Exploring probability

Through teacher guidance, students will experiment with objects to generate probable outcomes to consider probability.

A lesson plan for grades 4 and 7 Mathematics

By John Cleveland

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Learning outcomes

Students will:

• consider the probable outcomes by using manipulatives.
• convert results of experiments into graphs charts, and fractions to show outcomes.

Teacher planning

Time required for lesson

3 hours

Materials/resources

• pencils
• paper
• coins (one for each two students)
• dice (one for each two students)
• a kick ball
• 7 different geometric shapes; felt cloth (to be affixed to the surface of the ball)
• rubber cement
• blow-up model of the earth with continents displayed
• overhead projector
• clipboard
• overhead marker & black transparency

Technology resources

Access to a computer program which utilizes probabilities could provide enrichment.

Pre-activities

Introduce/re-introduce the game “Jan-Kem-Po” (paper-rock-scissors) to students and allow them to play the game as partners. Model organizing the data of each round played into a chart. Require students to record data after 3-5 minutes of play. Pick specific students and show the class how the data can be organized onto a chart to show the probability of one choice being made (paper or rocks or scissors). Also suggest how students can interpret data into a fraction form.

Activities

Day 1

1. Initiate the lesson with the “Jan Kem Po.”
2. Distribute coins to student pairs. Tell students to flip coin ten times and record each result (head or tail). When finished, collect coins to avoid off-task play.
3. Using overhead projector, show students how to convert data into fraction form. Have students convert their data into fraction form.

Day 2

Prior to lesson, glue felt shapes to ball; this will be the probability ball.

1. Set purpose for lesson and line up students. Once students are outside, have them form a circle.
2. Have students toss the ball to each other. Each time a student catches the ball have them call out the location of their right pointer finger on the probability ball. Record if the ball lands on a shape or on the bare surface of the ball each time a student catches it.
3. Introduce the blow-up globe for a geography connection. Have students give the blow-up a few tosses and record the results.
4. Students return to the classroom to record the results of the tosses. Use the overhead to show the results of the tosses and the total number of tosses.
5. Guide students in recording the data onto a chart to show the number of times a specific place was landed on by a pointer finger. (Be sure to demonstrate converting data into a fraction).
6. Discuss the data, asking the students higher level thinking questions:
   • Based on the pattern, what place would be pointed to if we were to toss the ball one more time?
   • Does the number of choices (two sides on a coin, eight different areas to point to on the ball) affect the chances of one of the choices being revealed?
7. Conclude the lesson with a summary of the topics discussed.

Assessment

Students should be evaluated based on participation during the lesson. Also the teacher should use the data derived from the tosses to create a handout to give students a hard copy of the concepts covered. Several open-ended questions could also be included on a test to check understanding. In your own words, describe how we used probability in our ball tossing activity.

Supplemental information

Comments

Explaining probability to students can be a real challenge due to the fact that it is abstract and indefinite. This is an example of an activity I will use in my classroom to explain probability. Before attempting this lesson, create a vocabulary bank for yourself on probability.