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

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

Ratio Tables · Ratio table · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do ratio tables work?
1To keep a ratio the same, multiply both numbers by the same scale factor.
  • A ratio table lists equal ratios in rows. To make a new row, you multiply BOTH numbers by the same amount, called the scale factor. 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. The pancake recipe is 2 cups of mix for every 3 cups of milk, so the ratio is 2:3.
  2. To make 2 batches, my scale factor is 2.
  3. I multiply both numbers by 2: 2 x 2 = 4 cups of mix, and 3 x 2 = 6 cups of milk.
  4. Now my row is 4:6, which is the same ratio as 2:3.
  5. I do NOT add 2 to each number; I multiply both by the same factor.
3Mathematical Word Bank
  • Ratio Tables (Tablas de razones) — Tables that organize pairs of equivalent ratios.
  • Ratio table (Tabla de razones) — A table of equal ratios that shows a pattern.
  • Equivalent ratio (Razón equivalente) — Two ratios that mean the same thing, like 1:2 and 2:4.
  • Scale factor (Factor de escala) — The number you multiply both parts of a ratio by to get an equal ratio.
  • Pattern (Patrón) — A rule that numbers follow again and again.
  • Additive pattern (Patrón aditivo) — Building new rows of a ratio table by adding each column's own constant amount, so the two columns grow together.
4Watch out
  • A common mistake in Ratio Tables is scaling only ONE part of the ratio, or adding the scale factor to a part instead of multiplying by it — for example, turning 2:3 into 6:3 (multiplying only the first number by 3 and forgetting the second) or into 4:5 (adding the scale factor 2 to the second number instead of multiplying, since 3+2=5 but 3×2=6). Before you submit, multiply BOTH numbers by the same scale factor and check that your new ratio simplifies back to the original.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    A cookie recipe uses 2 cups of butter for every 5 cups of flour. Complete the ratio table.

    BatchesButter (cups)Flour (cups)
    1
    2
    3
    ✏️ Scratchpad / Reasoning
  2. 2 FILL TABLE

    Complete the ratio table for lemon juice to water in Chef Reyes's lemonade recipe (1 cup lemon juice for every 4 cups water).

    PitchersLemon Juice (cups)Water (cups)
    1
    2
    5
    10
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    A recipe uses 3 eggs for every 5 cups of flour. How many eggs are needed for 15 cups of flour?

    1. A9
    2. B6
    3. C10
    4. D12
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    Which row does NOT belong in a ratio table for 4:5?

    1. A6:10
    2. B8:10
    3. C12:15
    4. D16:20
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    A ratio table shows 3:7, 6:14, and 9:21. What is the next row?

    1. A12:28
    2. B10:24
    3. C12:24
    4. D15:28
    ✏️ Workspace & Solution Steps
  4. 6 MULTIPLE CHOICE

    A ratio table for 2:5 starts with 2:5, 4:10. What is the third row?

    1. A6:15
    2. B6:12
    3. C8:15
    4. D5:10
    ✏️ 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