Grade 8 Workbook — Chapter 17: The Data Cycle and Scatterplots

SOL 8.PS.3 · Companion to Textbook Chapter 17

Each page below is one Canva page. Headings are sized for direct paste: page title as H1, section labels as H2. Figures referenced by filename live in ../figures/. Every numbered item is the same problem as in the textbook, so one answer key serves both. Item numbers run continuously from 1 to 112.

PAGE 1 — Chapter opener

Chapter 17 · The Data Cycle and Scatterplots

Standard 8.PS.3

In this chapter you will:

Ask a question about the relationship between two numerical quantities
Collect or acquire paired data — no more than 20 pairs — and keep the pairs together
Plot bivariate data as a scatterplot, by hand and with technology
Describe a scatterplot as showing a positive linear relationship, a negative linear relationship, or no relationship
Justify what you see using the points themselves
Sketch a line of best fit and use it honestly to estimate

Words to know: data cycle · univariate data · bivariate data · ordered pair · independent variable · dependent variable · scatterplot · positive linear relationship · negative linear relationship · no relationship · lurking variable · line of best fit · slope · y-intercept · interpolation · extrapolation

Two limits from the standard: a data set has no more than 20 items, and relationships are described in words — positive linear, negative linear, or no relationship. The line of best fit is sketched, never computed.

PAGE 2 — The data cycle, with two variables

17.1 The Data Cycle with Two Variables

FIGURE: fig1-data-cycle-scatterplots.png (full width)

Fill in the blanks.

The four stages are: ____________ questions · ____________ or acquire data · organize and ____________ data · ____________ data and communicate results.

A data set is bivariate when ______ numbers are recorded for each item and kept ____________.

The independent variable goes on the ____________ axis. The dependent variable goes on the ____________ axis.

Name the four stages of the data cycle in order.
1. _______________ 2) _______________ 3) _______________ 4) _______________
What makes a data set bivariate? _______________________________________________
A class records only the height of each student. Univariate or bivariate? ______

Why? _______________________________________________
Which stage are you in when you plot each ordered pair on a coordinate grid?
In a study of hours practiced and free throws made, which quantity goes on the horizontal axis? _______________ That variable is called the ____________ variable.
Correct the statement. "The data cycle ends as soon as the scatterplot is drawn."

PAGE 3 — Stages and variables

Naming Stages and Variables

Name the stage for each action.

Action	Stage
a) Measuring the length and the width of each of 16 leaves
b) Writing "Is there a relationship between shoe length and height?"
c) Plotting 16 ordered pairs on a coordinate grid
d) Telling the class that longer leaves tend to be wider

Put these in order: organize and represent data; analyze data and communicate results; formulate questions; collect or acquire data.
1. _______________ 2) _______________ 3) _______________ 4) _______________
Univariate or bivariate?

Data described	U or B
a) Minutes each of 20 students exercised yesterday
b) Age and resting heart rate of each of 20 people
c) Mass of each of 12 backpacks
d) Mass of each of 12 backpacks and the number of books in each

Name the independent and dependent variable.

Pair of quantities	Independent	Dependent
a) Hours of practice, free throws made
b) Age of a used car, its price
c) Days since planting, plant height

Write one question about your class that needs bivariate data.

Two quantities recorded per student: _______________ and _______________

PAGE 4 — Apply and reason

Why the Pairing Matters

Apply it. The school nurse wants to know whether eighth graders who sleep longer have lower resting heart rates. One sentence per stage.

Formulate: _______________________________________________

Collect: _______________________________________________

Organize: _______________________________________________

Analyze: _______________________________________________
Reasoning. Explain why a histogram cannot answer "Do students who study more score higher?" even if you have every study time and every score.

PAGE 5 — Exit ticket 17.1

Exit Ticket · Lesson 17.1

Name: ________________________ Date: ____________

The four stages, in order: _______________________________________________
One bivariate data set: _______________ One univariate data set: _______________
Days since planting and plant height: which goes on the vertical axis? _______________

It is called the ____________ variable.
Why must the two measurements in a bivariate set stay paired?

PAGE 6 — Asking a bivariate question

17.2 Asking a Bivariate Question

A question that needs a scatterplot has this shape:

Is there a relationship between $\underline{\hspace{4cm}}$ and $\underline{\hspace{4cm}}$ ?

Both blanks must hold a ____________ quantity.

A sharp question names four things:

the ____________ 2) the first quantity and its ____________ 3) the second quantity and its ____________ 4) the ____________ frame

Fill in the shape of a scatterplot question: "Is there a relationship between ______ and ______?"
Why must both quantities be numerical? _______________________________________________
Name the four things a sharp bivariate question states.
Rewrite "Does studying help?" as a question a scatterplot could answer.
A class collects 22 pairs. What does the standard say? _______________________________________________
A student has a study time but no quiz score. Can that student be plotted? ______

Why? _______________________________________________

PAGE 7 — Questions, methods, and sources

Collecting Paired Data

Could a scatterplot answer it? If not, why not?

Question	Yes / No	Why not
a) How many hours did each eighth grader sleep?
b) Hours of sleep and minutes of homework?
c) Favorite subject and quiz score?
d) Age of a used car and its price?

Sharpen each question. Name a population, both quantities with units, and a time frame.

a) Are tall people faster? _______________________________________________

b) Does cold weather sell hot chocolate? _______________________________________________
Name the method and the two numbers recorded per item.

Investigation	Method	Two numbers
a) Do taller students have longer arm spans?
b) Do colder days bring more coats?
c) Do students who sleep more do less homework?
d) Does a steeper ramp make a car roll farther?

PAGE 8 — Acquired data and record keeping

When You Did Not Collect It Yourself

A class wants rainfall and cloudy days for 15 U.S. cities.

Why acquire rather than collect? _______________________________________________

Two questions to ask about the data: _______________________________________________
A table lists last year's average temperature for each month. Another lists the store's total sales for each of the last five years. Why can these not be combined into a scatterplot?
Apply it. Does more practice mean more free throws made?

Sharpened question: _______________________________________________

Two numbers per student: _______________ and _______________

Method: _______________ Why it fits: _______________________________________________
Reasoning. A student writes all the sleep hours on one page and all the homework minutes on another, in the order people answered.

Why can the data no longer be plotted? _______________________________________________

How should it have been recorded? _______________________________________________

PAGE 9 — Exit ticket 17.2

Exit Ticket · Lesson 17.2

Name: ________________________ Date: ____________

A scatterplot question about your class: _______________________________________________
Its two quantities, with units: _______________ and _______________
Why can "favorite subject" not be one of the two quantities?
Largest number of data items allowed in this chapter: ______

PAGE 10 — Plotting a pair

17.3 Building a Scatterplot

FIGURE: fig2-plotting-a-pair.png (half width)

Fill in the blanks. To plot $(3, 81)$ , go across to $x =$ ______, then up to $y =$ ______, and mark the point. One point on a scatterplot represents ____________________.

FIGURE: fig3-study-time-scatterplot.png (half width)

What does one point on a scatterplot represent? _______________________________________________
A student read $45$ minutes and scored $18$ out of $20$ . Ordered pair: ( ______ , ______ )
$x$ runs from $1$ to $10$ ; $y$ runs from $70$ to $190$ .

Horizontal scale: from ______ to ______ in steps of ______

Vertical scale: from ______ to ______ in steps of ______
Two students both practiced $3$ hours. How are their points drawn?
The two labels every scatterplot's axes must carry: _______________ and _______________
A data set has 20 rows and 4 rows are missing the second measurement. Points plotted: ______

PAGE 11 — Plot the hot chocolate data

Cups Sold and Temperature

For each of 10 school days, the noon temperature and the cups of hot chocolate sold.

Temperature (°F)	20	25	30	35	40	45	50	55	60	65
Cups sold	116	92	94	75	77	54	53	36	35	18

Write the 10 ordered pairs, temperature first.

( ____ , ____ ) ( ____ , ____ ) ( ____ , ____ ) ( ____ , ____ ) ( ____ , ____ )

( ____ , ____ ) ( ____ , ____ ) ( ____ , ____ ) ( ____ , ____ ) ( ____ , ____ )
Horizontal scale: from ______ to ______ in steps of ______ Label: _______________

Vertical scale: from ______ to ______ in steps of ______ Label: _______________
Draw the scatterplot. Use the right-hand grid below.

FIGURE: fig13-blank-grids.png (full width — label the axes on the grid you use)

Number of items in this data set: ______

Why it satisfies the limit: _______________________________________________

PAGE 12 — Scales, axes, and stacks

Reading a Scatterplot Carefully

A student puts quiz score on the horizontal axis and hours studied on the vertical axis. Is the graph wrong? ______

What changes: _______________________________________________

What does not change: _______________________________________________
Why may the score axis start at $50$ instead of $0$ ?

What must the reader be shown? _______________________________________________
Apply it. Shoe length and height for you and 15 classmates.

Horizontal axis: _______________ Vertical axis: _______________ Why: _______________

Sketch the table you would build:

TABLE SPACE: 3 columns (student, shoe length in cm, height in cm), 6 rows, full width
Reasoning. "Two points that share an $x$ -value must be an error, because a graph can only have one $y$ for each $x$ ."

Why a scatterplot need not be a function: _______________________________________________

What the vertical stack means: _______________________________________________

PAGE 13 — Exit ticket 17.3

Exit Ticket · Lesson 17.3

Name: ________________________ Date: ____________

Independent value $8$ , dependent value $95$ . Ordered pair: ( ______ , ______ )
One reason the two axes usually need different scales: _______________________________________________
A spreadsheet chart puts the dependent variable on the horizontal axis. What went wrong?
Why does a scatterplot keep every individual pair instead of grouping the data?

PAGE 14 — Three relationships

17.4 Positive, Negative, or No Relationship

FIGURE: fig4-three-relationships.png (full width)

Fill in the blanks.

As $x$ increases, $y$ tends to increase → ____________ linear relationship.

As $x$ increases, $y$ tends to decrease → ____________ linear relationship.

As $x$ increases, $y$ shows no consistent direction → ____________ relationship.

FIGURE: fig5-hot-chocolate-scatterplot.png (half width)

FIGURE: fig6-no-relationship-scatterplot.png (half width)

The three descriptions used in this chapter: _______________, _______________, _______________
Points trend downward from upper left to lower right: _______________________________________________
No consistent direction: _______________________________________________
The three parts of a good justification:
1. _______________ 2) _______________ 3) _______________
Why does one pair that runs against the trend not change the relationship's name?
"Correlation is not causation" means: _______________________________________________

PAGE 15 — Classify three plots

Name It and Justify It

FIGURE: fig8-practice-scatterplots.png (full width)

Plot A relationship: _______________

Evidence — two points: ( ____ , ____ ) and ( ____ , ____ )
Plot B relationship: _______________ Justification: _______________________________________________
Plot C relationship: _______________

Evidence — two points: ( ____ , ____ ) and ( ____ , ____ )
Plot C in context, one sentence with units: _______________________________________________
Predict the relationship.

Pair of quantities	Prediction	Reason
a) Hours of practice, free throws made
b) Age of a used car, its price
c) Height, house number
d) Outside temperature, cups of hot chocolate sold

Improve it. Rewrite "It kind of goes down" so it names the relationship, cites evidence, and speaks in context.

PAGE 16 — Correlation is not causation

Two Things Rising Together

FIGURE: fig7-correlation-not-causation.png (full width)

Apply it. Cones sold and sunburns both rise across ten summer days.

Relationship: _______________

Why the shop should not conclude ice cream causes sunburns: _______________________________________________

Lurking variable: _______________
Find the error. "The plot of hours studied and quiz score has no relationship, because one student studied $2$ hours and beat a student who studied $3$ hours."

Error: _______________________________________________

Correct description with justification: _______________________________________________
Reasoning. Sleep hours and reaction time show a negative linear relationship. Give three explanations.

Sleep causes it: _______________________________________________

The causation runs the other way: _______________________________________________

A lurking variable: _______________________________________________

PAGE 17 — Exit ticket 17.4

Exit Ticket · Lesson 17.4

Name: ________________________ Date: ____________

Points trend upward from lower left to upper right: _______________________________________________
Points scatter with no direction. What do you report? _______________

Is the investigation a failure? ______ Why? _______________________________________________
One sentence justifying the temperature and cups relationship, citing two points:
Why can a scatterplot alone not prove causation? _______________________________________________

PAGE 18 — The line of best fit

17.5 Sketching the Line of Best Fit

FIGURE: fig9-line-of-best-fit.png (full width)

Four tests of a good sketch.

It follows the ____________ of the trend.
It runs through the ____________ of the cloud, with roughly as many points ____________ it as ____________ it.
It stays ____________ to the points overall.
It is a single ____________ line, not a curve and not a set of segments.

FIGURE: fig10-good-and-poor-fit-lines.png (full width)

The line of best fit can be written $y = mx + b$ . The slope $m$ tells you ____________________. The y-intercept $b$ is the value at $x =$ ______.

What does a line of best fit summarize? _______________________________________________
The two most important tests: _______________________________________________
In $y = mx + b$ , which number tells the direction of the relationship? ______
For $y = -2x + 150$ , the slope $-2$ means: _______________________________________________
Use $y = 6x + 60$ at $x = 4$ : $y = 6(\underline{\hspace{1cm}}) + 60 = \underline{\hspace{2cm}}$
Should you sketch a line on a plot with no relationship? ______ Why? _______________

PAGE 19 — Sketch and estimate

Sketch the Line, Then Read It

Sketch a line of best fit on the study-time grid below, then answer items 78–79. Plot the 12 pairs first: $(0, 63)$ , $(0, 57)$ , $(1, 68)$ , $(1, 62)$ , $(2, 77)$ , $(2, 70)$ , $(3, 81)$ , $(3, 75)$ , $(4, 88)$ , $(4, 80)$ , $(5, 92)$ , $(5, 87)$ .

FIGURE: fig13-blank-grids.png (full width — use the left-hand grid; x: hours studied, y: quiz score)

Points above my line: ______ Points below my line: ______

A line on an upward cloud of $12$ points has $11$ below it and $1$ above.

What is wrong: _______________________________________________

Fix: _______________________________________________
Using $y = 6x + 60$ :

a) At $x = 1$ : $y = \underline{\hspace{2cm}}$

b) At $x = 3$ : $y = \underline{\hspace{2cm}}$

c) Actual scores at $3$ hours were $81$ and $75$ . Why does neither equal your estimate?

PAGE 20 — Estimating honestly

Interpolation and Extrapolation

FIGURE: fig11-prediction-from-a-sketched-line.png (full width)

Using $y = -2x + 150$ :

a) At $x = 30$ : $y = \underline{\hspace{2cm}}$

b) At $x = 60$ : $y = \underline{\hspace{2cm}}$

c) Actual sales were $94$ cups at $30$ °F and $35$ cups at $60$ °F. Compare: _______________________________________________
The study data run from $0$ to $5$ hours. Use $y = 6x + 60$ at $x = 10$ : $y = \underline{\hspace{2cm}}$

Why the estimate should not be trusted (mention the maximum possible score):
Interpolation is ____________________. Extrapolation is ____________________.

More trustworthy: _______________ Why: _______________________________________________
Two students sketch slightly different lines and their estimates at $x = 3$ differ by $2$ points. Is one wrong? ______

Explain: _______________________________________________

PAGE 21 — Apply, reason, and repair

Using the Line Without Overclaiming

Apply it. A bean plant, measured every two days for 20 days, has sketched line $y = x + 1$ ( $x$ = days, $y$ = height in cm).

Height on day $15$ : ______ cm

The slope means: _______________________________________________

Why not day $200$ : _______________________________________________
Reasoning. When is a y-intercept meaningful? Use $y = 6x + 60$ and $y = -2x + 150$ .

$y = 6x + 60$ : _______________________________________________

$y = -2x + 150$ : _______________________________________________
Find the error. "This proves that studying $5$ hours will get you a $90$ ."

Problem 1: _______________________________________________

Problem 2: _______________________________________________

Rewrite: _______________________________________________

PAGE 22 — Exit ticket 17.5

Exit Ticket · Lesson 17.5

Name: ________________________ Date: ____________

The test that involves counting points above and below the line:
$y = -2x + 150$ at $x = 25$ : $y = \underline{\hspace{2cm}}$
Why report an estimate with the word "about"? _______________________________________________
The data run from $x = 0$ to $x = 5$ . Why is an estimate at $x = 12$ unreliable?

PAGE 23 — Review, Parts A and B

Chapter 17 Review · Questions and Data

Words to know: data cycle · univariate · bivariate · ordered pair · independent variable · dependent variable · scatterplot · positive linear · negative linear · no relationship · lurking variable · line of best fit · slope · y-intercept · interpolation · extrapolation

Could a scatterplot answer it?

Question	Yes / No	Why not
a) Minutes each eighth grader exercised yesterday
b) Minutes of exercise and resting heart rate
c) Favorite sport and minutes of exercise
d) Age of a used car and its price

Sharpen "Do bigger backpacks weigh more?"
Your own bivariate question: _______________________________________________

Horizontal axis: _______________ Vertical axis: _______________ Why: _______________
Method and the two numbers recorded per item.

Investigation	Method	Two numbers
a) Taller students, longer arm spans
b) Warmer days, fewer cups sold
c) More sleep, fewer homework minutes
d) Steeper ramp, farther roll

A class collects paired values from 24 students. Problem: _______________ Fix: _______________
15 students give study hours; 2 miss the quiz. Points plotted: ______

Why the 2 unmatched times cannot be paired with someone else's score: _______________________________________________

PAGE 24 — Review, Part C

Building the Plot

For each of 8 students: weeks of free-throw practice and free throws made out of 20.

Weeks of practice	1	2	3	4	5	6	7	8
Free throws made	4	6	5	9	8	11	12	14

The 8 ordered pairs:

( ____ , ____ ) ( ____ , ____ ) ( ____ , ____ ) ( ____ , ____ )

( ____ , ____ ) ( ____ , ____ ) ( ____ , ____ ) ( ____ , ____ )
Horizontal scale: from ______ to ______ in steps of ______ Label: _______________

Vertical scale: from ______ to ______ in steps of ______ Label: _______________
Draw the scatterplot.

GRID SPACE: 4.5 in square, gridlines every 0.25 in, axes drawn and unlabeled
Why does the week- $3$ point sit below the week- $2$ point, and why is the table not wrong?

PAGE 25 — Review, Parts D and E

Describing and Justifying

FIGURE: fig12-review-scatterplot-set.png (full width)

Plot D relationship: _______________
Plot E relationship: _______________
Height and house number: _______________ Reasoning: _______________________________________________
Points show no consistent direction. Report: _______________

Should a line of best fit be drawn? ______ Why? _______________
Justify item 101. Two points from Plot D: ( ____ , ____ ) and ( ____ , ____ )

In context: _______________________________________________
Justify item 102. Two points from Plot E: ( ____ , ____ ) and ( ____ , ____ )

In context: _______________________________________________
Rewrite "The plot proves that getting older makes a car cheaper."

Supported version: _______________________________________________

What causation would require: _______________________________________________
Reasoning. Cones sold and sunburns rise together.

Relationship: _______________ Lurking variable: _______________

Why neither causes the other: _______________________________________________

PAGE 26 — Review, Parts F and G

The Line, and the Whole Cycle

The four tests of a well-sketched line of best fit.
Plot D's line is $y = -13x + 200$ ( $x$ = years, $y$ = value in hundreds of dollars).

a) At $x = 5$ : $y = \underline{\hspace{2cm}}$ hundred dollars

b) The slope $-13$ means: _______________________________________________

c) Why not a $30$ -year-old car: _______________________________________________
Plot E's line is $y = x + 1$ ( $x$ = days, $y$ = height in cm).

a) At $x = 15$ : $y = \underline{\hspace{2cm}}$ cm

b) The slope $1$ means: _______________________________________________

c) Data run from day $2$ to day $20$ . Interpolation or extrapolation? _______________
All four stages for "Is there a relationship between hours of sleep last night and minutes spent on homework last night?"

Formulate: _______________________________________________

Collect: _______________________________________________

Organize: _______________________________________________

Analyze: _______________________________________________

Graph you would draw: _______________