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MARCH MADNESS
INTRODUCTION
Let's get ready to rumble! It's March Madness time which means, you guessed it - Basketball! Basketball is not only a sport filled with excitement, slam dunks, and unbelievable athletes; it also is full of mathematical concepts, as you will find in this project!
TASK
In this project, you will look at many different areas of math found in the NCAA basketball tournament. You will use the NCAA bracket to look at all the teams participating in the tournament. The world of math will come alive as you find fractions, decimals, and percents; probability statistics; use proportions and measurement; make predictions; and look for patterns. By the end of this project, you will be able to relate a variety of math facts to the NCAA tournament and explain the importance of Mathematics in basketball.
PROCEDURES
Find a copy of this year's NCAA Basketball Tournament bracket in the resources provided. You can use the copy provided or print a copy to use through the rest of the project.
Internet Scavenger Hunt-the students will be searching for information on the tournament’s background and its history.
SCALING DOWN MEASUREMENTS & Drawing a Basketball Court-the students will use their mapping and proportional skills to recreate a miniature basketball court to scale.
Research the STATS of the teams. You may work in-groups of two, four, or individually. HOWEVER, your grade will be done individually. You need to decide this before you begin. Please choose your group wisely. If you are working in teams, each member may be responsible for one region (south, east, midwest, and west). You will be looking for information about their past NCAA wins and their records for this year. You will need to use the Team Statistics worksheet to record your data. Answer all the questions on the worksheet.
Probability is our next area of focus. Use the resources provided to find out where each college or university is located. If you are working in teams, locate the states for the schools in your region. Only the state is needed. You may record this information on your bracket out beside the name of each school. Answer the probability questions on the Take Your Chances worksheet & the NCAA Probability worksheet with this information.
How do patterns relate to the NCAA Tournament? Fill out The Elimination worksheet. Look at your bracket to answer the questions.
Dribbling Test-the students will see how many times they can dribble in 30 seconds. They will find the mean, median, and mode in their set of data. The mean of each student will be contributed to the class as we create a stem and leaf plot of our data.
How does ALGEBRA relate to the NCAA Tournament? We will be defining variables, creating and solving equations with the game of basketball.
Go, Math! Students practice teamwork, cooperation and sporting behavior as they compete in solving review problems in sports math.
Mathematical Article Review- Select a newspaper article from the resources that deals with one game or team from the end of the tournament. This needs to be done independently. Print the article from a website or cut it out from a newspaper or magazine. From that article, record all the statistics that are mentioned. Write a brief paragraph explaining the importance of Mathematics in basketball.
This will be due __________________________
RESOURCES Here are some sites that might be helpful in your project. Official NCAA Site -http://www.ncaabasketball.net/ NCAA Championships -http://www.ncaasports.com/ Final Four & Team info - http://www.ncaasports.com/basketball/mens/schedules History of NCAA Basketball -http://live.sportsline.com/u/madness/1998/history/atoz/index.html Complete Listing of- Colleges and Universities - http://www.globalcomputing.com/universy.html Big Ten Converence http://bigten.collegesports.com/default/big10-default.html College Sports Links - http://chili.collegesportsnews.com/websitht.htm Fans Only - College Sports -http://www.fansonly.com/
EVALUATION HOW YOU ARE GRADED
You will be evaluated on the completeness and accuracy of your worksheets (Answers need to be given using complete sentences!) and the paragraph written about your article. Please see the attached RUBRIC.
CONCLUSION
Have we found a winner? You can consider yourself an NCAA champion if you can now see all of the mathematics that surrounds the NCAA basketball tournament. Through this project, you located patterns; used proportions; calculated fractions, decimals, and percents; and found many connections with probability. See if you can relate these same facts to any tournament. Do the same math facts still apply? You'll see!
Mrs. Mann’s March Madness Tentative Schedule
The dates given are the day of the lesson The homework will be due the following school day unless notified differently in class. All dates & topics are subject to change based on progress of the individual classes.
¨ introduction of project (3-8-10) ¨ Internet Scavenger Hunt -(3-8 & 3-9) due the 10th ¨ Proportions & Scale drawings (3-10,11) due the 15th
¨ Research of stats (3-15) due the 18th ¨ Probability (3-16 & 3-17)
¨ Patterns & Elimination (3-18) ¨ Algebra (3-21)
¨ Defense & Rebounds (3-22) ¨ Dribbling test (3-23)
¨ Research Articles (3-24) Review is due on the 28th ¨ Team Competition (3-25
¨ Mathematical Article Review Due Mar 28
MARCH MADNESS RUBRIC
Beginning 1
Developing 2
Accomplished 3
Exemplary 4
Worksheets Worksheets were
incomplete with no explanations.
Worksheets had a few incomplete questions with little explanation
for answers.
All worksheets were completed with few errors.
Expanations were given for all answers required.
All worksheets were completed accurately
and completely. Explanations to questions were
precise and
Paragraph about article
Article chosen was about a team or game from the
conference. Few or no statistics in the article were listed. The paragraph did
not explain the importance of mathematics in
basketball.
Article chosen was about a team or game from the conference. Most statistics in the
article were listed. The paragraph had at least one explanation of the
importance of mathematics in basketball but
provided no examples.
Article chosen was about a team or game from the
conference. All statistics in the article were listed. The
paragraph had explanations of the
importance of mathematics in basketball but provided
no examples.
Article chosen was about a team or game from the conference. All statistics in the article were listed. The paragraph had
clear explanations of the importance of mathematics in basketball and
provided examples.
** Answers need to be given using complete sentences!**
Answers need to be given using complete sentences!)
NCAA MARCH MADNESS INTERNET HUNT
Use the Internet locations and your problem solving skills to answer the following questions and become a March Madness Expert. Please use the links listed, but if you are having problems, you may search google to find your answers. v Open your Internet browser. Enter the URL:
http://library.thinkquest.org/10615/no-frames/basketball/history.html v Read the History of Basketball and answer these questions:
Who was the inventor of Basketball?_________________________________________________________________________________________________ When was it invented?____________________________________ Where:_______________________________________________ At who’s request and why was it invented? ____________________________________________________ v Navigate to the web site at http://library.thinkquest.org/6413/rules1.htm v Locate and read the information about the rules of the game. v Compare these rules to the original 13 rules listed at
http://inventors.about.com/library/inventors/blbasketball_rules.htm and answer the question below. HINT: Look at Rule #3 on the original 13 rules.
What is one difference in how the game was originally played compared to how it is played now? (Answer using a complete sentence.)
Answers need to be given using complete sentences!)
v Go to http://sportspl.com/collbsrl.html v Click on Rule Differences v Look under the NCAA Column v Find the answers to these questions
What is the duration of a men’s college basketball game?
What is the distance of the 3 point line? _____________________________________________________
What is the foul limit? _____________________________________________________ v Navigate to http://www.cbssports.com/collegebasketball/mayhem/history and
locate the following information. v Click on COMPLETE LIST under Year-By-Year Tournament History. v Click on the desired year bracket to complete the following questions.
This year there will be 64 teams in the NCAA tournament. How many teams played in 1979?________________________________________________
What was the first year of the tournament? _____________________________________________________
How many teams played the first year? _____________________________________________________ v Navigate to http://www.tourneytravel.com/history/schoolstats.htm and locate the
following information.
What team has made the most tournament appearances? _____________________________________________________
How many?_____________________________________________
Which team has the most NCAA Titles?
Answers need to be given using complete sentences!) How many?_____________________________________________
Which team was the lowest seed to win a championship? _____________________________________________________
What year?_________________ What seed?________________ v Locate http://www.ncaa.com v Click on Mens Sports D-I v Answer the questions below:
Where will the Men’s NCAA Final Four be played? _____________________________________________________ When?______________________________________________ v Click on Venue and answer the following questions.
What is the approximate seating capacity of this stadium? _____________________________________________________
This stadium is home to what football team? _____________________________________________________
How much is a green level ticket? _____________________________________________________
How much is a red level ticket? ____________________________________________________ v Go to http://www.ncaa.com v Along the top click on CHAMPIONSHIPS v Scroll down and look under Women’s Basketball. Click on D-1: Championship
Home Page v Click on ENTER SITE and answer the following questions.
Where will the Women’s NCAA Final Four be played? ____________________________________________________ When?______________
Answers need to be given using complete sentences!) v Click on Venue and answer the following questions.
What is the seating capacity for the Women’s NCAA final four? _____________________________________________________
This was the home to what team? _____________________________________________________
How do the seating capacities compare? What is a possible explanation for the difference? v Go to http://www.championshiphistory.com/ncaahoops.php v Scan the list of winners.
Kentucky has won the championship how many times?______________ What was Kentucky’s average score for these wins?______________ SHOW YOUR WORK! What is the average number of points that UCLA has won by during its tournament history? (HINT: There are 10 games. You must first calculate the point difference in each of the games and then calculate the average). SHOW YOUR WORK!
v Navigate back to http://www.cbssports.com/collegebasketball/mayhem/history v Scroll down to Single-Game Scoring Performances v Click on COMPLETE LIST
v Use the space below to calculate the following information and answer the questions.
Range in Points:_______________
Average number of points:_______________
Median:_______________
SHOW YOUR WORK! v Find the AP College Men’s Basketball Poll at
http://www.sportsline.com/collegebasketball/polls v Scan the list.
Answers need to be given using complete sentences!)
Based on the AP Poll which four teams would you predict would be in the Final Four tournament? Why?
Answers need to be given using complete sentences!)
v Under the Associated Press Top 25 click on Complete Details. v Select Gonzaga from the list.
Which conference does Gonzaga play in?____________________ v Click the back button to return to the Associated Press Top 25. v Find DUKE and click on it.
What is Duke’s Mascot?____________________________ v Click the back button to return to the Associated Press Top 25 and locate another
team of your choice. Click on it. Draw the team symbol here.
¨ Find the NCAA Shop. Click on 2011 Final Four Gear. ¨ Choose four items that you would like to have as souvenirs.
DO NOT CLICK ON “BUY IT”! List them below and your total cost. (show your work)
Items: Total Cost:__________
Drawing a Basketball Court You will be creating an actual basketball court to scale. Complete all of the calculations first before drawing each step. Complete the court in pencil first and make sure you use a ruler and a compass. Also, don’t forget to include a scale on your court. NEATNESS COUNTS! Take your time!
(Draw a picture of a court on a blank piece of computer paper!)
SCALE: 1 INCH=8 FEET
1. An NCAA basketball court is 94 feet long and 50 feet wide.
a. Use 2 proportions to find your drawing length & width
Your court: _________inches long
_________Inches wide
ü Draw the sidelines and baselines of your court.
USE AREA FORMULAS
· What is the area of an NCAA court? __________ft2
· What is the area of your court? __________ in2
2. The center line (half court line) runs through the exact center of
the court. Find the center of one sideline. (show work)
Your Center line is located ________inches on the sideline.
ü Show how you got this answer.
ü Draw the half court line on your court.
3. A basket is centered on each base line.
Your basket is located _________ inches on the end line.
· Make a mark for the center of the end line.
4. The basket is placed 4 feet onto the court from the endline.
a. Use a proportion to find where your basket will be placed.
Your Basket: _________inches onto the court.
ü Draw a basket on each side of the court.
5. The lane or key area under each basket is 12 feet wide and 17
feet long centered on the base line.
a. Use proportions to find the length & width of the free
throw lane.
Your court’s lane: ___________Inches long
___________inches wide
Use your PRIOR knowledge to find PERIMETER. (show your work)
· What is the perimeter of an NCAA lane?___________ feet
· What is the perimeter of your court’s lane?___________ Inches
6. The free throw circle, centered at the midpoint of the free
throw line, is with a universally-recognized 6 feet radius from the
free throw line, with boundaries of the half of the free throw
circle farthest from the backboard traced in solid lines.
Mark the spot and use your compass to create an arc where
the free throw circle line is. Continue to draw the three
point line arc from the circle. When the arc becomes
parallel with the side line, use a ruler to extend a straight
line to the base line.
Your 3 point line: ___________ inches from the center of the
basket.
7. Find the center of the middle line on your court. This is where
you will draw the center circle that has a radius of 2 feet.
Your center circle: ________ inch
ü Use your ruler and compass to create the center circle in
your court.
8. Go back to STEP 1 and double check that you have completed
each step as directed! Add or correct anything that is necessary.
9. Once all of your lines are drawn in pencil, use a black marker or
colored pencil to make them darker. Make sure to use a ruler and
compass while doing this. NEATNESS COUNTS!!
10. Think of different things that you have seen on a basketball
court. Use these ideas to personalize your basketball court.
Basketball Court Rubric: Accurate Calculations: ____/13 Accurate Drawings: ____/13 Neatness: ____/14 Creativity: ____/10 Total Points: ____/50 Letter Grade: ______
Answers need to be given using complete sentences!)
STATS FOR THE TEAMS
1. From your bracket, put the record of each team in the table. 2. On the left side of the table, use abbreviations to label the state where the
team is located. 3. Then find the percent of wins for each team
(remember, the first number listed in the record is the number of wins.) MAKE SURE TO SHOW YOUR WORK!!!
4. Find the amounts of past wins for each team in the tournament. 5. Based on only the information in your tables, no prior knowledge or bias,
determine and support mathematically which NCAA team you would expect to win the tournament.
The team that I predict to win is _____________________ because _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________
East REGION – Newark, NJ
West REGION – Anaheim, CA
Southwest REGION – San Antonio, Texas
Southeast REGION- New Orleans, LA
Name:_____________________________________________ Hour:______________
TAKE YOUR CHANCES!
(ALL answers need to be given using complete sentences!)
1. If the names of all the teams in the NCAA Basketball Tournament were put into a bag, what would be the probability of drawing the winning team out of the bag? Explain how you arrived at your answer.
2. How many states are represented in this year’s tournament? 3. How many teams are from ILLINOIS? How many teams from North Carolina? 4. From which state would you have the best chances of choosing a team if the teams were drawn from a bag? Explain your answer. 5. What percentage of all 50 states is represented? Show your work below.
(ALL answers need to be given using complete sentences!)
Probabilities in Basketball Name____________________________________________________ Date_____________________Hour________________________
Imagine that the 18 letters in the phrase
“NCAA STUDENT-ATHLETE”
have each been written on one of 18 cards, the cards have been carefully shuffled and one is drawn. Find the following probabilities as a fraction, a decimal and a percent. Round decimals to the nearest hundredth
and round percents to the nearest whole percent. 1. P(N) = ____ = ____ = ____ 2. P(C) = ____ = ____ = ____ 3. P(A)= ____ = ____ = ____ 4. P(T) = ____ = ____ = ____ 5. P(vowel) = ____ = ____ = ____ 6. P(not a vowel)= ____ = ____ = ____ 7. P(N or T) = ____ = ____ = ____ 8. P(N, E or T) = ____ = ____ = ____ 9. P(Z) = ____ = ____ = ____
Use the information in the table to compute the probabilities in the following problems.
10. Find the probability that a male high school senior wins an NCAA® freshman roster position. 11. Find the probability that a male high school senior becomes an NCAA senior student-athlete. 12. Find the probability that a female high school senior wins an NCAA freshman roster position. 13. Find the probability that a female high school senior becomes an NCAA senior student-athlete. 14. Find the probability that a male high school student-athlete becomes an NCAA senior student-athlete. 15. P(you will have an NCAA roster position next year) = ____________________. 16. P(math teacher will not have an NCAA roster position next year)
= ____________________.
Answers need to be given using complete sentences!) Name:_____________________________________________ Hour:______________
THE ELIMINATION!!
(Answers need to be given using complete sentences!) 1. Find the number of teams eliminated after each round. 2. Tell what fraction of the teams are eliminated after each round. Record your
data in the table above. 3. Change each fraction to a decimal and percent. 4. Do you see any patterns in the way teams are eliminated? Describe what you
see. 5. Use this information to determine how many teams are necessary if one more round were added to the tournament. 5. Describe the pattern in the fraction of teams eliminated.
Answers need to be given using complete sentences!) 7. Use this information to determine what fraction of the teams would be eliminated if two more rounds were added to the tournament. 8. Add all the fractions in your table together. How many more rounds will it take until they equal 1? Explain your answer. 9. Use the information you found in #8 to predict the sum of the decimal and percent columns. Justify your answers. Decimal sum prediction__________ Justification (explain your prediction): Percent sum prediction__________ Justification (explain your prediction): 10. Find the sum of the decimal column. Show your work below. 11. Find the sum of the percent column. Show your work below. 12. How do each of these answers (#10 and #11) compare to your predictions?
Answers need to be given using complete sentences!)
Algebra in Basketball Name____________________________________________________ Date_____________________ Hour:_____________________ Define the variables, write an equation, solve and check. Remember to look back and make sure you answered the question.
To find the total number of points a player makes in a game using this formula: 3x + 2y + f = t,
where x = the number of three-point field goals, y = the number of two-point field goals, f = the number of free throws t = total points.
Answer these questions on a separate piece of paper if needed. 1. Marcus played three games with his basketball team and made a total of 38 points. What was his average number of points per game? 2 . Juanita’s favorite basketball player scored 177 points in a tournament for an average of 35.4 points per game. How many tournament games did she play? 3. In the 1986 Division I women’s basketball tournament, Drake University’s Wanda Ford played two games and made an average of 33.5 points per game. How many points did she make in all? 4. Ricky made eight two-point field goals, one three-point field goal and five free throws in his game at the YMCA. How many points did he make in all? 5. Jackie Stiles, the 2001 NCAA® women’s Division I tournament scoring leader, scored 140 points. She made a total of 46 two-point field goals and 42 free throws. How many three-point field goals did she make? 6. Jamal’s math teacher watched his junior high basketball game and pointed out the next day that the number of Jamal’s free throws and the number of his two-point field goals were two consecutive odd numbers. He had made more two-point field goals than free throws and no three-point field goals. If Jamal made a total of 19 points, how many field goals did he make? 7. Patricia was playing one-on-one with her younger sister. If the ratio of Patricia’s baskets to her sister’s baskets was 4:3 for a total of 21 baskets, how many baskets did Patricia make? 8. Monique has been keeping track of her points while playing basketball in PE. So far the ratio of her field goals to her free throws is 6:1. She has made no three-point goals. If she has made 39 points, how many field goals has she made? 9. Tenzin plays basketball with the park district. The ratio of his free throws to two-point field goals to three-point field goals was 6:8:1. He has made a total of 50 points. What is his total number of field goals made?
Rebounds! Name____________________________________________________ Date_____________________ Hour:_________________________ Use this stem plot to answer questions 1 through 3.
1. The top five all-time women rebounders are listed below. Look at the stem plot and find the number of rebounds for each player. List the highest value for problem A, then next highest for problem B and so on.
3. Three rebounding leaders made scores between 140 and 150. What were those
scores? 4. How many scores are under 140?
5. Starting with the 1973 season, the men’s Division I rebounding champion team has
been defined as the one with the highest margins (margin = defensive rebounds – offensive rebounds). Make a stem plot.
Remember to include the key and the title. You can use graph paper to help line up the numbers. The margin for the men’s champion Division I team for each year from 1973 to 2000 is listed:
How many times can you dribble in 30 seconds?
Have your partner count each dribble you take in a 30 second period. Record your results on the table below:
Trial #: Dribbles in 30 seconds: Trial #1
Trial #2
Trial #3
Trial #4
Trial #5
**Take your 5 trials and calculate the following statistics: (show your work)
Mean:____________ Mode:_____________ Median:___________ Range:____________
HOMEWORK: Finish this worksheet & create a stem & leaf plot from the class data
Reporting the average amount of dribbles to the class Record your average number of dribbles as well as your classmates’ averages in the table below & find your CLASS AVERAGE (with work shown)
Class Data-Average Number of Dribbles:
Take the class data and arrange it into a stem and leaf plot. Don’t forget to put them in order!
Class Data-Average Number of Dribbles:
Stem-10s Leaf-1s
Math Team Competition Name____________________________________________ Date_____________________ Unless otherwise noted, reduce fractions, round decimals to the nearest tenth and use 3.14 for Pi. Use a separate sheet of paper if necessary. 1. How many lines of symmetry are in a perfectly drawn square? 2. Luiz made 14 two-point field goals, five free throws and a three-point field goal. Find his total points for the game. 3. Megan played four basketball games and made a total of 64 points. What was her average number of points per game? 4. Field Goals Made in Tournament Play 2 : 4 5 9 3 : 2 2 2 7 4 : 6 9 Key: stem value is tens place Use the key to determine the data value represented by the underlined number. (Remember to use the stem.) 5. The circle in the center of a basketball court has a diameter of 12 feet. A square has a side of 12 feet.How much larger is the perimeter of the square than the circumference of the circle? 6. A player makes an assist by passing the ball to a teammate who then makes a basket. Juan made 48 assists in five games. Find his average number of assists per game. 7. Each letter in the word “student-athlete” is written on one of 14 cards that are shuffled and placed facedown. Find the exact probability of drawing a t. 8. The ratio of Yaun’s free throws made to free throws attempted is 10:15. Find her PCT (percent made) to the nearest tenth of a percent. 9. Which of the following have point symmetry?
■ # ✶ ● Z 10. There are one red, two blue and four yellow pencils in Tera’s bag. When she reaches in (without looking) to take a pencil, what is the probability that she does not remove a yellow pencil? 11. A team emblem (logo) contains a circle with circumference 9.42 cm. How long is the radius? 12. The ratio of Sandy’s three-point field goals to his two-point field goals is 1 to 4. He made five free throws, giving him a total of 27 points for the game. How many two-point goals did he make?
PARAGRAPH GRADING RUBRIC F-D D- C C- B A
Paragraph about article
Article chosen was about a team or game from the
conference. Few or no statistics in the article were listed. The paragraph did
not explain the importance of
mathematics in basketball.
Article chosen was about a team or game from the conference. Most statistics in the
article were listed. The paragraph had at least one explanation of the
importance of mathematics in basketball but
provided no examples.
Article chosen was about a team or game from the conference. All statistics in the article were listed.
The paragraph had explanations of the
importance of mathematics in basketball but provided no examples.
Article chosen was about a team or game from the conference. All statistics in the article were listed. The paragraph had clear
explanations of the importance of
mathematics in basketball and provided
examples.
The Paragraphs ARE DUE when you come to class on MAR _____
