Objectives: Students will guess the
answers to a 5--question T/F quiz based on Lewis Carroll's nonsense poem,
Jabberwocky, of which they have no prior knowledge. After the class
tallies the results of the quizzes (thereby calculating the experimental
probability), students will determine the theoretical probability of earning
a passing grade of at least 80% (without preparation) on a 5--question T/F
quiz. Students will then compare the theoretical and experimental
probabilities of this simple compound event and explain why there might be
differences.
·
KY Program of Studies: Students will determine
theoretical probabilities, compare to experimental results, and explain why
there might be differences.
·
KY Core Content: Students will compute
probabilities for simple, compound events, using such methods as organized
lists, tree diagrams, and area models.
Connections: Kentucky Learner Goal 2: Apply Core
Concepts and Principles
Academic Expectation 2.13: Students understand and appropriately use
statistics and probability.
NCTM Principles and Standards for Data Analysis and Probability:
Understand and apply basic concepts of probability.
Context: This lesson should follow class work on
conducting simple probability experiments, such as drawing a number from a
box containing numbers 1 to 100, and dice games in which students compete
for particular products or sums. Also, prior exposure to simple compound
experiments such as flipping several coins at once will provide a sufficient
basis for scaffolding. Further, students should have previously learned the
meanings of probability language such as sample space, outcomes, desired
outcomes, randomness, and complementary and mutually exclusive events.
Students should have had experience in generating various visual
representations of data, such as circle diagrams, bar graphs, box plots,
stem and leaf plots.
Following this lesson, students can wrestle with the problem of
deciding which games of chance are fair and which are not, wherein they will
be conducting experiments and calculating the theoretical probability of
other simple, compound events.
·
Materials/Technology:
Copies of
The Jabberwocky quiz for each
student, or one on the overhead projector.
Large sheets of paper or write-on overhead transparencies for group
presentations.
Calculators as needed.
·
Procedures:
ATTENTION
1. Ask students to raise their hands if they ever neglected to study before
a test.
2. Ask them to raise their hands if they ever got a good grade without
studying.
3. Ask students to predict the chance of passing a test without adequate
preparation.
THE EXPERIMENT
4. Students will complete a 5-question T/F quiz for which they are
unprepared. Any quiz content is acceptable, as long as the students have to
guess at random. I chose Jabberwocky by Lewis Carroll, since 7th
graders love strange language, and integration of language arts content adds
interest.
5. Read the poem and have students grade their own quizzes, stressing that
students will not be penalized or rewarded for their answers. Explain that
the quiz was an experiment and that the class needs an accurate count of the
results.
6. Tally the results as directed through class discussion. Ask each group
to give a visual representation of the experimental data. (The variety of
responses may include a bar graph, a circle graph, a box and whiskers plot,
a stem and leaf plot, or other physical models.)
7. Invite a few groups with creative & unique responses to share with the
class.
THE PROBLEM
8. Ask students to work with their groups to find the mathematical
(theoretical) probability for passing the test. Remind students that their
goal is to find the desired outcomes/total outcomes. Ask the class
to give the specifics for this situation, which is number of ways to earn
an 80% or more/total number of ways to pass the test.
9. Observe as students discuss methods within their groups. Various
approaches may include organized lists, tree diagrams, building onto shorter
quizzes while looking for a pattern (Pascal's Triangle!), or the natural
counting principle.
10. Ask groups with creative & unique responses to share.
11. Guide the class to build Pascal's Triangle as a solution to the
problem. 12. Discuss the easiest method for finding probabilities of
passing a 10--question quiz. Build Pascal’s Triangle to explore the
solution.
ANALYSIS
13. Ask the groups to compare the experimental and theoretical
probabilities with a visual representation. Ask them to devise possible
explanations for any differences found.
14. Ask groups with creative and unique responses to share.
