Lesson 9.1Explore Relationships Between Two Variables
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.
Why This Matters Akela planted three trays of bean seeds for a science experiment. Each tray sat in a different spot, so each got a different amount of sunlight per day. After three weeks she measured the average plant height in every tray. Two quantities in that experiment are related: change the sunlight and the height changes with it. One of them Akela chose, and the other one answered back. Today you will name which quantity is the independent one and which depends on it, and you will find pairs like this in a jogging tracker and a pizza shop.
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 example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A bike rental costs $5 for each hour. Name the variables.
- The quantities are hours rented and total cost.
- Cost changes when hours change.
- “Total cost depends on hours rented” makes sense.
Answer: hours = independent; cost = dependent
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
Claire burned 123 Calories on a 30-minute jog and 246 Calories on a 60-minute jog.
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 out!A common mistake
Naming the variables backward
Lesson 9.1Explore Relationships Between Two Variables
Level 0Most support · every hint printed
Learning target I can recognize when two quantities change together, and identify which one is the independent variable and which is the dependent variable.
Why This Matters Akela planted three trays of bean seeds for a science experiment. Each tray sat in a different spot, so each got a different amount of sunlight per day. After three weeks she measured the average plant height in every tray. Two quantities in that experiment are related: change the sunlight and the height changes with it. One of them Akela chose, and the other one answered back. Today you will name which quantity is the independent one and which depends on it, and you will find pairs like this in a jogging tracker and a pizza shop.
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A bike rental costs $5 for each hour. Name the variables.
- The quantities are hours rented and total cost.
- Cost changes when hours change.
- “Total cost depends on hours rented” makes sense.
Answer: hours = independent; cost = dependent
-
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?
- APlant height
- BHours of sunlight
- CNumber of trays
- DNumber of seeds
Steps to try- Which quantity did Akela get to decide?
- Sunlight was set by where she put the tray.
- The one subject to choice is independent.
Show your work -
2Circle the letter of the best answer. Show how you know.
In Akela's experiment, which is the DEPENDENT variable?
- AHours of sunlight
- BThe kind of seed
- CThe size of the tray
- DPlant height
Steps to try- Which quantity RESPONDED to the other?
- Akela did not choose how tall the plants grew.
- The responding quantity is dependent.
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?
- ACalories she burns
- BHer heart rate
- CMinutes she jogs
- DThe weather
Steps to try- What does Claire decide before she starts?
- She sets the time on the tracker.
- Calories are the result, not the choice.
Show your work -
4Circle the letter of the best answer. Show how you know.
Which sentence is written in the correct order?
- AMinutes jogged depends on Calories burned.
- BCalories burned depends on Calories burned.
- CNeither quantity depends on the other.
- DCalories burned depends on minutes jogged.
Steps to try- Say both versions out loud. Which one is true?
- Claire chooses the minutes.
- The responder goes first: 'responder depends on chooser.'
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.