3.4 Small Group · Group 1
Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems
Graph Ratio Tables · Coordinate plane · Procedural Fluency · Reasoning & Critique
- 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.
- The recipe uses 2 ounces of sauce for every 1 sundae.
- I put sundaes on the x-axis and ounces of sauce on the y-axis.
- For 1 sundae I need 2 ounces, so I plot the ordered pair (1, 2): right 1, up 2.
- For 2 sundaes I need 4 ounces, so I plot (2, 4): right 2, up 4.
- When I connect (1, 2), (2, 4), (3, 6), they form a straight line through the origin (0, 0).
- 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.
- 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?
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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?
- A4:1
- B1:4
- C2:8
- D3:4
✏️ Workspace & Solution Steps -
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?
- AStudent B
- BStudent A
- CSame steepness
- DCannot tell
✏️ Workspace & Solution Steps -
3 MULTIPLE CHOICE
Recipe: 1 cup berries to 2 scoops yogurt. With cups on x and scoops on y, which pair shows 3 cups?
- A(3, 6)
- B(6, 3)
- C(3, 5)
- D(3, 3)
✏️ Workspace & Solution Steps -
4 MULTIPLE CHOICE
On the smoothie graph, every point follows the rule scoops = 2 × cups. Which equation describes the pattern between x (cups) and y (scoops)?
- Ay = 2x
- By = x + 2
- Cy = x ÷ 2
- Dx = 2y
✏️ Workspace & Solution Steps
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5 ERROR ANALYSIS
Level 1 — Spot the Common Mistake
- 1Read the ratio:A recipe uses 1 cup of sugar for every 2 cups of flour. Plot the point for 3 cups of sugar.
- 2Find the flour:3 cups of sugar means 3 + 2 = 5 cups of flour.
- 3Write the ordered pair:(3, 5)
Which step contains the error? Explain the mathematical misconception and write the correct calculation below.
✏️ Corrected Mathematical Work & Explanation -
6 ERROR ANALYSIS
On Level — Spot the Common Mistake
- 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.
- 2List the points:(1, 4), (2, 8), (3, 12)
- 3Add another point:The student also plots (4, 14) and says it belongs on the same line.
- 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
Writing Task: Justify why your mathematical solution is accurate and complete.