6.AT.1 Lesson 3-1-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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3.1 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each statement: does it describe a ratio or NOT describe a ratio?

    Target Categories: IS a Ratio NOT a Ratio
    • 2 DRAG SORT

      Sort each statement — is it a part-to-part ratio or a part-to-whole ratio?

      Target Categories: Part-to-Part Part-to-Whole
      SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
      1. 3 MULTIPLE CHOICE

        A recipe uses 4 cups of milk and 1 cup of cream. What is the ratio of milk to cream?

        1. A4:1
        2. B1:4
        3. C4:5
        4. D5:1
        ✏️ Workspace & Solution Steps
      2. 4 MULTIPLE CHOICE

        Chef Reyes uses 6 strawberries and 2 bananas in a smoothie. What is the part-to-whole ratio of bananas to total fruit?

        1. A2:8
        2. B6:2
        3. C2:6
        4. D8:2
        ✏️ Workspace & Solution Steps
      3. 5 MULTIPLE CHOICE

        In a class of 30 students, 18 are girls. What is the part-to-part ratio of boys to girls?

        1. A12:18
        2. B18:12
        3. C18:30
        4. D12:30
        ✏️ Workspace & Solution Steps
      4. 6 MULTIPLE CHOICE

        A pet store has 5 dogs and 9 cats. What is the ratio of dogs to cats?

        1. A5:9
        2. B9:5
        3. C5:14
        4. D14:5
        ✏️ Workspace & Solution Steps
      🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

      Group Discussion Prompt: How does your visual model justify your mathematical solution?

      🗣️ Partner A:
      Partner A: "I modeled this by identifying the relationship and..."
      👂 Partner B:
      Partner B: "I agree with your step because the standard mathematical rule states..."
      ✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

      Complete each sentence stem to demonstrate precise mathematical reasoning:

      BECAUSE The ratio remains equivalent because both quantities are scaled by the exact same multiplicative factor.
      BUT Two ratios may look similar, but inverting the order of terms fundamentally changes the comparison.
      SO The recipe requires 3 parts flour to 2 parts water, so the unit rate is 1.5 cups of flour per cup of water.
      📐 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