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Enhanced Instructional Transition Guide
Grade 8/Mathematics
Unit 08:
Suggested Duration: 6 days
Unit 08: Probability (6 days)
Possible Lesson 01 (6 days)
POSSIBLE LESSON 01 (6 days)
This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing with districtapproved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and districts may modify the time
frame to meet students’ needs. To better understand how your district is implementing CSCOPE lessons, please contact your child’s teacher. (For your convenience, please
find linked the TEA Commissioner’s List of State Board of Education Approved Instructional Resources and Midcycle State Adopted Instructional Materials.)
Lesson Synopsis:
Students investigate experimental and theoretical probability and the probabilities of dependent and independent events.
TEKS:
The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas law. Any standard
that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit.
The TEKS are available on the Texas Education Agency website at http://www.tea.state.tx.us/index2.aspx?id=6148
8.2
Number, operation, and quantitative reasoning.. The student selects and uses appropriate operations to solve problems and justify
solutions. The student is expected to:
8.2B
Use appropriate operations to solve problems involving rational numbers in problem situations. Readiness Standard
8.11
Probability and statistics.. The student applies concepts of theoretical and experimental probability to make predictions. The student
is expected to:
8.11A
Find the probabilities of dependent and independent events. Readiness Standard
8.11B
Use theoretical probabilities and experimental results to make predictions and decisions. Supporting Standard
8.11C
Select and use different models to simulate an event.
Underlying Processes and Mathematical Tools TEKS:
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Grade 8/Mathematics
Unit 08:
Suggested Duration: 6 days
8.14
Underlying processes and mathematical tools.. The student applies Grade 8 mathematics to solve problems connected to everyday
experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:
8.14A
Identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with
other mathematical topics.
8.14C
Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking
for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards
to solve a problem.
8.14D
Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation,
and number sense to solve problems.
8.15
Underlying processes and mathematical tools.. The student communicates about Grade 8 mathematics through informal and
mathematical language, representations, and models. The student is expected to:
8.15A
Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or
algebraic mathematical models.
8.16
Underlying processes and mathematical tools.. The student uses logical reasoning to make conjectures and verify conclusions. The
student is expected to:
8.16A
Make conjectures from patterns or sets of examples and nonexamples.
8.16B
Validate his/her conclusions using mathematical properties and relationships.
Performance Indicator(s):
Grade 08 Mathematics Unit 08 PI 01
Create a presentation (e.g., brochure, poster, etc.) with the experimental and theoretical probabilities of dependent and independent events within a given real-life situation (e.g.,
baseball, snakes, sandwiches, etc.). Make conjectures from the probabilities of the real-life situation, and validate conclusions using mathematical properties and
relationships. Design and simulate an in-class experiment with math manipulatives to compare the theoretical and experimental probabilities of a dependent real-life situation.
Sample Performance Indicator:
There are over 3,000 species of snakes in the world, and only 15% are considered dangerous to humans. Texas has 15 of the 25 species of
poisonous snakes identified in North America. With each bite, one­half are “dry”, which means that the snake does not inject venom into the
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Grade 8/Mathematics
Unit 08:
Suggested Duration: 6 days
victim.
Create an informational brochure to inform tourists about the venomous snakes that inhabit Texas. Include the probability of not receiving a “dry”
bite from each type and category of snake, and predict which habitat is most likely to yield the least and most snake bites. Validate the predictions
with mathematical properties and relationships. The rattlesnake is one of the most notorious snakes in the Lone Star State; identify the probability
of being bitten by a snake in a wooded area and it being a rattlesnake. Design and simulate an in-class experiment with math manipulatives to
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Unit 08:
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determine the experimental probability of being bitten by a venomous snake in a wooded area and it being a rattlesnake. In writing, compare the
experimental and theoretical probabilities of being bitten by a snake in a wooded area and it being a rattlesnake.
Standard(s): 8.2B , 8.11A , 8.11B , 8.11C , 8.14A , 8.14C , 8.14D , 8.15A , 8.16A , 8.16B ELPS ELPS.c.1C , ELPS.c.1G , ELPS.c.5F , ELPS.c.5G
Key Understanding(s):
To find the probability of real-life event(s), a problem-solving plan or strategy is required to examine the sample space and favorable outcomes.
Theoretical and experimental probabilities are represented from the concepts of desired outcome compared to sample space.
Theoretical probabilities, experimental results, and proportional reasoning can be used to make predictions and decisions in real-life problem
situations.
Conjectures from real-life problem situations, involving theoretical probability of an event or experimental results of a simulation, are helpful in
validating predictions and decisions in situations involving probability.
The probability of a dependent event represents the probability that one event will occur given that a second event already occurred.
The quantity in the sample space of the second event of a dependent event decreases as all outcomes from the first event are not replaced to the
sample space.
Models used to simulate a real-life event and to communicate the experimental probability must be able to represent the sample in the event(s).
Misconception(s):
Some students may not accurately reflect the total possible outcomes of an event which may be affected by the outcome of another event,
specifically when items are not replaced to the original set.
Some students may confuse the words “and” and “or” when solving for the probability of dependent or independent events in a problem situation.
Underdeveloped Concept(s):
Some students may think the probability of an event can be greater than 1.
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Grade 8/Mathematics
Unit 08:
Suggested Duration: 6 days
Vocabulary of Instruction:
composite events
dependent events
experimental probability
independent events
probability
sample space
theoretical probability
Materials List:
6-sided die (1 per student)
coin (2 per student)
color tiles (15 per student)
color tiles (5 red, 3 green, 2 yellow) (1 set per teacher)
color tiles (72 red, 72 yellow, 72 blue, 72 green) (1 set per teacher)
computer with Internet access (1 per 3 – 4 students)
marker (1 per teacher)
paper lunch sack (1 per student)
paper lunch sack (1 per 2 students)
paper lunch sack (1 per teacher)
paper lunch sack (12 per teacher)
scissors (1 per 2 students)
spinner (blank) (1 per student)
Attachments:
All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments
that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website.
Group Tally Sheet
Spinner Sample
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Grade 8/Mathematics
Unit 08:
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Hands on with Simple Probability and Sample Spaces KEY
Hands on with Simple Probability and Sample Spaces
Simple Probability and Sample Spaces KEY
Simple Probability and Sample Spaces
Composite Events and Problem Solving Strategies KEY
Composite Events and Problem Solving Strategies
Composite Events and Problem Solving Practice KEY
Composite Events and Problem Solving Practice
Looking at the Third Dimension KEY
Looking at the Third Dimension
Find the Probabilities of Dependent and Independent Events KEY
Find the Probabilities of Dependent and Independent Events
GETTING READY FOR INSTRUCTION
Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to
teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using
the Content Creator in the Tools Tab. All originally authored lessons can be saved in the “My CSCOPE” Tab within the “My Content” area. Suggested
Day
1
Suggested Instructional Procedures
Notes for Teacher
Topics:
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Grade 8/Mathematics
Unit 08:
Suggested Duration: 6 days
Suggested Instructional Procedures
Notes for Teacher
Spiraling Review
Experimental probability
Theoretical probability
Engage 1
Students use experience and reasoning to conduct an experiment and compare data for theoretical versus
experimental probability.
ATTACHMENTS
Teacher Resource: Group Tally
Sheet (1 per teacher)
Handout: Group Tally Sheet (1 per
student)
Instructional Procedures:
MATERIALS
1. Prior to instruction, create a set of Probability Bags for each teacher by labeling 12 paper
lunch sacks 1 – 12 and placing 15 red tiles, 3 yellow tiles, 3 blue tiles, and 3 green tiles in
paper lunch sacks 1, 5, and 9; 3 red tiles, 15 yellow tiles, 3 blue tiles, and 3 green tiles in a
paper lunch sacks 2, 6, and 10; 3 red tiles, 3 yellow tiles, 3 blue tiles, and 15 green tiles in
paper lunch sacks 3, 7, and 11; and 3 red tiles, 3 yellow tiles, 15 blue tiles, and 3 green tiles
in paper lunch sacks 4, 8, and 12.
2. Place students in groups of 3 – 4. Distribute handout: Group Tally Sheet to each group.
marker (1 per teacher)
paper lunch sack (12 per teacher)
color tiles (72 red, 72 yellow, 72 blue,
72 green) (1 set per teacher)
TEACHER NOTE
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Unit 08:
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Notes for Teacher
Explain to students that the Franklin Medical Center is training their lab techs to test blood
samples for specific diseases.
3. Display the following for the class to see:
4. Display the set of Probability Bags for the class to see. Explain to students that each paper
bag contains 24 color tiles with at least 3 of each color (red, blue, green, yellow) and it will
be their job to discover which bag represents which disease. A bag with more blue squares
represents Sickle Cell Anemia, a bag with more green squares represents Diabetes, a bag
with more yellow squares represents Leukemia, and a bag with more red squares
represents a Normal Blood Cell.
State Resources
TEXTEAMS: MS Proportionality: What’s in the
Bag?
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Unit 08:
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Notes for Teacher
TEACHER NOTE
5. Instruct a representative from each group to randomly select a displayed Probability Bag.
Remind students to not look in the bag. Instruct student groups to shake the bag, without
looking, randomly draw a tile from the bag, record a tally mark in the appropriate location on
their group handout: Group Tally Sheet, and replace the tile back in the bag before
drawing another tile. When a group thinks they can identify the disease their bag
represents, they are to stop drawing tiles and record this prediction on their tally sheet.
Allow time for students to complete the activity. Monitor and assess student group to check
for understanding. Facilitate a class discussion to summarize student predictions.
The terms “theoretical probability” and
“experimental probability" are formally introduced
in Grade 6. Although, in Grade 5 students used
experimental results to make predictions and
described the results of an experiment with a
fraction. In high school, experimental probability is
referred to as empirical probability.
6. Instruct student groups to compare and discuss their tally marks from their handout: Group
Tally Sheet with another group that predicted the same disease. Remind students to still
not look at the tiles in their bag. Allow time for student groups to discuss their predictions to
determine if they are still confident in their prediction. If groups are unsure of their
prediction after discussing the activity with another group, allow them to continue to test
their bag by drawing more tiles and recording each draw on their handout. Allow time for
students to complete the activity. Monitor and assess student groups to check for
understanding.
7. Instruct student groups to validate their prediction by dumping all tiles from their Probability
Bag, counting the number of red, yellow, green, and blue tiles, and compare the tiles in the
bag to the information displayed about the diseases. Allow time for students to complete the
activity. Monitor and assess student groups to check for understanding. Facilitate a class
discussion to debrief student solutions.
Ask:
How many pulls did you make before deciding the disease your bag
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Notes for Teacher
represents? Answers may vary. 10; etc.
Did comparing the tally marks with another group help identify the disease
correctly? (yes)
How did this affect your prediction? (The more trials (tally marks) there are, the
more accurate the prediction.)
There are two types of probability: Experimental and Theoretical. What type of
probability is this activity? Why? (Experimental, because the prediction was based on
the data from the actual trials experienced.
How is experimental probability related to theoretical probability? (To find the
experimental probability of winning a game, one must play the game many times, and
then divide the number of games won by the total number of games played. For
theoretical probability, spinning a 4 on a fair spinner with 4 equal sections numbered 1 –
4 is
or 25%, because there is one possibility in four to spin a 4, and under ideal
circumstances one out of every four spins would be a 4.)
2 – 3
Topics:
Spiraling Review
Probability
Explore/Explain 1
Students review concepts of probability from lower grades, which include likelihood, sample spaces, and how
to calculate the probability of an event.
Instructional Procedures:
ATTACHMENTS
Teacher Resource: Spinner Sample
Teacher Resource: Hands on with
Simple Probability and Sample
Spaces KEY (1 per teacher)
page 10 of 51 Grade 8/Mathematics
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Enhanced Instructional Transition Guide
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Notes for Teacher
Handout: Hands on with Simple
Probability and Sample Spaces (1
per student)
1. Display teacher resource: Spinner Sample. Facilitate a class discussion about the
probability of an event occurring.
Ask:
If the spinner is spun, how many possible outcomes are there? (12)
TEACHER NOTE
Students constructed sample spaces using lists
Explain to students that the list of all possible outcomes is called the sample space.
and tree diagrams in Grade 6. In Grade 7, students
What is the sample space for spinning the spinner? (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12)
Would you describe the probability of each outcome in the sample space as
equally likely, less likely, or more likely? Explain. (The probability of each outcome
occurring is equally likely, because each section of the spinner is the same size and
each number occurs only once.)
What is the probability of spinning a 3 on the spinner? (P(3)=
)
constructed sample spaces for simple or
composite events.
TEACHER NOTE
The Fundamental Counting Principle was
introduced in Grade 4. However, it may be
necessary to demonstrate creating tree diagrams
of the experiments.
2. Demonstrate recording the correct notation for the probability of the event for the class to
see.
P(3) =
Ask:
What is the probability of spinning an odd number? Explain. (P(odd)=
)
Answers may vary. Half of the numbers on the spinner are odd; etc.
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Enhanced Instructional Transition Guide
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Notes for Teacher
What is the probability of spinning a number greater than 5? Explain. (P(greater
than 5)=
) Answers may vary. Six of the numbers are greater than 5 which
represents half of the spinner; etc.
What is the probability of spinning a number that is a factor of 8? Explain.
(P(factor of 8)=
) Answers may vary. The numbers 1, 2, 4, and 8 are factors of 8
which represents one-third of the spinner; etc.
What is the probability of spinning a prime number? Explain. (P(prime)=
)
Answers may vary. The numbers 2, 3, 5, 7, and 11 are prime; etc.
What is the probability of spinning a multiple of 3? Explain. (P(multiple of 3)=
) Answers may vary. The numbers 3, 6, 9, and 12 are multiples of 3; etc.
3. Facilitate a class discussion about probability.
Ask:
What is the probability of spinning a number greater than 12? Explain. (P(greater
than 12)=
) Answers may vary. There are no numbers greater than 12 on the
spinner; etc.
What is the probability of spinning a number less than 13? Explain. (P(less than
13)=
) Answers may vary. All the numbers on the spinner are less than 13; etc.
Remind students that the probability of an event occurring is always between 0 and 1.
4. Facilitate a class discussion about the probability of an event and its complement.
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Notes for Teacher
Ask:
What is the probability of spinning a number less than 10? Explain. (P(less than
10)=
) Answers may vary. Nine of the 12 numbers are less than 10, which
represents three-fourths of the spinner; etc.
What is the probability of not spinning a number less than 10? Explain. (P(not
less than 10)=
) Answers may vary. Three of the 12 numbers are not less than
10, which represents one-fourth of the spinner; etc.
Remind students that the sum of an event occurring and its complement is 1.
P(event) + P(complement of event) = 1
5. Instruct students to consider the experiment of flipping a coin two times. Facilitate a class
discussion about how to use the Fundamental Counting Principle to determine how many
different outcomes are possible for an event.
Ask:
How is the Fundamental Counting Principle used to determine the number of
outcomes in an experiment? (If the experiment has two events, multiply the number of
outcomes for each event together to determine the number of possible outcomes for the
experiment.)
What is an example of an experiment with 2 events? Answers may vary. If I flip a
coin, the coin can land on either heads or tails. So, when flipping a coin two times, there
are 2 outcomes for the first flip, and there are 2 outcomes for the second flip. So, if I
multiply 2 times 2, that is the number of possible outcomes for the experiment; etc.
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Notes for Teacher
What is the probability of flipping 2 coins and both coins will land on heads? (
)
6. Place students in pairs. Distribute handout: Hands on with Simple Probability and
Sample Spaces to each student. Instruct students to list all the possible outcomes for each
experiment and identify the probability of a specified outcome occurring. Allow time for
students to complete the activity. Monitor and assess student pairs to check for
understanding. Facilitate a class discussion to debrief student solutions.
Topics:
Spiraling Review
Probability of independent events
Probability of dependent events
Explore/Explain 2
Students use the Fundamental Counting Principle to find the probabilities and their complements of simple
and composite events. Students find the probabilities of independent and dependent events
Instructional Procedures:
1. Model placing 5 red, 3 green, and 2 yellow color tiles in a paper lunch sack. Facilitate a
class discussion about the probability of an event and its complement.
Ask:
What is the probability of reaching in the bag and not selecting a yellow color
ATTACHMENTS
Teacher Resource: Composite
Events and Problem-Solving
Strategies KEY (1 per teacher)
Handout: Composite Events and
Problem-Solving Strategies (1 per
student)
Teacher Resource: Simple
Probability and Sample Spaces
KEY (optional) (1 per teacher)
Handout: Simple Probability and
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Enhanced Instructional Transition Guide
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tile? (Since there are 8 tiles that are not yellow, the probability will be
Notes for Teacher
.)
2. Remind students that this probability is also called the complement of picking a yellow and
that the sum of a probability and its complement is always 1.
Ask:
What is the probability of drawing a blue tile? (zero)
What is the probability of not drawing a blue tile? (1)
3. Model reaching into the paper lunch sack, drawing a tile, recording its color, replacing the
tile in the bag, drawing another tile, and recording its color. Facilitate a class discussion
about composite events.
Ask:
How would you determine the probability of this event occurring? Answers may
vary. The fundamental counting principle; tree diagram; etc.
How could you determine how many ways there are to select two red tiles by
reaching in and drawing a tile, recording it, replacing it, and then selecting a
second tile? (You can pick any of the 5 red tiles each time you draw, since you are
replacing the tile each time.)
4. Explain to students that since you can draw any of the 5 tiles on the first draw and any of
the 5 tiles on the second draw, these are called independent events because the outcome
of the second event does not depend on the outcome of the first event. Facilitate a class
discussion about independent events.
Sample Spaces (optional) (1 per
student)
Teacher Resource: Composite
Events and Problem-Solving
Practice (optional) KEY (1 per
teacher)
Handout: Composite Events and
Problem-Solving Practice
(optional) (1 per student)
MATERIALS
color tiles (5 red, 3 green, 2 yellow)
(1 set per teacher)
paper lunch sack (1 per teacher)
TEACHER NOTE
The concept of finding the complement to a simple
event was introduced in Grade 6.
ADDITIONAL PRACTICE
Handout (optional): Simple Probability and
Sample Spaces and handout (optional):
page 15 of 51 Grade 8/Mathematics
Unit 08:
Suggested Duration: 6 days
Enhanced Instructional Transition Guide
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Notes for Teacher
Ask:
Composite Events and Problem-Solving Practice
may be used as additional practice, if needed.
How would you find the probability of these two independent events
occurring? (First, find the probability of each event, then, multiply them together.)
How many possible outcomes are there for the first draw? (10)
What is the probability of selecting a red tile on the first draw? (
State Resources
)
How many possible outcomes are there for the second draw if the tile from the
first draw is replaced? (10)
What is the probability of selecting a red tile on the second draw? (
)
MTR 6 – 8: How Many Boxes? may be used to
reinforce these concepts or used as alternate
activities
What is the probability that both tiles drawn will be red? (The probability of
drawing of two red tiles is
, or
.)
What if you repeated the same experiment, except after the first draw you did
not replace the tile, what type of event would occur for the second event?
Explain. (dependent event) Answers may vary. It is a dependent event because the
outcome of the second event depends on the outcome of the first event; the outcome of
the first event affects the outcome of the second event; etc.
How is the total number of possible outcomes for the experiment affected
when a tile is not replaced? (The first event has 10 outcomes, but the second event
has only 9 outcomes. 9 times 10 is 90, so there are 90 possible outcomes for drawing 2
red tiles in a row rather than 100 possible outcomes.)
If you do not replace the tile after the first draw, what is the probability of
drawing a green tile and then a red tile? (There are 3 ways to draw a green tile and
5 ways to draw a red tile, so there are 15 ways to draw a green tile followed by a red tile;
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Unit 08:
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Suggested Instructional Procedures
or
Notes for Teacher
.)
What is the probability of drawing a red tile, then a green tile, and then a yellow
tile without replacing the tiles after they have been drawn? (5 times 3 times 2 out
of 10 times 9 times 8;
or
)
5. Distribute handout: Composite Events and Problem-Solving Strategies to each
student as independent practice and/or homework.
4
Topics:
Spiraling Review
Probability of independent events
Probability of dependent events
Explore/Explain 3
Students determine the probabilities of independent and dependent events while reviewing concepts and
attributes of three-dimensional figures.
Instructional Procedures:
1. Place students in pairs. Distribute handout: Looking at the Third Dimension to each
student and a pair of scissors and brown paper bag to each pair. Instruct student pairs to
cut out the three-dimensional figures from the table at the top of their handout and use the
figures to complete the remainder of the handout. Allow time for students to complete the
activity. Monitor and assess student pairs to check for understanding. Facilitate a class
discussion to debrief student solutions.
ATTACHMENTS
Teacher Resource: Looking at the
Third Dimension KEY (1 per
teacher)
Handout: Looking at the Third
Dimension (1 per student)
MATERIALS
scissors (1 per 2 students)
paper lunch sack (1 per 2 students)
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Notes for Teacher
Ask:
TEACHER NOTE
How do you determine the probability of an event? (number of favorable outcomes
to number of total possible outcomes)
How do you find the probability of drawing a three-dimensional figure from the
bag? (number of favorable outcomes to 8 total possible outcomes)
How many cards are in the bag? (8)
Is the event described in problem 1 simple or compound? (Arvis drawing from his
bag is simple and Sylvia drawing from her bag is simple, but the event of Arvis drawing a
shaded figure AND Sylvia drawing a pyramid is a compound event.)
Is the event dependent or independent? (independent)
Which probabilities are experimental and which are theoretical? (The actual
drawing is experimental. Problem 1 is theoretical.)
Is the event described in problem 3 dependent or independent? (dependent)
5 – 6
As student pairs are completing the activity, walk
around and continue to ask, “How many cards are
in the bag?” for students to realize when the total
number of cards in the bag changes.
Topics:
Spiraling Review
Probability of independent events
Probability of dependent events
Elaborate 1
Students determine the probabilities of independent and dependent events.
Instructional Procedures:
ATTACHMENTS
Teacher Resource: Find the
Probabilities of Dependent and
Independent Events KEY (1 per
teacher)
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Grade 8/Mathematics
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Suggested Instructional Procedures
1. Place students in pairs. Distribute handout: Find the Probabilities of Dependent and
Independent Events. Instruct students to find the probability for each event. Allow time for
students to complete the activity. Monitor and assess student pairs to check for
understanding. Facilitate a class discussion to debrief student solutions and clarify
misconceptions and vocabulary.
Evaluate 1
Instructional Procedures:
1. Assess student understanding of related concepts and processes by using the
Performance Indicator(s) aligned to this lesson.
Notes for Teacher
Handout: Find the Probabilities of
Dependent and Independent
Events (1 per student)
MATERIALS
coin (2 per student)
6-sided die (1 per student)
spinner (blank) (1 per student)
color tiles (15 per student)
paper lunch sack (1 per student)
Performance Indicator(s):
Grade 08 Mathematics Unit 08 PI 01
Create a presentation (e.g., brochure, poster, etc.) with the experimental and theoretical probabilities of
dependent and independent events within a given real-life situation (e.g., baseball, snakes, sandwiches,
etc.). Make conjectures from the probabilities of the real-life situation, and validate conclusions using
mathematical properties and relationships. Design and simulate an in-class experiment with math
manipulatives to compare the theoretical and experimental probabilities of a dependent real-life situation.
Sample Performance Indicator:
There are over 3,000 species of snakes in the world, and only 15% are considered
dangerous to humans. Texas has 15 of the 25 species of poisonous snakes identified
in North America. With each bite, one­half are “dry”, which means that the snake does
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Notes for Teacher
not inject venom into the victim.
Create an informational brochure to inform tourists about the venomous snakes that
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Notes for Teacher
inhabit Texas. Include the probability of not receiving a “dry” bite from each type and
category of snake, and predict which habitat is most likely to yield the least and most
snake bites. Validate the predictions with mathematical properties and relationships.
The rattlesnake is one of the most notorious snakes in the Lone Star State; identify
the probability of being bitten by a snake in a wooded area and it being a rattlesnake.
Design and simulate an in-class experiment with math manipulatives to determine the
experimental probability of being bitten by a venomous snake in a wooded area and it
being a rattlesnake. In writing, compare the experimental and theoretical probabilities
of being bitten by a snake in a wooded area and it being a rattlesnake.
Standard(s): 8.2B , 8.11A , 8.11B , 8.11C , 8.14A , 8.14C , 8.14D , 8.15A , 8.16A , 8.16B
ELPS ELPS.c.1C , ELPS.c.1G , ELPS.c.5F , ELPS.c.5G
05/09/13
page 21 of 51 Grade 8
Mathematics
Unit: 08 Lesson: 01
Group Tally Sheet
Franklin Medical Center is training their lab techs to test blood samples for specific diseases.

Sickle Cell Anemia:

Diabetes:

Leukemia:

Normal Blood Cell:
Group Name:
Color
Tally
Frequency
Red
Yellow
Blue
Green
Prediction and explanation of thinking:
©2012, TESCCC
10/12/12
page 1 of 1
Grade 8
Mathematics
Unit: 08 Lesson: 01
Spinner Sample
8
10
4
1
6
9
30
12
3
5
11
7
2
©2012, TESCCC
04/18/13
page 1 of 1
Grade 8
Mathematics
Unit: 08 Lesson: 01
Hands on with Simple Probability and Sample Spaces KEY
Directions: List the possible outcomes for each problem. The first one is done for you.
1. What is the probability of a nickel landing tails when you flip it?
Possible outcomes: Heads or Tails
1
Probability of tails: 1 in 2 or
2
2. What is the probability of rolling a 2 with a fair number cube (1-6)?
Possible outcomes: 1, 2, 3, 4, 5, 6
1
Probability of rolling a 2:
6
3. What is the probability of rolling a 4 with a fair number cube (1-6)?
Possible outcomes: 1, 2, 3, 4, 5, 6
1
Probability of rolling a 4:
6
4. What is the probability of rolling a 2 or a 4 with a fair number cube (1-6)?
Possible outcomes: 1, 2, 3, 4, 5, 6
2
1
Probability of rolling a 2 or 4:
or
6
3
5. A small black cloth bag holds two red counters, two green counters, two blue counters, and
two black counters. All are the same size. Without looking into the bag, what is the probability
of drawing a blue counter from the bag?
Possible outcomes: red, red, green, green, blue, blue, black, black
2
1
Probability of drawing the blue counter:
or
8
4
6. What is the probability of drawing either the red or black counter from the bag?
Possible outcomes: red, green, blue, black
4
1
Probability of drawing the red or black counter:
or
8
2
7. What is the probability of drawing a purple counter?
Possible outcomes: red, green, blue black
0
Probability of drawing a purple counter:
or 0
8
8. What is the probability of drawing either a red, green, or black counter from the bag?
Possible outcomes: red, green, blue, black
6
3
Probability of drawing the red, green or black counter from the bag:
or
8
4
9. What is the probability of one head and one tail landing when you flip the two coins, a nickel
and a quarter at the same time?
Possible outcomes: Nickel: H, Nickel: T, Quarter: H, Quarter: T
The possible outcomes together are as follows in Nickel/Quarter format: H/H, H/T, T/H, T/T
2
1
Probability of one head and one tail:
=
4
2
©2012, TESCCC
05/01/13
page 1 of 1
Grade 8
Mathematics
Unit: 08 Lesson: 01
Hands on with Simple Probability and Sample Spaces
Directions: List the possible outcomes for each problem. The first one is done for you.
1. What is the probability of a nickel landing tails when you flip it?
Possible outcomes: Heads or Tails
1
Probability of tails: 1 in 2 or
2
2. What is the probability of rolling a 2 with a fair number cube (1-6)?
Possible outcomes: ___________
Probability of rolling a 2: ________
3. What is the probability of rolling a 4 with a fair number cube (1-6)?
Possible outcomes: ______________
Probability of rolling a 4: ___________
4. What is the probability of rolling a 2 or a 4 with a fair number cube (1-6)?
Possible outcomes: ______________
Probability of rolling a 2 or 4: _______
5. A small black cloth bag holds two red counters, two green counters, two blue counters, and
two black counters. All are the same size. Without looking into the bag, what is the probability
of drawing a blue counter from the bag?
Possible outcomes: ________________
Probability of drawing the blue counter: _________________
6. What is the probability of drawing either the red or black counter
from the bag?
Possible outcomes: ___________
Probability of drawing the red or black counter: ___________
7. What is the probability of drawing a purple counter?
Possible outcomes: _____________
Probability of drawing a purple counter: ______________
8. What is the probability of drawing a red, a green, or a black counter from the bag?
Possible outcomes: ____________
Probability of drawing the red, green or black counter from the bag: ___________
9. What is the probability of one head and one tail landing when you flip the two coins, a nickel
and a quarter at the same time?
Possible outcomes: _______________
Probability of one head and one tail: _____________
©2012, TESCCC
10/12/12
page 1 of 1
Grade 8
Mathematics
Unit: 08 Lesson: 01
Simple Probability and Sample Spaces KEY
Probability is the likelihood that a particular event or occurrence will take place. Probability is
expressed as a ratio in fraction form. The probability ratio compares the number of favorable
outcomes to the total possible outcomes.
Example: What is the probability of a coin landing tails up on one toss? There are two sides to the
coin so there are two possible outcomes to the toss. There is one favorable outcome—
1
tails! The probability is 1 out of 2 or .
2
The letters of the words “possible outcomes” are put in a bag. Find the probability of picking each
letter.
1. p:
1
16
5. b:
1
16
2. o:
3
16
6. l:
3. s:
3
16
7. e:
2
1
=
16
8
11. m:
4. i:
1
16
8. u:
1
16
12. r:
1
16
9. t:
1
16
10. c:
1
16
1
16
0
=0
16
What is the probability of rolling the following number situations with a fair number cube (1-6)?
Express each answer in lowest terms.
Sample Space: 1, 2, 3, 4, 5, 6
13. odd number:
3
1
=
6
2
14. even number:
3
1
=
6
2
15. a number less than 4:
3
1
=
6
2
16. a number greater than 2:
©2012, TESCCC
4
2
=
6
3
10/12/12
page 1 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Simple Probability and Sample Spaces KEY
Using a standard deck of playing cards, what is the probability of choosing each of the following
cards? Express each answer in lowest terms.
4
1
=
52
13
26
1
18. a black card:
=
52
2
4
1
19. a queen:
=
52
13
1
20. a two of spades:
52
17. a king:
21. a 10 of diamonds or a 10 of hearts:
22. a red three:
2
1
=
52
26
23. a king, queen or jack of any suit:
24. a red card:
2
1
=
52
26
12
3
=
52
13
26
1
=
52
2
A glass jar contains 100 jellybeans. There are 25 cherry-flavored, 20 grape-flavored, 12 licorice
flavored, 24 coconut-flavored and 19 lime-flavored. What is the probability of choosing a given flavor?
Express each answer in lowest terms.
25. grape:
20
1
=
100
5
26. coconut or licorice:
27. cherry or lime:
28. lemon:
44
11
=
100
25
0
=0
100
29. grape or cherry:
30. cherry:
©2012, TESCCC
36
9
=
100
25
45
9
=
100
20
25
1
=
100
4
10/12/12
page 2 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Simple Probability and Sample Spaces KEY
Area models of geometric figures can be used to represent simple probabilities. The whole figure
represents the total number of possible outcomes and the shaded part represents the desired
outcomes. Figures can be broken up into equal sections or areas can be calculated and
compared.
31. What simple probability is represented by each of the following area models? Assume divided
sections within a figure are equal in area.
45
1
8
1
2
1
2
32. Split the rectangle into equal sections to represent a probability of 0.2.
Sample answer, others possible such as ten sections with two shaded
33. Split the circle into equal sections to represent a probability of 75%. Sample answer
90
34. What is the probability that a randomly dropped penny would fall inside the square grid, but
outside the shaded rectangular region?
Area of square grid = 8 • 8 = 64 u2
Area of shaded rectangle = 6 • 4 = 24 u2
P(falling inside shaded rectangle) =
(Area of square grid ─ Area of shaded
rectangle) ÷ Area of square grid =
64  24
40
5
=
=
= 0.625 = 62.5%
64
64
8
©2012, TESCCC
10/12/12
page 3 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Simple Probability and Sample Spaces
Probability is the likelihood that a particular event or occurrence will take place. Probability is
expressed as a ratio in fraction form. The probability ratio compares the number of favorable
outcomes to the total possible outcomes.
Example: What is the probability of a coin landing tails up on one toss? There are two sides to the
coin so there are two possible outcomes to the toss. There is one favorable outcome—
1
tails! The probability is 1 out of 2 or .
2
The letters of the words “possible outcomes” are put in a bag. Find the probability of picking each
letter.
1. p:
5. b:
9. t:
2. o:
6. l:
10. c:
3. s:
7. e:
11. m:
4. i:
8. u:
12. r:
What is the probability of rolling the following number situations with a fair number cube (1-6)?
Express each answer in lowest terms.
13. odd number:
14. even number:
15. a number less than 4:
16. a number greater than 2:
©2012, TESCCC
10/12/12
page 1 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Simple Probability and Sample Spaces
Using a standard deck of playing cards, what is the probability of choosing each of the following
cards? Express each answer in lowest terms.
17. a king:
18. a black card:
19. a queen:
20. a two of spades:
21. a 10 of diamonds or a 10 of hearts:
22. a red three:
23. a king, queen or jack of any suit:
24. a red card:
A glass jar contains 100 jellybeans. There are 25 cherry-flavored, 20 grape-flavored, 12 licorice
flavored, 24 coconut-flavored, and 19 lime-flavored. What is the probability of choosing a given
flavor? Express each answer in lowest terms.
25. grape:
26. coconut or licorice:
27. cherry or lime:
28. lemon:
29. grape or cherry:
30. cherry:
©2012, TESCCC
10/12/12
page 2 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Simple Probability and Sample Spaces
Area models of geometric figures can be used to represent simple probabilities. The whole figure
represents the total number of possible outcomes and the shaded part represents the desired
outcomes. Figures can be broken up into equal sections or areas can be calculated and
compared.
31. What simple probability is represented by each of the following area models? Assume divided
sections within a figure are equal in area.
45
__________
__________
__________
32. Split the rectangle into equal sections to represent a probability of 0.2.
33. Split the circle into equal sections to represent a probability of 75%.
34. What is the probability that a randomly dropped penny would fall inside the square grid, but
outside the shaded rectangular region?
©2012, TESCCC
10/12/12
page 3 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Composite Events and Problem-Solving Strategies KEY
Solve problems using the strategy of systematically organizing data, including using tree
diagrams, lists, tables, and acting it out.
A standard deck of cards (without jokers) has 52 cards.
There are 4 “suits”: hearts ♥ (red), diamonds ♦ (red), clubs ♣
(black), and spades ♠ (black). Each suit has cards numbered
2 through 10, a Jack, a Queen, a King, and an Ace.
Box A
Box B
Box C
Answer each question. Support your answer with a tree diagram, a list, or an explanation. For probability of composite
events, justify the individual simple probability numbers that you use to obtain the desired probability of the composite
events. Show your “thought processes” and support for your answer choices on another sheet of paper.
1. What is the probability of randomly picking shapes and getting a non-quadrilateral from Box A
3
2
2
and a polygon from Box C?
=
•
7
3
7
2. What is the probability of randomly picking shapes and getting a heart from Box B and a
3
3
9
regular polygon from Box A?
•
=
5
7
35
3. What is the probability of drawing a non-polygon from Box C (with your eyes closed) and
1
1
1
getting tails when you flip a fair coin once?
•
=
2
6
3
4. What is the probability of closing your eyes and picking a quadrilateral from Box A and picking
4
3
12
a heart from Box B?
•
=
7
5
35
5. What is the probability of closing your eyes and picking a polygon from Box C and a trapezoid
2
1
2
from Box A?
=
•
3
7
21
6. What is the probability of closing your eyes and picking a regular polygon from Box A and a
3
2
6
non-heart from Box B?
•
=
7
5
35
©2012, TESCCC
05/01/13
page 1 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Composite Events and Problem-Solving Strategies KEY
7. What is the probability of closing your eyes and picking a rhombus from Box A and a non2
2
1
polygon from Box C?
•
=
3
21
7
8. What is the probability of getting Tails when you flip a fair coin once and picking a regular
3
1
3
polygon Box A (with your eyes closed)?
•
=
7
2
14
9. What is the probability of rolling a double five with one roll of a pair of fair number cubes (1-6)?
1 1 1
• =
6 6 36
10. What is the probability of rolling a “3” with one roll of a fair number cube (1-6) and getting
1
1 1
1
heads-heads when you flip a fair coin twice?
•
• =
6
2 2
24
11. What is the probability of not rolling a 5 on a fair number cube?
5
6
12. What is the probability of drawing 5 queens from a standard deck of cards? 0
13. What is the probability of getting heads when you flip a fair coin once and drawing an ace of
1
1
1
spades when you draw one card from a standard deck of cards?
=
•
2
52
104
14. What is the probability of getting a sum of 13 with one roll of a pair of fair number cubes (1-6)?
0
15. What is the probability of getting an Ace and then another Ace, if you draw two cards from a
4
3
1
standard deck WITHOUT REPLACING the 1st card?
•
=
52
51 221
©2012, TESCCC
05/01/13
page 2 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Composite Events and Problem-Solving Strategies KEY
16. Stephanie, Bryana, and Jackie went to McDonald’s® for breakfast. McDonald’s® had a
breakfast special deal which included one main entrée, one side item, and one drink for $1.99.
The two choices for the main entrée were pancakes or eggs; the three side dish choices were
hash browns, bacon, or sausage; the two drink options were apple juice or milk.
How many different breakfast special deal combinations are possible? 12
Illustrate your answer by completing a tree diagram showing all possible combinations, a TChart showing all possible combinations, and a list showing all possible combinations, THEN
answer the related questions. 12
Sides
Drinks
Apple
Hash Browns
pancakes
Main Entrée
Bacon
Milk
Apple
Milk
Apple
Sausage
Milk
Apple
Hash Browns
eggs
Bacon
Milk
Apple
Milk
Apple
Sausage
List showing ALL possible
combinations (outcomes)
Pancakes, Hash Browns, Apple
Pancakes, Hash Browns, Milk
Pancakes, Bacon, Apple
Pancakes, Bacon, Milk
Pancakes, Sausage, Apple
Pancakes, Sausage, Milk
Eggs, Hash Browns, Apple
Eggs, Hash Browns, Milk
Eggs, Bacon, Apple
Eggs, Bacon, Milk
Eggs, Sausage, Apple
Eggs, Sausage, Milk
Milk
To make a T-Chart showing all combinations, list
the items in 1 category across the top of the
columns of the T-Chart, then just do simpler
combinations with the remaining categories.
pancakes
Hash Brown, Apple
Hash Brown, Milk
Bacon, Apple
Bacon, Milk
Sausage, Apple
Sausage, Milk
©2012, TESCCC
eggs
Hash Brown, Apple
Hash Brown, Milk
Bacon, Apple
Bacon, Milk
Sausage, Apple
Sausage, Milk
If McDonald’s® has one of each possible meal
bagged on the counter and each girl picks one at
random, what is the probability that. . .
4
1
 Stephanie’s meal contains bacon?
=
12
3
6
1
 Bryana’s meal contains pancakes?
=
12
2
 Jackie’s meal contains bacon & pancakes?
2
1
=
12
6
05/01/13
page 3 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Composite Events and Problem-Solving Strategies
Solve problems using the strategy of systematically organizing data, including using tree
diagrams, lists, tables, and acting it out.
A standard deck of cards (without jokers) has 52 cards.
There are 4 “suits”: hearts ♥ (red), diamonds ♦ (red), clubs ♣
(black), and spades ♠ (black). Each suit has cards numbered
2 through 10, a Jack, a Queen, a King, and an Ace.
Box A
Box B
Box C
Answer each question. Support your answer with a tree diagram, a list, or an explanation. For probability of composite
events, justify the individual simple probability numbers that you use to obtain the desired probability of the composite
events. Show your “thought processes” and support for your answer choices on another sheet of paper.
1. What is the probability of randomly picking shapes and getting a non-quadrilateral from Box A
and a polygon from Box C?
2. What is the probability of randomly picking shapes and getting a heart from Box B and a
regular polygon from Box A?
3. What is the probability of drawing a non-polygon from Box C (with your eyes closed) and
getting tails when you flip a fair coin once?
4. What is the probability of closing your eyes and picking a quadrilateral from Box A and picking
a heart from Box B?
5. What is the probability of closing your eyes and picking a polygon from Box C and a trapezoid
from Box A?
6. What is the probability of closing your eyes and picking a regular polygon from Box A and a
non-heart from Box B?
©2012, TESCCC
10/12/12
page 1 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Composite Events and Problem-Solving Strategies
7.
7. What is the probability of closing your eyes and picking a rhombus from Box A and a nonpolygon from Box C?
8. What is the probability of getting Tails when you flip a fair coin once and picking a regular
polygon Box A (with your eyes closed)?
9. What is the probability of rolling a double five with one roll of a pair of fair number cubes (1-6)?
10. What is the probability of rolling a “3” with one roll of a fair number cube (1-6) and getting
heads-heads when you flip a fair coin twice?
11. What is the probability of not rolling a 5 on a fair number cube (1-6)?
12. What is the probability of drawing 5 queens from a standard deck of cards?
13. What is the probability of getting heads when you flip a fair coin once and drawing an ace of
spades when you draw one card from a standard deck of cards?
14. What is the probability of getting a sum of 13 with one roll of a pair of fair number cubes (1-6)?
15. What is the probability of getting an “Ace”, if you draw two cards from a standard deck
WITHOUT REPLACING the 1st card?
©2012, TESCCC
10/12/12
page 2 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Composite Events and Problem-Solving Strategies
16. Stephanie, Bryana, and Jackie went to McDonald’s® for breakfast. McDonald’s® had a
breakfast special deal which included one main entrée, one side item, and one drink for $1.99.
The choices for the main entrée were pancakes or eggs; the three side dish choices were hash
browns, bacon, or sausage; drink options were apple juice or milk.
How many different breakfast special deal combinations are possible?
Illustrate your answer by completing a tree diagram showing all possible combinations, a TChart showing all possible combinations, and a list showing all possible combinations, THEN
answer the related questions.
Sides
Drinks
List showing ALL possible
combinations (outcomes)
Main Entrée
pancakes
eggs
To make a T-Chart showing all combinations, list
the items in 1 category across the top of the
columns of the T-Chart, then just do simpler
combinations with the remaining categories.
pancakes
eggs
If McDonald’s® has one of each possible meal
bagged on the counter and each girl picks one at
random, what is the probability that. . .
 Stephanie’s meal contains bacon?
 Bryana’s meal contains pancakes?
 Jackie’s meal contains bacon & pancakes?
©2012, TESCCC
10/12/12
page 3 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Composite Events and Problem-Solving Practice KEY
1.
Henry’s mom had 3 types of bread: white, wheat, and sourdough; 3 types of lunchmeat: ham,
turkey, and chicken; 2 types of cheese: American and Cheddar. (She only has Miracle Whip®,
so Henry won’t get a choice of dressing.) Henry’s sandwich will have 1 type bread, 1 type of
meat, and 1 type of cheese.
How many different types of sandwiches can Henry’s mom build for him for his lunch? 18
Illustrate your answer by completing the tree diagram showing all possible combinations, a TChart showing all possible combinations, and a list showing all possible combinations, THEN
answer the related questions.
meat
Ham
Turkey
White
bread
Chicken
Ham
Turkey
Wheat
Chicken
Sourdough
Ham
Turkey
Chicken
List showing ALL possible
combinations (outcomes)
cheese
White, Ham, American
White, Ham, Cheddar
White, Turkey, American
White, Turkey, Cheddar
White, Chicken, American
White, Chicken, Cheddar
Wheat, Ham, American
Wheat, Ham, Cheddar
Wheat, Turkey, American
Wheat, Turkey, Cheddar
Wheat, Chicken, American
Wheat, Chicken, Cheddar
Sourdough, Ham, American
Sourdough, Ham, Cheddar
Sourdough, Turkey, American
Sourdough, Turkey, Cheddar
Sourdough, Chicken, American
Sourdough, Chicken, Cheddar
American
Cheddar
American
Cheddar
American
Cheddar
American
Cheddar
American
Cheddar
American
Cheddar
American
Cheddar
American
Cheddar
American
Cheddar
To make a T-Chart showing all combinations, list
the items in 1 category across the top of the
columns of the T-Chart; then just do simpler
combinations with the remaining categories.
white
H, A
H, C
T, A
T, C
C, A
C, C
wheat
H, A
H, C
T, A
T, C
C, A
C, C
s-dough
H, A
H, C
T, A
T, C
C, A
C, C
What is the probability that Henry’s
sandwich will have. . .
 Chicken?
 White Bread?
 Cheddar Cheese?
 Chicken and Cheddar Cheese?
 Chicken and Cheddar Cheese and White Bread?
rd
If a 3 cheese option (Swiss) is added, then the number of
different sandwiches becomes 27.
©2012, TESCCC
10/12/12
page 1 of 1
Grade 8
Mathematics
Unit: 08 Lesson: 01
Composite Events and Problem Solving Practice
1. Henry’s mom had 3 types of bread: white, wheat, and sourdough; 3 types of lunchmeat: ham,
turkey, and chicken; 2 types of cheese: American and Cheddar. (She only has Miracle Whip®, so
Henry won’t get a choice of dressing.) Henry’s sandwich will have 1 type bread, 1 type of meat,
and 1 type of cheese.
How many different types of sandwiches can Henry’s mom build for him for his lunch?
Illustrate your answer by completing the tree diagram showing all possible combinations, a TChart showing all possible combinations, and a list showing all possible combinations, THEN
answer the related questions.
List showing ALL possible
combinations (outcomes)
cheese
bread
meat
To make a T-Chart showing all combinations, list
the items in 1 category across the top of the
columns of the T-Chart, then just do simpler
combinations with the remaining categories.
white
wheat
What is the probability that Henry’s
sandwich will have. . .
s-dough
 Chicken?
 White Bread?
 Cheddar Cheese?
 Chicken & Cheddar Cheese?
 Chicken & Cheddar Cheese & White Bread?
rd
If a 3 cheese option (Swiss) is added, then the number of
different sandwiches becomes ____.
©2012, TESCCC
10/12/12
page 1 of 1
Grade 8
Mathematics
Unit: 08 Lesson: 01
Looking at the Third Dimension KEY
In Mr. Dimension’s math class, each student is given a set of three-dimensional figure cards to cut
out. The three-dimensional figure cards are either shaded or not shaded as shown above. Sylvia and
Arvis each cut out their cards and put them in their own brown paper bag. You and your partner need
to do the same.
Answer the following questions.
1. Arvis draws a three-dimensional card from his bag and then Sylvia draws a three-dimensional
card from her bag. If they each draw from the bag 50 times and replace the three-dimensional
cards each time before drawing again, how many times would Arvis be expected to draw a
shaded three-dimensional figure and Sylvia draw a pyramid?
Multiply the probabilities. P(drawing a shaded three-dimensional figure from Arvis’s bag) ●
5 2 5
 
P(drawing a pyramid from Sylvia’s bag) =
8 8 32
5
250
If the experiment is conducted 50 times, multiply the probability by 50. 50●
=
= 7.8125
32
32
2. Model the experiment with your partner with one of you acting as Arvis and the other acting as
Sylvia. What happens in your experiment with your partner? Did you get the same results?
Why or why not?
Answers will vary.
3. Arvis draws twice from his bag of three-dimensional cards and after the first draw he does not
put the three-dimensional cards back in the bag. Predict the number of times that he might
draw a prism and then a pyramid if he conducts the experiment 25 times?
1
The probability of pulling a prism the first time is 2 out of 8 or .
4
If the three-dimensional figure is not replaced, there are now 7 three-dimensional figures in the
bag. The probability of pulling a pyramid is now 2 out of 7, because there could be 2 pyramids
left in the bag.
1 2 2
1
1
 

 1.8
If Arvis conducts the experiment 25 times, 25●
4 7 28 14
14
©2012, TESCCC
10/12/12
page 1 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Looking at the Third Dimension KEY
4. Four of the students each put five of their three-dimensional cards into the same bag. They do
not tell which of the three-dimensional figures they placed into the bag. They conduct an
experiment to see if they can tell which of the three-dimensional figures were placed in the bag
by drawing a card out 100 times with replacement. The results are shown below. Predict the
contents of the bag. Justify your reasoning.
Type
Number
of times
drawn
Probability
14
14
7

100 50
9
9
100
12
12
3

100 25
22
22 11

100 50
5
5
1

100 20
10
10
1

100 10
0
28
0
28
7

100 25
Now multiply each by 20. This is the number of three-dimensional figures in the bag.
7
 20  2.8  3
Cylinder =
50
9
 20  1.8  2
Triangular Prism =
100
3
 20  2.4  2
Three-dimensional Heart =
25
11
 20  4.4  4
Rectangular Prism =
50
1
 20  1
Triangular Pyramid =
20
1
 20  2
Rectangular Pyramid =
10
Cone = 0
7
 20  5.6  6
Sphere =
25
All of these values should sum to approximately 20, since there are 20 three-dimensional figures in
the bag.
©2012, TESCCC
10/12/12
page 2 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Looking at the Third Dimension KEY
5. Working with another pair, do the experiment and afterwards predict what is in the bag.
Type
Number
of times
drawn
ANSWERS MAY VARY
Use the space below to show your work.
Answers may vary.
6. Twelve of the students in the class place all of their three-dimensional cards into a bag. What
is the probability of drawing a prism? They are asked to remove 24 three-dimensional cards
from the bag. How can they do this so that the probability of drawing a prism remains the
same?
There are 12 groups of 8 or 96 three-dimensional figures in the bag. In each group, there are 2
prisms, one shaded and one not shaded. There are 24 prisms in the bag. So the probability of
24 1
 . Twenty-four of the cards must be removed with exactly six of these
drawing a prism is
96 4
being prisms and the other eighteen being any of the other three-dimensional figures.
©2012, TESCCC
10/12/12
page 3 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Looking at the Third Dimension
In Mr. Dimension’s math class each student is given a set of three dimensional figure cards to cut out.
The three-dimensional cards are either shaded or not shaded, as shown above. Sylvia and Arvis cut
out each of their cards and put them in their own brown paper bag. You and your partner need to do
the same.
Answer the following questions.
1. Arvis draws a three-dimensional card from his bag and then Sylvia draws a three-dimensional
card from her bag. If they each draw from the bag 50 times and replace the three-dimensional
cards each time before drawing again, how many times would Arvis be expected to draw a
shaded three-dimensional figure and Sylvia draw a pyramid?
2. Model the experiment with your partner with one of you acting as Arvis and the other acting as
Sylvia. What happens in your experiment with your partner? Did you get the same results?
Why or why not?
3. Arvis draws twice from his bag of three-dimensional cards and after the first draw he does not
put the three-dimensional cards back in the bag. Predict the number of times that he might
draw a prism and then a pyramid if he conducts the experiment 25 times?
©2012, TESCCC
10/12/12
page 1 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Looking at the Third Dimension
4. Four of the students each put five of their three-dimensional cards into the same bag. They do
not tell which of the three-dimensional figures they placed into the bag. They conduct an
experiment to see if they can tell which of the three-dimensional figures were placed in the bag
by drawing a card out 100 times with replacement. The results are shown below. Predict the
contents of the bag. Justify your reasoning.
Type
Number
of times
drawn
Probability
©2012, TESCCC
14
14
7

100 50
9
9
100
12
12
3

100 25
22
22 11

100 50
10/12/12
5
5
1

100 20
10
10
1

100 10
0
28
0
28
7

100 25
page 2 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Looking at the Third Dimension
5. Working with another pair, do the experiment and afterwards predict what is in the bag.
Type
Number
of times
drawn
Use the space below to show your work.
6. Twelve of the students in the class place all of their three-dimensional cards into a bag. What
is the probability of drawing a prism? They’re asked to remove 24 three-dimensional cards
from the bag. How can they do this so that the probability of drawing a prism remains the
same?
©2012, TESCCC
10/12/12
page 3 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Find the Probabilities of Dependent and Independent Events KEY
1. A spinner and a fair number cube are used in a bet. The spinner has an equal chance of
landing on 1 of 4 colors: purple, green, blue, or yellow. The faces of the cube are labeled 1
through 6. What is the probability of a player spinning the color green and then rolling a 5 or 6?
Sample Space: purple: 1, 2, 3, 4, 5, 6, green: 1, 2, 3, 4, 5, 6, blue: 1, 2, 3, 4, 5, 6, yellow: 1, 2,
3, 4, 5, 6
1
2
1
•
=
4
6 12
3
A.
10
1
B.
8
1
C.
12
1
D.
24
2. Diana has a box containing 6 blue, 8 red, 5 purple, 9 green, and 2 clear marbles that are all the
same size and shape. What is the probability of randomly choosing a clear marble on the first
pick, replacing it, and then randomly choosing a purple marble on the second pick?
1
A.
6
1
B.
15
1
C.
87
1
2
5
1
•
=
D.
:
30
90
90 30
3. If Diana uses the same box of marbles, but this time in her experiment she does not replace
the marble, what is the probability of randomly choosing a clear marble on the first pick and
then randomly choosing a purple marble on the second pick?
1
A.
6
1
B.
15
1
2
5
1
•
=
C.
:
87 30
29
87
1
D.
90
©2012, TESCCC
05/04/13
page 1 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Find the Probabilities of Dependent and Independent Events KEY
4. Ryan tosses 4 fair coins. What is the probability that all four coins will land tails up?
1 1 1 1 1 1
: • • • =
A
16 2 2 2 2 16
1
B
8
1
C
4
1
D
2
5. In the spinner below, the pointer stopped on the blank region. What color should the blank
1
region be so that the probability of the pointer landing on this color is ?
2
Pink
Red
Green
Blue
Red
Blue
A
B
C
D
©2012, TESCCC
Red
Red
White
Blue
Green
05/04/13
page 2 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Find the Probabilities of Dependent and Independent Events KEY
6. The probability of a football being defective is
1
. About how many footballs would be
10
defective in a shipment of 725 footballs?
A 1
1
• 725 = 72.5
B 7
10
C 73
D 80
7. The results of a magazine survey showed that 42 out of 80 people plan to vote for Mr. Smith
for President. Which is the best prediction of the total number of votes he will receive if 2,000
people vote?
A 25
42
21 21 • 50
1050
B 50
=
;
=
80
40 40 • 50
2000
C 120
D 1,000
8. Charlotte took a math test. There were 15 questions of which she answered 3 incorrectly. At
this rate, how many questions should Charlotte expect to answer incorrectly if she answers a
total of 135 questions?
A 45
3 • 9
27
=
B 27
15 • 9 135
C 9
D 5
9. Jose and Vidal each have a bag containing 4 blue, 2 red, 1 yellow, and 3 green marbles. Jose
replaces marbles after each draw. Vidal does not replace marbles after each draw. Find the
probability of Jose drawing a red and then a green marble. Find the probability of Vidal drawing
a red and then a green marble. Write a summary that explains why the probabilities are
different and which simulation illustrates independent probability and which simulation
illustrates dependent probability.
2 3
3
2 3 1
•
=
= 0.06 Vidal P(red and then green) =
• =
≈ 0.067
10 10 50
10 9 15
Answers vary. Sample: The simulation for Jose represents independent probability, because he
replaced the marbles and the first draw does not impact the probability on the second draw. Jose’s
probability of success will be less because he has more marbles to draw from when trying to get the
green. The simulation for Vidal represents dependent probability, because he does not replace the
marble he first draws. This impacts the probability of the second draw, because there will only be nine
marbles remaining in the bag. This will give him a greater probability of success on the second draw.
Jose P(red and then green) =
10. Sara and Laura each have a bag containing 2 blue, 3 red, 4 yellow, and 1 green marbles. Sara
replaces marbles after each draw. Laura does not replace marbles after each draw. Find the
probability of Sara of drawing a red and then another red marble. Find the probability of Laura
drawing a red and then another red marble.
Sara P(red and then red) =
3 3
9
•
=
= 0.09
10 10 100
Laura P(red and then red) =
3 2 1
• =
≈ 0.067
10 9 15
Since Laura does not replace the marble, there is one less red marble after the first marble is chosen.
Therefore, when Laura chooses the second marble, there are only 2 red marbles left, and only 9
marbles in total.
©2012, TESCCC
05/04/13
page 3 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Find the Probabilities of Dependent and Independent Events
1. A spinner and a fair number cube are used in a bet. The spinner has an equal chance of
landing on 1 of 4 colors: purple, green, blue, or yellow. The faces of the cube are labeled 1
through 6. What is the probability of a player spinning the color green and then rolling a 5 or 6?
3
A
10
1
B
8
1
C
12
1
D
24
2. Diana has a box containing 6 blue, 8 red, 5 purple, 9 green, and 2 clear marbles that are all the
same size and shape. What is the probability of randomly choosing a clear marble on the first
pick, replacing it, and then randomly choosing a purple marble on the second pick?
1
A
6
1
B
15
1
C
87
1
D
90
3. If Diana uses the same box of marbles, but this time in her experiment she does not replace
the marble, what is the probability of randomly choosing a clear marble on the first pick and
then randomly choosing a purple marble on the second pick?
1
A
6
1
B
15
1
C
87
1
D
90
©2012, TESCCC
05/04/13
page 1 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Find the Probabilities of Dependent and Independent Events
4. Ryan tosses 4 fair coins. What is the probability that all four coins will land tails up?
1
A
16
1
B
8
1
C
4
1
D
2
5. In the spinner below, the pointer stopped on the blank region. What color should the blank
1
region be so that the probability of the pointer landing on this color is ?
2
Pink
Red
Green
Blue
Red
Blue
A
B
C
D
Red
Red
White
Blue
Green
©2012, TESCCC
05/04/13
page 2 of 3
Grade 8
Mathematics
Unit: 08 Lesson: 01
Find the Probabilities of Dependent and Independent Events
6. The probability of a football being defective is
1
. About how many footballs would be
10
defective in a shipment of 725 footballs?
A
B
C
D
1
7
73
80
7. The results of a magazine survey showed that 42 out of 80 people plan to vote for Mr. Smith
for President. Which is the best prediction of the total number of votes he will receive if 2,000
people vote?
A
B
C
D
25
50
120
1,000
8. Charlotte took a math test. There were 15 questions of which she answered 3 incorrectly. At
this rate, how many questions should Charlotte expect to answer incorrectly if she answers a
total of 135 questions?
A
B
C
D
45
27
9
5
9. Jose and Vidal each have a bag containing 4 blue, 2 red, 1 yellow, and 3 green marbles. Jose
replaces marbles after each draw. Vidal does not replace marbles after each draw. Find the
probability of Jose drawing a red and then a green marble. Find the probability of Vidal drawing
a red and then a green marble. Write a summary that explains why the probabilities are
different and which simulation illustrates independent probability and which simulation
illustrates dependent probability.
10. Sara and Laura each have a bag containing 2 blue, 3 red, 4 yellow, and 1 green marbles. Sara
replaces marbles after each draw. Laura does not replace marbles after each draw. Find the
probability of Sara drawing a red and then another red marble. Find the probability of Laura
drawing a red and then another red marble.
©2012, TESCCC
05/04/13
page 3 of 3