Lesson 3.4Determine Equivalent Ratios Using Graphs
Start hereWords, worked example, and sentence starters
Learning target I can graph the values from a ratio table as points on the coordinate plane.
Why This Matters The organizers of a soccer league ordered 6 of the bags shown to hold soccer balls. Each bag holds the same number of soccer balls. How many soccer balls will the bags hold?
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| Coordinate planeSpanish: Plano cartesiano | A grid with a line going across and a line going up to plot points. | x across, y up |
| Ordered pairSpanish: Par ordenado | Two numbers (x, y) that tell where a point is on a grid. | (2, 14) |
| Linear patternSpanish: Patrón lineal | Points that make a straight line on a grid. | (1,2), (2,4), (3,6) all line up |
| ProportionalSpanish: Proporcional | Two amounts that grow together at the same rate. | A straight line from (0,0) through (2,6) and (4,12) |
| OriginSpanish: Origen | The point (0, 0) where the two grid lines cross. | 0 pages, 0 stickers |
| Ratio tableSpanish: Tabla de razones | A table of equal ratios that shows a pattern. | Cups of juice: 2, 4, 6 | Cups of water: 3, 6, 9 |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Each tray holds 8 muffins (x = trays, y = muffins). Write and plot three points.
- Table: 1 tray = 8, 2 trays = 16, 3 trays = 24.
- Pairs: (1, 8), (2, 16), (3, 24).
- Plot each pair from (0, 0): across x, then up y.
Answer: The points lie on one straight line through (0, 0)
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A recipe uses 1 cup of sugar for every 3 cups of flour.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The point ( , ) means .
- The origin means .
- I found y by multiplying x by .
- The points form a straight line because .
Word bank coordinate planeordered pairoriginx-axisy-axisplotpointstraight linetablemultiplyacrossup
Watch out!A common mistake
A common mistake in Graph Ratio Tables is writing the ordered pair in the wrong order
Lesson 3.4Determine Equivalent Ratios Using Graphs
Version ASupported practice
Learning target I can graph the values from a ratio table as points on the coordinate plane.
Why This Matters The organizers of a soccer league ordered 6 of the bags shown to hold soccer balls. Each bag holds the same number of soccer balls. How many soccer balls will the bags hold?
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1Plot and label each point on the grid.
A recipe uses 1 cup of sugar for every 2 cups of flour. Plot the ordered pairs: (1, 2), (2, 4), (3, 6).
Hint Each pair is (sugar, flour): the first number tells you how far RIGHT, the second how far UP.
Show your thinking
-
2Circle the letter of the best answer. Show how you know.
A ratio table shows (2, 6), (4, 12), and (6, 18). Which ordered pair comes next if the pattern continues?
- A(7, 20)
- B(8, 24)
- C(8, 22)
- D(10, 24)
Hint Watch each coordinate separately: x goes 2, 4, 6, … and y goes 6, 12, 18, …
Show your work -
3Circle the letter of the best answer. Show how you know.
When you graph equivalent ratios, the points will always form what shape?
- AA curved line
- BA straight line through the origin
- CA zigzag
- DA circle
Hint Think about what happened when you plotted equivalent-ratio points earlier in this lesson.
Show your work -
4Circle the letter of the best answer. Show how you know.
A ratio table shows (2, 8), (3, 12), and (5, 20). What is the y-value when x = 7?
- A21
- B24
- C28
- D35
Hint Compare each pair: 2 → 8, 3 → 12, 5 → 20. What is done to x to get y every time?
My work — one step per line What I did to both sides - 1LookWhat is done to the variable?
- 2UndoDo the opposite — both sides.
- 3SimplifyOne side at a time.
- 4CheckPut it back in.
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5Circle the letter of the best answer. Show how you know.
Which point would NOT be on the graph of the ratio 1:5?
- A(2, 10)
- B(3, 10)
- C(4, 20)
- D(5, 25)
Hint On the 1:5 graph, every y-value is exactly 5 times its x-value.
Show your work
-
6Find the mistake. Explain it, then show the correct work.
Level 1 — Spot the Common Mistake
- 1Read the ratioA recipe uses 1 cup of sugar for every 2 cups of flour. Plot the point for 3 cups of sugar.
- 2Find the flour3 cups of sugar means 3 + 2 = 5 cups of flour.
- 3Write the ordered pair(3, 5)
Which step has the mistake? Explain what went wrong, then show the correct work.
Hint Look at Step 2. The student added 2 to the sugar instead of multiplying by 2.
Correct workCorrect answer:
Explain your thinkingWhat pattern do the plotted points make? How does the graph show the ratio of 1 sundae to 2 ounces of sauce?
Sentence starter Every time the sundaes go up by ___, the ounces go up by ___, so the points line up in a ___ starting from ___.
Lesson 3.4Determine Equivalent Ratios Using Graphs
Version BCore practice
Learning target I can graph the values from a ratio table as points on the coordinate plane.
Why This Matters The organizers of a soccer league ordered 6 of the bags shown to hold soccer balls. Each bag holds the same number of soccer balls. How many soccer balls will the bags hold?
-
1Plot and label each point on the 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).
Show your thinking -
2Complete the table. Show how you found each value.
Use the graph pattern y = 5x to complete the ratio table, then identify what the ordered pairs would be.
x y Ordered Pair 1 5 (1, 5) 2 4 6 Show your work
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3Circle the letter of the best answer. Show how you know.
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?
- A1:4
- B2:8
- C3:4
- D4:1
Show your work -
4Circle the letter of the best answer. Show how you know.
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 A
- BSame steepness
- CCannot tell
- DStudent B
Show your work
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5Find the mistake. Explain it, then show the correct work.
On Level — Spot the Common Mistake
- 1Read the ratioA 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 pointThe student also plots (4, 14) and says it belongs on the same line.
- 4ConclusionAll four points form a straight line.
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer:
Explain your thinkingWhat pattern do the plotted points make? How does the graph show the ratio of 1 sundae to 2 ounces of sauce?
Lesson 3.4Determine Equivalent Ratios Using Graphs
ChallengeExtension
Learning target I can graph the values from a ratio table as points on the coordinate plane.
Why This Matters The organizers of a soccer league ordered 6 of the bags shown to hold soccer balls. Each bag holds the same number of soccer balls. How many soccer balls will the bags hold?
-
1Plot and label each point on the grid.
Two recipes are graphed: Recipe A uses 2 cups of mix per 1 serving, and Recipe B uses 3 cups of mix per 2 servings. Plot both sets of points and determine which recipe uses more mix per serving.
Show your thinking
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2Find the mistake. Explain it, then show the correct work.
Find Jada's Mistake
- 1Read the ratio tableCookies: 2, 4, 6 | Cups of milk: 1, 2, 3
- 2Write ordered pairs(1, 2), (2, 4), (3, 6)
- 3Plot the pointsPlotted (1,2), (2,4), (3,6) on the grid
- 4ConclusionThe x-axis is cookies and y-axis is cups of milk
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer: -
3Answer in complete sentences.
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.
Write your answer