Summary
Students will begin to understand the concept of probability through hands on activities.
Materials
Invitation to Learn
Flip the Coin Activity:
Bag of Colors
Probability Posters
- Colored chips
- Dice
- Colored marbles
- Colored centimeter
cubes
- Small circles or tiles
(numbered 1-20)
- Spinners
- Probability Recording
Sheet
- Poster board / chart
paper
Additional Resources
Books
Probability, by Sarah Jane Brian; ISBN 0590373676
Background for Teachers
Students need to understand the correct terms and vocabulary
while discussing probability. It is important for students to learn to
distinguish between theoretical and experimental probability. Students
can also be introduced to the mathematical formulas.
Theoretical probability:
- The numerical measure of the likelihood that an event will
happen or the ratio of the number of ways the event can occur
to the total number of possibilities.
- It is the fraction of times we expect an event to occur if the
same experiment is repeated over and over.
- It is the represented by the fraction:
Number of ways the event can occur
Total number of possible outcomes
- Theoretical probability does not change.
Example:
What is the probability of getting a number less than 3 when
tossing an ordinary dice? There are six possible outcomes: 1,
2, 3, 4, 5, or 6; all of which are equally likely to occur. Two of
these, 1 and 2, are less than 3; so the theoretical probability of
getting a number less than 3 is: 2/6 = 1/3.
Experimental probability:
- The numerical measure of what actually happens in an
experiment.
- It is the fraction of times an event actually occurs when the
same experiment is repeated over and over.
- It is represented by the fraction:
Number of actual outcomes
Total number of possible outcomes
- The experimental probability may vary from the theoretical
probability, but the more times the experiment is repeated, the
closer the experimental probability approaches the theoretical
probability.
Instructional Procedures
Invitation to Learn
Provide four slips of paper for each student. Ask them to write
their name on a paper each time they can answer "yes" to the following
questions:
- Do you have black hair?
- Are you an only child in your family?
- Is your birthday in January or July?
- Is there the letter "w" found in your first, middle, or last name?
Have students place the pieces of paper that have their names on
them in a container.
Ask students to predict whether they think their name will be
chosen. Draw one slip of paper out of the container. Compare
students' predictions with the actual results. Tell students that today
they will learn how to use mathematics to make better predictions.
Instructional Procedures
Flip the Coin Activity:
Conduct the following activity as a class:
- Trial 1: Hold up a coin and ask the students: "if I flip this
coin one time, how many possible outcomes are there?" (2:
heads or tails)
- Trial 2: Now ask: If I flip it ten times how many times would
you predict that I would get heads? (1/2 of 10 or 5 times.)
Pass one coin and paper to record to each student and direct
them to flip the coin ten times and record the results. Ask:
Did your outcomes match your prediction? Collect samplings
from several students and record on board or overhead chart,
pointing out that there was some variance.
- Trial 3: Have the students predict how many times they will get
heads if they flip the coin 30 times. (1/2 of 30 or 15 times) Have
them flip the coin 30 times and record the results. Ask: Did
your outcomes match your prediction? Again collect samplings
from several students and record on board or overhead chart.
- Trial 4: Have the students repeat the experiment, this time
flipping the coin 100 times. Again take class samplings and
record.
Class discussion:
- Through guided questioning, lead students to an understanding
of the difference between what they predicted would
occur, Theoretical Probability, and what actually occurred,
Experimental Probability, then place words on the board.
- Also discuss the ways they used to record their results. Again
through guided questioning, help students to determine the
best ways to record results (e.g., tally marks, T-charts, boxes, or
columns).Be sure to use vocabulary such as: event, likely, unlikely,
possible, impossible, outcomes, theoretical probability, and
experimental probability during discussion.
- Introduce the Theoretical Probability formula:
Number of ways the event can occur
Total number of possible outcomes
and the Experimental Probability formula:
Number of actual outcomes
Total number of possible outcomes
- Lead the discussion to an understanding of the idea that
the experimental probability may vary from the theoretical
probability, but the more times the experiment is repeated, the
closer the experimental probability approaches the theoretical
probability. Use the classes total results to illustrate this
concept.
Bag of Colors
- Put students into cooperative learning groups with no more than
four to a group
- Give each group a bag of tiles and a recording sheet for each
student
- With the class, go through the three steps in writing a
Theoretical Probability, found at the top of the Bag of Colors
Recording Sheet.<
- Step 1: Count the number of red tiles.
- Step 2: Count all of the tiles.
- Step 3: Write a fraction-Theoretical Probability.
- Allow each group time to write the Theoretical Probability
fraction for the remaining three colors. Do a quick check to
make sure they are correct.
- On their own, each group will fill out the chart and conduct
their experiment.
Probability Posters
A collection of various manipulatives to be used in conducting
experiments with probability such as:
- Put students into cooperative learning groups with no more
than four to a group.
- Each group will be given a different set of manipulatives to
conduct probability experiments.
- Each group will then prepare a short visual presentation of
their experiment.
- Give them time to conduct experiments, record results, and
prepare presentation.
Extensions
- Put manipulatives from Probability Station in a center and have
students continue conducting probability experiments with
materials that they didn't use before. Use Probability Recording
Sheet.
- In a center, provide manipulatives for students to create new
probability experiments and share with the class.
Family Connections
- Share experiments with family.
- Look for ways at home where probability can be used.
Assessment Plan
- Completion of Bag of Colors and Probability Recording Sheet.
- Group presentation of poster or chart displaying results and
findings using probability journal.
- Write a journal entry about what they have learned about
theoretical and experimental probability.
Bibliography
Rivero, V. (2006) let technology be your guide. American school board journal, November,
p52-53.
The author gives seven tips for integrating tools of technology to
help bolster students' knowledge in math and science education in the
classrooms and schools.
Blessman, J., Myszczak, B. (2001). Mathematics vocabulary and its effect on student
comprehension. ERIC Source (ED455112). Retrieved January 12, 2007, from http://
www.eric.ed.gov.
In this action research project, interventions were used for
improving fifth grade students' comprehension of mathematical
vocabulary. The following were used: math journals, student-created
math dictionaries, children's literature to introduce and reinforce
mathematical concepts, graphic organizers, visual aids, and written
explanations of open-ended word problems. These interventions
resulted in an increase in comprehension and use of mathematical
vocabulary in math performance and in communication of
mathematical ideas.
Created: 07/16/2007
Updated: 02/01/2018
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