Materials Needed:

Three paper "ballots" for each student (Note: these ballots could be slips of paper or sticky-notes)
Several envelopes to hold the collected ballots.
Candy bar or snack pack to be used as a prize.
Ruler
Access to (or printed copy of ) this map.
Access to (or printed copy of)  Lulu's map.
A printed copy of the worksheet

Preparation:

Distribute the ballots to each student.
Place envelopes at the end of the rows.

Lesson Activity:

1. Hold up the prize with an explaination that you have an extra candy bar and would like to award it to one of the students in the class. Ask, "How can I give someone the candy bar and be fair to everyone?"

If the students respond that you should cut the candy bar into smaller pieces and give everyone a piece, explain that such an approach would be a good example of sharing, but today's topic requires that we selecte a single student and keep the prize whole.

If the students have no response then ask, "Should I give the prize to the hungriest student or to the student who lives the greatest distance from school? How can I give away just one candybar and still be fair to everyone?

2. The students should now write their name on one of the slips of paper. Assign a student to collect the slips in the envelope.

3. When the envelope with the student names has been returned to the teacher ask, "What rules should I follow to make this a fair drawing?" Record any suggested rules that tend to ensure that every student has an equal chance of being selected (shake up the envelope, select with your eyes closed, have an objective bystander draw).

4. Have the students write the defintion for "fairness" in their notebook or on the second ballot: Fair means having an equal chance of being selected.

5. Following the rules for fairness draw out the student to receive the prize.

1. In this activity the class will select its favorite Super Hero (Note: you may need to substitute an age appropriate term for Super Hero such as Pokemon character, Disney character, or famous American).

2. To make the selection as fair as possible, ask the students to write down their favorite Super Hero on the thrid ballot. Turn the ballot over so that others cannot see your vote.

3. When everyone has voted, explain that you would like to predict in advance of the vote count, who the class will pick.

4. Ask the student to count the votes of the four closest students to their seat (or count the votes within their cooperative learning group). Have them write the winner below their definition of Fairness.

5. Point out that based on this small sample, the students may have some idea of who the class will pick as its favorite Super Hero. But is your survey an accurate prediction? How fair was the sampling process? Did every student have an equal chance of having their vote counted in the group's survey?

6. Encourage the students to write down the definition of a systematic sample: Systematic Sampling counts every Nth result. In other words, when you use a systematic sampling method, you skip over equal number of votes.

7. The teacher now carries out a systematic sample by collecting every third student's ballot. Calculate the most popular Super Hero in your sample and write your prediction on the board.

8. Count all the votes and compare the results from the small group sample, the systematic sample, and the final vote count. Ask, "how do we account for the different results? Do we believe any sample will tell us the same thing as when we count all the votes? Is fairness in the sampling process important?

9. Discuss with the class how you could have improved your systematic sampling to make it more fair ( drawing randomly from a hat or flipping a coin to determine the starting point for your systematic sample).

Note to Fourth Grade Teachers: Your students can carry out the measurement aspects of this section, but probably cannot solve the ratio problems used here. You may wish to work out the ratios for your students after they measure the distances on the map.

1. Visit the following web site and display the map on a projection device. Each student will need a printed copy of the map so that they can measure carefully the distances involved: Map

2. The web page shows the location of an American Bald Eagle wearing a satellite transmitter. While there are a large number of factors which make it difficult to sample in a completely fair manner, the map can help us predict how fast the eagle is flying. Note: the scale at the bottom of the map reveals that every 18 cm is equivalent to 50 miles.

3. Ask your students to study this map for clues to the sampling process. Does it appear to be a systematic sample method? (No, they skipped unequal blocks of time between posted sample times).

4. Due to many factors (when the satellite passes overhead, if the transmitter is sending, the way in which locations were selected on the map), the sample is not systematic so we will need to estimate the speed of the eagle without a great deal of confidence that our samples will be accurate. Still it will be fun to compare our estimate of the eagle's speed with the widely accepted view of an eagle's speed.

5. Compare the scale on the bottom of the map to the distance flown between 9:00 and 1:15. The distance appears to be about 100 miles (Note: the distance between 9:00 and 1:15 is acutually closer to 34 cm. or 97.2 miles).

6. Divide the distance traveled by the time between the 9:00 and 1:15 sightings (100 miles divided by 4.25 hours yields an estimate of 23.5 miles per hour. Using 97.2 miles we get a speed of 22.8 miles per hour).

7. We can use a similar process to predict the distance between the 1:15 and the 3:15 sightings ( 2 hours at 22.8 mph predicts 45.6 miles). How well does our prediction hold up? Careful measurement leads us to see that the sightings are 12 cm apart for a distance of 33 miles. Why didn't the eagle fly the expected 45 miles? Students should consider other factors such as headwind, presence of prey, terrain, endurance, weather, etc.

8. Compare your calculations to the average cruising speed recorded for the eagle by the Sedgwick County Zoo website at http://scz.org/animals/e/bald.html

From the map it appears that it is about 50 more miles to the closest point on the Montana border. About what time would we predict the eagle will cross into Montana based on our earlier calculations (2 hours later or about 5:15 p.m.)? Based on the Sedgwick County Zoo website information?

Can you find the cruising speed of the Tundra Swan and compare it to the data at Swan Archive? Why is or is not this data a good sample of the cruising speed of the Tundra Swan?

Compare the migatory flight of Lulu on December 19,2000 with the generally accepted cruising speed of the Tundra Swan.  How does Lulu's speed compare to what you expected to find?