6.AT.3a Lesson 3-4-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.4 · Part II

Supported Application · Guided Entry to Today's Problem

Graph Ratio Tables · Coordinate plane

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 3.4 · Part II
1Graphing Equivalent Ratios
2Strategy Model — step by step
  1. Form ordered pairs (x, y) from columns or rows in a ratio table
  2. Plot the points on the coordinate plane
  3. Proportional Relationship: Points form a straight line passing 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?
  1. 1 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
  2. 2 MULTIPLE CHOICE

    (Lesson 3.1) 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
  3. 3 MULTIPLE CHOICE

    (Lesson 3.1) 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
📐 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
6.AT.3a Lesson 3-4-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.4 · Part II

On-Level Application · Standard Rigor

Graph Ratio Tables · Coordinate plane

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 3.4 · Part II
1Graphing Equivalent Ratios
2The Structural Procedure
  1. Form ordered pairs (x, y) from columns or rows in a ratio table
  2. Plot the points on the coordinate plane
  3. Proportional Relationship: Points form a straight line passing 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?
  1. 1 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
  2. 2 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
  3. 3 MULTIPLE CHOICE

    Recipe: 1 cup berries to 2 scoops yogurt. With cups on x and scoops on y, which pair shows 3 cups?

    1. A(3, 6)
    2. B(6, 3)
    3. C(3, 5)
    4. D(3, 3)
    ✏️ Workspace & Solution Steps
📐 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
6.AT.3a Lesson 3-4-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.4 · Part II

Extension & Non-Routine Application

Graph Ratio Tables · Coordinate plane

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 3.4 · Part II
1Graphing Equivalent Ratios
2The Structural Procedure
  1. Form ordered pairs (x, y) from columns or rows in a ratio table
  2. Plot the points on the coordinate plane
  3. Proportional Relationship: Points form a straight line passing 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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A ratio table pairs 1 hour with 45 miles, 2 hours with 90 miles, and 3 hours with 135 miles. Which ordered pair belongs on the graph of this relationship?

    1. A(4, 180)
    2. B(4, 45)
    3. C(180, 4)
    4. D(4, 140)
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 2 OPEN RESPONSE

    A student plots the points (1, 3), (2, 6), (3, 9), and (4, 15) from a ratio table. She says they form a straight line because they go up. Is she correct? Explain how to check.

    ✏️ Mathematical Justification & Response
📐 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