Trashketball: Part 1

Inform students they will be investigating data about shooting percentages. Ask students to work with a partner to create a definition for shooting percentage.

After a few minutes, ask for volunteers to share their definitions. Record the given definition on the board, and ask other pairs how it differs from their own. Ask if any pair thinks the definition needs to be altered. Continue the discussion until the class agrees on the definition.

Have students work with their partners to create a mathematical definition, or formula, for shooting percentage.

Have each of the student pairs write their formulas on a standard size piece of paper, large enough for the class to see. Post these papers around the room (or have students hold them up) so the other groups can view them. Ask if all of the formulas are equivalent or if there are differences. Have students discuss the differences they see. Ask students if these differences would result in different shooting percentage values and have them explain their thinking. Through this discussion, students should work together to create one formula for the class to use to determine shooting percentages.

Make sure students save the papers on which they wrote their formulas. They will use these papers later to play trashketball.

Give each student a green sticky note and a red sticky note. For each of the examples below, have students hold up a green sticky if they think the example should result in a high shooting percentage, or a red sticky if they think the example should result in a low shooting percentage.

Example 1: 7 attempts, 3 shots made

Example 2: 9 attempts, 8 shots made

Example 3: 5 attempts, 0 shots made

Example 4: 12 attempts, 12 shots made

Example 5: 15 attempts, 16 shots made

Once they have made a prediction for each example, have students use their formula to calculate the shooting percentage. Have students verify that the values they get from the formula match the predictions they made.

Once the class is convinced that the formula they created accurately measures shooting percentage, introduce students to the game of trashketball. Place an empty wastebasket somewhere in the room so that there is space free of obstacles in front of it. The wastebasket can be placed on a desk, table, or on the floor. Wad up a piece of paper and demonstrate shooting it into the wastebasket and retrieving it afterwards.

Ask students to consider if and how moving away from the basket will affect the shooting percentage. Tell students to use the words increase, decrease, or constant to create a hypothesis that describes what will happen to the shooting percentage as the distance between the shooter and the basket increases. Students should record their hypotheses as a complete sentence on the attached Trashketball handout.

Ask students to identify the independent and dependent variables for their hypotheses and record them on their handouts for question 2.

Ask students to identify the control variables and record these for question 2.

Move students, an empty wastebasket, and several tape measures outside (or to the gym, cafeteria, or other area of the school with a large floor space). Have students bring their Trashketball handouts, a writing utensil, and the papers on which they wrote their shooting percentage formulas.

Place the wastebasket in the middle of the floor and use the tape measure to measure a radius of 8 feet from the basket. Have students form a circle around the basket at that distance, standing next to the partner with whom they originally wrote their shooting percentage formulas.

Tell students to tear their formula papers in two. Each partner in a pair gets half of their paper to make a trashketball. Explain that every student will crumple up the half-sheet of paper and try to shoot it into the wastebasket. Ask students what that means about the values in the chart for question 3 of their Trashketball handout. Students should be able to explain that the attempts made will equal the number of students in the class. Have them record this information on their charts and then ask students to make their first attempt from 8 feet.

Once all students have taken their shots, go to the wastebasket and count out how many wads of paper made it into the wastebasket. Have students retrieve a wad of paper (it does not have to be the one they threw) and then form a new circle nine feet from the basket. Continue shooting, recording, and forming circles at distances increasing by 1 foot each time until you run out of room in your space or on the chart.

Once all of the data is collected, let students work in groups of two or three to find the shooting percentages for question 3 of the handout. Students may use calculators but should be sure to check their group's work before recording it on their own papers.

Once all of the shooting percentages are calculated, call on one group at a time to share their result for the shooting percentage at a specific distance. Have the other groups check the other groups' work. All groups should have the same result. If not, have disagreeing groups share their work and reasoning to settle differences. Continue calling on groups to share results until the class agrees on all of the shooting percentages. Once the class has reached agreement, have each student use the data to create a scatter plot for question 4 on the Trashketball handout.