"They don't want to comment on what they've found in their research. Let your students know that it is now their turn to solve the challenge that Elton Brand posed to the teams in the video.

Skinner, an avid basketball fan, was inspired to analyze the game when he heard a talk at an American Physical Society meeting in 2007 on the flow of traffic. I did my IA on the use of mathematics in the courtroom, as I aspire to be a lawyer and find doing work on an area I am extremely passionate about to be both interesting and manageable. Compare and contrast the various algebraic and graphical representations possible for the problem. Are you looking for free math basketball games that you can play online? Their first question was simple: “What’s the best free throw?” Should the shooter aim towards the front of the hoop or the back? With tournament play underway, I’m reminded of how competitive the game has become, and how it has truly become a game of inches. At what time(s) does the ball reach 10 feet? A player needs to memorize the motion of her entire body during release to impart the same speed consistently. Is there only one path or trajectory for this to occur using Elton’s stats? Explain that in the activity, students should use the Fast Break Facts for information about the three key variables and Elton’s stats to figure out the maximum height the ball reaches on its way into the basket when making a free throw shot. To simulate millions of trajectories without the code taking too long to run, we tried any trick we could think of. Ask students to discuss how they selected the equation and graphs used, and how they calculated the values for time and height using each set of player stats. (The ball, at the highest point of its arc, should reach the top of the backboard.) Ask students to brainstorm other real-world situations which involve the type of math and problem solving that they used in this lesson. Review the directions listed on the handout. He factors in the probability that a given shot will go in, the quality of future shots the team is likely to generate, and the number of seconds left before the players must either shoot or forfeit the ball to the opposing team. Write an article and join a growing community of more than 115,700 academics and researchers from 3,762 institutions. How does the approach used to solve the challenge affect the choice of representations? At what time does the ball reach the maximum height? Please note that difference between HL and SL IAs is the level of math expected of students which is reflected in slightly different rubrics and consequently the HL and SL grades differ slightly. Discuss why you would need to maximize the height of the basketball trajectory.

After students have written their reflections, lead a group discussion where students can discuss their responses. In that angle, the launch speed is the lowest, and the probability of the shot being successful is the greatest. Next, assuming the player releases the ball at 7 feet above the ground, a launch angle of about 52 degrees is best. Maths and Time: Exploring ideas regarding time dilation; Plotting Planets: Using log functions to track planets!

So there we have it, 50 IB Maths IA topic ideas to give you a head-start for attacking this piece of IB coursework! On this website you can find a variety of games designed to supplement your math lessons and to make the learning process a fun experience. A new article provides mathematical guidelines about when a basketball player should attempt to score and when the team is better off waiting for another chance. His equations follow the ball from the inbound pass until it reaches the hoop. I got 18/20 at the end. As students complete the challenge, encourage them to use the following 6-step mathematical modeling cycle to solve the problem: How can you combine the three key variables: acceleration of gravity, initial vertical velocity, and release height, to determine the maximum height of the basketball? We learned how to turn large numbers of trajectories into statistical probabilities. IB Math SL IA are exploration and IB Math Studies IAs are more like a project. Analysts had noticed that in games from which Ewing or other big scorers on a team were absent, that team was more likely to win. Some 20 years ago, my colleague Dr. Chau Tran and I developed a way to simulate the trajectories of millions of basketballs on the computer.

Ask students what sports they like to watch and how they keep track of their team’s progress. Copyright © 2010–2020, The Conversation US, Inc. Preview all of the video segments and web interactives used in this lesson. Ask students to brainstorm how they think mathematics might be used in the sport. "The most interesting case is the conventional situation of NBA basketball with a ticking shot clock," which analysts often ignore in evaluating the role and contributions of a player, he adds. Assess deeper understanding: Ask your students to reflect upon and write down their thoughts about the following: How did you determine an effective strategy for solving the challenges in this lesson?

We even created fictitious trajectories in which the ball magically passes through all of the physical obstacles (hoop, backboard, back plate) except for one, to see where it collides first. Where is it now? Basically, the back of the rim is more forgiving than the front of the rim.

I took Math SL, and got a 7. By Ron Cowen Aug. 2, 2011 , 1:00 PM. But what is its long-term plan? As an old basketball player, like many of you, I enjoy watching the game – and, every so often, catching a glimpse of that perfect free throw. Elton Brand, basketball player and NBA star, describes how he got involved in sports, gives an introduction to the mathematics used in maximizing a free throw shot, and poses a related math … Release the ball too slowly and the shot is short; release it too fast and the shot is long. "When you're a nerd, you can't turn it off.". Theory is one thing, but putting the models into practice is whole other ballgame. View Math_IA_sample2.pdf from MATH ENG 111 at ESSEC. However, launch speed is quite the opposite. Math Basketball Games.

Get colored stickers (optional) and colored markers, for students to mark the points and construct the trajectory, or path, of the basketball in Learning Activity 1 & 2. Larry M. Silverberg does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment. Line up the ball to eliminate the side angle. What are some ways to represent, describe, and analyze patterns that occur in our world?

(, Explain that today’s lesson features video segments and web interactives from. The last release condition was the most surprising: the aim point of the free throw. Distribute the “Math in Basketball: Try other challenges” handout. Does it depend on whether the shooter is short or tall? © 2020 American Association for the Advancement of Science. To shoot, or not to shoot, that is the question. In addition, the diagrams and flow of players in basketball also resembled the traffic models Skinner had seen. Download the video clips used in the lesson to your classroom computer(s) or prepare to watch them using your classroom’s internet connection. The Mathematics of Basketball. After students have completed the activity, ask students to share their solutions and problem-solving strategies with the class through discussion and visual materials, such as chart graph paper, grid whiteboards, overhead transparency grids. I was thinking maybe to do something slightly physics-y with projectile motion, so I was thinking to first model the trajectory of a cannonball.

Once again, new Antarctic reserves fail to win backing, United Kingdom lights up its unusual fusion reactor. In the new paper, Skinner wanted to see if his model could predict the best time to take a shot.

1 Improving the free throw percentage in basketball IB Mathematics SL 2 Table of content Introduction .3 Topic Background .3 Rationale . After students have completed the activity, lead a group discussion and encourage students to share their strategies and solutions to the challenges. Professional basketball players face that quandary multiple times in every game. For instance, if any of your students play a sport, ask them to discuss the math they have used as athletes. MEDIA RESOURCES FROM THE GET THE MATH WEBSITE, (Note: These activities can either be conducted with handouts provided in the lesson and/or by using the web interactives on the Get the Math website.). It has a rate at which it is spinning backwards (called backspin), and it has a launch speed and a launch angle. The fate of a free throw is set the instant the ball leaves the player’s fingertips, so we looked closely at the “launch conditions” of the shot. You can play these games alone on the computer or in two teams. Because of the money at stake, professional teams are also reluctant to share data that might be compared with the models, Skinner says. Use the “Math in Basketball: Take the challenge” answer key as a guide to help students as they complete the activity. Ask students to describe the challenge that Elton Brand posed to the teens in the video segment. How do you know? It’s the hardest variable for a player to control. Our research suggests that players should aim the ball beyond the center of the rim. However, Skinner's equations show that for a scenario in which if team B shoots, on average, every 20 seconds, team A should shoot every 13 seconds rather than every 10. Conventional wisdom would indicate that team A's best prescription for success would be to shoot twice as often as B. It speeds up the amount of time it takes to see the patterns behind the best shots. "Brian's paper poses an intuitive theoretical model of the way basketball players should select shots in a variety of situations," says Matthew Goldman, a graduate student in economics at the University of California, San Diego, who also models basketball games. Math offers a unique perspective. Suppose, Skinner says, that team A and team B each have the same chance of scoring on a given shot but that A passes the ball twice as fast as B. Skinner further assumes that both teams have the same ball turnover rate and have plenty of seconds left on the shot clock. From a mathematical viewpoint, basketball is a game of trajectories. To shoot, or not to shoot, that is the question.

What are your conclusions and the reasoning behind them? Why is it useful to represent real-life situations algebraically? We found that the player should aim the ball to the back of the rim. Still feeling confused? The extra 3 seconds allows team A to be more selective about which shots to take, which turns out to be the winning strategy. The free throw was the first shot that my colleague and I studied in detail. The difference was that the 90 percent players were being consistent at the right shot - the best trajectory. Does this math IA topic for SL sound any good?

(NBA teams must shoot within 24 seconds of possessing the ball, whereas men's college basketball teams have 35 seconds.). "There's more receptiveness" to these ideas among basketball coaches and managers than ever before, says sports statistician Dean Oliver, who became director of production analytics at ESPN in March after working with the Denver Nuggets since 2006. All else being the same, players who release from higher above the floor have a higher shooting percentage. We studied the free throw for about five years.

Professor of Mechanical and Aerospace Engineering, North Carolina State University. It takes about 1 second for a ball to reach the basket, so 3 hertz equates to three revolutions in the air, from the instant the ball leaves the player’s hands to when it reaches the basket. One of the first things we learned from our simulations and by watching TV footage was that players with the same consistency can shoot free throws with anywhere from 75 to 90 percent accuracy. All rights Reserved. These trajectories are unique in that the ball’s motion doesn’t change much when it’s flying through the air, but then rapidly changes over milliseconds when the ball collides with the the hoop or the backboard.

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