Graph Ratio Tables
I can graph the values from a ratio table as points on the coordinate plane.
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🎯 Content Objective / Objetivo de contenido
I can graph the values from a ratio table as points on the coordinate plane.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
The sundae recipe uses 2 ounces of chocolate sauce for every 1 sundae. Before you graph, what do you predict the points will look like, and which quantity goes on each axis?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Scenario Launch
Chef Academy students are tracking how much chocolate sauce they need for different numbers of sundaes. They know the recipe uses 2 ounces of sauce for every 1 sundae. Chef Reyes challenges them to plot the ratio table values on a coordinate grid to see the pattern. Will the points form a straight line?
Concept Launch
💡 How do we graph a ratio table?
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).
The points from equal ratios form a straight line that passes through the origin (0, 0).
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Coordinate plane Plano cartesiano |
A grid with a line going across and a line going up to plot points. Una cuadrícula con una línea horizontal y una vertical para marcar puntos. |
A + shape made by two number lines crossing at the center point (0, 0) | |
| Ordered pair Par ordenado |
Two numbers (x, y) that tell where a point is on a grid. Dos números (x, y) que dicen dónde está un punto en una cuadrícula. |
(3, 6) means go right 3, up 6 | |
| Linear pattern Patrón lineal |
Points that make a straight line on a grid. Puntos que forman una línea recta en una cuadrícula. |
(1,2), (2,4), (3,6) all line up | |
| Proportional Proporcional |
Two amounts that grow together at the same rate. Dos cantidades que crecen juntas al mismo ritmo. |
A straight line from (0,0) through (2,6) and (4,12) | |
| Origin Origen |
The point (0, 0) where the two grid lines cross. El punto (0, 0) donde se cruzan las dos líneas de la cuadrícula. |
The starting corner of the grid at (0, 0) |
Which Word Fits?
The flat grid formed by a horizontal and a vertical number line is the ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
The sundae recipe uses 2 ounces of chocolate sauce for every 1 sundae. Before you graph, what do you predict the points will look like, and which quantity goes on each axis?
👂 Listen For
A strong answer chooses sundaes (x) and ounces of sauce (y), and predicts a straight line because each sundae always needs 2 more ounces.
Extend: Predict whether the line will pass through the origin (0, 0). Justify your prediction using what 0 sundaes would mean.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
The ratio table shows sundaes to ounces of chocolate sauce (1 sundae = 2 oz). Plot each ordered pair on the coordinate grid.
✍️ Explore Discourse
Explain your strategy and reasoning.
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
After plotting (1,2), (2,4), (3,6)... what pattern do you notice, and how does it show the chocolate-sauce ratio?
👂 Listen For
Listen for 'straight line through the origin' and the connection that the constant 2-ounce step shows a proportional relationship.
Extend: Critique this claim: 'Any points that go up to the right form a proportional graph.' What would the points (1,2),(2,4),(3,7) show instead, and why?
Practice Check A
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?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
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?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Equivalent Ratio Sort
Complete the interactive activity using today's strategy.
✍️ Justify Your Thinking
The smoothie line follows the rule y = 2x (2 scoops per cup). Sort each ordered pair: is it ON the line or OFF the line?
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "The points from equal ratios form a straight line that passes through the origin (0, 0)." — and it works because ___.
Because Coordinate plane means ___, but a tricky part is ___, so I have to ___.
A common mistake with Coordinate plane is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Ordered pair to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
The points from equal ratios form a straight line that passes through the origin (0, 0). because ___
The points from equal ratios form a straight line that passes through the origin (0, 0). but ___
The points from equal ratios form a straight line that passes through the origin (0, 0). so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
The ratio table shows sundaes to ounces of chocolate sauce (1 sundae = 2 oz). Plot each ordered pair on the coordinate grid.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
A ratio table shows (2, 6), (4, 12), and (6, 18). Which ordered pair comes next if the pattern continues?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
A food truck tracks how many tacos it sells and how much salsa it uses. After recording data for a week, the owner plots the points on a graph and notices they form a straight line. This helps the owner predict exactly how much salsa to prepare for any number of tacos.
✍️ Connection Reasoning
This is like our graphing work because ___ and ___ are related by ___.
This is like our graphing work because ___ and ___ are related by ___.
Turn & Talk — Connect
The food truck plots tacos vs. salsa and gets a straight line. What does that graph tell the owner about preparing salsa for ANY number of tacos?
👂 Listen For
A strong answer says the proportional line lets the owner read off (or extend to) salsa amounts for taco counts not in the table.
Extend: Generalize: if the food-truck line were steeper than another truck's line, what would that tell you about how much salsa each truck uses per taco?
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
A ratio table shows cups of rice to cups of water: (1, 2), (2, 4), (3, 6). If you plot these points, the line passes through which point?
Bonus Exit Check
A ratio table shows (2, 6), (4, 12), and (6, 18). Which ordered pair comes next if the pattern continues?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• A strong answer chooses sundaes (x) and ounces of sauce (y), and predicts a straight line because each sundae always needs 2 more ounces.
• Listen for 'straight line through the origin' and the connection that the constant 2-ounce step shows a proportional relationship.
• A strong answer says the proportional line lets the owner read off (or extend to) salsa amounts for taco counts not in the table.
• Listen for students naming a specific strategy tied to 6.AT.3a — not just "I multiplied." They should connect steps to the key idea.
Common mistake: A common mistake in Graph Ratio Tables is skipping the key idea: "The points from equal ratios form a straight line that passes through the origin (0, 0)." — always check your work against this rule before you submit.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 4:1 — For each point: 4÷1 = 4, 8÷2 = 4, 12÷3 = 4. The ratio of y to x is always 4:1.
✓ Practice 2: Student B — Student A's ratio is 1:2 (y goes up 2 for each 1 in x). Student B's ratio is 1:3 (y goes up 3 for each 1 in x). A higher rate of change means a steeper line, so Student B's is steeper.
✓ Practice 3: (8, 24) — The pattern adds 2 to x and 6 to y each time. After (6, 18): x = 6+2 = 8, y = 18+6 = 24. The next point is (8, 24).
✓ Practice 4: A straight line through the origin — Equivalent ratios are proportional, so their graph is always a straight line that passes through the origin (0, 0).
✓ Exit ticket: (5, 10) — The ratio is 1:2, so for 5 cups of rice you need 5 × 2 = 10 cups of water. The point (5, 10) continues the pattern.