Lesson 9.1Tables of Values
Start hereWords, worked example, and sentence starters
Learning target I can recognize when two quantities change together, and identify which one is the independent variable and which is the dependent variable.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| independent variableSpanish: variable independiente | The input quantity in a model, chosen or observed. | Miguel picks the number of MONTHS — nothing else decides it for him. |
| dependent variableSpanish: variable dependiente | The quantity that changes in response to the independent variable. | Total cost = $24.95 × months — the cost RESPONDS to the months. |
| depends onSpanish: depende de | One quantity depends on another when changing the first causes the second to change. | “Total cost depends on the number of months.” Responder first, chooser last. |
| quantitySpanish: cantidad | Something that can be counted or measured. | 24.95 dollars per month, 12 months — each is a number with a meaning. |
| relationshipSpanish: relación | How two quantities change together. | 1 month → $24.95, 2 months → $49.90: the two quantities move together. |
| Table of valuesSpanish: Tabla de valores | A list of matched input and output pairs. | x: 2, 4 | y: 14, 28 |
How it worksWorked examplebuilding a table of values
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A copier prints 35 pages each minute. Make a table of values for 1, 2, and 3 minutes.
- Name the variables: minutes is independent (x); pages printed is dependent (y).
- Column 1 holds x, the minutes. Column 2 holds y, the pages printed.
- Multiply each minute by the rate: 1 → 35 · 2 → 70 · 3 → 105
- Check: each time x grows by one minute, y grows by the same 35 pages.
Answer: x: 1, 2, 3 minutes and y: 35, 70, 105 pages. Pages printed depends on minutes.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A faucet fills a tub with 11 gallons each minute. Make a table of values for 1, 2, and 4 minutes.
- Name the variables: is independent (x); is dependent (y).
- Fill column 1 (x): 1, 2, 4 minutes. Then find column 2 (y): , ,
- Multiply each number of minutes by gallons.
- Check: each time x grows by one minute, y grows by gallons.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The independent variable is , so it goes in column .
- The dependent variable is , so it goes on the axis.
- Each time x increases by one, y increases by .
- The table shows that depends on .
Word bank table of valuesinputoutputcolumnpairhorizontal axisvertical axisindependentdependentincreasesraterule
Watch outA common mistake
Naming the variables backward — calling the responding quantity 'independent' because it is the one the question asks about.
Lesson 9.1Tables of Values
Apply Day · Version ASupported practice
Learning target I can recognize when two quantities change together, and identify which one is the independent variable and which is the dependent variable.
-
1Complete each step, then write the final answer.
Leo chooses how many plants to water. He measures the cups of water he uses. Which is the dependent variable: plants or cups?
Show your workHint Leo chooses the plants. The other quantity responds.
Final answer: -
2Complete each step, then write the final answer.
Gina chooses how many songs to download. Each song costs $1. Is the number of songs independent or dependent?
Show your workHint Did Gina choose the number of songs?
Final answer: -
3Complete each step, then write the final answer.
Ty picks how many laps to walk. He counts his steps. Which is the independent variable: laps or steps?
Show your workHint The independent variable is the one Ty picks.
Final answer:
Lesson 9.1Tables of Values
Apply Day · Version BCore practice
Learning target I can recognize when two quantities change together, and identify which one is the independent variable and which is the dependent variable.
-
1Circle the letter of the best answer. Show how you know.
Which pair of quantities does NOT change together?
- AA student's height and the color of her shirt
- BHours worked and money earned
- CGallons of gas and the cost of the gas
Show your work -
2Complete each step, then write the final answer.
A recipe uses 3 eggs for each cake. A baker chooses how many cakes to make. Which is the dependent variable: cakes or eggs?
Show your workFinal answer: -
3Complete each step, then write the final answer.
Nora chooses how many laps to swim. She records her time. Is the time independent or dependent?
Show your workFinal answer:
Lesson 9.1Tables of Values
Apply Day · ChallengeExtension
Learning target I can recognize when two quantities change together, and identify which one is the independent variable and which is the dependent variable.
-
1Circle the letter of the best answer. Show how you know.
Devon adds a different number of scoops of plant food to each tray of seedlings. Two weeks later he counts the new leaves on every tray. Which pair correctly names the variables?
- AIndependent: new leaves counted; Dependent: scoops of plant food
- BIndependent: scoops of plant food; Dependent: new leaves counted
- CIndependent: the number of trays; Dependent: scoops of plant food
- DIndependent: new leaves counted; Dependent: the two weeks of growing time
Show your work -
2Circle the letter of the best answer. Show how you know.
A movie theater is open 12 hours every day. On Monday it sells 150 tickets. On Tuesday it sells 210 tickets. Do the hours open depend on the tickets sold?
- ANo. The hours stay 12 when the tickets change.
- BYes. Selling more tickets means more hours.
- CYes. The hours are the dependent variable.
Show your work -
3Complete each step, then write the final answer.
Ben wants to run exactly 5 laps. He records how many minutes it takes. Is the number of laps independent or dependent?
Show your workFinal answer: