Course 3 Think Smart for the Smarter Balanced Assessment

Scatter Plots

Course 3

Think Smart for the Smarter Balanced Assessment

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NAME

DATE

PERIOD

Chapter 9 Performance Task

For this Performance Task, your teacher will ask you to conduct a survey and do research to provide the data for your analysis and data displays.

SCORE

Make a Run for It

Running is great exercise. Some runners enter races and join track teams, while others run to condition themselves for other sports or just to stay fit. Some of the greatest runners in the world compete in the Olympics.

For this task, survey 32 students and ask them if they run for exercise or participate in an organized sport. Then do research to find Olympic gold medalist times in the men's 100-meter dash from 1900 to the present.

Write your answers on another piece of paper. Show all your work to receive full credit.

Part A

Create a two-way table to show the results of your survey. Label the columns "Runs" and "Does Not Run" and the rows "Sport" and "No Sport." Find the relative frequencies for the values in the table related to all the students surveyed. Round the relative frequencies to the nearest hundredth. Use this information to describe the students in your survey.

Copyright ? McGraw-Hill Education. Permission is granted to reproduce for classroom use.

Part B

Find the relative frequencies from your table by column, rounded to the nearest hundredth. Are students who run likely to play sports? Are students who do not run likely to play sports? Explain.

Part C

Find the relative frequencies from your table by row, rounded to the nearest hundredth. Are students who play sports more likely to run? Are students who do not play sports likely to run? Explain.

Course 3 ? Chapter 9 ? Scatter Plots and Data Analysis 123

In the Summer Olympics, male and female athletes participate in a variety of track and field events. These events involving running, jumping, and throwing. One track-and-field running event is the men's 100-meter dash.

Part D

Make a scatter plot of the data you collected about the Olympic men's 100-meter dash. Record the years since 1900 on the x-axis and the gold medalists' times on the y-axis. Then draw a line of best fit. Describe the association shown by the scatter plot.

Part E

Calculate the slope and y-intercept of your line of best fit. Then write an equation for your line of best fit. Use the equation to predict the times for the gold medalists in the men's 100-meter dash at the Olympics in 2020 and in 2056. Compare the results to the 2012 results.

124 Course 3 ? Chapter 9 ? Scatter Plots and Data Analysis

Copyright ? McGraw-Hill Education. Permission is granted to reproduce for classroom use.

Chapter 9 Performance Task Rubric

Page 123 ? Make a Run for It

Note to teacher: For this Performance Task, have students survey 32 students about whether they run for exercise or participate in an organized sport. Then have students research Olympic gold medalist times in the men's 100-meter dash from 1900 to the present.

Task Scenario

Students will collect data about sports and Olympic times, display their data in two-way tables and scatter plots, and interpret relative frequencies and a line of best fit.

CCSS Content Standard(s)

8.SP.1, 8.SP.2, 8.SP.3, 8.SP.4

Mathematical Practices MP1, MP2, MP3, MP4, MP5, MP6, MP7

Depth of Knowledge DOK2, DOK3, DOK4

Part

Maximum Points

Scoring Rubric

A

3

Full Credit:

Sample survey data and relative frequencies:

Sample answer:

Sport No Sports Total

Runs 11; 0.34 5; 0.16

16

Does Not Run 9; 0.28 7; 0.22 16

Total 20 12 32

About 34% of students run and play a sport. The least percentage

of students (16%) run but do not play a sport.

Partial credit (1 point) will be given for each of the 3: correct twoway table OR correct relative frequencies OR a correct analysis.

No credit will be given for an incorrect or incomplete answer.

B

2

Full Credit:

Sample table and answer: More than two thirds of runners play a sport. Students who do not run

Sport No Sports

Runs 0.69 0.31

Does Not Run 0.56 0.44

are also more likely to play a sport.

Partial Credit (1 point) will be given for correct relative frequencies OR an accurate analysis of the frequencies.

No credit will be given for an incorrect or incomplete answer.

C

2

Full Credit:

Sample table and answer: Students who play sports are slightly more likely to run. 42% of students who

Sport No Sports

Runs 0.55 0.42

Does Not Run 0.45 0.58

do not play sports still run for exercise.

Partial Credit (1 point each) will be given for correct relative frequencies OR an accurate analysis of the frequencies.

No credit will be given for an incorrect or incomplete answer.

266

Course 3 ? Chapter 9 ? Performance Task Rubric

Copyright ? McGraw-Hill Education. Permission is granted to reproduce for classroom use.

Chapter 9 Performance Task Rubric, continued

Copyright ? McGraw-Hill Education. Permission is granted to reproduce for classroom use.

Time (s) Performance Task Rubrics

Part

D

Maximum Points

3

Scoring Rubric

Full Credit: Data, given as "year, time in seconds": 1900, 11; 1904, 11; 1908, 10.8; 1912, 10.8; 1920, 10.8; 1924, 10.6; 1928, 10.8; 1932, 10.3; 1936, 10.3; 1948, 10.3; 1952, 10.4; 1956, 10.5; 1960, 10.2; 1964, 10; 1968, 9.9; 1972, 10.14; 1976, 10.06; 1980, 10.25; 1984, 9.99; 1988, 9.92; 1992, 9.96; 1996, 9.84; 2000, 9.87; 2004, 9.85; 2008, 9.69; 2012, 9.63

y 11.2 11.0 10.8 10.6 10.4 10.2 10.0 9.8 9.6 9.4

08

Men's 100-Meter Dash Results

x 16 24 32 40 48 56 64 72 80 88 96 104 112

Olympic Year Since 1900

A sample line of fit is shown. Sample answer: As the year increases, the time in seconds decreases, so a negative association exists. The points lie close to the line, so the data appear linear. There are no outliers.

Partial Credit (1 point) will be given for each of 3 answers: a correct scatter plot OR an accurate line of best fit OR a description of the associations in the data.

No credit will be given for an incorrect or incomplete answer.

E

3

Full Credit:

Sample answer:

slope = -10-6.24--??-210-4.-6 = ?0.01; 10.6 = ?0.01(24) + b; b = 10.84, so

y-intercept = 10.84

line of best fit: y = ?0.01x + 10.84

In 2020: y = ?0.01(120) + 10.84 = 9.64 s In 2056: y = ?0.01(156) + 10.84 = 9.28 s

The result of the 2020 race should be fairly similar to the 2012 result, but in 2056, the gold medalist is expected to be almost 0.4 second faster than in 2012.

Partial Credit (1 point) will be given for each of 3 answers: an accurate equation for the line of best fit OR correct predictions for 2020 and 2056 OR an accurate comparison.

No credit will be given for an incorrect and incomplete answer.

TOTAL

13

Course 3 ? Chapter 9 ? Performance Task Rubric

267

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