6.AT.3a Lesson 3-4-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.4 Small Group · Group 1

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

Graph Ratio Tables · Coordinate plane · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do we graph a ratio table?
1The points from equal ratios form a straight line that passes through the origin (0, 0).
  • An ordered pair (x, y) tells where to plot a point: go right x, then up y. When you graph equal ratios, the points make a straight line through the origin (0, 0). 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 recipe uses 2 ounces of sauce for every 1 sundae.
  2. I put sundaes on the x-axis and ounces of sauce on the y-axis.
  3. For 1 sundae I need 2 ounces, so I plot the ordered pair (1, 2): right 1, up 2.
  4. For 2 sundaes I need 4 ounces, so I plot (2, 4): right 2, up 4.
  5. When I connect (1, 2), (2, 4), (3, 6), they form a straight line through the origin (0, 0).
3Mathematical Word Bank
  • Graph Ratio Tables (Representar tablas de razones en una gráfica) — Plot the paired values from a ratio table as ordered pairs.
  • Coordinate plane (Plano cartesiano) — A grid with a line going across and a line going up to plot points.
  • Ordered pair (Par ordenado) — Two numbers (x, y) that tell where a point is on a grid.
  • Linear pattern (Patrón lineal) — Points that make a straight line on a grid.
  • Proportional (Proporcional) — Two amounts that grow together at the same rate.
  • Origin (Origen) — The point (0, 0) where the two grid lines cross.
4Watch out
  • A common mistake in Graph Ratio Tables is writing the ordered pair in the wrong order — putting the second table value first instead of matching (x, y) to the table's column order. For example, if a recipe table shows 2 cups of sugar for every 4 cups of flour, a student might plot (4, 2) instead of (2, 4), landing the point in a completely different spot on the grid. Before you plot, check: which quantity goes on the x-axis, and does your ordered pair start with that number?
SECTION 1 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
  1. 1 COORDINATE GRID

    A recipe uses 1 cup of sugar for every 2 cups of flour. Plot the ordered pairs: (1, 2), (2, 4), (3, 6).

    ✏️ Workspace & Solution Steps
  2. 2 COORDINATE GRID

    Chef Reyes uses 3 cups of flour for every 1 cup of sugar. Plot the ordered pairs from the ratio table: (1,3), (2,6), (3,9), (4,12).

    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    A ratio table shows (2, 6), (4, 12), and (6, 18). Which ordered pair comes next if the pattern continues?

    1. A(8, 24)
    2. B(7, 20)
    3. C(8, 22)
    4. D(10, 24)
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    When you graph equivalent ratios, the points will always form what shape?

    1. AA straight line through the origin
    2. BA curved line
    3. CA zigzag
    4. DA circle
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    A ratio table shows (2, 8), (3, 12), and (5, 20). What is the y-value when x = 7?

    1. A28
    2. B24
    3. C21
    4. D35
    My work — one step per lineWhat I did to both sides
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.
  4. 6 MULTIPLE CHOICE

    Which point would NOT be on the graph of the ratio 1:5?

    1. A(3, 10)
    2. B(2, 10)
    3. C(4, 20)
    4. D(5, 25)
    ✏️ 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