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Accuracy Versus Precision Beanbag Toss

By Shana McAlexander
Product Developer
Carolina Biological Supply Company

This fun, interactive beanbag-toss game lets students release pent-up energy while they measure and manipulate data. Students make a protractor and target for the game, then form teams for activities that improve their math and motor skills. They calculate the mean, median, and mode of distances from the bull’s eye, and determine the accuracy or precision of their tosses across trials. Graphing options, provided for students of varying levels of expertise, visually represent the collected performance data.

Content standards

• Unifying Concepts and Processes: Constancy, Change, and Measurement

Background concepts

 Precision: The quality of being reproducible in amount or performance Accuracy: The quality of being near to the true or desired value Mean: The average Equation: Add the values and divide by the number of values. Of the set of values 2, 6, and 7, the sum is 15. There are 3 values, therefore 15 ÷ 3 = 5; the mean is 5. Median: The middle value in an ordered set of values Of the set of values 2, 6, and 7, the median is 6. Mode: The most frequent value in a set of values Of the set of values 2, 6, and 7, there is no mode. Of the set of values 2, 6, 7, and 6, the mode is 6. Range: The change or difference between extremes in a set of values Equation: Subtract the lowest value from the highest value. Of the set of values 2, 6, and 7, 7 – 2 = 5; the range is 5.

Materials (per group)

• 8 Bean Bags (4 each of 2 colors)
• Paper, 35 × 35 cm
• Scissors
• Meter Stick or Metric Ruler
• Twine, 20 cm
• Colored Marking Pen
• Scorecard (see master below)

Preparation (teacher)

1. Gather materials and print scorecards for each group.
2. Review concepts with students.

Procedure

1. Divide your class into groups of 2 to 4 students.
2. Have students construct a target of 3 concentric circles around a center point.
• Students measure a length of twine and use the pen to mark distances 5, 10, and 15 cm from the end.
• A student tapes the end of the twine to the center point of the paper.
• Another student, keeping the string taut while rotating it around the center point, serves as a protractor. Holding the string too taut will pull the taped end loose.
• As the protractor moves, a student traces the route of a mark on the twine. The student repeats the process for each mark. Students can make a continuous line or points along the circle to connect after removing the twine.
• Teaching moment:

What happens as you attempt to draw the circle with more and more points (more sides)? How many sides does a circle have? Describe the infinite points of a circle. Students observe that they can’t draw a perfectly round target; but the more points used, the more the shape resembles a circle.

Figure 1: Shaded space represents the difference in area between the polygon and circle. As the number of its sides increases, the polygon resembles the circle more and more. A circle has an infinite number of sides, but this may not be obvious as we draw it because of the thickness of our drawn line. Click here for a larger image.

3. Direct each group to find an open space on the floor, free of obstacles, and tape down their target.
4. Instruct students to measure 3 meters from the bull’s eye and use tape to indicate the toss-from line.
5. Have students take turns, as teams or individuals, tossing the beanbags toward the target.
6. After all 8 bags are tossed, have students take measurements.
• Measure the distance between the closest edge of each bag and the center point of the target. Record the data on the scorecard.
• Measure the distance between the 2 bags farthest from each other. Record the data on the scorecard.
7. Repeat step 6 for trials 2 and 3 with the same teams.
8. Have students calculate mean, median, mode, and range for each trial.
9. If desired, have students graph the data. Many graphical approaches are acceptable for visualizing the collected data. Choose the graph(s) appropriate for your class’s ability. A few examples are below. Utilize graph paper or graphical software.
10. Have students discuss results and answer questions.

Graphing examples

Accuracy between trials: Mean distance from target (cm)
Team A Team B
Trial 1 13 10
Trial 2 11 12
Trial 3 5 7
Precision between trials: Graphing the distance between the most disparate throws (cm)
Team A Team B
Trial 1 16 13
Trial 2 9 12
Trial 3 12 5
Frequency of binned distances
Distance from center Team A: All trials Team B: All trials
0–5 cm 2 3
6–10 cm 4 1
11–15 cm 4 0
16–20 cm 2 6
> 20 cm 0 2
NOTES:

Student questions

1. Which value represents accuracy: the mean, median, mode, range from center, or distance between farthest beanbags?
2. Which value represents precision: the mean, median, mode, range from center, or distance between farthest beanbags?
• Answer: The distance between the 2 beanbags farthest from each other (not the distance from the farthest beanbag in relation to the target) quantifies precision.
3. Was your team more accurate with each trial? Explain what contributed to becoming more or less accurate.
4. Was your team more precise with each trial? Explain what contributed to becoming more or less precise.

Extensions

1. Have students investigate other values.
• Percent accuracy: Number of hits to target ÷ total number of throws
• Percent accuracy within 5 cm, 10 cm, or 20 cm
2. Discuss outliers and their effect on the mean, median, and mode.
3. Create a beanbag-toss tournament to determine the most accurate and most precise teams.
4. Increase or decrease distance between the target and toss line. Compare data from the 3-m distance.

Beanbag Toss Scorecard

Trial 1
 Team: Toss 1 Toss 2 Toss 3 Toss 4 Distance from center (cm)
Mean:
Median:
Mode:
Range from target:
Distance between farthest bags:
 Team: Toss 1 Toss 2 Toss 3 Toss 4 Distance from center (cm)
Mean:
Median:
Mode:
Range from target:
Distance between farthest bags:

Trial 2
 Team: Toss 1 Toss 2 Toss 3 Toss 4 Distance from center (cm)
Mean:
Median:
Mode:
Range from target:
Distance between farthest bags:
 Team: Toss 1 Toss 2 Toss 3 Toss 4 Distance from center (cm)
Mean:
Median:
Mode:
Range from target:
Distance between farthest bags:

Trial 3
 Team: Toss 1 Toss 2 Toss 3 Toss 4 Distance from center (cm)
Mean:
Median:
Mode:
Range from target:
Distance between farthest bags:
 Team: Toss 1 Toss 2 Toss 3 Toss 4 Distance from center (cm)
Mean:
Median:
Mode:
Range from target:
Distance between farthest bags: