Grade 6 Mathematics · Unit 9: Relationships Between Two VariablesStandard 6.AT.11

Lesson 9.1Explore Relationships Between Two Variables

Start hereWords, worked example, and sentence starters

Name Date Period

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.	hours studied
dependent variableSpanish: variable dependiente	The quantity that changes in response to the independent variable.	quiz score
depends onSpanish: depende de	One quantity depends on another when changing the first causes the second to change.	Score depends on study time.
quantitySpanish: cantidad	Something that can be counted or measured.	minutes, dollars, laps
relationshipSpanish: relación	How two quantities change together.	more time → higher score
Table of valuesSpanish: Tabla de valores	A list of matched input and output pairs.	x: 2, 4 paired with y: 14, 28

How it worksWorked examplenaming the independent and dependent variables

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Jaden walks dogs after school. The more hours he walks, the more money he earns. Which variable is independent, and which is dependent?

Name the two quantities: hours walked and money earned.
Which is chosen? Jaden picks his hours — hours walked is the independent variable.
Which responds? The money changes because the hours change — money earned is dependent.
Sentence check: 'Money earned depends on hours walked.' The sentence makes sense.

Answer: Independent variable: hours walked. Dependent variable: money earned.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A bakery decides how many trays of muffins to bake. The more trays it bakes, the more flour it uses. Label the two variables.

Name the two quantities: and
Which is chosen or controlled? is the independent variable.
Which responds? is the dependent variable.
Sentence check: depends on .

Answer:independent variable; dependent variable; sentence check

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

The independent variable is because you it.
The dependent variable is because it .
depends on .
If the changes, then the changes in response.

Word bank independentdependentvariablequantitydepends oninputoutputcauserespondchoosechangesrelationship

Watch outA common mistake

Naming the variables backward — calling the responding quantity 'independent' because it is the one the question asks about.

Grade 6 Mathematics · Unit 9: Relationships Between Two VariablesStandard 6.AT.11

Lesson 9.1Explore Relationships Between Two Variables

Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

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.
Akela chooses how many hours of sunlight each tray gets. Which is the INDEPENDENT variable?
1. APlant height
2. BHours of sunlight
3. CNumber of trays
4. DNumber of seeds
Hint Which quantity did Akela get to decide?
Show your work
2Circle the letter of the best answer. Show how you know.
In Akela's experiment, which is the DEPENDENT variable?
1. AHours of sunlight
2. BThe kind of seed
3. CThe size of the tray
4. DPlant height
Hint Which quantity RESPONDED to the other?
Show your work
3Circle the letter of the best answer. Show how you know.
Claire burned 123 Calories on a 30-minute jog. Which quantity is subject to choice?
1. ACalories she burns
2. BHer heart rate
3. CMinutes she jogs
4. DThe weather
Hint What does Claire decide before she starts?
Show your work
4Circle the letter of the best answer. Show how you know.
Which sentence is written in the correct order?
1. AMinutes jogged depends on Calories burned.
2. BCalories burned depends on Calories burned.
3. CNeither quantity depends on the other.
4. DCalories burned depends on minutes jogged.
Hint Say both versions out loud. Which one is true?
Show your work
5Circle the letter of the best answer. Show how you know.
A tray that got 2 hours of sun grew to 4 cm. A tray that got 6 hours grew to 12 cm. As sunlight increases, plant height…
1. Adecreases
2. Bstays the same
3. Cincreases
4. Dcannot be determined
Hint Compare the two trays.
Show your work
6Circle the letter of the best answer. Show how you know.
You buy tickets at $45 each. Which quantity depends on the other?
1. ATotal cost depends on number of tickets
2. BNumber of tickets depends on total cost
3. CThe price per ticket depends on the total cost
4. DNothing depends on anything here
Hint Which number do you pick at the counter?
Show your work

Explain your thinkingTake a card you and your partner put in different columns. Say the sentence 'The _ depends on the _' out loud both ways — which version is true, and how does that settle which variable is independent?

Sentence starter The ___ depends on the ___, so ___ is the independent variable.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 9: Relationships Between Two VariablesStandard 6.AT.11

Lesson 9.1Explore Relationships Between Two Variables

Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

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.
A gym charges $24.95 per month. Which pair correctly names the variables?
1. AIndependent: months; Dependent: total cost
2. BIndependent: total cost; Dependent: months
3. CIndependent: $24.95; Dependent: months
4. DIndependent: months; Dependent: $24.95
Show your work
2Circle the letter of the best answer. Show how you know.
Claire jogs 30 minutes and burns 123 Calories. At the same rate, how many Calories would a 90-minute jog burn?
1. A246
2. B300
3. C369
4. D410
Show your work
3Circle the letter of the best answer. Show how you know.
Which of these pairs is NOT a dependent relationship?
1. ANumber of pizzas sold and weekly cost of cheese
2. BNumber of pizzas sold and number of employees the shop has
3. CHours jogged and Calories burned
4. DTickets bought and total cost
Show your work
4Circle the letter of the best answer. Show how you know.
A plant grows 2 cm for every hour of daily sunlight. Which table row is correct?
1. A4 hours to 8 cm
2. B4 hours to 6 cm
3. C4 hours to 2 cm
4. D4 hours to 4 cm
Show your work
5Circle the letter of the best answer. Show how you know.
Which question would you ask to find the DEPENDENT variable?
1. AWhich quantity responds when the other one changes?
2. BWhich quantity is larger?
3. CWhich quantity has units?
4. DWhich quantity comes first alphabetically?
Show your work
6Circle the letter of the best answer. Show how you know.
Claire decides to walk instead of jog for the same 30 minutes. What happens to the two variables?
1. ACalories burned becomes the independent variable
2. BNeither is a variable any more
3. CTime stays the independent variable; Calories burned still depends on it
4. DTime becomes the dependent variable
Show your work

Explain your thinkingTake a card you and your partner put in different columns. Say the sentence 'The _ depends on the _' out loud both ways — which version is true, and how does that settle which variable is independent?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 9: Relationships Between Two VariablesStandard 6.AT.11

Lesson 9.1Explore Relationships Between Two Variables

ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can recognize when two quantities change together, and identify which one is the independent variable and which is the dependent variable.

Part 1Understand the ideamodels and meaning

1Circle the letter of the best answer. Show how you know.
Two quantities are related. Which statement is ALWAYS true?
1. AThe independent variable is always the larger number
2. BThe independent variable is the input used to describe the relationship
3. CThe dependent variable is always measured in dollars
4. DThe independent variable is always listed first in a table
Show your work
2Write the letter of the matching item on each line.
Match each scenario to its (independent → dependent) pair.
1. Gym membership
2. Seedling experiment
3. Jogging
4. Buying movie tickets
- Amonths → total cost
- Bhours of sunlight → plant height
- Cminutes → Calories burned
- Dtickets → total price

Part 2Apply itreal-world problems

3Circle the letter of the best answer. Show how you know.
Give an example where the SAME quantity can be independent in one problem and dependent in another.
1. ATime is always independent
2. BTime: chosen when you pick how long to jog, but measured as a result when you run a set distance
3. CTime is always dependent
4. DA quantity can never switch roles
Show your work
4Circle the letter of the best answer. Show how you know.
The pizza shop spends $1.15 on cheese per pizza. Which weekly total is correct if it makes 200 pizzas?
1. A$115
2. B$201.15
3. C$230
4. D$1,150
per 1
5Circle the letter of the best answer. Show how you know.
Which relationship is NOT a case of one quantity depending on the other?
1. AHours studied and quiz score
2. BMinutes jogged and Calories burned
3. CPizzas made and cheese used
4. DA student's height and their house number
Show your work
6Circle the letter of the best answer. Show how you know.
Write the relationship as a sentence: a printer prints 12 pages per minute.
1. AMinutes running depends on pages printed
2. B12 depends on the number of pages
3. CPages printed depends on minutes running
4. DThe printer depends on the pages
Show your work

Explain your thinkingTake a card you and your partner put in different columns. Say the sentence 'The _ depends on the _' out loud both ways — which version is true, and how does that settle which variable is independent?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help




per 1

Start hereWords for this lesson

How it worksWorked examplenaming the independent and dependent variables

Now you trySame steps, your turn

Say it and write itSentence starters

Watch outA common mistake

Explain your thinkingTake a card you and your partner put in different columns. Say the sentence 'The ___ depends on the ___' out loud both ways — which version is true, and how does that settle which variable is independent?

Explain your thinkingTake a card you and your partner put in different columns. Say the sentence 'The ___ depends on the ___' out loud both ways — which version is true, and how does that settle which variable is independent?

Explain your thinkingTake a card you and your partner put in different columns. Say the sentence 'The ___ depends on the ___' out loud both ways — which version is true, and how does that settle which variable is independent?

Explain your thinkingTake a card you and your partner put in different columns. Say the sentence 'The _ depends on the _' out loud both ways — which version is true, and how does that settle which variable is independent?

Explain your thinkingTake a card you and your partner put in different columns. Say the sentence 'The _ depends on the _' out loud both ways — which version is true, and how does that settle which variable is independent?

Explain your thinkingTake a card you and your partner put in different columns. Say the sentence 'The _ depends on the _' out loud both ways — which version is true, and how does that settle which variable is independent?