6.AT.3a Lesson 3-4-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.4 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

Graph Ratio Tables · Coordinate plane · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do we graph a ratio table?
1The points from equal ratios form a straight line that passes through the origin (0, 0) — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
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).
3Second Model — Try it together — then prove it
  1. A recipe uses 1 cup of sugar for every 3 cups of flour.
  2. For 1 cup of sugar, the ordered pair is (1, 3): right 1, up 3.
  3. For 2 cups of sugar, what is the pair? It is (2, 6): right 2, up 6.
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 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. 2 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. 3 MULTIPLE CHOICE

    Points from a ratio table are plotted at (1, 4), (2, 8), and (3, 12). What is the ratio of y to x for each point?

    1. A4:1
    2. B1:4
    3. C2:8
    4. D3:4
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    Two students graph ratio tables. Student A plots (1,2), (2,4), (3,6). Student B plots (1,3), (2,6), (3,9). Whose line is steeper?

    1. AStudent B
    2. BStudent A
    3. CSame steepness
    4. DCannot tell
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Points from a ratio table are plotted at (1, 4), (2, 8), and (3, 12). What is the ratio of y to x for each point?
    2. 2A classmate at our table answered:1:4

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    On Level — Spot the Common Mistake

    1. 1Read the ratio:A recipe uses 4 cups of water for every 1 cup of rice (rule: y = 4x). A student is plotting points for the line.
    2. 2List the points:(1, 4), (2, 8), (3, 12)
    3. 3Add another point:The student also plots (4, 14) and says it belongs on the same line.
    4. 4Conclusion:All four points form a straight line.

    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
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