Neft Teacher · Learn It

Unit 9 · Standard 6.AT.11

Explore Relationships Between Two Variables

Lesson 9-1 · Learn It — how the math works

Why we're learning this

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.

✱ Math Workbench

Learn It

Which quantity is doing the changing — and which is responding?

When two quantities are related, one of them depends on the other. Naming which is which is the whole job of this lesson.

Picture itSee what the math looks like before you read about it

Three trays of bean seedlings sit on a windowsill. The tray closest to the glass is tall and leafy. The tray in the middle is shorter. The tray pushed back into the corner is barely up out of the soil.
Where you see this in real lifeThree trays of bean seedlings sit on a windowsill. The tray closest to the glass is tall and leafy. The tray in the middle is shorter. The tray pushed back into the corner is barely up out of the soil.

Watch me solve itI do — read one step at a time

The problem looks like this
Table sorting Akela's two quantities: sunlight is the independent variable, plant height is the dependent variable.Independent (chosen)sunlightDependent(responded)plant height
  1. The two quantities are hours of sunlight per day and average plant height after 3 weeks.
  2. Akela CHOSE where to put each tray, so she chose the sunlight. Sunlight is subject to choice — that makes it the .
  3. She did not choose how tall the plants got. Height responded. That makes height the .
  4. Say it as a sentence: plant height sunlight.

Watch out — mistakes students make here

  • Both quantities can't be independent — one has to respond to the other.
  • One of these two quantities does respond to the other — they aren't unrelated.
  • $24.95 is a fixed rate, not a variable that changes.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Claire burned 123 Calories on a 30-minute jog and 246 Calories on a 60-minute jog.
  2. Which did Claire choose — the minutes, or the Calories?
  3. She chose how long to jog. So time is independent, and Calories burned is dependent.
  4. Sentence frame: ___ ___ .

On your ownYou do — solve this one by yourself

Before you start, remember:

  • For each pair below, decide which is subject to choice.
  • Then finish the sentence: ___ ___ .

Solve: A gym charges $24.95 per month. Which pair correctly names the variables?

My answer

Stuck? Open one hint at a time.

Hint 1

Which number can the member change?

Hint 2

Months is the choice.

Hint 3

Cost responds to months.

Check my answer
✅ Answer: Independent: months; Dependent: total cost
You choose how many months to stay a member. The total cost responds to that.

Turn & TalkSay it out loud with a partner

Akela put her three bean trays in three different spots, so each got a different amount of sunlight. After three weeks she measured the height of the plants. Which of those two quantities did Akela choose, and which one responded?

Try starting with:

  • Akela chose ___, so ___ is the independent variable.Akela eligió ___, así que ___ es la variable independiente.
  • Plant height is the dependent variable because it ___.La altura de la planta es la variable dependiente porque ___.
Use these wordsindependent variabledependent variabledepends on