Real World Performance Tasks

Real World Real Life, Real Data, Real-Time - These activities put students into real life scenarios where they use real-time, real data to solve problems. In the NLSN series, we use data from NBA.com and update our data regularly. Note - some data has been rounded or simplified in order to adjust the math to the appropriate level.

Engaging Relevant – Students today are very familiar with professional basketball, making these activities very relevant to their everyday lives. To pique their interest further, try asking the Your Challenge question to the class first. Authentic Tasks - Through these activity sheets students learn how to project a player’s efficiency rating and are prompted to form opinions and ideas about how they would solve real life problems. A glossary is included to help them with the unfamiliar terms used. Student Choice - Each set of activity sheets is available in multiple versions where students will do the same activities using data for different teams (e.g. Oklahoma City Thunder, Golden State Warriors, and Chicago Bulls). You or your students can pick the team that most interests them.

Modular Principal Activity - The activity sheets always start with repeated practice of a core skill matched to a common core standard, as set out in the Teacher Guide. This principal activity (or Level 1 as it is labeled to students) can be used in isolation. This should generally take around 10-15 minutes. Step Up Activity - For the Level 2 questions, students are required to integrate a different skill or set of skills with increasing complexity. The additional skills used to answer these questions are set out in the Teacher Guide. This should generally take around 20-30 minutes. Challenge - This is designed to require critical thinking skills and stretch students to reason with math and data to come to conclusions. They are matched up with one of the Common Core Standards for Mathematical Practice. These activities work well with students in pairs or small groups where they can discuss the math. Cross-Curricular Activity - Every activity sheet also includes a finale that you can use to extend the math lesson into another subject (usually ELA). These could be assigned in a second lesson or for homework.

Customizable All of the activity sheets are provided in Word so that they can be differentiated to add, remove, or edit questions or even add space for students to show their work. Suggested customizations for each activity sheet are given in the Teacher Guide.

Community We would love for you and your students to tell us about your experience. Join the conversation on Twitter starting your tweet with @nextlesson and using #NLSN.

Updated June 2015 © NextLesson 2015 Linear Functions

Teacher Guide

Sound Bite for Students: “In the real world, we use statistics to make projections into the future.”

Skills Practiced: Principal Activity (Level 1): - Construct linear functions - Evaluate and solve linear functions Step Up Activity (Level 2): - Construct linear functions - Evaluate and solve linear functions - Assess data for correlation

Common Core Math Standards Addressed: Interpret differences in shape, center, and spread in the context of the data HSS-ID.A.3 sets, accounting for possible effects of extreme data points (outliers). Represent data on two quantitative variables on a scatter plot, and describe Principal HSS-ID.B.6 how the variables are related. Activity: Fit a function to the data; use functions fitted to data to solve problems in the HSS-ID.B.6a context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Fit a function to the data; use functions fitted to data to solve problems in the HSS-ID.B.6a context of the data. Use given functions or choose a function suggested by Step-Up the context. Emphasize linear, quadratic, and exponential models. Activity: Interpret the slope (rate of change) and the intercept (constant term) of a HSS-ID.C.7 linear model in the context of the data.

Differentiation Tips: You can edit any of the activity sheets to: - Alter the tasks (e.g. add or remove players from the assignment, only introduce one new piece of data in the challenge) - Cue for differentiation purposes (e.g. can provide instruction for using TI calculators or provide labeled coordinate grids for scatterplots) - Utilize TI graphing technology Due to school paper restriction, the spacing provided is only for answers. However, you could modify the spacing to add room for work if desired. Students should be encouraged to show their work where possible.

Updates: At NextLesson we strive to engage students with data that is real and real-time. This lesson uses data as of June 2015. Please come back for the most recent updates.

Updated June 2015 © NextLesson 2015 Los Angeles Lakers

Name: ______

You are the Statistician for the Los Angeles Lakers and you are investigating the effectiveness and value of players on your roster.

Your Challenge: Who are the most effective players on the Los Angeles Lakers?

LEVEL 1

To analyze your roster after the 2014-2015 season, you are considering the new Player Efficiency Rating (PER) statistic that measures a player’s value to his team and how it may project for the next season.

The table below shows the last three seasons of player efficiency ratings for some of the players on the Los Angeles Lakers. The average NBA player has a PER score of 15.

Player 2012-13 PER 2013-14 PER 2014-15 PER Kobe Bryant 23.0 10.7 17.6 Carlos Boozer 17.1 14.4 16.4 Ronnie Price 6.8 7.6 10.2 Nick Young 13.3 16.0 14.2 Wayne Ellington 13.9 12.2 11.6 Jordan Hill 18.5 19.3 16.2 Ed Davis 17.2 15.9 20.0 Jeremy Lin 14.9 14.3 15.6

1 Updated June 2015 © NextLesson 2015 Los Angeles Lakers

1. Model the stats of each of player to produce a line of best fit and interpret its rate of change. Player Line of Best Fit Interpretation of Rate of Change Kobe Bryant Carlos Boozer Ronnie Price Nick Young Wayne Ellington Jordan Hill Ed Davis Jeremy Lin

2. Use the line of best fit to predict their player efficiency rating for the next season.

Player Line of Best Fit Rate of Change 2015-16 Prediction

Kobe Bryant Carlos Boozer Ronnie Price Nick Young Wayne Ellington Jordan Hill Ed Davis Jeremy Lin

3. Based on the projections, which players have the most significant expected increase and decrease?

4. Based on the projections, which three players are projected to have the highest player efficiency ratings in the 2015-2016 season? Is this a change from the current year?

5. If an average NBA player has a player efficiency rating of 15, how many of the Los Angeles Lakers players in the table are expected to be better than average next year?

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LEVEL 2

You want to know if the average number of minutes played per game is related to a player’s player efficiency rating.

You hope to observe a positive correlation between player efficiency rating and their minutes.

Average 2014-15 Player Player Minutes Played Efficiency Rating Kobe Bryant 34.5 17.6 Carlos Boozer 23.8 16.4 Ronnie Price 22.8 10.2 Nick Young 23.8 14.2 Wayne Ellington 25.8 11.6 Jordan Hill 26.8 16.2 Ed Davis 23.3 20.0 Jeremy Lin 25.8 15.6

6. Construct a scatterplot to display the relationship and determine a line of best fit.

7. Interpret the rate of change. What does it mean in the context of the problem?

8. If a player was playing 25 minutes a game, what would you expect his player efficiency rating to be based on the models?

9. If a player was playing 5 minutes a game, what would you expect his player efficiency rating to be based on the models?

10. If a player had a player efficiency rating of 18, how many minutes would you expect him to play?

11. If a player had a player efficiency rating of 6, how many minutes would you expect him to play?

12. Assess the decisions of the team’s coaches in this situation. Did they use players to give their team the best chance of winning?

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Challenge

To finalize your report you wanted to include two more variables into your analysis – a player’s salary and his +/- rating. The +/- rating is determined by how many more or less points a player’s team scored when they were on the court.

2014-15 Player Average 2014-15 Player Efficiency +/- Rating Minutes Played Salary ($) Rating Kobe Bryant 34.5 17.6 -11.8 23,500,000

Carlos Boozer 23.8 16.4 -9.0 3,250,000

Ronnie Price 22.8 10.2 -3.2 1,316,809

Nick Young 23.8 14.2 -2.8 4,944,420

Wayne Ellington 25.8 11.6 -3.6 923,780

Jordan Hill 26.8 16.2 -10.6 9,000,000

Ed Davis 23.3 20.0 -7.2 981,084

Jeremy Lin 25.8 15.6 -6.5 8,374,646

1. Select a relationship between two variables that you haven’t yet explored. Using the methods from your earlier research, determine a linear model and interpret the results.

2. Based on your research, which three players on the team do you believe bring the most value to the roster? Use evidence from your research to support your opinion.

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Finale

You could give students one of the following finale options or have them choose themselves.

1. In the NBA, there may be a significant difference between a player’s regular season and playoff performance. Select five players from playoff teams this year and compare their regular season and playoff statistics. Is there a relationship between the two? Write a blog post to share your findings.

2. Investigate the player efficiency rating system to determine how it is calculated. Construct an infographic that details aspects that go into the calculation. Do you believe other factors should be included?

3. In the NBA, while there is a salary cap, teams can exceed the cap but are then required to pay a luxury tax. Research how the luxury tax amount is calculated and create a Prezi that is either for or against a salary cap.

5 Updated June 2015 © NextLesson 2015 Los Angeles Lakers

Glossary

+/- Rating – the average number of points a Salary cap – a limit for spending money on players team scores more or less than their players. opponent while the player is on the court. Statistician – someone who specializes in Luxury tax – an additional tax that is using data to draw conclusions or make applied to teams who exceed the salary cap. predictions (see also Job Background section). Player efficiency rating – an advanced NBA stat that aims to determine a player’s value to his team.

Updated June 2015 © NextLesson 2015 Los Angeles Lakers

Job Background

Quick Facts: Statisticians $75,560 per year

2012 Median Pay $36.33 per hour

Entry-Level Education Master’s degree

Work Experience in a Related Occupation None

On-the-job Training None

Number of Jobs, 2012 27,600

Job Outlook, 2012-22 27% (Much faster than average)

Employment Change, 2012-22 7,400

What Statisticians Do Statisticians use statistical methods to collect and analyze data and help solve real-world problems in business, engineering, the sciences, or other fields.

Work Environment Although statisticians work mostly in offices, they may travel to oversee a survey’s design or implementation or to collect data. About a quarter of statisticians work for government; many others work for private businesses.

How to Become a Statistician Statisticians typically need a graduate degree in statistics or mathematics. However, there are an increasing number of positions available for those with only a bachelor’s degree.

Pay The median annual wage for statisticians was $75,560 in May 2012.

Job Outlook Employment of statisticians is projected to grow 27 percent from 2012 to 2022, much faster than the average for all occupations. Growth is expected to result from more widespread use of statistical analysis to make informed business, healthcare, and policy decisions.

ANSWER KEY LEVEL 1 1. Where t = time in seasons with season 2012-2013 being t=0 and E = Player Efficiency Rating Player Line of Best Fit Interpretation of Rate of Change Kobe Bryant's player efficiency rating is Kobe Bryant E = -2.7t + 19.8 decreasing 2.7 points per season. Carlos Boozer's player efficiency rating is Carlos Boozer E = -0.35t + 16.32 decreasing 0.35 points per season. Ronnie Price's player efficiency rating is Ronnie Price E = 1.7t + 6.5 increasing 1.7 points per season. Nick Young's player efficiency rating is Nick Young E = 0.45t + 14.05 increasing 0.45 points per season. Wayne Ellington's player efficiency rating Wayne Ellington E = -1.15t + 13.72 is decreasing 1.15 points per season. Jordan Hill's player efficiency rating is Jordan Hill E = -1.15t + 19.15 decreasing 1.15 points per season. Ed Davis's player efficiency rating is Ed Davis E = 1.4t + 16.3 increasing 1.4 points per season. Jeremy Lin's player efficiency rating is Jeremy Lin E = 0.35t + 14.58 increasing 0.35 points per season.

Player Line of Best Fit Rate of Change 2015-16 Prediction

Kobe Bryant E = -2.7t + 19.8 -2.7 11.7 Carlos Boozer E = -0.35t + 16.32 -0.4 15.27 Ronnie Price E = 1.7t + 6.5 1.7 11.6 Nick Young E = 0.45t + 14.05 0.5 15.4 Wayne Ellington E = -1.15t + 13.72 -1.2 10.27 Jordan Hill E = -1.15t + 19.15 -1.2 15.7 Ed Davis E = 1.4t + 16.3 1.4 20.5 Jeremy Lin E = 0.35t + 14.58 0.4 15.63

3. Ronnie Price is predicted to have the largest increase with 1.4 points and Kobe Bryant is predicted to have the largest decrease with -5.9 points.

ANSWER KEY

4. 4The predicted top 3 players for this upcoming season are Ed Davis, Jordan Hill, and Jeremy Lin. Jeremy Lin and Jordan Hill both move into the top 3 this season but they were not last season. Ed Davis was in the top 3 last season and is predicted to stay in the top 3

5. There are predicted to be 5 players who will play better than average next season.

LEVEL 2 6. Los Angeles Lakers: Minutes Played vs. Player Eﬃciency Rang

40 35 30 25 20 15

Minutes Played 10 5 0 0 5 10 15 20 25 Player Eﬃciency Rang

m = 0.348E + 20.529, where m = minutes played and E = player efficiency rating

7. The rate of change is 0.348. This means that for every increase of one point in a player's efficiency rating, that player will play about 0.348 additional minutes. This is equal to about 21 seconds.

8. Based on the model, that player would have a rating of 12.85

9. Based on the model, that player would have a rating of -44.62

10. Based on the model, that player would play about 26.79 minutes

11. Based on the model, that player would play about 22.62 minutes

12. The correlation of the model representing the relationship of Minutes vs. Player Efficiency Rating is 0.2919. This means the coaches did a mediocer job of playing the players with higher efficiency ratings more, which might have cost the team a few chances of winning some of their games.

ANSWER KEY Challenge

1. Answers will vary based on which two variables they decide to compare. For example, if a student chooses to do Salary vs. Player Efficiency Rating, their scatterplot would look like the following:

Los Angeles Lakers: Salary vs. Player Eﬃciency Rang

25000000

20000000

15000000

Salary ($) 10000000

5000000

0 0 5 10 15 20 25 Player Eﬃciency Rang

The linear regression is S = 869,841.8E - 6,706,999.09, where S = player’s salary and E = player efficiency rating. The rate of change is 869,841.8 per point, which means for each increase of one point of a player’s efficiency rating, the player will be paid about $869,841.8 more in their salary.

2. Answers will vary. For example, a student might claim that Ed Davis is one of the top three because he has one of the highest player efficiency rankings at 20, but one of the lower salaries at $981,084. Students may also want to consider plus/minus and minutes played into their decision of which three players bring the most value to the team.