Download Planned Course: Algebra I Remediation Mifflin County School

Mifflin County School District – Mathematics Department
Planned Course
Planned Course: Algebra I Remediation
Mifflin County School District
2014
Mifflin County School District – Mathematics Department
Planned Course
Glossary of Curriculum
Summative Assessment: Seeks to make an overall judgment of progress made at the end of a defined
period of instruction.
Formative Assessment: Used by teachers and students during instruction to provide feedback to adjust
ongoing teaching and learning to improve students’ achievement of intended instructional outcomes.
Benchmark Assessment: Designed to provide feedback to both the teacher and the student about how
the student is progressing towards demonstrating proficiency on grade level standards.
Diagnostic Assessment: Ascertains, prior to instruction, each student’s strengths, weaknesses,
knowledge, and skills.
Big Ideas: Declarative statements that describe concepts that transcend grade levels. Big Ideas are
essential to provide focus on specific content for all students.
Concepts: Describe what students should know (key knowledge) as a result of this instruction specific to
grade level.
Competencies: Describe what students should be able to do (key skills) as a result of this instruction,
specific to grade level.
Essential Questions: Questions that are specifically linked to the Big Ideas. They should frame student
inquiry, promote critical thinking, and assist in learning transfer.
Assessment Anchor: The Assessment Anchors represent categories of subject matter that anchor the
content of the Keystone Exams. Each Assessment Anchor is part of a module and has one or more
Anchor Descriptors unified under it.
Anchor Descriptor: The Anchor Descriptor level provides further details that delineate the scope of
content covered by the Assessment Anchor. Each Anchor Descriptor is part of an Assessment Anchor and
has one or more Eligible Content unified under it.
Eligible Content: The Eligible Content is the most specific description of the content that is assessed on
the Keystone Exams. This level is considered the assessment limit and helps educators identify the range
of the content covered on the Keystone Exams.
Enhanced Standard: Enhanced Standards correlate to the Eligible Content statement. Some Eligible
Content statements include annotations that indicate certain clarifications about the scope of an eligible
content.
Mifflin County School District – Mathematics Department
Planned Course
Course Description:
Algebra 1 Remediation is a data driven review of Keystone Exam Assessment Anchors and Eligible
Content. The course will use data from the Keystone Exam to identify areas of strength and weakness
for individuals as well as the class and then provide specific content area practice in order to further
develop Algebraic skills. At the conclusion of the course, students will retake the Keystone Algebra 1
Exam.
References:
Algebra I Standards, PA Department of Education
http://www.pdesas.org/Standard/Views#0|0|705|0
Common Core State Standards
http://www.corestandards.org/the-standards/mathematics/high-school-algebra/introduction/
National Council of Teachers of Mathematics
http://www.nctm.org/standards/content.aspx?id=3874
SAT – College Board
http://sat.collegeboard.com/practice/sat-subject-test-preparation/mathematics-level-1
Mifflin County School District – Mathematics Department
Planned Course
Mathematical Practice Standards
Mathematical Practice Standards describes the habits of mind required to reach a level of
mathematical proficiency.
Standards for Mathematical Practice
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Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and make sense of regularity in repeated reasoning.
Mifflin County School District – Mathematics Department
Planned Course
Subject: Algebra I Remediation
Unit Title: Operations with Real Numbers and Expressions
Grade levels: 11
Rational/Summary of Unit
There are some mathematical relationships that are always true. These relationships are used
as the rules of arithmetic and algebra and are useful for writing equivalent forms of
expressions and solving equations and inequalities.
Common Core Standards
Assessment Anchors and Eligible Content
 CC.2.1.8.E.1 Distinguish
between rational and irrational
numbers using their properties.
 A1.1.1.1 Represent and/or use numbers
in equivalent forms (e.g., integers,
fractions, decimals, percents, square
roots, and exponents).
 A1.1.1.1.1 Compare and/or order
any real numbers (rational and
irrational may be mixed).
 A1.1.1.1.2 Simplify square roots
(e.g., √24 = 2√6).
 CC.2.1.8.E.4 Estimate irrational
numbers by comparing them to
rational numbers.
 CC.2.1.HS.F.1 Apply and extend
the properties of exponents to
solve problems with rational
exponents.
 CC.2.1.HS.F.2 Apply properties
of rational and irrational numbers
to solve real world or
mathematical problems.
 CC.2.1.6.E.3 Develop and/or
apply number theory concepts to
find common factors and
multiples.
 CC.2.2.8.B.1 Apply concepts of
radicals and integer exponents to
generate equivalent expressions.
 CC.2.2.7.B.3 Model and solve
real-world and mathematical
problems by using and
connecting numerical, algebraic,
and/or graphical representations.
 A1.1.1.2.1 Apply number theory
concepts to show relationships between
real numbers in problem solving setting.
 A1.1.1.2.1 Find the Greatest
Common Factor (GCF) and/or the
Least Common Multiple (LCM) for
sets of monomials.
 A1.1.1.3 Use exponents, roots, and/or
absolute values to solve problems.
 A1.1.1.3.1 Simplify/evaluate
expressions involving properties/laws
of exponents, roots and/or absolute
value to solve problems (exponents
should be integers from -10 to 10).
 A1.1.1.4 Use estimation strategies in
problem-solving situations.
 A1.1.1.4.1 Use estimation to solve
problems.
Mifflin County School District – Mathematics Department
Planned Course
 CC.2.2.HS.D.9 Use reasoning to
solve equations and justify the
solution method.
 CC.2.2.HS.D.1 Interpret the
structure of expressions to
represent a quantity in terms of
its context.
 CC.2.2.HS.D.2 Write expressions
in equivalent forms to solve
problems.
 CC.2.2.HS.D.3 Extend the
knowledge of arithmetic
operations and apply to
polynomials.
 A1.1.1.5 Simplify expressions involving
polynomials.
 A1.1.1.5.1 Add, subtract and/or
multiply polynomial expressions
(express answers in simplest form –
nothing larger than a binomial
multiplied by a trinomial).
 A1.1.1.5.2 Factor algebraic
expressions, including difference of
squares and trinomials (trinomials
limited to the form ax2+bx+c where a
is equal to 1 after factoring out all
monomial factors).
 A1.1.1.5.3 Simplify/reduce a rational
algebraic expression.
 CC.2.2.HS.D.5 Use polynomial
identities to solve problems.
 CC.2.2.HS.D.6 Extend the
knowledge of rational functions to
rewrite in equivalent forms.
Big Ideas
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Numbers can be expressed and transformed to various equivalent forms.
Factoring can be used to break down composite expressions into primes.
Exponents model real world situations.
Rules are applied to numbers to develop universal precision and accuracy.
Essential Questions
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How can we show that algebraic properties and processes are extensions of arithmetic
properties and processes?
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How can we use algebraic properties and processes to solve problems?
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How do we use rules and properties to simplify algebraic expressions, combine simple
rational and/or polynomial expressions, and/or factor polynomial expressions?
Mifflin County School District – Mathematics Department
Planned Course
Concepts
Students will know…
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Numbers can be represented in
equivalent forms.
Radical numbers can be written in
many forms.
Every set of monomials has a
greatest common factor and a least
common multiple.
Expressions can be simplified
using properties and laws of
exponents, roots, and/or absolute
values.
Estimation is a strategy for
problem solving.
Polynomial expressions can be
simplified.
Factoring is a process to represent
algebraic expressions in equivalent
forms.
Algebraic expressions can be
represented in equivalent forms.
Competencies
Students will be able to…
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Identify irrational numbers at the
approximate location on a number line.
Compare and/or order any real numbers
(rational and irrational may be mixed).
Estimate the value of an irrational
number.
Use prime factorization to rewrite a
composite number (numerical).
Find the square root of an integer to the
nearest tenth using either a calculator or
estimation.
Use perfect square factors to write square
roots in simplest radical form.
Evaluate expressions using substitution
for an unknown quantity and apply the
order of operations (absolute value,
positive & negative exponents, square
roots, power rules).
Simplify expressions involving…
 absolute value
 + and - exponents
 roots
 multiplying with exponents
 powers of powers
 powers of products
(integer exponents from -10 to 10)
Add and subtract polynomial
expressions.
Multiply a monomial by a polynomial
using the distributive property.
Multiply polynomial expressions
(express answers in simplest form –
nothing larger than a binomial multiplied
by a trinomial).
Use prime factorization to rewrite a
composite number (algebraically).
Find the Greatest Common Factor (GCF)
for sets of monomials.
Find the Least Common Multiple (LCM)
for sets of monomials.
Recognize and factor out a GCF, if
applicable.
Mifflin County School District – Mathematics Department
Planned Course
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Absolute value
Algebraic expression
Base
Binomial
Composite number
Difference of squares
Distributive Property
Evaluate
Exponent
Expression
Factor (monomials &
polynomials)
Greatest common factor(GCF)
Integers
Completely factor algebraic expressions
(difference of squares and trinomials:
trinomials limited to the form ax2+bx+c
where a is equal to 1 after factoring out
all monomial factors).
 Simplify and reduce a rational algebraic
expression.
 Use the factoring process to reduce
algebraic expressions.
Vocabulary
Irrational number
Prime factorization
Least common multiple
Prime number
(LCM)
Product of powers
Like terms
Radical expression
Monomial
Rational expression
Natural number
Rational number
Negative exponent
Real number
Number line
Simplest form
Order of operations
Simplify
Perfect square number
Square root
Polynomial
Term
Positive exponent
Trinomial
Powers
Whole number
Power of a power
Evidence of Learning
Formative Assessments
Summative Assessments
Daily Participation
5 min warm ups
Quizzes
Performance Assessment
Anchor Assessments
Resources
KEYSTONE Finish Line
Supplemental Materials on “R:” drive
Kuta Software (search by topic and customize)
Hippo Math
Khan Academy
Other print and digital resources at teacher’s discretion.
Mifflin County School District – Mathematics Department
Planned Course
Subject: Algebra I Remediation
Unit Title: Linear Equations
Grade levels: 11
Rational/Summary of Unit
Represent a linear equation and systems of equations in multiple ways, including tables,
algebraic rules, graphs, and contextual situations and make connections among these
representations.
Choose the appropriate representation to model, solve and interpret problems relating to real
world situations and justify the solution.
Linear inequalities can be used to model real-world situations and can represent various
mathematical relationships.
Common Core Standards
 CC.2.2.8.B.3 Analyze and solve
linear equations and pairs of
simultaneous linear equations.
 CC.2.1.HS.F.3 Apply quantitative
reasoning to choose and interpret
units and scales in formulas,
graphs and data displays.
 CC.2.1.HS.F.4 Use units as a way
to understand problems and to
guide the solution of multi-step
problems.
 CC.2.1.HS.F.5 Choose a level of
accuracy appropriate to limitations
on measurement when reporting
quantities.
 CC.2.2.HS.D.7 Create and graph
equations or inequalities to
describe numbers or relationships.
 CC.2.2.HS.D.8 Apply inverse
operations to solve equations or
formulas for a given variable.
Assessment Anchors and Eligible Content
 A1.1.2.1 Write, solve, and/or graph
linear equations using various methods.
 A1.1.2.1.1 Write, solve and/or apply
a linear equation (including problem
situations).
 A1.1.2.1.2 Use and/or identify an
algebraic property to justify any step
in an equation solving process (linear
equations only).
 A1.1.2.1.3 Interpret solutions to
problems in the context of the
problem situation (linear equations
only).
 A1.1.2.2 Write, solve, and/or graph
systems of linear equations using various
methods.
 A1.1.2.2.1 Write and/or solve a
system of linear equations (including
problem situations) using graphing,
substitution and/or elimination (limit
systems to 2 linear equations).
 A1.1.2.2.2 Interpret solutions to
problems in the context of the
problem situation (systems of 2
linear equations only).
Mifflin County School District – Mathematics Department
Planned Course
 CC.2.2.HS.D.9 Use reasoning to
solve equations and justify the
solution method.
 CC.2.2.HS.D.10 Represent, solve
and interpret equations/inequalities
and systems of
equations/inequalities algebraically
and graphically.
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CC.2.2.HS.C.3 Write functions or
sequences that model relationships
between two quantities.
Big Ideas
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Mathematical operations have inverse operations that “undo” what other operations
perform.
Rules can be applied to equations to determine the input for a given output.
Systems of linear equations can be used to model real world problems.
Essential Questions
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How can we use algebraic properties and processes to solve problems and justify the
solution process?
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How do you decide which linear representation to choose when modeling a real world
situation, and how would you explain and justify your solution to the problem?
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How do you write, solve, graph, and interpret linear equations to model relationships
between quantities?
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How do you write, solve, and interpret systems of two linear equations using various
techniques, and how do you apply them to real world situations?
Concepts
Students will know…
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Algebraic properties can be used to
solve one variable equations in
multiple steps.
Competencies
Students will be able to…
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Identify properties of equality.
 Emphasize Inverse, Identity,
Commutative, Associative (for
solving) & Substitution (for
checking)
Mifflin County School District – Mathematics Department
Planned Course
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Algebraic properties can be used to
manipulate equations to a
particular form (slope intercept,
point-slope, standard).
Linear equations model real world
problems.
Algebraic properties illustrated in
mathematical relationships are
always true.
Linear equations can be used to
model real world problems.
A system of linear equations can
be used to model real world
problems that can be solved in
multiple ways.
Solutions of linear equations can
be used to predict real world
situations.
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Recognize a linear relationship given
data.
Translate between algebraic and verbal
statements.
Write linear equations.
Use properties of equality to solve linear
equations…
 Multi – step
 Variables on both side
 Proportional form
Use the substitution property to check
solutions.
Model real world situations by writing
and solving equations.
Apply linear equations in problem
solving situations.
Solve literal equations (formulas) for a
specified variable.
Model real world situations writing and
solving equations.
Solve a system of equations in two
variables by graphing (manually and
with technology).
Solve a system of equations in two
variables by the substitution method.
Solve a system of equations using linear
combination/elimination method.
Identify the number of solutions to a
system of equations.
 Identify when a system has one
solution, no solution, or infinite
solutions.
Write systems of equations from tables,
graphs and data.
Apply a system of linear equations to
solve word problems.
 Identify which systems of
equations will model the
situation.
 Evaluate reasonability of a
solution and what that tells you
about your solution.
 Identify what the parts of the
ordered pair represent.
Mifflin County School District – Mathematics Department
Planned Course
Additive inverse
Associative Property
Coefficient
Commutative Property
Compound inequality
Constant
Dependent variable
Distributive Property
Vocabulary
Equation
Identity (addition &
multiplication)
Independent variable
Inequality
Inverse operations
Inverse Property
Linear equation
Proportion
Multiplicative inverse
Reciprocal
Solution
Systems of Linear Equations
Variable
Evidence of Learning
Formative Assessments
Summative Assessments
Daily Participation
5 min warm ups
Quizzes
Performance Assessment
Anchor Assessments
Resources
KEYSTONE Finish Line
Supplemental Materials on “R:” drive
Kuta Software (search by topic and customize)
Hippo Math
Khan Academy
Other print and digital resources at teacher’s discretion.
Mifflin County School District – Mathematics Department
Planned Course
Subject: Algebra I
Unit Title: Linear Inequalities
Grade levels: 11
Rational/Summary of Unit
Rules of arithmetic and algebra are useful for writing equivalent forms of expressions, solving
inequalities, and systems of linear inequalities.
Common Core Standards
Assessment Anchors and Eligible Content
 CC.2.2.HS.D.7 Create and graph
equations or inequalities to
describe numbers or relationships.
 CC.2.2.HS.D.8 Apply inverse
operations to solve equations or
formulas for a given variable.
 CC.2.2.HS.D.10 Represent, solve
and interpret
equations/inequalities and systems
of equations/inequalities
algebraically and graphically.
 CC.2.1.HS.F.5 Choose a level of
accuracy appropriate to
limitations on measurement when
reporting quantities.
.
 A1.1.3.1 Write, solve, and/or graph
linear inequalities using various methods.
 A1.1.3.1.1 Write or solve compound
inequalities and/or graph their
solution sets on a number line (may
include absolute value inequalities).
 A1.1.3.1.2 Identify or graph the
solution set to a linear inequality on a
number line.
 A1.1.3.1.3 Interpret solutions to
problems in the context of the
problem situation (limit to linear
inequalities).
 A1.1.3.2 Write, solve, and/or graph
systems of linear inequalities using
various methods.
 A1.1.3.2.1 Write and/or solve a
system of linear inequalities using
graphing (limit systems to 2 linear
inequalities).
 A1.1.3.2.2 Interpret solutions to
problems in the context of the
problem situation (systems of 2
linear inequalities only).
Big Ideas
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The intersection of two linear functions can be found through various techniques.
Systems of inequalities can be used to model real world situations.
Essential Questions
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How do you write, solve, graph, and/or interpret linear inequalities to model
relationships between quantities?
Mifflin County School District – Mathematics Department
Planned Course
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How do you decide which linear inequality representation to choose when modeling a
real world situation, and how would you explain your solution to the problem
How do you write, solve, and/or interpret systems of two linear inequalities using
various techniques?
Concepts
Students will know…
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Competencies
Students will be able to…
Algebraic properties can be used to
solve one variable equations in
multiple steps.
Algebraic properties illustrated in
mathematical relationships are
always true.
Compound inequalities have
multiple solutions, and the graph is
a visual representation of these
solutions.
Inequalities have multiple
solutions, and the graph is a visual
representation of these solutions.
Linear inequalities represent realworld situations with feasible
solutions.
Systems of linear inequalities have
multiple solutions, and the graph is
a visual representation of these
solutions.
Systems of linear inequalities
represent real-world situations
with feasible solutions.
Absolute value inequality
Linear combination/elimination
method
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Write, graph, and solve compound
inequalities.
Solve and graph absolute-value
inequalities in one variable.
Read and interpret algebraic inequalities.
Write an inequality from a graph on a
number line.
Create a graph from the solution to a
linear inequality.
Use the solution to a linear inequality to
solve a real world problem.
Write a system of linear inequalities for a
given situation.
Solve a system of linear inequalities
using graphing (manually and with
technology).
Justify the solution to a system of linear
inequalities by showing any point in the
overlapping shaded region satisfies both
inequalities.
Use the solution of a system of linear
inequalities to solve a real world
problem.
Vocabulary
Linear inequality
Solution set
Substitution
Systems of linear inequalities
Mifflin County School District – Mathematics Department
Planned Course
Evidence of Learning
Formative Assessments
Summative Assessments
Daily Participation
5 min warm ups
Quizzes
Performance Assessment
Anchor Assessments
Resources
KEYSTONE Finish Line
Supplemental Materials on “R:” drive
Kuta Software (search by topic and customize)
Hippo Math
Khan Academy
Other print and digital resources at teacher’s discretion.
Mifflin County School District – Mathematics Department
Planned Course
Subject: Algebra I Remediation
Unit Title: Functions
Grade levels: 11
Rational/Summary of Unit
Functions can be used to analyze patterns and relations using multiple representations,
including words, graphs, tables and equations.
Functions can be transformed and composed to model real world situations.
Common Core Standards
 CC.2.2.HS.C.2 Graph and
analyze functions and use their
properties to make connections
between the different
representations.
 CC.2.2.HS.C.1 Use the concept
and notation of functions to
interpret and apply them in terms
of their context.
 CC.2.2.HS.C.3 Write functions
or sequences that model
relationships between two
quantities.
 CC.2.4.HS.B.2 Summarize,
represent, and interpret data on
two categorical and quantitative
variables.
 CC.2.2.8.B.2 Understand the
connections between proportional
relationships, lines, and linear
equations.
 CC.2.1.HS.F.3 Apply quantitative
reasoning to choose and interpret
units and scales in formulas,
graphs and data displays.
Assessment Anchors and Eligible Content
 A1.2.1.1 Analyze and/or use patterns or
relations.
 A1.2.1.1.1 Analyze a set of data for
the existence of a pattern and
represent the pattern algebraically
and/or graphically.
 A1.2.1.1.2 Determine if a relation is
a function given a set of points or a
graph.
 A1.2.1.1.3 Identify the domain or
range of a relation (may be presented
as ordered pairs, a graph, or a table).
 A1.2.1.2 Interpret and/or use linear
functions and their equations, graphs, or
tables.
 A1.2.1.2.1 Create, interpret and/or
use the equation, graph or table of a
linear function.
 A1.2.1.2.2 Translate from one
representation of a linear function to
another (graph, table and equation).
Mifflin County School District – Mathematics Department
Planned Course
 CC.2.1.HS.F.4 Use units as a way
to understand problems and to
guide the solution of multi-step
problems.
 CC.2.2.HS.C.4 Interpret the
effects transformations have on
functions and find the inverses of
functions.
 CC.2.2.HS.C.6 Interpret
functions in terms of the situation
they model.
Big Ideas
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The regularity and predictability of patterns can be used as a vehicle to stimulate
thinking about variables and functions.
Patterns can be represented by functions, graphically, numerically, and algebraically.
Functions can be used to describe the relationship between two quantities.
Essential Questions
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How do you decide which functional representation to choose when modeling a real
world situation, and how would you explain your solution to the problem?
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How do you use functions to analyze relationships and make predictions?
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How do you determine if a relation is a function?
Concepts
Students will know…
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Various representations of data
allow us to interpret and make
predictions.
A set of points or a graph can
represent a relation and/or a
function.
Competencies
Students will be able to…
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Analyze a set of data for the existence of
a pattern.
Represent the pattern of a set of data
algebraically and graphically (manually
and with technology).
 Given a set of data, write an
equation.
Mifflin County School District – Mathematics Department
Planned Course
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The domain and range of a relation
can be related to its graph and,
where applicable, to real world
situations.
Graphs, tables and equations
represent real life situations.
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Functions can be represented in
different forms.
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Arithmetic sequence
Coordinate plane
Domain
Function
Function notation
Geometric sequence
 Represent a set of data in different
formats.
 Analyze and/or interpret x,y
tables.
 Identify patterns.
Determine if a relation is a function
given a graph or given a set of points
(ordered pairs).
 Plot the points on the coordinate
plane and perform the vertical
line test.
 Determine whether each member
of the domain is paired with one
and only one member of the
range.
 Use mapping techniques to test for
a function.
Determine the domain by identifying the
x-coordinates in a relation.
Determine the range by identifying the ycoordinates in a relation.
Use the equation to find the range, given
the domain.
Identify the values along the vertical axis
as the range and the horizontal axis as the
domain, given the graph.
Identify the domain, range and the
inverse of a relation.
Interpret linear functions to solve
problems using linear equations, tables,
or graphs.
Write the function rule, given a table.
Make a table, given the equation.
Plot the points of a line, given a table.
Vocabulary
Linear function
Mapping
Ordered pair
Pattern (or sequence)
Quadrants
Range
Relation
Table
Slope/rate of change
Vertical line test
Mifflin County School District – Mathematics Department
Planned Course
Evidence of Learning
Formative Assessments
Summative Assessments
Daily Participation
5 min warm ups
Quizzes
Performance Assessment
Anchor Assessments
Resources
KEYSTONE Finish Line
Supplemental Materials on “R:” drive
Kuta Software (search by topic and customize)
Hippo Math
Khan Academy
Other print and digital resources at teacher’s discretion.
Mifflin County School District – Mathematics Department
Planned Course
Subject: Algebra I Remediation
Unit Title: Coordinate Geometry
Grade levels: 11
Rational/Summary of Unit
Coordinate geometry can be used to interpret the rate of change (slope) and initial value (yintercept) of a linear function in terms of the situation it models.
Coordinate geometry can be used to create a linear model using various methods to describe
the given relationship.
Common Core Standards
Assessment Anchors and Eligible Content
 CC.2.2.8.C.1 Define, evaluate,
and compare functions.
 CC.2.2.8.C.2 Use concepts of
functions to model relationships
between quantities.
 CC.2.2.HS.C.1 Use the concept
and notation of functions to
interpret and apply them in terms
of their context.
 CC.2.2.HS.C.3 Write functions
or sequences that model
relationships between two
quantities.
 A1.2.2.1 Describe, compute, and/or use
the rate of change (slope) of a line.
 A1.2.2.1.1 Identify, describe and/or
use constant rates of change.
 A1.2.2.1.2 Apply the concept of
linear rate of change (slope) to solve
problems.
 A1.2.2.1.3 Write or identify a linear
equation when given the graph of the
line 2 points on the line, or the slope
and a point on a line (linear equation
may be in point-slope, standard
and/or slope-intercept form).
 A1.2.2.1.4 Determine the slope
and/or y-intercept represented by a
linear equation or graph.
 CC.2.2.HS.C.5 Construct and
compare linear, quadratic and/or
exponential models to solve
problems.
Big Ideas
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Relationships between two quantities can be described using equations, graphs, tables,
and verbal representations.
Rate of change (slope) models how one quantity affects another.
Mifflin County School District – Mathematics Department
Planned Course
Essential Questions
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How do you identify, describe and apply the rate of change (slope)?
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How do you write, solve, graph and interpret linear equations to model relationships
between quantities?
Concepts
Students will know…
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Rate of change can be determined
from various forms of data.
Slope can be correlated to real life
data.
Slope shows how two variables are
related.
Linear equations can be written to
represent relationships between
quantities.
Linear equations or graphs can be
used to determine slope or yintercept.
Competencies
Students will be able to…
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Explain the rate of change given a graph,
equation or two points.
Calculate rate of change (slope) from a
set of data.
Find the slope given two points or from a
graph.
Determine whether slopes are undefined,
zero, positive or negative.
Find another point on the graph, given a
point and slope.
Graph a line given data.
Graph the line given the standard form.
Graph the line given the intercepts.
Identify the slope and y-intercept from a
graph, data points or equation.
Write the equation/inequality of a line in
slope-intercept form given…
 Slope and y -intercept
 Slope and a point
 Two points
 Graph
 Table of data
Graph linear functions/equations/
inequalities on a coordinate plane
(manually and with technology).
Interchange point-slope, slope-intercept,
and standard form of a linear
equation/inequality.
Identify the equations of horizontal,
vertical and oblique lines.
Determine the relationship of lines using
their slopes (parallel or perpendicular).
Mifflin County School District – Mathematics Department
Planned Course
Graph of linear equation
Horizontal lines
Oblique lines
Ordered pair
Origin
Parallel lines
Vocabulary
Perpendicular lines
Point slope form
Quadrant
Rate of change
Slope
Slope intercept form
Standard form
Vertical lines
X-axis
X-intercept
Y-axis
Y-intercept
Evidence of Learning
Formative Assessments
Summative Assessments
Daily Participation
5 min warm ups
Quizzes
Performance Assessment
Anchor Assessments
Resources
KEYSTONE Finish Line
Supplemental Materials on “R:” drive
Kuta Software (search by topic and customize)
Hippo Math
Khan Academy
Other print and digital resources at teacher’s discretion.
Mifflin County School District – Mathematics Department
Planned Course
Subject: Algebra I Remediation
Unit Title: Data Analysis & Probability
Grade levels: 11
Rational/Summary of Unit
Bivariate data can be modeled with mathematical functions that approximate the data well
and help us make predictions based on the data.
Apply probability to real world situations.
Common Core Standards
 CC.2.4.HS.B.1 Summarize,
represent, and interpret data on a
single count or measurement
variable.
 CC.2.4.HS.B.3 Analyze linear
models to make interpretations
based on the data.
 CC.2.4.HS.B.5 Make inferences
and justify conclusions based on
sample surveys, experiments, and
observational studies.
 CC.2.4.HS.B.4 Recognize and
evaluate random processes
underlying statistical
experiments.
 CC.2.4.HS.B.7 Apply the rules
of probability to compute
probabilities of compound events
in a uniform probability model.
 CC.2.4.HS.B.2 Summarize,
represent, and interpret data on
two categorical and quantitative
variables.
 CC.2.2.HS.C.6 Interpret
functions in terms of the situation
they model.
Assessment Anchors and Eligible Content
 A1.2.3.1 Use measures of dispersion to
describe a set of data.
 A1.2.3.1.1 Calculate and/or interpret
the range, quartiles and interquartile
range of data.
 A1.2.3.2 Use data displays in problemsolving settings and/or to make predictions.
 A1.2.3.2.1 Estimate or calculate to
make predictions based on a circle,
line, bar graph, measures of central
tendency, or other representations.
 A1.2.3.2.2 Analyze data, make
predictions, and/or answer questions
based on displayed data (box-andwhisker plots, stem-and-leaf plots,
scatter plots, measures of central
tendency, or other representations).
 A1.2.3.2.3 Make predictions using
the equations or graphs of best-fit
lines of scatter plots.
 A1.2.3.3 Apply probability to practical
situations.
 A1.2.3.3.1 Find probabilities for
compound events (e.g., find
probability of red and blue, find
probability of red or blue) and
represent as a fraction, decimal or
percent).
Mifflin County School District – Mathematics Department
Planned Course
 A1.2.2.2 Analyze and/or interpret data on a
scatter plot.
 A1.2.2.2.1 Draw, find and/or write
an equation for a line of best fit for a
scatter plot.
Big Ideas
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Data are gathered, displayed, summarized, examined, and interpreted to discover
patterns and deviations from patterns.
Statistics provide tools for describing variability in data and for making informed
decisions or predictions.
Essential Questions
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How can we use univariate and bivariate data to analyze relationships and make
predictions?
How do you decide which functional representation to choose when modeling a real
world situation, and how would you explain your solution to the problem?
How do you identify, apply, and analyze uses of probabilities in real world situations?
Concepts
Students will know…
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A box and whisker plot can be
used to describe data.
Outliers can skew data.
Mean, median and mode are
all measures of central
tendency but average is most
commonly used in reference to the
mean.
Various data displays can be
created and used to make
predictions.
The line of best fit can be used to
determine a general relationship or
to predict trends.
Probability can be used to
determine the likelihood of a
particular outcome.
Competencies
Students will be able to…
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Make predictions based on the scatter
plot and/or line of best fit.
 Draw a scatter plot from existing
data.
 Draw the line of best fit from data.
 Create an equation for the line of
best fit (manually and with
technology).
 Make predictions based on the
graph(s).
 Determine the reasonableness of a
prediction.
Create, analyze and interpret circle, line
and/or bar graphs.
Calculate upper and lower quartile
numbers.
Mifflin County School District – Mathematics Department
Planned Course
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Bar graph
Box and whisker plot
Circle graph
Complement
Compound (or combined
event)
Conjunction
Dependent events
Disjunction
Experimental probability
Extremes
Create, analyze and interpret a box and
whisker plot.
 Compare data sets.
 Determine if any of the data
values are outliers.
Create stem and leaf plots (including
back to back).
Determine which type of graph best
represents the data set.
Find probabilities for compound events.
Find the probability of independent and
dependent events (conjunction).
Find the probability of mutually
exclusive or not mutually exclusive
events (disjunction).
Vocabulary
Favorable and unfavorable
outcomes
Frequency
Independent events
Interquartile range
Line graph
Mean
Median
Measures of central
tendency
Mode
Mutually exclusive
Outliers
Probability (compound and
simple)
Quartiles
Range
Sample space
Stem and leaf plot
Theoretical probability
Evidence of Learning
Formative Assessments
Summative Assessments
Daily Participation
5 min warm ups
Quizzes
Performance Assessment
Anchor Assessments
Resources
KEYSTONE Finish Line
Supplemental Materials on “R:” drive
Kuta Software (search by topic and customize)
Hippo Math
Khan Academy
Other print and digital resources at teacher’s discretion.
Mifflin County School District – Mathematics Department
Planned Course