Download TEKS Lesson Plan/Unit Plan - Texarkana Independent School District

Focus Plan
Texarkana Independent School District
GRADING
PERIOD:
Teacher:
4th Six Weeks
PLAN CODE:
Tipton
Course/subject:
Mathematics
Grade(s):
8
Time allotted
for instruction:
1 – 1 ½ hours
Title:
Simulation and Probability Fun
Lesson TOPIC:
Simulating Events
TAKS Objective:
Objective 5: The student will demonstrate an understanding of
probability and statistics.
FoCUS TEKS and
Student Expectation:
(11) Probability and Statistics. The student applies concepts of
theoretical and experimental probability to make predictions. The
student is expected to:
(C) select and use different models to simulate an event
11) Probability and Statistics. The student applies concepts of
theoretical and experimental probability to make predictions. The
student is expected to:
(B) use theoretical probabilities and experimental results to make
predictions and decisions
Supporting TEKS and
Student Expectations:
Concepts
Enduring Understandings/Generalizations/Principles
The student will understand that
Simulation is the process of acting out a problem.
Simulation
Experimental Probability
Experimental probability is an estimated probability based on the relative
frequency of positive outcomes occurring during an experiment.
Theoretical Probability
Theoretical probability is the long-term probability of an outcome based on
mathematical principals.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
I.
Sequence of Activities (Instructional Strategies)
A.
Focus/connections
Prior to this lesson, you will need the following:
 One glass goldfish bowl
 400 Pepperidge Farm cheddar goldfish crackers
 100 Pepperidge Farm pretzel (or parmesan) goldfish crackers
 Small paper cups
 20 die (for Probability Worksheet activity)
 20 blue number cubes, 20 red number cubes (for Probability Worksheet activity)
 20 brown paper sacks (for Probability Worksheet activity)
Before students enter the class, mix all of the fish crackers together and put in the fish bowl. Tell the class
that they are going to predict how many pretzel goldfish you have in your bowl. Tell the class that there
are currently 400 cheddar goldfish in the bowl. Have four volunteers come to the front of the class. Each
student will use a net (small paper cup) to capture some fish. They will count the total number of fish in
their sample and how many of the fish are pretzels. Record the results on the board. The students should
return their fish to the bowl before the next student takes their sample.
B.
Instructional activities
(demonstrations, lectures, examples, hands-on experiences, role play, active
learning experience, art, music, modeling, discussion, reading, listening, viewing,
etc.)
This activity uses sampling techniques to estimate the population of a certain species within a defined
area. Tell the class that our goal is to make a reasonable prediction about the number of pretzel goldfish
that are in the bowl. Explain to the class that in the real world, probabilities are often based on
frequencies obtained by conducting experiments. There are two types of probabilities to consider:
experimental probabilities and theoretical probabilities. Experimental probabilities are based on
frequencies obtained by conducting experiments. Theoretical Probabilities are probabilities based on
known characteristics or facts. Ask the class to classify what type of probability they are currently
conducting with the goldfish.
C.
Guided activity or strategy
Each student will estimate the total number of pretzel fish in the bowl using only the data on the board.
After time has been given for calculations, have each student tell you what they have predicted. Discuss
the calculations determined by the class. After discussion, have students write an explanation about the
differences between their estimates using only their data and then the class’s pooled data. Place
students in pairs to complete the Probability Worksheet.
D.
Accommodations/modifications
Students requiring modifications may be paired with a peer to complete the guided activity.
E.
II.
Enrichment
STUDENT PERFORMANCE
A.
Description
Students will complete the Probability Worksheet in a small group setting.
B.
Accommodations/modifications
Students requiring modifications may be paired with a peer to complete the Probability Worksheet.
C.
Enrichment
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
Students requiring enrichment may reteach the lesson in a small group setting to their peers.
iii.
Assessment of Activities
A.
Description
Individual student grades may be taken on the Probability Worksheet if desired.
B.
Rubrics/grading criteria
Grades may be taken based on the Probability Worksheet Grading Rubric.


IV.
C.
Accommodations/modifications
D.
Enrichment
E.
Sample discussion questions
In what real world situations would you use experimental probability?
What occupations would utilize theoretical and experimental probability?
TAKS Preparation
A.
Transition to TAKS context
The teacher will lead the students in a discussion of how simulation problems may look in test format by
placing the TAKS questions below on the board/overhead.
B.
Sample TAKS questions
1. Fidel tosses four fair coins. What is the probability that all four coins will land heads up?
A. 1/16
B. 1/8
C. 1/4
D. 1/2
2. The probability of a table-tennis ball being defective is 1/10. About how many balls would be defective
in a case of 725 table-tennis balls?
A. 1
B. 7
C. 73
D. 80
3. The results of a random survey showed that 42 out of 80 people plan to vote for Mr. Vu for city council.
Which is the best prediction of the total number of votes he will receive if 2000 people vote?
F. 25
G. 50
H. 120
J. 1000
4. A spinner and a fair number cube are used in a game. The spinner has an equal chance of landing on
1 of 4 colors: red, purple, blue, or green. The faces of the cube are labeled 1 through 6. What is the
probability of a player spinning the color red and then rolling a 5 or 6?
F. 3/10
G. 1/8
H. 1/12
J. 1/24
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
V.
Key Vocabulary
Simulation, Experimental Probability, Theoretical Probability
VI.
Resources
A.
Textbook
Glencoe Mathematics ~ Applications and Connections
Chapter 12: Investigating Discrete Math and Probability
 Experimental Probability, pp. 540-543
 Using Sampling to Predict, pp. 546-548


B.
Supplementary materials
Probability Worksheet
Probability Worksheet Grading Rubric
C.
Technology

Students could design random simulations to use with technology. For example, students can
program the Random Number Generator on a calculator to produce random numbers from 200 to
999. In this range, there are an equal number of digits in each place-value position that are even
or odd; in other words, the probability of getting an even digit in any one position is 1/2, and the
probability of getting an odd digit in any one position is 1/2. If an even digit represents red, and an
odd digit represents yellow, then when the calculator’s RNG shows 356, it is the same as tossing
three two-color counters and getting one red and two yellows.

Students can create a simulation on a computer to extend the experimental results to 1,000 trials
and compare the results to the theoretical probability.
VII.
follow up activities
(reteaching, cross-curricular support, technology activities, next lesson in sequence, etc.)
The following scenario could be used for reteaching:
Given that the probability of getting a broken CD player from Bad CD Players, Inc., is 1/3, students select
and use a model to simulate buying a CD player. For example, students could place two blue marbles
(representing good CD players) and one red marble (representing a defective CD player) in a bag and
draw one; or they could spin a spinner that is 1/3 red and 2/3 blue, with red representing a defective CD
player. Students could use the model to simulate the event and then analyze their data.
VIII.
Teacher Notes
Probability is a subject that demonstrates the importance of understanding fractions, decimals and
percents. Probability is introduced as a measure of uncertainty or chance. The difference between
theoretical probability and experimental probability needs to be emphasized. Uses of probability in
weather reports, insurance, risk analysis and polls can be discussed to reinforce understanding.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District