Practice Set · Part 1
Determine Equivalent Ratios Using Graphs
Pick up where we left off
Where we left off
Our goal: I can graph the values from a ratio table as points on the coordinate plane, explain what each part stands for, and build one for a situation I have not seen before.
The big idea: The 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.
Model to copy — Watch me
- 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).
Start here
You did these with your group. Now do them on your own — the model above is yours to copy.
- 1
Same stepsFinish what the group started. Use the model above, step for step.
Try it together — then prove it: A recipe uses 1 cup of sugar for every 3 cups of flour. For 1 cup of sugar, the ordered pair is (1, 3): right 1, up 3. For 2 cups of sugar, what is the pair? It is (2, 6): right 2, up 6. Now prove it: say why that move had to work at all — not just that it did.Show your work - 2
Warm restartA ratio table for 2:5 starts with 2:5, 4:10. What is the third row?
- A6:12
- B6:15
- C8:15
- D5:10
How do you know?
- 3
Warm restartWhich row does NOT belong in a ratio table for 4:5?
- A8:10
- B12:15
- C6:10
- D16:20
How do you know?
- 4
Warm restartA ratio table shows 3:7, 6:14, and 9:21. What is the next row?
- A10:24
- B12:24
- C12:28
- D15:28
How do you know?
Practice Set · Part 2
Determine Equivalent Ratios Using Graphs
Keep going
You answered these out loud. Now write them.
Answer, then say how you know — the reason is the part that counts.
- 5
Think it throughThe graph shows 1 taco uses 2 oz of salsa. How much salsa for 15 tacos?
- A30 oz
- B17 oz
- C7.5 oz
- D20 oz
Why is that the answer?
- 6
Think it throughWhy do the points form a straight line through (0, 0)?
- ABecause the quantities are proportional — the same ratio holds for every pair
- BBecause the owner sold the same number of tacos every day
- CBecause all graphs of data are straight
- DBecause salsa is measured in ounces
How do you know? Give a second reason as well.
- 7
Think it throughWhich point would NOT be on this line?
- A(4, 8)
- B(10, 20)
- C(6, 12)
- D(5, 12)
Explain your thinking. What would have to change for a different choice to be right?
- 8
Back to the modelWhat pattern do the plotted points make? How does the graph show the ratio of 1 sundae to 2 ounces of sauce?
Practice Set · Part 3
Determine Equivalent Ratios Using Graphs
Words and reasoning
Word bank · Banco de palabras
Use the words
Fill each blank with a word from the bank.
- Each row of a ratio table becomes one ___ ___ on the coordinate plane.
- The flat grid formed by a horizontal and a vertical number line is the ___.
- A set of two numbers (x, y) that names a point is an ___.
- When graphed points form a straight line, they show a ___.
Explain the thinking
- 9
Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.
The mistake: 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. - 10
Say moreAfter plotting (1,2), (2,4), (3,6)... what pattern do you notice, and how does it show the chocolate-sauce ratio?
- 11
Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Chef Reyes keeps a table for sundae sauce: 1 sundae takes 2 ounces of chocolate sauce, 2 sundaes take 4 ounces, and 3 sundaes take 6 ounces. She starts plotting the (sundaes, ounces) pairs on a coordinate grid.
Show your work
Practice Set · Part 4
Determine Equivalent Ratios Using Graphs
Show what you know
Last check
These two come from Lesson 3.3. If they are shaky, that is the lesson to revisit — not this one.
- 12
Show what you knowExplain your thinking — 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?
- A(5, 10)
- B(4, 6)
- C(5, 8)
- D(6, 10)
Explain your choice.
- 13
From Lesson 3.3Explain your thinking — A salad dressing recipe uses 2 tablespoons of oil for every 5 tablespoons of vinegar. How many tablespoons of oil are needed for 20 tablespoons of vinegar?
- A8
- B10
- C7
- D12
How do you know?
- 14
From Lesson 3.3Which pair is NOT equivalent to 3:2?
- A9:6
- B6:4
- C30:20
- D5:4
How do you know?
Be honest — this tells your teacher what to do next
| I can… | Not yet | Getting there | Got it |
|---|---|---|---|
| I can graph the values from a ratio table as points on the coordinate plane, explain what each part stands for, and build one for a situation I have not seen before. | |||
| I can explain why it works: The points from equal ratios form a straight line that passes through the origin (0, 0)… | |||
| I can justify my answer to a skeptic and connect it to a second strategy or representation. |
One question I want to ask my group next time