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HCPSS Worthwhile Math Task
Who Do You Pass The Ball To?
Common Core Standard
Summarize, represent, and interpret data on two categorical and quantitative variables.
S.ID.B.5 Summarize categorical data for two categories in two-way frequency tables. Interpret
relative frequencies in the context of the data (including joint, marginal, and conditional relative
frequencies). Recognize possible associations and trends in the data.
MP2: Reason abstractly and quantitatively.
MP3: Construct viable arguments and critique the reasoning of others.
MP6: Attend to precision.
Common Core Algebra I, Unit 4
The Task
Pe’Shon Howard is under pressure. There are 1.5 seconds left in the game against Duke
University and his Maryland Terrapins team is down by 2 pts. They are in the bonus for nonshooting fouls. (If they are fouled when not shooting, they will have a 1 and 1 situation – only if
they make the first do they get to shoot a second time.) He is inbounding the ball at half line and
he doesn’t know which of his teammates should get the ball so he calls a time out.
The players below are on the court with him. To whom should he try to pass the ball? Support
the decision with statistical evidence, making sure to include why you chose the player and why
you did not choose the other 3 players. The table columns with percentages were left blank in
case you would like to fill them in.
Maryland Terrapins Men’s Basketball Season Statistics 2011-12, Listed alphabetically:
Player
FGM
FGA
FG%
FTM
FTA
FT%
3PM
3PA
Nick
96
257
70
113
23
85
Faust
Sean
100
259
91
109
36
99
Mosely
James
102
198
79
140
0
0
Padgett
Terrell
220
553
159
202
91
237
Stoglin
KEY:
FGM = Field Goals Made – 2 pts each
3P%
FGA = Field Goals Attempted
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
FTM = Free Throws Made – 1 pt each
3PM = 3 Point Field Goals Made
FTA = Free Throws Attempted
3PA = 3 Point Field Goals Attempted
Source: http://espn.go.com/mens-college-basketball/team/stats/_/id/120/maryland-terrapins
Facilitator Notes
1. Not all students may be familiar with the game of basketball and a scenario like this. It
may be helpful to show a quick video clip and take some time to discuss some basic
terms as a class to make sure that groups feel comfortable completing the task.
2. After students are finished completing the task, have them present their results to the
class. Determine overall which player students would pass the ball to and if the data
supports their decision. Most likely all groups will not agree on the same player, which
leads to a great discussion of how data can support different solutions. (Look for
evidence of MP2, MP3, and MP6.)
Follow-Up Questions
1. Are the Terrapins home or away and does that have an impact on the decision? (Look for
evidence of MP2.)
2. Do certain players match up better against Duke? (Look for evidence of MP2.)
3. Are there any substitute players on the bench that might be a better pick?
4. What are the stats for the game up to the last second? Which players are shooting well
today? (Look for evidence of MP6.)
5. What are recent stats for the players, i.e. the last 3 games?
6. What is the team’s record in overtime overall and against Duke? This would influence
whether to concentrate on going for the win (3pt play) or the tie. (Look for evidence of
MP2 and MP6.)
Solutions
Completed Table with sample solution:
Player
FGM
FGA
FG%
FTM
Nick
96
257
37.4%
70
Faust
Sean
100
259
38.6%
91
Mosely
James
102
198
51.5%
79
Padgett
Terrell
220
553
39.8%
159
Stoglin
FTA
113
FT%
61.9%
3PM
23
3PA
85
3P%
27.1%
109
83.5%
36
99
36.3%
140
56.4%
0
0
0%
202
78.7%
91
237
38.3%
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
If students decide to look at the overall percentage of shots made (field goals made + free throws
made + 3 points made) over shots attempted (field goals attempted + free throws attempted + 3
points attempted) these are the results:
Terrell Stoglin: 470/992 = 47.4%, Sean Mosely: 227/467 = 48.6%,
Nick Faust: 189/455 = 41.5%, James Padgett: 181/338 = 53.6%
If students look at an overall shooter (from the data above) Padgett appears to be the best,
making 53.6% of all the shots he attempts. However he is also the player who takes the least
amount of shots and he has not taken a 3 point shot all season. Furthermore, if he gets the ball
and gets fouled he has the worst free throw shot average at 56.4%.
If the students want Maryland to win the game by giving the ball to the person who makes the
most 3 point shots, then Howard should pass it to Terrell Stoglin who has the largest percent of 3
point shots made at 38.3%. Although Stoglin has the best percentage, Mosely isn’t far behind.
Mosely hasn’t taken as many shots overall as Stoglin so perhaps he is more cautious with his
shots and is a better choice. It would be nice if we had the stats for both players against Duke to
make a better decision. Faust’s 3 point percentage is at least 10% less than Stoglin so we
shouldn’t consider him unless Duke puts some of its best defenders on Stoglin and Mosely and a
pass to either isn’t possible. Hopefully, it is obvious if they want to win the game, he should not
pass it to Padgett who hasn’t taken any attempts at this type of shot.
If the students want to tie the game for a chance to go into overtime, they might go with Padgett
who has the highest field goal percentage of 51.5%. However if he is fouled, he has the lowest
percentage of free throws made at 56.4%. If he misses his first free throw Maryland will lose.
Knowing that Duke might know who the better players are and that we are unsure if a foul might
occur, we might choose Sean Mosely. Although he doesn’t have the highest 3 point or field goal
percentage of the 4 players, he does have a good percentage overall, 48.6%, and the best free
throw percentage, 83.5%, in case he is fouled. Hopefully, by passing the ball to him he will shoot
either a 3 pointer to win the game, a 2 pointer to tie the game, or try to get fouled so that he can
get 2 free throws, make both and tie the game.
Follow Up Questions:
Statistics to support answers to questions 1-5 can be found by accessing the source website listed
and looking at the various categories as they might apply: home and away games, previous
match ups against Duke, relevant statistics for all players, individual game statistics for players
in each game, the team’s record and results, including those that resulted in overtime.
Although Question #6 will not have direct statistics available, since most of the game has been
played (all but 1.5 seconds), the students could look at statistics for a previous game and use
those – possibly they would use a previous game against Duke.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.