The Winning Edge: Probability in Basketball

SCORE Mathematics

Standards Connections

The Winning Edge: Probability in Basketball

Lesson 1: Calculating Free-throw Percentages

Introduction: Time has run out in the big basketball game, and the score is tied. However, Up-State College has the ball with time out. You're the coach. Which players should you put into the game to give you the best chance of winning? This is one in a series of on-line interactive pages exploring probability and statistics in real life. These lessons utilize on-line simulations to generate data.

Prior Knowledge: Calculating percentages from given ratios; concept of average; definition of a "free-throw"; rules of basketball.

Grade Levels: 6th and 7th grades (this lesson); 6th through 12th grades for the entire series.

Objective: Students will calculate percentages based upon simulated performances of a statistically significant number of discrete events (i.e. endgame free-throw attempts).

Resources: Student worksheet 1 (html) / (pdf), Student worksheet 2 (html) / (pdf), javascript-enabled browser, pencil, calculator, if desired.

Process: Start Here: Click Starting Page
    First -- Students will use an on-line simulation to "shoot" free throws for 5 selected players on a fictional basketball team.
    Second -- They will then compile the results and calculate the free-throw percentages for each of the five players.
    Third -- Lastly, students will use their findings to decide which "player" they would choose to shoot at the end of the game.

Learning Advice:
Due to the random function of the computer simulation, results for any given set of trials for any given player will vary -- just like in real life. Checking the accuracy of the results thus requires matching the data from the simulation (free throws made versus free throws attempted) with the resulting percentage.
If only one "station" computer is available, it is suggested that students be grouped in teams of 5, each member would then choose a different player and would do the "shooting", recording and calculating of free-throw percentages for his/her selected player, the group would then combine results. The lesson can be completed (worksheet 2) either as a group or individually.

Evaluation: Completeness of the free-throw data; accuracy of the derived percentage; student conclusions based upon their data

Extensions: Other lessons in the series

Conclusion: "Which of the 5 players whom you chose would you most want to have shooting free throws to decide the outcome of the game? Why?" (see Student worksheet 2 (html) / (pdf))

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California Academic Content Standards:

Grade 6:
Statistic, Data Analysis and Probability
2.0 Students use data samples of a population and describe the characteristics and limitations of the samples.
2.5 identify claims based on statistical data and, in simple cases, evaluate the validity of the claims

3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events.

3.2 use data to estimate the probability for future events (e.g., batting averages or number of accidents per mile driven)

Grade 7:
Mathematical Reasoning
1.0 Students make decisions about how to approach problems.

1.1 analyze problems by identifying relationships, discriminating relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns

NCTM 5-8:

STANDARD 1: MATHEMATICS AS PROBLEM SOLVING
STANDARD 3: MATHEMATICS AS REASONING
STANDARD 7: COMPUTATION AND ESTIMATION
STANDARD 10: STATISTICS