Download Unit 5 - Cleburne Independent School District

Grade 7- Pre- AP
Math Unit 5
Title
Suggested Time Frame
Time Frame : 4th & 5th 6 Weeks
Suggested Duration : 20 Days
Probability
CISD Safety Net Standards: 7.6I
Big Ideas/Enduring Understandings
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Guiding Questions
The way a set of data is displayed influences its interpretation.
Central tendency and range can be used to describe a set of
data.
A physical or mathematical model can be used to describe the
experimental and theoretical probability of real-life events.
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How can I use multiple representations to determine the number
of outcomes for an action?
• How can you predict the outcome of future events?
• How can I select tools and techniques to determine if a game is
fair?
• To what extent does the way a graph is displayed influence the
interpretation of the graph?
• What is the most efficient way to use central tendency and range
to describe data?
• How are types of models used to describe probability of real-life
events?
Vertical Alignment Expectations
*TEKS one level below*
*TEKS one level above*
TEA Vertical Alignment 5th Grade – Algebra I
Sample Assessment Question
Coming Soon……………………………………………………..
CISD 7th Math Pre-AP Unit 5
Updated November 30, 2016
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Grade 7- Pre- AP
Math Unit 5
The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper
depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the
suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the
district curriculum. Some resources are protected by copyright. A username and password is required to view the copyrighted material. A portion of the District Specificity and
Examples are a product of the Austin Area Math Supervisors TEKS Clarifying Documents available on the Region XI Math website.
Ongoing TEKS
Math Processing Skills
7.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The
student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
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Focus is on application
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Students should assess which tool to apply rather than trying only one
or all
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Students should evaluate the effectiveness of representations to ensure
they are communicating mathematical ideas clearly
Students are expected to use appropriate mathematical vocabulary and
phrasing when communicating ideas
Students are expected to form conjectures based on patterns or sets of
examples and non-examples
(B) use a problem-solving model that incorporates analyzing given information, formulating a
plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
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(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
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(G) display, explain, and justify mathematical ideas and arguments using precise mathematical
language in written or oral communication
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CISD 7th Math Pre-AP Unit 5
Updated November 30, 2016
Precise mathematical language is expected.
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Grade 7- Pre- AP
Math Unit 5
Knowledge and Skills
with Student
Expectations
7.6 Proportionality –
The student applies
mathematical process
standards to use
probability and
statistics to describe or
solve problems involving
proportional
relationships. The
student is expected to:
District Specificity/ Examples
Supplemental Vocabulary: Simple experiment, Composite
experiment, Qualitative, Quantitative Complement, Prediction(s),
Experimental data, Frequency tables, Independent event,
Dependent event, Simple event
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•7.6A represent
sample spaces for
simple and compound
events using lists and
tree diagrams
Supporting Standard
•7.6B select and use
different simulations to
represent simple and
compound events with
CISD 7th Math Pre-AP Unit 5
Updated November 30, 2016
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Analyze and solve problems using concepts of probability and
statistics.
Construct sample spaces for simple and composite
experiments using tree diagrams, tables and organized lists.
Determine the probability of an independent event and
dependent events.
Compare theoretical and experimental probabilities.
Determine differences between experimental and theoretical
probabilities.
Find the probability of a simple event and its complement to
add up to 1 or 100%.
Ex: 1/6 (simple event) + 5/6 (complement) = 1 whole
Use qualitative (impossible, unlikely, possible, as likely as not,
certain) and quantitative (numbers) predictions from
experiments.
Determine an appropriate graphical representation: bar
graph, circle graph, line plots (dot plot), Venn diagram, and
box plot.
Select and construct bar graphs to compare sets of data.
Select and sketch circle graphs to show parts of a whole and
part to part comparisons.
Vocabulary
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Compound event
List
Probability
proportional
reasoning
sample space
simple event
tree diagram
experiment
simulation
experimental data
theoretical
probability
experimental
probability
complement
Suggested Resources
Resources listed and categorized to
indicate suggested uses. Any
additional resources must be aligned
with the TEKS.
Textbook Resources:
McGraw Hill Ch 5
Web Resources:
• Probability Overview
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Probability Explained
(Videos)
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Compound
Independent Events
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Dependent
Probability
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Working with Tree
Diagrams
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Binomial Distribution
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Supreme Court
Handshake
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and without technology
Supporting Standard
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•7.6C make predictions •
and determine solutions
using experimental data •
for simple and
compound events
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Supporting Standard
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•7.6D make predictions
and determine solutions •
using theoretical
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probability for simple
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and compound events
Supporting Standard
•7.6E find the
probabilities of a simple
event and its
complement and
describe the
relationship between
the two Supporting
Standard
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Grade 7- Pre- AP
Math Unit 5
Justify the selection of a graphical representation.
Draw conclusions or make inferences based on an analysis of
the given or collected data.
Support conclusions based on an analysis of data with
convincing arguments.
Use vocabulary appropriate to communicate the conclusion
drawn.
Analyze and solve problems using concepts of probability and
statistics.
Calculate or identify the median to describe the middle
number.
Determine the range to describe the spread of the data.
Use the median to describe the middle number.
Construct a table from a Venn diagram and a Venn diagram
from a table.
Construct sample spaces for simple and composite
experiments using tree diagrams, tables and organized lists.
Determine the probability of an independent event and
dependent events.
Compare theoretical and experimental probabilities.
Describe the relationship between the probability of a simple
event and its complement.
7.6ABCDEFGHI
Students will recognize an appropriate design for conducting an
•7.6F use data from a
experiment with simple probability events, understanding that
random sample to make
the experimental data give realistic estimates of the probability of
inferences about a
an event but are affected by sample size. Students use tree
population Supporting
diagrams, frequency tables, and organized lists, and simulations
Standard
to determine the probability of simple and compound events.
CISD 7th Math Pre-AP Unit 5
Updated November 30, 2016
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•7.6G solve problems
using data represented
in bar graphs, dot plots,
and circle graphs,
including part-to-whole
and part-to-part
comparisons and
equivalents Readiness
Standard
•7.6H solve problems
using qualitative and
quantitative predictions
and comparisons from
simple experiments
Readiness Standard
*CISD Safety Net*
•7.6I determine
experimental and
theoretical probabilities
related to simple and
compound events using
data and sample spaces
Readiness Standard
CISD 7th Math Pre-AP Unit 5
Updated November 30, 2016
Example 1: (7.6 I)
Jason is tossing a fair coin. He tosses the coin ten times and it
lands on heads eight times. If Jason tosses the coin an eleventh
time, what is the probability that it will land on heads?
Grade 7- Pre- AP
Math Unit 5
Example 2: (7.6 A)
How many ways could the 3 students, Amy, Brenda, and Carla,
come in 1st, 2nd and 3rd place?
Represent this information using a list and tree diagram.
Example 3: (7.6 C)
Conduct an experiment using a Styrofoam cup by tossing the cup
and recording how it lands.
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How many trials were conducted?
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How many times did it land right side up?
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How many times did it land upside down/
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How many times did it land on its side?
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Determine the probability for each of the above results
Solution:
Making an organized list will identify that there are 6 ways for the
students to win a race A, B, C
A, C, B
B, C, A
B, A, C
C, A, B
C, B, A
Example 4: (7.6 I)
Students conduct a bag pull experiment. A bag contains 5
marbles. There is one red marble, two blue marbles and two
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purple marbles. Students will draw one marble without
replacement and then draw another. What is the sample space
for this situation? Explain how the sample space was determined
and how it is used to find the probability of drawing one blue
marble followed by another blue marble.
Grade 7- Pre- AP
Math Unit 5
Example 5: (7.6 D)
A fair coin will be tossed three times. What is the probability that
two heads and one tail in any order will results?
Solution:
HHT, HTH and THH so the probability would be ⅜ .
Misconceptions:
• Vocabulary related to probability is frequently used in the
“real-world” but not necessarily in the true mathematical
meanings, for example probability and odds are often used
interchangeably
CISD 7th Math Pre-AP Unit 5
Updated November 30, 2016
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