pieces of melon, 3 pieces of pineapple, and 2 grapes. What is the ratio of pineapple to melon?

    1. A3:5
    2. B5:3
    3. C3:10
    4. D3:2
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    A parking lot has 10 cars and 6 trucks. What is the part-to-whole ratio of trucks to total vehicles?

    1. A6:16
    2. B10:6
    3. C6:10
    4. D16:6
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Prep Bowl A: Chef Reyes stirs 7 cups of flour with 4 cups of water to make dough. What is the part-to-part ratio of flour to water?

    1. A7:4
    2. B4:7
    3. C7:11
    4. D11:4
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    A class has 5 chefs and 7 helpers (12 total). What is the part-to-whole ratio of chefs to the whole class?

    1. A5:12
    2. B5:7
    3. C7:12
    4. D12:5
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Spot the Mistake — Order of a Ratio

    1. 1Read the problem:A salad bar has 5 bowls of soup and 8 sandwiches. Write the ratio of soup to sandwiches.
    2. 2Identify the amounts:Soup = 5 and sandwiches = 8.
    3. 3Write the ratio:A student writes the ratio of soup to sandwiches as 8:5.
    4. 4Answer:The ratio of soup to sandwiches is 8:5.

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Spot the Mistake — Part-to-Whole Ratio

    1. 1Read the problem:A class has 9 boys and 6 girls. Write the part-to-whole ratio of girls to the whole class.
    2. 2Count the whole:9 + 6 = 15 students in all.
    3. 3Write the ratio:A student writes girls to the whole class as 6:9.
    4. 4Answer:The part-to-whole ratio of girls to the whole class is 6:9.

    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