## SCIENCE OF GOLF: Calculating a Golf Handicap Index - STEM Lesson Plan (Grades 6-12)

##### Objective:

Students will investigate questions about the handicap index and its role in golf competition by making models and carrying out calculations.

##### Introduction Notes:

Science of GOLF

Calculating a Golf Handicap Index

Lesson plans produced by the National Science Teachers Association.

Video produced by NBC Learn in partnership with the USGA and Chevron.

Background and Planning Information.............................................................. 2

Video Timeline ........................................................................................................................ 2

Next Generation Science Standards........................................................................................ 2

Common Core Standards for Mathematics............................................................................ 3

Promote STEM with Video................................................................................ 3

Connect to Science................................................................................................................... 3

Connect to Technology............................................................................................................ 3

Connect to Engineering........................................................................................................... 4

Connect to Math...................................................................................................................... 4

Facilitate MATH Inquiry.................................................................................... 5

Explore Understanding............................................................................................................ 5

Possible Materials........................................................................................................ 6

Open Choice Approach................................................................................................ 6

Focused Approach........................................................................................................ 6

Media Research Option............................................................................................... 8

Make a Claim Backed by Evidence.......................................................................................... 8

Compare Findings.................................................................................................................... 8

Reflect on Learning.................................................................................................................. 8

Inquiry Assessment.................................................................................................................. 9

Incorporate Video into Your Lesson Plan........................................................... 9

Integrate Video in Instruction................................................................................................. 9

Visualize Concepts....................................................................................................... 9

Real World Application................................................................................................ 9

Using the 5E Approach?............................................................................................... 9

Connect to … Language Arts.................................................................................................. 10

Connect to … Social Studies.................................................................................................. 10

Use Video as a Writing Prompt............................................................................................. 10

Copy Masters ................................................................................................. 11

Open Choice Inquiry Guide for Students.............................................................................. 11

Focused Inquiry Guide for Students .................................................................................... 12

Assessment Rubric for Inquiry Investigations...................................................................... 14

(1)

Background and Planning Information

This video discusses the history and current practice of calculating handicap index, a system by which players of different abilities can compete equitably by means of adjustments to their scores. It features Eric Lahman, Manager of Course Rating and Handicapping for the United States Golf Association (USGA). The video discusses the reasons for having a handicapping procedure, along with the reasons for including course and slope ratings. It is a good example of how mathematic procedures can evolve as new needs are discovered, and how people create solutions to address these needs.

Video Timeline

0:00     0:15     Series opening

0:16     0:51     Describes a handicap index

0:52     1:32     Introduces Eric Lahman and describes the purpose of a handicap index

1:33     2:04     Defines course ratings and slope ratings

2:05     2:31     Explains calculation of slope ratings and its importance to handicap

2:32     3:25     Explains the formula for a handicap calculation

3:26     4:01     Explains how a player’s potential is considered by the formula

4:02     4:36     Explains the bonus for excellence

4:37     5:08     Describing how specific course and slope ratings are used with the index

5:08     5:34     Summary

5:35     5:53     Closing credits

Language Support:  To aid those with limited English proficiency or others who need help focusing on the video, click on the Transcript tab on the side of the video window, then copy and paste into a document for student reference.

Next Generation Science Standards

The investigation described in Facilitate MATH Inquiry supports Practices for K–12 Science Classrooms.

Science and Engineering Practices

Plan and conduct an investigation individually and collaboratively to produce data to serve as the basis for evidence, and in the design: decide on types, amount, and accuracy of data needed to produce reliable measurements; consider limitations on the precision of the data (e.g., number of trials, cost, risk, time), and refine the design accordingly.

Analyze data using tools, technologies, and/or models (e.g., computational, mathematical)  to make valid and reliable scientific claims, or determine an optimal design solution.

Develop a model to predict and/or describe phenomena.

Use mathematical representations of phenomena to describe explanations.

Construct and interpret graphical displays of data to identify linear and nonlinear relationships.

(2)

Common Core Standards for Mathematics

The investigation described in Facilitate MATH Inquiry supports mathematics instruction. The complete text for the following standards can be accessed at: http://www.corestandards.org.

Standards for Mathematical Practice

CCSS.Math.Practice.MP1Make sense of problems and persevere in solving them.

CCSS.Math.Practice.MP2Reason abstractly and quantitatively.

CCSS.Math.Practice.MP4Model with mathematics.

CCSS.Math.Content.6.EE.C.9Use variables to represent two quantities in a real-world problem that change in relationship to one another….

CCSS.Math.Content.6.SP.B.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as….

CCSS.Math.Content.7.EE.B.4Use variables to represent quantities in a real-world or mathematical problem, and….

CCSS.Math.Content.8.EE.B.5Graph proportional relationships, interpreting the unit rate as the slope of the graph….

CCSS.Math.Content.HSA-SSE.A.1 Interpret expressions that represent a quantity in terms of its context.

Promote STEM with Video

Connect to Science

Science is involved in the handicap calculation in that a large amount of data (alluded to in the video) had to be accumulated and analyzed to develop and adjust the system, and must also be used in the routine process of determining course and slope ratings for new and existing courses.

Take Action with Students

Use the video as a springboard to start students brainstorming examples of other activities, including sports, where handicapping might be appropriate or at least possible. An example might be running road races, where large amounts of data exist online (an Internet search on “5K race results” will provide a wealth of data). Students might develop “course ratings” and “slope ratings” using such data.

Connect to Technology

Modern technology, particularly computers, makes the rather complex task of calculating handicap index much easier.  Computers not only speed up the calculations, they store golfers’ scores for very quick recall.  Computers store scores from many different golfers and combine those scores to calculate the level of challenge of a particular course in comparison to other courses. Additionally, a golfer can walk into competitive play on a course almost anywhere with an appropriate handicap for that course, because of the handicapping computer set up in the clubhouse.

(3)

Take Action with Students

Show the portion of the video (about 1:33–1:36) that shows scores being entered or accessed via a touch-screen. Have students do Internet searches to find software or smartphone applications for calculating handicap index. You or the students might obtain and experiment with such applications.

Connect to Engineering

The engineering design process involves identifying problems and finding solutions, usually as part of an ongoing cycle of innovation. The handicapping system was simple at first, but had shortcomings that were addressed and improved with experimentation using layers of complexity. This same complexity can be cumbersome, requiring expertise and technology to deal with in practice. A feature of engineering is that different people or teams of people will often arrive at different solutions to the same problem. This is apparent in the variety of handicapping systems that golf associations in different countries have created.

Take Action with Students

Have students do research to trace the history of and reasons for each innovation in the USGA handicapping system – e.g., course rating, slope rating, and “bonus for excellence.” Have them clearly identify the problem that motivated the changes, and how these changes made the system better. Also, ask students on what basis one would decide that the system had in fact been improved. A good source is the series starting with http://www.usga.org/news/2011/October/History-Of-Handicapping--Part-I/

Have students do research to compare the USGA’s handicap system with those in other countries.  Note: At least three other systems are noted in the Wikipedia article on “Handicap (golf).”  Have students identify and explain any differences, and make arguments for how and why these may – or may not – be an improvement over the USGA system.

Connect to Math

Math is the essential tool for determining handicap index. Many mathematical concepts are involved in calculating the index, including statistics (such as the “better half average,” or mean, of scores as a measure of player potential), and algebra (noting especially the slope-intercept form of the score compared to the handicap index graph shown). Some high school students may have taken a course focused on statistics, and most high school and many middle school students will have seen the equation y = mx + b, describing a line with a slope of m and the y-intercept at b.

Take Action with Students

If students have experience with statistics, have them discuss reasons for using the last 20 rounds, as opposed to a lifetime average, and also the reasons for using the “better half” of scores instead of all of them. Additionally, have them discuss the reason for using the table to determine how many scores to use when less than 20 are available, and the reason for the 0.96 factor. Help them understand that without this last one, the handicapping system would remove almost all incentive for improvement, as the system would essentially erase the differences between players of widely varying abilities.

(4)

If students have experience with modeling situations with equations, have them label the “x” and “y” axes on the given graphs, and identify the meaning of the y-intercept (course rating) and slope (slope rating).  Have students brainstorm to imagine what a golf course with all four combinations of low/high course rating and low/high slope rating would look like on the graph, and how the actual courses might be different from each other to necessitate these values.

Explain to students that they will use the concepts from the video to calculate a handicap index from data you supply to them. Show the segment from about 1:15–3:40, showing it at least twice before expecting students to complete the calculations – or pause the video enough so they can complete the calculations as the examples are shown. Because several mathematical steps are required, this can serve as an assessment of practical math skills, such as solving formulas given different values.

Another interesting discussion:  have students consider the difference between rounding (such as when calculating individual differentials, the score is rounded to the nearer tenth), and truncating (such as when determining your handicap, the score is truncated). What is the effect of different processes in these two instances? Why might the scores be expressed in this way?

Facilitate MATH Inquiry

Encourage inquiry using a strategy modeled on the research-based science writing heuristic. Student work will vary in complexity and depth depending on grade level, prior knowledge, and creativity. Use the prompts liberally to encourage thought and discussion. Student Copy Masters begin on page 11.

Explore Understanding

Set the stage for a discussion of handicapping in golf:  elicit from volunteers what impact a participant’s skill level has on how any type of competition plays out. Use prompts such as the following.

To make the competition fairer when people playing _____ have different skill levels, they might….

Some ways that people “level the playing field” in _____ are….

Handicapping in races, golf, and some other sports involves….

Some concerns or problems that might arise in developing a handicapping system are….

Show the video “Science of Golf: Handicap Index.” Continue the discussion of handicapping, with prompts such as the following:

When I watched the video, I thought about….

According to the video, the reasons for having a handicapping system are….

According to the video, some problems that must be addressed in a system are….

According to the video, the two variables describing the course are….

The USGA handicapping system has become complex because….

(5)

Stimulate small-group discussion with the prompt: This video makes me think about these questions…. Then have groups list questions they have about the challenges that must be surmounted to develop a handicapping index that takes into account not only the skill of the golfer, but the challenges of a particular course for golfers of different skill levels. Ask groups to choose one question and phrase it in such a way as to be researchable and/or testable. The following are some examples.

How does the USGA system take into account the skill of the golfer?

How does this system take into account the overall difficulty of the course?

How does this system take into account how the course affects different skill-level golfers?

How does this system retain an incentive to improve?

How can different systems of handicapping accomplish the same goals?

Choose one of the following options based on your students’ knowledge, creativity, and ability level and your available materials. Actual materials needed would vary greatly based on these factors as well.

Possible Materials: Allow time for students to examine and manipulate the materials you have available. Doing so often aids students in refining their questions, or prompts new questions  that should be recorded for future investigation. In this inquiry, students might use materials such as several dozen pennies or other small objects, and a bowl, bucket, or large can into which these small objects can be tossed.

Safety Considerations: To augment your own safety procedures, see NSTA’s Safety Portal at http://www.nsta.org/portals/safety.aspx.

Open Choice Approach (Copy Master page 11)

Groups might come together to agree on one question for which they will explore an answer, or each group might explore something different. Students should brainstorm to form a plan they would have to follow in order to answer the question, which might include researching background information. Work with students to develop safe procedures that control variables and enable them to gather valid data. Encourage students with prompts such as the following:

Information we need to understand before we can start our investigation is….

A game or other application for which we might develop and use a handicapping system is….

The variables in developing a handicapping system might be….

We might test our system by….

To conduct the investigation safely, we will….

Focused Approach (Copy Master pages 12–13)

Note to teachers: This investigation can vary in scope and length, depending on how many aspects of the handicap index calculation you want to simulate.  At a minimum, it would involve two rounds (sets of tossing objects) on a single course (the can at a certain distance)—the first to establish a simple handicap index, and the second to use it in competition. At maximum,

many rounds could be played, on multiple courses, and the results analyzed more thoroughly, to more fully parallel the video. Here, an intermediate path is described, including simplified versions of course and slope ratings.  The following exemplifies how students might play a golf-like game, and use the results to calculate a somewhat simplified handicap index to be used in further competition.                                               (6)

1.     After students examine the materials  you have available for devising a scoring game, ask them questions such as the following to help them envision their investigation.

How might we play a game in which, like golf, a lower score is better?

How can we establish conditions that make the game challenging, but playable?

What will constitute the scoring system?

2.     Students might first experiment with tossing objects into the can from different distances – ranging from a few to perhaps 10 feet (for a can between 6 and 12 inches in diameter – to  find a distance at which most students can get at least half the objects in the can, but very few can get all of them in. A definition similar to the following could be used: 36 tosses to get 30 objects in the can could be par (on nine holes); 45 could be bogey.

We determined that the distance at which the most accurate tossers can get most of the objects in the can was….

We calculated a typical average score by….

3.     After a bit of practice, a formal game could be played to establish handicap indices. A simple subtraction of 36 from the score could be taken as the handicap index. If more time is available, 60 sunk objects could be required (par = 72), or more rounds could be played, to allow a “best half” determination.

One round is/is not sufficient to establish a reliable handicap because….

Additional rounds might impact the handicap by….

The range of handicaps in the class is….

What we have done is (the same as/different from) what was done in the video in that….

4.     Having established handicap indices, students can now have a tournament in which they play a round and then subtract their handicap indices:

The range of scores after handicapping is (narrower/wider) than before because….

There is still a range of scores in spite of handicapping because….

This method (is/is not) a fair way to compete because….

5. Students might use their handicaps to compete on different courses, to replicate the concept of course and slope ratings. To do so, they might move the can further away: a 10 to 20% increase can be sufficient to make a more challenging course that results in higher scores. Students will likely notice that the score of bogey players – perhaps defined as those scoring 45 or some other number, or alternately, the higher scoring half -- increases more than that of the best players.

A good distance to make a noticeably harder course might be….

We will define scratch and bogey golfers by….

Assuming the first course to have a course rating of 36, this course gets a rating of….

Assuming the first course to have a bogey rating of 45, this course gets a rating of….

If the slope of the first course was 9, the slope of more difficult course is….

6. Students might then play the more challenging course, using handicap indices that incorporate the difference in slope ratings.

In order to calculate course handicaps, without regard to slope, we must….

In order to include slope in our handicap index calculations, we must….

The effect of multiplying handicap indices by 0.96, as in the video, would be to….

To conduct the investigation safely, we will….

(7)

Media Research Option

Groups might have questions that are best explored using print media and online resources. Students should brainstorm to form a list of key words and phrases they could use in Internet search engines to locate resources that will help them answer the question. Review how to safely browse the Web, how to evaluate information on the Internet for accuracy, and how to correctly cite the information found. Suggest students make note of any interesting tangents they find in their research effort for future inquiry. Encourage students with prompts such as:

Words and phrases associated with our question are….

The reliability of our sources was established by….

The science and math concepts that underpin a possible solution are….

Our research might feed into an engineering design solution such as….

To conduct the investigation safely, we will….

Make a Claim Backed by Evidence

Students should analyze their data and then make one or more claims based on the evidence their data shows. Encourage students with this prompt: As evidenced by… we claim… because….

An example claim might be:  As evidenced by the greater difference between bogey and scratch players when playing the harder course, we claim that the harder (higher course rating) course also has a higher slope rating, because increases in scores were more multiplicative than additive.

Compare Findings

Encourage students to compare their ideas with others, such as classmates who investigated a similar (or different) question or system, or to compare their ideas with material they found on the Internet or in their textbooks, or heard from an expert they chose to interview. Remind students to credit their original sources in their comparisons. Elicit comparisons from students with prompts such as:

My ideas are similar to (or different from) those of the experts in the video in that….

My ideas are similar to (or different from) those of my classmates in that….

My ideas are similar to (or different from) those that I found on the Internet in that….

Students might make comparisons like the following:  My ideas on what constitutes a fair and effective handicapping system are similar to those discussed by presenters in the video and practiced by the USGA. However, I found that there are a variety of ways this might be done, and different methods each have their merits and drawbacks.

Reflect on Learning

Students should reflect on their understanding, thinking about how their ideas have changed or what they know now that they didn’t know before. Encourage reflection, using prompts such as the following:

The claim made by the expert in the video is….

I support or refute the expert’s claim because in my investigation….

When thinking about the expert’s claims, I am confused as to why….

Another investigation I would like to explore is….

(8)

Inquiry Assessment

See the rubric included in the student Copy Masters on page 14.

Incorporate Video into Your Lesson Plan

Integrate Video in Instruction

Visualize Concepts:  Show the portion of the video starting about 1:37, pausing it to allow students to carefully inspect the graph at about 2:15, showing a slope and an intercept. The concept of a quantity changing steadily from some initial value arises not only in algebra classes in the abstract sense, but also in numerous other subjects, especially science. Have students identify topics they have learned in your class or other classes, which involve similar looking graphs. Have them identify what the slope and the intercept represent in these applications.

Real World Application: Have students individually (or as part of small teams) generate a list of 10 to 15 pretend golf scores, making an effort to represent fluctuation (good days/bad days) about some roughly predetermined average (say 75, 85, or 100). Have them look up two or three local courses on which they played these rounds, incorporating the course handicaps and slope ratings. Students might also use actual scorecards obtained from local courses or downloaded from famous course websites. Have them follow through the series of calculations to come up with their own handicap index. If time and interest allow, you could have the students “play” another course, and compete, using the handicap indices. Finally, you could have them use software applications or calculators to verify their manual calculations.

Using the 5E Approach?

If you use a 5E approach to lesson plans, consider incorporating video in these Es:

Explore:  Use the Design Investigations section of the Facilitate Inquiry to support any lessons you may be teaching entailing probability, statistics, or relationships among variables. For example, in the object-tossing activity, students might try to find a relationship (linear, exponential, square root) between mean score and distance from the bowl.  It might, for example, be modeled as square law (twice as far away, requiring four times as many pitches). Students could brainstorm to come up with reasons for whatever relationship they find.

Elaborate:  Sample size is an important concept in statistics, and the decision of the creators of the handicap system to use 20 rounds, from which to extract the best 10, was made as a balance of a large sample size versus a representation of relatively recent scores. Likewise, the use of more than half the scores if there are less than 20 is a compromise between sample size and the desire to represent a player’s potential (as defined by average of better half of scores). To illustrate this, have students randomly generate 20 scores – including a few bad outings – and then compute the average of the best 10. Then have them follow the guidelines in the table for the number to use out of less than 20, and use, for example, only the last 16, 12, or 8  to recompute the averages. Have students discuss any variations they see, and whether they see any trends as the number of scores decreases.

(9)

Connect to … Language Arts

In watching this video or others in the Science of Golf series, students may notice the use of many words, such as scratch or bogey, which are not familiar outside of golf. These are an example of jargon. Have students research to develop a list of golf terms, along with interesting stories about their etymology. Then, have students identify other sports or professions known for having distinct jargon of their own. Have them debate whether or not jargon plays a positive role in a sport or profession.

Connect to … Social Studies

Debate:  Golf is a game that is often thought of as elitist – yet it has many egalitarian aspects, such as the handicapping system and even some of its historical roots. Along with this, golf tradition emphasizes courtesy and honesty in play. Have students research the meanings of elitist and egalitarian and, after doing some research, debate whether golf is more one than the other in practice. Students might also comment about how democratic golf is, and on who plays golf, ranging from wealthy country club members to shift workers playing at an inexpensive public course in the morning before their workday begins.

Use Video as a Writing Prompt

Have students consider other activities in life—sports, employment, education, government, and so on—where something like handicapping is or could be practiced.  Ask them to identify circumstances under which handicapping is appropriate, and under which it is not, as well as to explain the criteria by which they are making such judgments.

(10)

Copy Master: Open Choice Inquiry Guide for Students

Science of Golf: Handicap Index

Use this guide to investigate handicap index and its role in golf competition. Write your lab report in your science notebook.

The video makes me think about these questions….

Choose one question. How can you answer it? Brainstorm with your teammates. Write a procedure that controls variables and makes accurate measurements. Look up information as needed. Add safety precautions.

Information we need to understand before we can start our investigation is….

The aspect(s) of golf handicapping we will be working on is….

This (these) aspect(s) of handicapping is (are) important because….

The variables we will be working with are….

We will evaluate or test our system by….

To conduct the investigation safely, we will….

Record Data and Observations

Record your observations. Organize your data in tables or graphs as appropriate.

Make a Claim Backed by Evidence

Analyze your data and then make one or more claims based on the evidence your data show. Make sure that the claim goes beyond summarizing the relationship between the variables.

 My Evidence My Claim My Reason

Compare Findings

Review the video and then discuss your results with classmates who investigated the same or a similar question. Or do research on the Internet or talk with an expert. How do your findings compare? Be sure to give credit to others when you use their findings in your comparisons.

My ideas are similar to (or different from) those of the experts in the video in that….

My ideas are similar to (or different from) those of my classmates in that….

My ideas are similar to (or different from) those that I found on the Internet in that….

Reflect on Learning

Think about what you found out. How does it fit with what you already knew? How does it change what you thought you knew?

The claim made by the expert in the video is….

I support or refute the expert’s claim because in my investigation….

When thinking about the expert’s claims, I am confused as to why….

Another investigation I would like to explore is….

(11)

COPY MASTER: Focused Inquiry Guide for Students

Science of Golf: Handicap Index

Use this guide to investigate handicap index and its role in golf competition. Write your lab report in your science notebook.

How does a handicapping system impact golf competition?

What factors should be taken into account in developing such a system?

How will we actually make the calculations?

The reason for having a handicap index is….

We will initially determine individual handicap indices by….

We will determine overall course difficulty by….

We will determine how the course affects players of different skills by….

We will incorporate course rating and slope in our calculations by….

We predict that using our handicap index will largely erase differences among players because….

To conduct the investigation safely, I need to….

Record Data and Observations

Organize your observations in tables and graphs such as the examples presented. Be sure to include the number of tosses and the distance to the cup in each course.

Results of Simple Handicap System Course 1

 Student Name Score #1 Score #2 Score #3 Average best 2 of 3 Handicap (average minus ____) Tournament score Score after handicap

Results of Simple Handicap System Course 2

 Student Name Score #1 Score #2 Score #3 Average best 2 of 3 Handicap (average minus ____) Course 1 handicap minus Course 2 handicap

(12)

Ideas for Analyzing Data

Taking all students into account after the tournament on the first course, how did average score compare to the average score after handicapping? How did the amount of variation in scores compare before and after handicapping?

How different, on average, were scores on the second course compared to the first?  How different were the scores of the players in the lower-scoring half of the group between the two courses (considering the same individuals)? If the first course warrants a scratch rating of 36, what would be an appropriate rating for the second course?

How different were the scores of the players in the higher-scoring half of the group between the two courses (considering the same individuals)? If the first course warrants a bogey rating of 45 (or some other value you want to define), what would be an appropriate rating for the second course?

Based on the above, how would you define slope ratings for the two courses? How would you take this into account in calculating individual handicap indices?

If you played another tournament on the second course, did the scores stay in as narrow a range as on the first course?

What sources of error might remain in this experiment? How might you make the handicap index determination more consistent?

Make a Claim Backed by Evidence

Analyze your data and then make one or more claims based on the evidence shown by your data. Make sure that the claim goes beyond summarizing the relationship between the variables.

 My Evidence My Claim My Reason

Compare Findings

Review the video and then discuss your results with classmates who did the investigation using the same or a similar system, or with those who did the investigation using a different system. Or do research on the Internet or talk with an expert. How do your findings compare? Be sure to give credit to others when you use their findings in your comparisons.

My ideas are similar to (or different from) those of the experts in the video in that….

My ideas are similar to (or different from) those of my classmates in that….

My ideas are similar to (or different from) those that I found on the Internet in that….

Reflect on Learning

Think about what you found out. How does it fit with what you already knew? How does it change what you thought you knew?

The claim made by the expert in the video is….

I support (or refute) the expert’s claim because in my investigation….

When thinking about the expert’s claims, I am confused as to why….

Another investigation I would like to explore is….

(13)

Copy Master: Assessment Rubric for Inquiry Investigations

(14)

Close

FILTERING

If you are trying to view the videos from inside a school or university, your IT admin may need to enable streaming on your network. Please see the Internet Filtering section of our Technical Requirements page.

DVDs AND OTHER COPIES

Videos on this page are not available on DVD at this time due to licensing restrictions on the footage.

Still have questions?

Close

INTERNATIONAL VISITORS

The Science of the Olympic Winter Games videos are only available to visitors inside the United States due to licensing restrictions on the Olympics footage used in the videos.

FILTERING

If you are trying to view the videos from inside a school or university, your IT admin may need to enable streaming on your network. Please see the Internet Filtering section of our Technical Requirements page.

DVDs AND OTHER COPIES

The Science of the Olympic Winter Games is not available on DVD at this time due to licensing restrictions on on Olympic footage.

Still have questions?

Close