INVESTIGATING THE PROBABILITY
Grades 4 - 6

In this lesson the students will discover the importance of data collection as it relates to the scientific method or in mathematical investigations and how this data is utilized by scientists to make predictions. Through the experience of gathering and recording their own data the students will gain an understanding of how collected data can influence scientists' predictions.

The students will be actively involved in probability investigations using coins and dice. The activities in this lesson will provide the students with opportunities to generate data for themselves, graph, organize and interpret data, and communicate their findings to one another. Students will predict, describe, compare, compute, and draw conclusions that will lead them to predictions based on what they have observed, recorded, and learned.

THE VOYAGE OF THE MIMI I: EPISODE 4A: Counting Whales

Students will be able to:

• Define vocabulary terms related to probability.
• Generate and record data during probability investigations.
• Create bar graphs using the information from their data sheets.
• Compare and describe individual graphs and make and state their predictions based on the recorded data.

Previewing Activities

• index cards (two for each child)
• paper and pencil for recording data

Teacher Also Needs:

• jar or basket for job cards
• chalkboard or overhead projector/ pens

Coin Flip

• 1 penny for each pair of students
• 2 data sheets for each student

Dice Roll

• 1 die for each pair of students
• data sheet for each student
• crayons/colored pencils
• graph paper for each student

Whole Class Graphs

• butcher paper ( 3-4 feet section)
• water soluble markers
• calculators (optional)

It would be helpful if students have some prior knowledge of the scientific method and understand the process scientists use to make predictions based on observations and recorded data. It would also be appropriate for students to understand that in scientific or mathematical inquiries, investigations and observations generate the data that scientists will analyze and interpret helping them to formulate their predictions.

This first activity can be done in a whole group setting. Have the students brainstorm jobs that are done around the house, such as mow the lawn, clean the garage, do the laundry, wash the dishes, and so on. As the students volunteer their responses write each job on an index card and put them into a job jar. (Have equal number of inside and outside jobs.) Ask questions like the following:

"What are the chances of choosing an outdoor job?"

"What are the chances that you won't pick "mow the lawn?" (The answer will depend on the number of jobs.)

Ask several volunteers to choose and replace jobs and record the data on the chalkboard. Define the word "data" as information that you observe and record.

For this next activity divide the students into groups of four and hand out an index card to each student. Ask each student to write his or her name on the index card. Each group should shuffle the cards and place them face down on the desk. One of the students then chooses a card and records the results on a piece of paper. The cards are shuffled, and the next person chooses. Continue this process until all the students have chosen a card. Ask questions like the following to the whole group:

"What is the chance that you will choose the card with your name on it?" (1 out of 4)

"What were the groups' results." (Answers will vary.)

"What if we combined two groups so that there was a total of 8 students in each group? What is the chance that you will choose the card with your name on it?" (1 out of 8)

Help the students to realize that as the number of cards is increased the "chance" of selecting the card with their name on it decreases.

Introduce the term probability. Ask the students if they know what it means. Define probability as "the chance that a certain event will happen." Relate the term to the completed pre-viewing activities by asking, "What was the probability that in our first game you would select an outside job?"

Students may be more familiar with the word "chance" as it is used in weather forecasts. For example, "There is a 20% chance of rain tomorrow." Help the students relate the two and explain that there is a 20% probability it will rain.

Explain that one of the things that scientists and mathematicians do is investigate the chance or likelihood that something will or will not happen. Emphasize that probability tells us approximately, but not exactly what will happen. Scientists collect, record, and interpret data to help them make more accurate or reasonable predictions.

The focus for viewing is a specific responsibility or task(s) that the students are responsible for during or after watching the video to focus and engage students' viewing attention.

Give students these specific responsibilities while viewing the video segment:

Ask students to watch for the kind of information or data that these scientists are collecting and be ready to share this information with the class.

Ask students to watch to see if and how the data is initially recorded.

Ask students to watch to see how a computer is used to help the scientists in their interpretation of the data.

START the video at the point where the Mimi crew are gathering in the galley for breakfast and Anne, pointing to a navigational chart, says to the Captain, "This part of the bank is where we want to sample the whale population."

PAUSE the video after the Captain says "All hands on deck!" Ask the students to clarify what this phrase means to the other people on the ship. Explain that this is a nautical expression. RESUME the video.

PAUSE the video after C.T. says "We're at 67 degrees, 42 minutes west longitude, 41 degrees, 30 minutes north latitude." Ask students what kind of information we get from using longitude and latitude. (exact location) RESUME the video.

PAUSE the video after Anne says, "Okay Arthur and Rachel, any whales you spot give me the behavior, its compass bearing and the distance." Ask the students to repeat the information that Anne needs from Arthur and Rachel. Write these on the chalkboard or overhead as students give responses. RESUME the video so students can watch as scientists continue to collect and record data.

PAUSE the video after Arthur says, " . . . 56 degrees." Ask students what instrument Arthur used to find the bearing. (a compass) Explain that the bearing is the direction from one object (the ship) to another (the whale) in compass degrees. Ask the students what unit of measurement is being used to determine distance. (meters)

Review with students the information that the scientists on the Mimi are collecting: time, behavior (sighting cue as Anne explains it), distance (from ship to the spotted whale), and species. Add any of these to the list that were left out in the first discussion. It would be appropriate to explain that the behaviors or sighting cues of whales could include the blow (the spray from the blow hole), breaching (jumping into the air and belly flopping), or lobtailing (slapping the tail against the water), actions of the whale. RESUME the video.

PAUSE the video after Anne says, "That's it no more sightings for this transect." Ask students why Anne and the others would look at their watches. (to establish time of sighting which is part of their data). Ask the students how the information from these sightings recorded. (on clipboard using pencil/paper) RESUME the video to see how this recorded information is then entered into the ship's computer.

PAUSE the video after Anne explains what the computer screen is showing (the number of whales sighted in an area called a transect).

REWIND THE VIDEO AND FREEZE THE FRAME so that the computer image showing the line representing the Mimi's course and the X's indicating whales is on the screen. Pointing to the screen image, review with the students that the straight line represents the course of the Mimi and the X's indicate whales that were spotted in the transect.

Remind students that the data collected for this investigation included the time, behavior, compass bearing, distance (in meters), and species. Ask the students if this information could have been plotted on a map instead of having been entered into a computer. Ask the students what the advantage was of using the computer?" RESUME the video.

STOP the video after Arthur says, "That's why we will do a series of census transects at several different places over the next two weeks and we have three more to do today." Ask students to explain what Arthur meant by this statement. This would be a good time to make the students aware that investigations or observations are often done over long periods of time and that scientists will sometimes collect data over days, weeks, months, and years. This information provides them with a sampling or realistic picture of what is likely to occur. The information or data gathered on the humpbacks during this investigation on the Mimi will help scientists estimate or predict the whale population in a given area. The more data collected the greater the probability that the information is accurate. That is why this process will be repeated many times.

Review with students the data collected, how it was recorded, interpreted, and what these scientists learned about the whale population in a given area. Discuss what they did with this information and how this information would help them to make predictions about the whale population. Remind students that scientists make better predictions with the collection of more data and that was why this investigation on the Mimi would need to be done several times a day during the next two weeks.

Ask students if they understand now, how and why scientists collect and record data for scientific investigations (to make more accurate predictions). The class could discuss other examples of scientists collecting and interpreting data such as the weather service.

Explain to the students that since it is not possible for us to go whale watching with the crew of the Mimi, we will be involved in some classroom investigations that will enable us to generate and collect our own data, chart, and graph this data to help us better understand it, and make predictions based on this collected data. Explain that when a prediction is made without any information it is more of a guess, but when predictions are made based on information or collected data they tend to be more accurate.

Coin Flip Activity

Hand out one penny and one data sheet to each student. Before students begin this activity have them make a prediction which side of the coin will come up more often - heads or tails (this first prediction is more of a guess). Have the students mark their prediction on the top of their data sheet.

In this first activity students will need to flip a coin for a total of 40 times and record which side the coin lands for each flip. Have students work in pairs while one student flips the coin the other student can record the outcome on the data sheet for his/her partner. Then switch. Students will be recording the outcome of their coin flips as well as keeping track of the number of times they flip the coin. After each pair of students has recorded their individual data they will need to add their final outcomes to the class graph. The teacher or students can use butcher paper and markers to create a class bar graph.

A discussion should follow after all the data has been recorded and added to the class graph about the chance of landing on heads or tails. Ask the students how many predicted correctly. Ask how many students would like to change their prediction now that they have the seen the class data. Hand out a second data sheet and have the students repeat this coin flip activity again. When this activity has been completed, discuss the difference between the guessing prediction and the prediction based on collected data.

Dice Roll Activity

For this activity students will roll a die and record how the die landed. Before the activity begins have the students make their predictions and mark the top of their data sheet. Again, have students work in pairs and help each other as they record their outcomes on the data sheet. Each student will throw the die a total of 60 times. The students will be recording the outcome of the die roll and keeping track of how many times they have rolled the die. When they have completed this activity students will create their own bar graph on graph paper with colored pencils showing their individual outcomes.

When everyone has completed their individual graphs ask the students to raise their hands to indicate which number they think will come up the most often when we complete a class total. Write these predictions on the board to compare later. Next have the students share their outcomes for each number and record this on a class graph using butcher paper and markers.

After the graph is completed ask the students which number the die landed on most often, least often, etc. Discuss together the final class outcomes. Ask how many students predicted correctly and how many students would change their predictions based on the information displayed on the class graph. These two activities could be done again on another day to see how the data compares. Ask if students would predict differently based on the collection of more data. Review with students the kind of data the Mimi scientists were collecting and the kind of data that they collected in the coin and dice activities. Help students clarify in their own minds the importance of collecting data as part of the process of making predictions.

Have the Education Liaison at the World Center for Birds of Prey visit the classroom or arrange for a class field trip to the center to learn about what kind of data biologists collect on the birds of prey. What kind of information and how it is collected, recorded, and interpreted could be explained to the students as well as, how the biologists and other scientists at the center use this data or information.

Visit the local fish hatchery to see what kind of information or data scientists collect on the fish. Students could learn how this information is collected and recorded and discuss what kind of predictions scientists make with the data? Students could inquire about the use of computers in interpreting data.

Visit the U.S. Weather Service to see how information is collected and interpreted in regards to weather forecasting. Students could discover what kind of equipment is used to gather the data, how is it interpreted and reported.

Language Arts:
Have the students survey other students in other classrooms about their favorite hot lunch. Make predictions by grade level. After surveys have been tallied have students create graphs that show the top 5 favorites. Display these in the cafeteria or write an article for the school newspaper disclosing the results.

Send e-mail messages to other classes asking them for data on their favorite pizza topping, or ice cream flavor. Collect and record data and with the help of high school students or a computer specialist, create a spread sheet that displays their information.

Science:
Have students set up experiments with plants keeping track of growth. Teams could be responsible for measuring and collecting data to add to a class chart or graph. Make predictions about conditions for growth (sunlight vs. dark room).

Math:
Create other games or activities involving dice or spinners to allow students additional opportunities to generate and record their own data. Make predictions and create graphs that display their results.

Social Studies:
Students can survey other classrooms to determine the names of the states (or countries) they were born in. Display this data on a bulletin board or on a map of the U.S.

WHERE TO GET THE VIDEO
Sunburst Communications Inc.
101 Castleton Street
Pleasantville, NY 10570
(800-321-7511)

Lesson Plan Created by Master Teacher Wendy Eveland, Frontier Elementary School, Meridian, Idaho

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NOTE TO TEACHER

This video is about scientists on the ship called the "Mimi" collecting data on humpback whales. This should provide students with a real life situation where scientists are collecting, recording, and interpreting data and finally making estimations or predictions on the humpback whale population. Even if students are not familiar with some of the terms, they are explained in the video segment and a discussion can take place.

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