Daniel Patrick Dillon
Math TEDU 522
Lesson Plan (Probability)
Purpose:
The focus of this lesson will be to teach students about outcomes, events, and
favorable outcomes. The activities will use dice and rock, paper scissors to produce
data to examine theoretical probability versus actual outcomes of events.
SOLs: Probability and Statistics
5.14 - The student will make predictions and determine the probability of
an outcome by constructing a sample space. 5.15 The student, given a problem
situation, will collect,
5.15 - The student, given a problem situation, will collect, organize, and
interpret data in a variety of forms, using stem-and-leaf plots and line graphs.
Objective:
Given two dice and a chart of possible outcomes, 100 percent of the students
will be able to accurately collect data from experimental trials. Given questions from
an accompanying worksheet, students will be able to correctly answer 80 percent (4
out of 5) questions. These skills will be shown on their charts, and in their answers to
the associated questions.
Procedure:
Introduction:
 The teacher will begin by discussing experiments, outcomes, events and
favorable outcomes with the students.
 The teacher will ask to define the term.
 Is an experiment valid if it is only performed once?
 What if we know the possible results?
 Use a deck of cards or a coin to show this concept.
 What are outcomes? (Known possible results)
 Show how color, suit, and number are possible results. (Heads and tails for a
coin)
 What is it called when we actually carry out an experiment and
produce an outcome? (Event)
 Ask a student to choose the color of the next card (Favorable outcome) and
then carry out the experiment. Discuss whether the favorable outcome was
achieved.
 Greater number of events will produce more accurate data, which leads
to stronger validity claims.
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Development:
Inform the students that we will be using dice to explore these concepts further.
Introduce dice inside of dice,
Pass out possible outcomes chart.
 Have students find the theoretical probability of each total being
produced.
 2 and 12 (1/36) p= .027
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 3 and 11 (1/18) p= .055
 4 and 10 (1/12) p= .083
 5 and 9 (1/9) p= .11
 6 and 8 (5/36) p= .138
 7 (1/6) p= .166
 How many possible totals are there? (11)
 Why not 12? (1 is impossible with two dice)
 How many possible outcomes are there? (36)
 If there are questions as to the reason why, discuss as a class.
Instruct students to carry out an experiment in an attempt to produce results similar to
the theoretical probability.
 Students will be paired up based on a drawing.
 *Possible extension, have students calculate the probability of
their name/number being drawn during a given drawing.
 Each pair of students will be given a total to track so that the
results can be compared to the theoretical probability.
 Each pair of students will throw the double dice 50 times.
 They will record their results on the given chart.
The teacher will create a stem and leaf chart on the board for each outcome as
students work.
Once completed, the students will report their findings by listing their results on the
stem and leaf plot.
 For those who finish early: When done with their 50 rolls, students
should compare their results to the theoretical probability, until all
students are finished. Students could also:
 Find total number of events produced by the class.
 Take note of outliers as all results come in.
 Hypothesize whether they think the class results will be
accurate.
Once the numbers are all in, the class will calculate the results of the study. Each pair
of students will focus on the total they were given at the beginning of the experiment.
 *Extension: If there is enough time, the teacher can input the data into
a graphing program and produce a bar or pie graph to represent the
data.
Summary:
Students will answer parts b., c., and d. from the associated questions.
The class will reconvene and discuss:
 The actual results as compared to the theoretical probability.
 Discuss if the results matched what they thought would happen.
 Review experiments and their relation to outcomes, favorable
outcomes, and events.
*Extension:
 Have students complete questions 3 and 4 on the worksheet.
 Discuss independent and dependent probabilities using a deck of cards.
 Discuss how the theoretical probabilities of Rock Paper Scissors.
 How often would a win, loss, or tie occur (1/3)
 What a good format for that activity would be.
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Materials:
Double dice
Dice Chart/Worksheet
Random number generator or other random method of selection
*Graphing program (If doing extension)
Whiteboard to record results
Evaluation A:
When evaluating the charts the teacher should look for:
 Correct number of rolls
 Each roll clearly marked on the chart.
When evaluating student answers on parts b., c., and d. the teacher should look for:
 Correct terminology.
 Logical reasoning to justify their answer to part d.
When evaluating parts 3 and 4 the teacher should look for:
 Appropriate terminology
 Distinction made between an outcome and an event.
Evaluation B:
This lesson was the second one that I had taught in Mrs. Miller's fifth grade
class, and my third overall. As a result, I felt most comfortable and most competent
teaching this lesson. I had selected this lesson with Mrs. Miller from one of her
textbooks before we watched the video of a similar lesson on probability in class. I
decided to use the graphing portion of the activity in the video to combine with the
events that the students recorded on their graphic organizer. I came away with a sense
that this lesson was a success overall, and I found myself "thinking like a teacher" and
really reflecting on what was working and what wasn't during the lesson.
I would have changed the pacing of this lesson. I felt that my content was
strong for this lesson, and I focused on trying to do one main activity, and build in
possible extensions and alternate representations of the content. My problem came in
the recording of the data on the stem and leaf plots. I was informed prior to the lesson
that the students had not yet used a stem and leaf plot to record information. This
made me feel that I should record the data as the students completed their 50 events.
This was successful at first, but quickly became backed up as multiple groups
completed their events at the same time. I would have had the students report their
data on the stem and leaf plot if I were to do this lesson over, so I could focus on
assisting students with the associated questions.
I was most satisfied with the students level of comprehension from the lesson.
The students met my objectives, and were able to skillfully describe the resulting data
table and graph. All of the data was recorded and reported accurately, (100%) and
aside from, question four on the "What Is Your Answer" which addressed a term that
was not explicitly covered in the lesson, the students provided acceptable answers to
all the other questions. The graph itself showed an almost perfect bell curve and
allowed myself and Mrs. Miller to discuss and introduce the concept to the class. This
was an unexpected but wholly welcome opportunity to extend the lesson to introduce
new concepts, and show the students that what they produced was remarkably close to
the theoretical probability.
The introduction to the lesson allowed me to show probability using a deck of
cards, accessing students background knowledge of card games to have them think
about how probability influences many card games. I think this helped students to
consider probability in a concrete way. The students were then able to examine more
abstract ways to show probability concepts in their recording of the dice rolls, on their
graphic organizer, in a stem and leaf chart, and then finally on a bar graph. These
multiple representations allowed students to have multiple access points to the
concepts covered in the lesson.
During my debriefing, Mrs. Miller asked me what I thought I needed to work
on. I was able to pinpoint exactly what my weakness was, pace. I knew that the lesson
got a bit disjointed during the recording of the data, and that I needed a more efficient
way to have students report their findings. Mrs. Miller said that was her only grow for
me, and that understanding pacing is something that comes with experience. I was
able to complete my activity, but I did not get an opportunity to discuss with the class
after the lesson to the degree that I would have liked. Mrs. Miller paid me a great
compliment when she told me that I was one of the most reflective practicum students
she had ever worked with. I was prepared to honestly assess my performance, and
was accurate in what worked and what needed adjustment, even during the lesson.
Mrs. Miller also had the students write a glow and a grow for me, and I look forward
to this alternative assessment of my performance, which I will receive later this week.