Download Regional Integrated Algebra Curriculum

Regional Integrated Algebra Curriculum
UNIT: Set Theory and Probability
TOPIC: Set Theory
Timeframe for Unit: 12 days
Timeframe for Topic: 2 days
7th Grade Prior Knowledge
None specific to set theory
Contents Strand
A.A.29
Use set-builder notation and/or interval notation to illustrate the elements of a
set, given the elements in roster form
A.A.30
Find the complement of a subset of a given set, within a given universe
A.A.31
Find the intersection of sets (no more than three sets) and/or union of sets
(no more than three sets)
Concepts
Subsets of Real Numbers
Set builder and/or interval notation {x | x > 4}
Roster notation
Universal Set
Complement
Null Set
Union
Intersection
Venn diagrams
Essential Questions
What is the difference between the null set and a solution set of {x | x=0} ?
What are the main concepts of Set Theory and how do they apply to real life?
What is the difference between union and intersections of sets?
Process/Skills
A.PS.3
Observe and explain patterns to formulate generalizations and conjectures
A.RP.11 Use a Venn diagram to support a logical argument
A.CM.2
Use mathematical representations to communicate with appropriate accuracy,
including numerical tables, formulas, functions, equations, charts, graphs,
Venn diagrams, and other diagrams
A.CN.3
Model situations mathematically, using representations to draw conclusions
and formulate new situations
A.R.2
Recognize, compare, and use an array of representational forms
Vocabulary
Complement
Intersection
Null
Roster
Union
Universal Set
Suggested assessments
Formal
Pre-assessment
Regents/state exams
Tests and quizzes
a. T/F
b. Multiple choice
c. Constructed response
See Blackboard for specific Assessments
Resources
Informal
Projects
Class participation, discussions
On-spot checks of classwork
Ticket-out-the-door
Regional Integrated Algebra Curriculum
UNIT: Set Theory and Probability
TOPIC: Probability
Timeframe for Units: 12 Days
Timeframe for Topic: 7 days
7th Grade Prior Knowledge
7.S.8
Interpret data to provide the basis for predictions and to establish experimental
probabilities
7.S.9
Determine the validity of sampling methods to predict outcomes
7.S.10
Predict the outcome of an experiment
7.S.11
Design and conduct an experiment to test populations
7.S.12
Compare actual results to predicted results
Content Strands
A.S.18
Know the definition of conditional probability and use it to solve for
probabilities in finite sample spaces
A.S.19
Determine the number of elements in a sample space and the number of
favorable events
A.S.20
Calculate the probability of an event and its complement
A.S.21
Determine empirical probabilities based on specific sample data
A.S.22
Determine, based on calculated probability of a set of events, if:
some or all are equally likely to occur
one is more likely to occur than another
whether or not an event is certain to happen or not to happen
A.S.23
Calculate the probability of:
a series of independent events
a series of dependent events
two mutually exclusive events
two events that are not mutually exclusive
A.N.7
Determine the number of possible events, using counting techniques or the
Fundamental Principle of Counting
Concepts
Sample Space
Simple Probability of a Single Event
Probability With “ And” (Single Event)
Probability With “Or” (Single Event)
Complement
Empirical Probability (Based on specific sample data)
Impossible Events
Certain Events
Counting Principle
Replacement
Mutually exclusive
Essential Questions
Why do you use the Counting Principle? Why are the probabilities of events different?
Why does a dependent event differ from an independent event? Why can the words
“and/or” be associated with the mathematical operations of addition and multiplication?
Process/Skills
A.PS.3
Observe and explain patterns to formulate generalizations and conjectures
A.RP.11 Use a Venn diagram to support a logical argument
A.CM.2
Use mathematical representations to communicate with appropriate accuracy,
including numerical tables, formulas, functions, equations, charts, graphs,
Venn diagrams, and other diagrams
A.CN.3
Model situations mathematically, using representations to draw conclusions
and formulate new situations
A.R.2
Recognize, compare, and use an array of representational forms
Vocabulary
Appropriateness
Biased
Calculated probability
Conditional probability
Counting methods
Data
Dependent Events
Dependent variable
Independent events
Element
Mutually exclusive events
Empirical probability
Favorable event
Finite sample space
Fundamental Counting Principle
Suggested Assessments
Formal
Pre-assessment
Regents/state exams
Tests and quizzes
a. T/F
b. Multiple choice
c. Constructed response
See Blackboard for specific Assessments
Resources
Informal
Projects
Class participation, discussions
On-spot checks of classwork
Ticket-out-the-door
Regional Integrated Algebra Curriculum
UNIT: Set Theory and Probability
TOPIC: Permutations
Timeframe for Unit: 12 days
Timeframe for Topic: 1 day
7th Grade Prior Knowledge
None specific to permutations
Content Strands
A.N.6
Evaluate expressions involving factorials, absolute values, and exponential
expressions
A.N.7
Determine the number of possible events, using counting techniques or the
Fundamental Counting Principle (FCP)
A.N.8
Determine the number of possible arrangements (permutations) of a list of
items
Concepts
Factorials
FCP
Essential Questions
When do you use factorials? Why do you use the FCP? Why do you use permutations?
What is the difference between the FCP and permutations?
Process/Skills
A.PS.3
Observe and explain patterns to formulate generalizations and conjectures
A.CM.2 Use mathematical representations to communicate with appropriate accuracy,
including numerical tables, formulas, functions, equations, charts, graphs, Venn
diagrams, and other diagrams
A.CN.3 Model situations mathematically, using representations to draw conclusions and
formulate new situations
A.R.2
Recognize, compare, and use an array of representational forms
Vocabulary
Factorials
Permutations
FCP
Suggested assessments
Formal
Pre-assessment
Regents/state exams
Tests and quizzes
a. T/F
b. Multiple choice
c. Constructed response
See Blackboard for specific Assessments
Resources
Informal
Projects
Class participation, discussions
On-spot checks of classwork
Ticket-out-the-door