Download Algebra I- Curriculum Map 2014-2015

Youngstown City Schools - - CURRICULUM MAP – MATH (2014-2015)
Unit: # 1 Name: 1 Relationships Between Quantities and Reasoning with Equations Time: 31 days instruction, 10 days computer, 1 day assessment
CHAPTERS/LESSONS
Chapter 14
14.1
The Real Numbers …For
Realsies!
14.2
Getting Real, and Knowing
How…
Chapter 1
1.1
A Picture is Worth a
Thousand Words
1.2
A Sort of Sorts
MATH STANDARDS NS
MATH PRACTICES
N.RN.3 Explain why the sum or
product of two rational numbers is
rational; that the sum of a rational
number and an irrational number is
irrational; and that the product of a
nonzero rational number and an
irrational number is irrational.
N.RN.3 Explain why the sum or
product of two rational numbers is
rational; that the sum of a rational
number and an irrational number is
irrational; and that the product of a
nonzero rational number and an
irrational number is irrational.
N.Q.2 Define appropriate quantities
for the purpose of descriptive
modeling.
The 8 Practices are
Embedded Throughout
the Units
F.LE.1.b Recognize situations in
which one quantity changes at a
constant rate per unit interval relative
to another.
F.IF.1 Understand that a function
from one set (called the domain) to
another set (called the range) assigns
to each element of the domain
exactly one element of the range. If f
is a function and x is an element of
its domain, then f(x) denotes the
output of f corresponding to the input
x. The graph of f is the graph of the
5. Use appropriate tools
strategically.
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1. Make sense of
problems and persevere
in solving them.
SPECIAL EXPLANATIONS
Complete problem 1.
Do problem 2 time permitting
Complete Problems 1 and 2
2. Reason abstractly and
quantitatively.
3. Construct viable
arguments and critique
the reasoning of others.
Complete Problems 1 and 2
4. Model with
mathematics.
6. Attend to precision.
Complete Problems 1-3
7. Look for and make use
of structure.
8. Look for and express
regularity in repeated
reasoning
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CHAPTERS/LESSONS
MATH STANDARDS NS
MATH PRACTICES
SPECIAL EXPLANATIONS
equation y = f(x).
1.3
There are Many Ways to
Represent Functions
F.IF.5 Relate the domain of a
function to its graph and, where
applicable, to the quantitative
relationship it describes. For
example, if the function
h(n) gives the number of personhours it takes to assemble n engines
in a factory, then the positive integers
would be an appropriate domain for
the function.
F.IF.5 Relate the domain of a
function to its graph and, where
applicable, to the quantitative
relationship it describes. For
example, if the function
h(n) gives the number of personhours it takes to assemble n engines
in a factory, then the positive integers
would be an appropriate domain for
the function.
If graphing calculators are not
available, you can complete these
problems as a class by projecting a
graphing calculator on a board.
Complete Problems 1-3
F.IF.9 Compare properties of two
functions each represented in a
different way (algebraically,
graphically, numerically in tables, or
by verbal descriptions). For example,
given a graph of one quadratic
function and an algebraic expression
for another, say which has the larger
maximum.
A.REI.10 Understand that the graph
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CHAPTERS/LESSONS
MATH STANDARDS NS
MATH PRACTICES
SPECIAL EXPLANATIONS
of an equation in two variables is
the set of all its solutions plotted in
the coordinate plane, often forming
a curve (which could be a line).
F.IF.1 Understand that a function
from one set (called the domain) to
another set (called the range) assigns
to each element of the domain
exactly one element of the range. If f
is a function and x is an element of
its domain, then f(x) denotes the
output of f corresponding to the input
x. The graph of f is the graph of the
equation y = f(x).
F.IF.2 Use function notation,
evaluate functions for inputs in their
domains, and interpret statements
that use function notation in terms of
a context
1.4
Function Families for 200
Alex…
F.IF.7. Graph functions expressed
symbolically and show key features
of the graph, by hand in simple cases
and using technology for more
complicated cases.★
a. Graph linear and quadratic
functions and show intercepts,
maxima, and minima
F.IF.1 Understand that a function
from one set (called the domain) to
another set (called the range) assigns
to each element of the domain
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Complete Problem 2 and the Talk
the Talk graphic organizer
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CHAPTERS/LESSONS
MATH STANDARDS NS
MATH PRACTICES
SPECIAL EXPLANATIONS
exactly one element of the range. If f
is a function and x is an element of
its domain, then f(x) denotes the
output of f corresponding to the input
x. The graph of f is the graph of the
equation y = f(x).
F.IF.4 For a function that models a
relationship between two quantities,
interpret key features of graphs and
tables in terms of the quantities,
and sketch graphs showing key
features given a verbal description
of the relationship. Key features
include: intercepts; intervals where
the function is increasing,
decreasing, positive, or negative;
relative maximums and minimums;
symmetries; end behavior; and
periodicity
F.IF.7. Graph functions expressed
symbolically and show key features
of the graph, by hand in simple cases
and using technology for more
complicated cases.★
a. Graph linear and quadratic
functions and show intercepts,
maxima, and minima
F.IF.9 Compare properties of two
functions each represented in a
different way (algebraically,
graphically, numerically in tables, or
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CHAPTERS/LESSONS
MATH STANDARDS NS
MATH PRACTICES
SPECIAL EXPLANATIONS
by verbal descriptions). For example,
given a graph of one quadratic
function and an algebraic expression
for another, say which has the larger
maximum.
F.LE.1.b Recognize situations in
which one quantity changes at a
constant rate per unit interval relative
to another.
F.LE.2 Construct linear and
exponential functions, including
arithmetic and geometric sequences,
given a graph, a description of a
relationship, or two input-output pairs
(include reading these from a table).
Chapter 2
2.1
The Plane!
A.CED.2 Create equations in two or
more variables to represent
relationships between quantities; graph
equations on coordinate axes with
labels and scales.
A.REI. 1 Explain each step in
solving a simple equation as
following from the equality of
numbers asserted at the previous
step, starting from the
assumption that the original equation
has a solution. Construct a viable
argument to justify a solution
method.
Complete Problems 1 and 3
A.REI.3 Solve linear equations and
inequalities in one variable, including
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CHAPTERS/LESSONS
MATH STANDARDS NS
MATH PRACTICES
SPECIAL EXPLANATIONS
equations with coefficients
represented by letters.
A.REI.10 Understand that the graph
of an equation in two variables is
the set of all its solutions plotted in
the coordinate plane, often forming
a curve (which could be a line).
A.CED.1 Create equations and
inequalities in one variable and use
them to solve problems.Include
equations arising from linear and
quadratic functions, and simple
rational and exponential functions.
A.CED.2 Create equations in two or
more variables to represent
relationships between quantities; graph
equations on coordinate axes with
labels and scales.
N.Q.1 Use units as a way to
understand problems and to guide the
solution of multi-step problems;
choose and interpret units
consistently in formulas; choose and
interpret the scale and the origin in
graphs and
data displays.
A.SSE.1. Interpret expressions that
represent a quantity in terms of its
context.*
a. Interpret parts of an expression, such
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CHAPTERS/LESSONS
MATH STANDARDS NS
MATH PRACTICES
SPECIAL EXPLANATIONS
as terms, factors, and coefficients.
F.IF.2 Use function notation,
evaluate functions for inputs in their
domains, and interpret statements
that use function notation in terms of
a context
F.IF.6 Calculate and interpret the
average rate of change of a function
(presented symbolically or as a table)
over a specified interval. Estimate the
rate of change from a graph.*
2.2
What Goes Up Must Come
Down
A.REI.3 Solve linear equations and
inequalities in one variable, including
equations with coefficients
represented by letters.
Complete Problems 1and 2
A.CED.1 Create equations and
inequalities in one variable and use
them to solve problems.Include
equations arising from linear and
quadratic functions, and simple
rational and exponential functions.
A.CED.2 Create equations in two or
more variables to represent
relationships between quantities; graph
equations on coordinate axes with
labels and scales.
N.Q.1 Use units as a way to
understand problems and to guide the
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CHAPTERS/LESSONS
MATH STANDARDS NS
MATH PRACTICES
SPECIAL EXPLANATIONS
solution of multi-step problems;
choose and interpret units
consistently in formulas; choose and
interpret the scale and the origin in
graphs and data displays.
A.SSE.1.a
Interpret expressions that represent a
quantity in terms of its context.*
a. Interpret parts of an expression, such
as terms, factors, and coefficients.
A.REI.10 Understand that the graph
of an equation in two variables is
the set of all its solutions plotted in
the coordinate plane, often forming
a curve (which could be a line).
N.Q.3 Choose a level of accuracy
appropriate to limitations on
measurement when reporting
quantities.
F.IF.2 Use function notation,
evaluate functions for inputs in their
domains, and interpret statements
that use function notation in terms of
a context
F.IF.6 Calculate and interpret the
average rate of change of a function
(presented symbolically or as a table)
over a specified interval. Estimate the
rate of change from a graph.*
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CHAPTERS/LESSONS
2.3
Scouting for Prizes!
MATH STANDARDS NS
A.CED.1 Create equations and
inequalities in one variable and use
them to solve problems. Include
equations arising from linear and
quadratic functions, and simple
rational and exponential functions.
MATH PRACTICES
SPECIAL EXPLANATIONS
Complete Problems 1 - 3
A.CED.2 Create equations in two or
more variables to represent
relationships between quantities; graph
equations on coordinate axes with
labels and scales.
A.CED.3 Represent constraints by
equations or inequalities, and by
systems of equations and/or
inequalities, and interpret solutions as
viable or nonviable options in a
modeling context. For example,
represent inequalities describing
nutritional and cost constraints on
combinations of different foods.
A.REI.3 Solve linear equations and
inequalities in one variable, including
equations with coefficients
represented by letters.
A.REI.10 Understand that the graph
of an equation in two variables is
the set of all its solutions plotted in
the coordinate plane, often forming
a curve (which could be a line).
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CHAPTERS/LESSONS
2.4
We’re Shipping Out
MATH STANDARDS NS
N.Q.3 Choose a level of accuracy
appropriate to limitations on
measurement when reporting
quantities.
A.CED.1 Create equations and
inequalities in one variable and use
them to solve problems. Include
equations arising from linear and
quadratic functions, and simple
rational and exponential functions.
MATH PRACTICES
SPECIAL EXPLANATIONS
Complete Problems 1 - 3
A.CED.2 Create equations in two or
more variables to represent
relationships between quantities; graph
equations on coordinate axes with
labels and scales.
2.5
Play Ball!
A.REI.3 Solve linear equations and
inequalities in one variable, including
equations with coefficients
represented by letters.
A.CED.1 Create equations and
inequalities in one variable and use
them to solve problems. Include
equations arising from linear and
quadratic functions, and simple
rational and exponential functions.
Complete Problems 1and 2
A.CED.2 Create equations in two or
more variables to represent
relationships between quantities; graph
equations on coordinate axes with
labels and scales.
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CHAPTERS/LESSONS
MATH STANDARDS NS
MATH PRACTICES
SPECIAL EXPLANATIONS
A.CED.3 Represent constraints by
equations or inequalities, and by
systems of equations and/or
inequalities, and interpret solutions as
viable or nonviable options in a
modeling context. For example,
represent inequalities describing
nutritional and cost constraints on
combinations of different foods.
A.REI.3 Solve linear equations and
inequalities in one variable, including
equations with coefficients
represented by letters.
2.6
Choose Wisely
A.REI.10 Understand that the graph
of an equation in two variables is
the set of all its solutions plotted in
the coordinate plane, often forming
a curve (which could be a line).
N.Q.1 Use units as a way to
understand problems and to guide the
solution of multi-step problems;
choose and interpret units
consistently in formulas; choose and
interpret the scale and the origin in
graphs and
data displays.
Complete Problems 1- 4
N.Q.2 Define appropriate quantities
for the purpose of descriptive
modeling.
A.CED.2 Create equations in two or
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CHAPTERS/LESSONS
MATH STANDARDS NS
MATH PRACTICES
SPECIAL EXPLANATIONS
more variables to represent
relationships between quantities; graph
equations on coordinate axes with
labels and scales.
A.CED.3 Represent constraints by
equations or inequalities, and by
systems of equations and/or
inequalities, and interpret solutions as
viable or nonviable options in a
modeling context. For example,
represent inequalities describing
nutritional and cost constraints on
combinations of different foods.
A.REI.10 Understand that the graph
of an equation in two variables is
the set of all its solutions plotted in
the coordinate plane, often forming
a curve (which could be a line).
F.IF.2 Use function notation,
evaluate functions for inputs in their
domains, and interpret statements
that use function notation in terms of
a context
F.LE.1.b Recognize situations in
which one quantity changes at a
constant rate per unit interval relative
to another.
F.LE.1.c Recognize situations in
which a quantity grows or decays by a
constant percent rate per unit interval
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CHAPTERS/LESSONS
MATH STANDARDS NS
MATH PRACTICES
SPECIAL EXPLANATIONS
relative to another.
Chapter 3
3.1
Is it Getting Hot in Here?
S.ID.6 Fit a linear function for a
scatter plot that suggests a linear
association.
Complete Problems 1 and 3
S.ID.7 Interpret the slope (rate of
change) and the intercept (constant
term) of a linear model in the context
of the data.
N.Q.2 Define appropriate quantities
for the purpose of descriptive
modeling.
3.2
Tickets for Sale
A.REI.3 Solve linear equations and
inequalities in one variable, including
equations with coefficients
represented by letters.
A.SSE.1.a Interpret parts of an
expression, such as terms, factors, and
coefficients.
Complete Problem 1and 3
A.SSE.1.b Interpret complicated
expressions by viewing one or more of
their parts as a single entity. For
example, interpret P(1+r)n as the
product of P and a factor not
depending on P.
A.CED.2 Create equations in two or
more variables to represent
relationships between quantities; graph
equations on coordinate axes with
labels and scales.
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CHAPTERS/LESSONS
MATH STANDARDS NS
MATH PRACTICES
SPECIAL EXPLANATIONS
A.CED.3 Represent constraints by
equations or inequalities, and by
systems of equations and/or
inequalities, and interpret solutions as
viable or nonviable options in a
modeling context. For example,
represent inequalities describing
nutritional and cost constraints on
combinations of different foods.
A.CED.4 Rearrange formulas to
highlight a quantity of interest, using
the same reasoning as in solving
equations. For example, rearrange
Ohm's law V = IR to highlight
resistance R.
A.REI.3 Solve linear equations and
inequalities in one variable, including
equations with coefficients
represented by letters.
N.Q.2 Define appropriate quantities
for the purpose of descriptive
modeling.
3.3
Cool As a Cucumber or Hot
like a Tamale!
F.IF.2 Use function notation,
evaluate functions for inputs in their
domains, and interpret statements
that use function notation in terms of
a context
A.CED.2 Create equations in two or
more variables to represent
relationships between quantities; graph
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Complete Problems 1and 3. Do
Problem 2 if time permits
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CHAPTERS/LESSONS
MATH STANDARDS NS
MATH PRACTICES
SPECIAL EXPLANATIONS
equations on coordinate axes with
labels and scales.
A.CED.4 Rearrange formulas to
highlight a quantity of interest, using
the same reasoning as in solving
equations. For example, rearrange
Ohm's law V = IR to highlight
resistance R.
3.4
A Growing Business
A.REI.1 Explain each step in solving
a simple equation as following from
the equality of numbers asserted at
the previous step, starting from the
assumption that the original equation
has a solution. Construct a viable
argument to justify a solution
method.
A.SSE.1.a Interpret parts of an
expression, such as terms, factors, and
coefficients.
Complete Problems 1 and 2
A.SSE.1.b Interpret complicated
expressions by viewing one or more of
their parts as a single entity. For
example, interpret P(1+r)n as the
product of P and a factor not
depending on P.
A.CED.2 Create equations in two or
more variables to represent
relationships between quantities; graph
equations on coordinate axes with
labels and scales.
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CHAPTERS/LESSONS
MATH STANDARDS NS
MATH PRACTICES
SPECIAL EXPLANATIONS
A.CED.3 Represent constraints by
equations or inequalities, and by
systems of equations and/or
inequalities, and interpret solutions as
viable or nonviable options in a
modeling context. For example,
represent inequalities describing
nutritional and cost constraints on
combinations of different foods.
A.REI.3 Solve linear equations and
inequalities in one variable, including
equations with coefficients
represented by letters.
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Youngstown City Schools - - CURRICULUM MAP – MATH (2014-2015)
Unit: #2
Name: Linear & Exponential Functions
CHAPTERS/LESSONS
Chapter 4: Sequences
4.1, 4.2, 4.3, 4.4, 4.5
Chapter 5: Exponential Functions
5.1, 5.2, 5.3, 5.4, 5.5, 5.6
Chapter 6: Systems of Equations
6.1, 6.2, 6.3, 6.4
Chapter 7: Systems of
Inequalities
7.1, 7.2, 7.3, 7.4
Time: 25 days instruction, 9 days computers, 4 days testing
1. MATH STANDARDS
Chapter 4
CCSS.MATH.CONTENT.HSF.LE.A.1.B
Recognize situations in which one quantity
changes at a constant rate per unit interval
relative to another.
CCSS.MATH.CONTENT.HSF.LE.A.2
Construct linear and exponential functions,
including arithmetic and geometric sequences,
given a graph, a description of a relationship,
or two input-output pairs (include reading
these from a table).
CCSS.MATH.CONTENT.HSF.BF.A.1.A
Determine an explicit expression, a recursive
process, or steps for calculation from a
context.
CCSS.MATH.CONTENT.HSF.BF.A.1
Write a function that describes a relationship
between two quantities.*
CCSS.MATH.CONTENT.HSF.BF.A.2
Write arithmetic and geometric sequences both
recursively and with an explicit formula, use
them to model situations, and translate
between the two forms.*
CCSS.MATH.CONTENT.HSA.SSE.A.1
Interpret expressions that represent a quantity
in terms of its context.*
CCSS.MATH.CONTENT.HSA.SSE.A.1.A
Interpret parts of an expression, such as terms,
factors, and coefficients.
CCSS.MATH.CONTENT.HSF.IF.A.1
MATH PRACTICES
1. Make sense of
problems and
persevere in solving
them.
2. Reason
abstractly and
quantitatively.
3. Construct viable
arguments and critique
the
reasoning of others.
4. Model with
mathematics.
5. Use appropriate
tools strategically.
6. Attend to
precision.
7. Look for and
make use of structure.
8. Look for and
express regularity in
repeated
reasoning
SPECIAL EXPLANATIONS
Chapter 4
4.1: Recognizing Patterns and Sequences
Do Problem 1 and 2.
4.2: Arithmetic and Geometric Sequences
Do the Warm Up or something similar, Problem 1,
and Students’ Understanding.
4.3: Using Formulas to determine Terms of a
Sequence.
Do the Warm up, Problem 1 and Problem 3, do
Check for Students’ Understanding.
4.4: Graphs of Sequences
Do the Warm up, Problem 1, Problem 2 (don’t cut
out, write in the book.)
4.5: Sequences and Functions
Do problems 1 and 2.
Chapter 5
5.1: Comparing Linear and Exponential Functions
Do problem 1 and check for students’
understanding.
Understand that a function from one set (called
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CHAPTERS/LESSONS
1. MATH STANDARDS
the domain) to another set (called the range)
assigns to each element of the domain exactly
one element of the range. If f is a function
and x is an element of its domain, then f(x)
denotes the output of f corresponding to the
input x. The graph of f is the graph of the
equation y = f(x).
CCSS.MATH.CONTENT.HSF.IF.B.4
For a function that models a relationship
between two quantities, interpret key features
of graphs and tables in terms of the quantities,
and sketch graphs showing key features given
a verbal description of the relationship. Key
features include: intercepts; intervals where
the function is increasing, decreasing, positive,
or negative; relative maximums and
minimums; symmetries; end behavior; and
periodicity.*
MATH PRACTICES
SPECIAL EXPLANATIONS
5.2: Graphs of Exponential Functions
Do the Warm up, Problem 1 and Problem 3.
5.3: Translations of Linear and Exponential
Functions
Do just problem 1.
5.4: Reflections of Linear and Exponential
Functions
Do the Warm up and Problem 1 and 3.
5.5: Properties of Rational Exponents
Do Problem 1 and 2, Warm up. This is a quick
review unit.
5.6: Solving Exponential Functions
CCSS.MATH.CONTENT.HSF.LE.A.2
Construct linear and exponential functions,
including arithmetic and geometric sequences,
given a graph, a description of a relationship,
or two input-output pairs (include reading
these from a table).
CCSS.MATH.CONTENT.HSF.LE.A.1
Distinguish between situations that can be
modeled with linear functions and with
exponential functions.
CCSS.MATH.CONTENT.HSF.LE.A.1.A
Prove that linear functions grow by equal
differences over equal intervals, and that
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Do Problem 2.
Chapter 6
6.1: Solving Linear Systems Graphically and
Algebraically
Problem 1 and Talk the Talk.
6.2: Using Linear Combinations to Solve a Linear
System.
Do Problems 1-3.
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CHAPTERS/LESSONS
1. MATH STANDARDS
exponential functions grow by equal factors
over equal intervals.
CCSS.MATH.CONTENT.HSF.LE.A.1.C
Recognize situations in which a quantity
grows or decays by a constant percent rate per
unit interval relative to another.
MATH PRACTICES
SPECIAL EXPLANATIONS
6.3: Solving More Systems.
Do warm up, and Problem 1, 2, and Talk the Talk or
give other practice.
6.4: Using graphing, substitution, and Linear
Combinations.
Do Problems 1-3 and extra practice.
CCSS.MATH.CONTENT.HSF.LE.B.5
Interpret the parameters in a linear or
exponential function in terms of a context.
CCSS.MATH.CONTENT.HSF.IF.A.2
Use function notation, evaluate functions for
inputs in their domains, and interpret
statements that use function notation in terms
of a context.
CCSS.MATH.CONTENT.HSF.IF.A.3
Recognize that sequences are functions,
sometimes defined recursively, whose domain
is a subset of the integers. For example, the
Fibonacci sequence is defined recursively by
f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
CCSS.MATH.CONTENT.HSF.BF.A.1
Write a function that describes a relationship
between two quantities.*
Chapter 7
7.1: Graphing Inequalities.
Do the Warm ups, Problem 1 and 2 and check for
Students’ Understanding.
7.2: Systems of Linear Inequalities
Do Problems 1 and 2 with extra practice.
7.3: Systems With More Than Two Linear Linear
Inequalities.
Do Problems 1 and 3.
7.4 Linear programming
Do Problems 1-3.
Chapter 5
CCSS.MATH.CONTENT.HSA.SSE.A.1.A
Interpret parts of an expression, such as terms,
factors, and coefficients.
CCSS.MATH.CONTENT.HSA.SSE.A.1.B
Interpret complicated expressions by viewing
one or more of their parts as a single
entity. For example, interpret P(1+r)n as the
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CHAPTERS/LESSONS
1. MATH STANDARDS
MATH PRACTICES
SPECIAL EXPLANATIONS
product of P and a factor not depending on P.
CCSS.MATH.CONTENT.HSA.CED.A.1
Create equations and inequalities in one
variable and use them to solve problems.
Include equations arising from linear and
quadratic functions, and simple rational and
exponential functions.
CCSS.MATH.CONTENT.HSA.CED.A.2
Create equations in two or more variables to
represent relationships between quantities;
graph equations on coordinate axes with labels
and scales.
CCSS.MATH.CONTENT.HSF.IF.A.3
Recognize that sequences are functions,
sometimes defined recursively, whose domain
is a subset of the integers. For example, the
Fibonacci sequence is defined recursively by
f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
CCSS.MATH.CONTENT.HSF.IF.B.6
Calculate and interpret the average rate of
change of a function (presented symbolically
or as a table) over a specified interval.
Estimate the rate of change from a graph.*
CCSS.MATH.CONTENT.HSF.IF.C.7.E
Graph exponential and logarithmic functions,
showing intercepts and end behavior, and
trigonometric functions, showing period,
midline, and amplitude.
CCSS.MATH.CONTENT.HSF.IF.B.4
For a function that models a relationship
between two quantities, interpret key features
of graphs and tables in terms of the quantities,
and sketch graphs showing key features given
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CHAPTERS/LESSONS
1. MATH STANDARDS
MATH PRACTICES
SPECIAL EXPLANATIONS
a verbal description of the relationship. Key
features include: intercepts; intervals where
the function is increasing, decreasing, positive,
or negative; relative maximums and
minimums; symmetries; end behavior; and
periodicity.*
CCSS.MATH.CONTENT.HSF.BF.A.1.A
Determine an explicit expression, a recursive
process, or steps for calculation from a
context.
CCSS.MATH.CONTENT.HSF.BF.A.1.A
Determine an explicit expression, a recursive
process, or steps for calculation from a
context.
CCSS.MATH.CONTENT.HSF.BF.B.3
Identify the effect on the graph of
replacing f(x) by f(x) + k, k f(x), f(kx),
and f(x + k) for specific values of k (both
positive and negative); find the value
of k given the graphs. Experiment with cases
and illustrate an explanation of the effects on
the graph using technology. Include
recognizing even and odd functions from their
graphs and algebraic expressions for them.
CCSS.MATH.CONTENT.HSF.LE.A.1.A
Prove that linear functions grow by equal
differences over equal intervals, and that
exponential functions grow by equal factors
over equal intervals.
CCSS.MATH.CONTENT.HSF.LE.A.1.B
Recognize situations in which one quantity
changes at a constant rate per unit interval
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CHAPTERS/LESSONS
1. MATH STANDARDS
MATH PRACTICES
SPECIAL EXPLANATIONS
relative to another.
CCSS.MATH.CONTENT.HSF.LE.A.1.C
Recognize situations in which a quantity
grows or decays by a constant percent rate per
unit interval relative to another.
CCSS.MATH.CONTENT.HSF.LE.A.2
Construct linear and exponential functions,
including arithmetic and geometric sequences,
given a graph, a description of a relationship,
or two input-output pairs (include reading
these from a table).
CCSS.MATH.CONTENT.HSF.LE.A.3
Observe using graphs and tables that a
quantity increasing exponentially eventually
exceeds a quantity increasing linearly,
quadratically, or (more generally) as a
polynomial function.
CCSS.MATH.CONTENT.HSF.LE.B.5
Interpret the parameters in a linear or
exponential function in terms of a context.
CCSS.MATH.CONTENT.HSA.REI.D.10
Understand that the graph of an equation in
two variables is the set of all its solutions
plotted in the coordinate plane, often forming a
curve (which could be a line).
CCSS.MATH.CONTENT.HSA.REI.B.3
Solve linear equations and inequalities in one
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CHAPTERS/LESSONS
1. MATH STANDARDS
MATH PRACTICES
SPECIAL EXPLANATIONS
variable, including equations with coefficients
represented by letters.
CCSS.MATH.CONTENT.HSA.REI.D.11
Explain why the x-coordinates of the points
where the graphs of the equations y = f(x)
and y = g(x) intersect are the solutions of the
equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph
the functions, make tables of values, or find
successive approximations. Include cases
where f(x) and/or g(x) are linear, polynomial,
rational, absolute value, exponential, and
logarithmic functions.*
CCSS.MATH.CONTENT.HSA.REI.C.5
Prove that, given a system of two equations in
two variables, replacing one equation by the
sum of that equation and a multiple of the
other produces a system with the same
solutions.
CCSS.MATH.CONTENT.HSA.REI.C.6
Solve systems of linear equations exactly and
approximately (e.g., with graphs), focusing on
pairs of linear equations in two variables.
CCSS.MATH.CONTENT.HSN.Q.A.2
Define appropriate quantities for the purpose
of descriptive modeling.
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CHAPTERS/LESSONS
1. MATH STANDARDS
MATH PRACTICES
SPECIAL EXPLANATIONS
Chapter 7
CCSS.MATH.CONTENT.HSA.REI.D.12
Graph the solutions to a linear inequality in
two variables as a half-plane (excluding the
boundary in the case of a strict inequality), and
graph the solution set to a system of linear
inequalities in two variables as the intersection
of the corresponding half-planes.
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Youngstown City Schools - - CURRICULUM MAP – MATH (2014-2015)
Unit: # 3
CHAPTERS/LESSONS
Chapter 11:
10 Instructional—6 Software—1 Assessment
11.1 Curve Ball
11.2 Just U and I
11.3 Walking the…Curve?
Name: Expressions and Equations
Time: 27 Instructional - 15 Software - 4 Assessment
MATH STANDARDS
MATH PRACTICES
1) HSA.SSE.A.1
Interpret expressions that represent a quantity in terms of its
context.*
a) HSA.SSE.A.1.A Interpret parts of an expression,
such as terms, factors, and coefficients.
b) HSA.SSE.A.1.B
Interpret complicated expressions by viewing one or
more of their parts as a single entity. For example,
interpret P(1+r)n as the product of P and a factor
not depending on P.
2) HSA.CED.A.1
Create equations and inequalities in one variable and
use them to solve problems. Include equations arising
from linear and quadratic functions, and simple rational
and exponential functions.
3) HSA.CED.A.2
Create equations in two or more variables to represent
relationships between quantities; graph equations on
coordinate axes with labels and scales.
4) CCSS.MATH.CONTENT.HSF.IF.B.4
For a function that models a relationship between two
quantities, interpret key features of graphs and tables in
terms of the quantities, and sketch graphs showing key
features given a verbal description of the relationship.
Key features include: intercepts; intervals where the
function is increasing, decreasing, positive, or negative;
relative maximums and minimums; symmetries; end
behavior; and periodicity.
5) CCSS.MATH.CONTENT.HSF.IF.C.7
Graph functions expressed symbolically and show key
features of the graph, by hand in simple cases and using
technology for more complicated cases.
6/3/2014








SPECIAL
EXPLANATIONS
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 express
regularity in repeated
reasoning.
Youngstown City Schools – Math Map – Algebra I – 2014-2015 25
CHAPTERS/LESSONS
11.4 Are You Afraid of Ghosts?
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
a) CCSS.MATH.CONTENT.HSF.IF.C.7.A
Graph linear and quadratic functions and show
intercepts, maxima, and minima.
1) HSA.SSE.A.1
Interpret expressions that represent a quantity in terms of its
context.*
a) HSA.SSE.A.1.A Interpret parts of an expression,
such as terms, factors, and coefficients.
b) HSA.SSE.A.1.B
Interpret complicated expressions by viewing one or
more of their parts as a single entity. For example,
interpret P(1+r)n as the product of P and a factor
not depending on P.
2) CCSS.MATH.CONTENT.HSA.SSE.B.3
Choose and produce an equivalent form of an
expression to reveal and explain properties of the
quantity represented by the expression.*
a) CCSS.MATH.CONTENT.HSA.SSE.B.3.A
Factor a quadratic expression to reveal the zeros of
the function it defines.
3) HSA.CED.A.1
Create equations and inequalities in one variable and
use them to solve problems. Include equations arising
from linear and quadratic functions, and simple rational
and exponential functions.
4) HSA.CED.A.2
Create equations in two or more variables to represent
relationships between quantities; graph equations on
coordinate axes with labels and scales.
5) CCSS.MATH.CONTENT.HSF.IF.B.4
For a function that models a relationship between two
quantities, interpret key features of graphs and tables in
terms of the quantities, and sketch graphs showing key
features given a verbal description of the relationship.
Key features include: intercepts; intervals where the
function is increasing, decreasing, positive, or negative;
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CHAPTERS/LESSONS
MATH STANDARDS
6)
11.5 Just Watch that Pumpkin Fly
1)
2)
11.6 The Form is “Key”
1)
2)
MATH PRACTICES
SPECIAL
EXPLANATIONS
relative maximums and minimums; symmetries; end
behavior; and periodicity.
CCSS.MATH.CONTENT.HSF.IF.B.5
Relate the domain of a function to its graph and, where
applicable, to the quantitative relationship it describes.
For example, if the function h(n) gives the number of
person-hours it takes to assemble n engines in a factory,
then the positive integers would be an appropriate
domain for the function.
CCSS.MATH.CONTENT.HSF.IF.B.4
For a function that models a relationship between two
quantities, interpret key features of graphs and tables in
terms of the quantities, and sketch graphs showing key
features given a verbal description of the relationship.
Key features include: intercepts; intervals where the
function is increasing, decreasing, positive, or negative;
relative maximums and minimums; symmetries; end
behavior; and periodicity.
CCSS.MATH.CONTENT.HSF.IF.B.5
Relate the domain of a function to its graph and, where
applicable, to the quantitative relationship it describes.
For example, if the function h(n) gives the number of
person-hours it takes to assemble n engines in a factory,
then the positive integers would be an appropriate
domain for the function.
CCSS.MATH.CONTENT.HSF.IF.B.4
For a function that models a relationship between two
quantities, interpret key features of graphs and tables in
terms of the quantities, and sketch graphs showing key
features given a verbal description of the relationship.
Key features include: intercepts; intervals where the
function is increasing, decreasing, positive, or negative;
relative maximums and minimums; symmetries; end
behavior; and periodicity.
CCSS.MATH.CONTENT.HSF.IF.B.5
Relate the domain of a function to its graph and, where
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CHAPTERS/LESSONS
MATH STANDARDS
3)
11.7 More Than Meets The Eye
Chapter 12
1)
1)
8 Instructional—4 Software—1 instructional
12.1 Controlling the Population
2)
3)
MATH PRACTICES
SPECIAL
EXPLANATIONS
applicable, to the quantitative relationship it describes.
For example, if the function h(n) gives the number of
person-hours it takes to assemble n engines in a factory,
then the positive integers would be an appropriate
domain for the function.
CCSS.MATH.CONTENT.HSF.IF.C.7
Graph functions expressed symbolically and show key
features of the graph, by hand in simple cases and using
technology for more complicated cases.
a. CCSS.MATH.CONTENT.HSF.IF.C.7.A
Graph linear and quadratic functions and show
intercepts, maxima, and minima.
CCSS.MATH.CONTENT.HSF.BF.B.3
Identify the effect on the graph of replacing f(x) by f(x) +
k, k f(x), f(kx), and f(x + k) for specific values of k (both
positive and negative); find the value of k given the
graphs. Experiment with cases and illustrate an
explanation of the effects on the graph using technology.
Include recognizing even and odd functions from their
graphs and algebraic expressions for them.
CCSS.MATH.CONTENT.HSA.SSE.A.1
Interpret expressions that represent a quantity in terms
of its context.*
a) CCSS.MATH.CONTENT.HSA.SSE.A.1.A
Interpret parts of an expression, such as terms,
factors, and coefficients.
CCSS.MATH.CONTENT.HSA.APR.A.1
Understand that polynomials form a system analogous
to the integers, namely, they are closed under the
operations of addition, subtraction, and multiplication;
add, subtract, and multiply polynomials.
HSA.CED.A.1
Create equations and inequalities in one variable and
use them to solve problems. Include equations arising
from linear and quadratic functions, and simple rational
and exponential functions.
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CHAPTERS/LESSONS
12.2 They’re Multiplying Like
Polynomials!
12.3 What Factored Into It?
12.4 Solving Quadratics by
Factoring
12.5 What Makes You So Special?
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
4) HSA.CED.A.2
Create equations in two or more variables to represent
relationships between quantities; graph equations on
coordinate axes with labels and scales.
1) HSA.APR.A.1
Understand that polynomials form a system analogous
to the integers, namely, they are closed under the
operations of addition, subtraction, and multiplication;
add, subtract, and multiply polynomials.
1) HSA.SSE.B.3
Choose and produce an equivalent form of an
expression to reveal and explain properties of the
quantity represented by the expression.*
a) HSA.SSE.B.3.A
Factor a quadratic expression to reveal the zeros of
the function it defines.
2) HSA.APR.A.1
Understand that polynomials form a system analogous
to the integers, namely, they are closed under the
operations of addition, subtraction, and multiplication;
add, subtract, and multiply polynomials.
HSA.REI.B.4
Solve quadratic equations in one variable.
b) HSA.REI.B.4.B
Solve quadratic equations by inspection (e.g., for x2
= 49), taking square roots, completing the square,
the quadratic formula and factoring, as appropriate
to the initial form of the equation. Recognize when
the quadratic formula gives complex solutions and
write them as a ± bi for real numbers a and b.
1) CCSS.MATH.CONTENT.HSA.SSE.A.2
Use the structure of an expression to identify ways to
rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus
recognizing it as a difference of squares that can be
factored as (x2 - y2)(x2 + y2).
1)
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CHAPTERS/LESSONS
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
2) HSA.APR.A.1
Understand that polynomials form a system analogous
to the integers, namely, they are closed under the
operations of addition, subtraction, and multiplication;
add, subtract, and multiply polynomials.
12.6 Could It Be Groovy to be
1) CCSS.MATH.CONTENT.HSA.SSE.B.3
Square?
Choose and produce an equivalent form of an
expression to reveal and explain properties of the
quantity represented by the expression.
2) CCSS.MATH.CONTENT.HSA.REI.B.4
Solve quadratic equations in one variable.
12.7 Another Method
1) HSA.SSE.B.3
Choose and produce an equivalent form of an
expression to reveal and explain properties of the
quantity represented by the expression.*
a) HSA.SSE.B.3.A
Factor a quadratic expression to reveal the zeros of
the function it defines.
b) CCSS.MATH.CONTENT.HSA.SSE.B.3.B
Complete the square in a quadratic expression to
reveal the maximum or minimum value of the
function it defines.
2) CCSS.MATH.CONTENT.HSA.REI.B.4
Solve quadratic equations in one variable.
a) CCSS.MATH.CONTENT.HSA.REI.B.4.A
Use the method of completing the square to
transform any quadratic equation in x into an
equation of the form (x - p)2 = q that has the same
solutions. Derive the quadratic formula from this
form.
Chapter 13
1) CCSS.MATH.CONTENT.HSA.REI.B.4
5 Instructional—3 Software—1 Assessment
Solve quadratic equations in one variable.
13.1 Ladies and Gentlemen: Please
a) CCSS.MATH.CONTENT.HSA.REI.B.4.A
Welcome the Quadratic formula!
Use the method of completing the square to
transform any quadratic equation in x into an
equation of the form (x - p)2 = q that has the same
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CHAPTERS/LESSONS
13.2 It’s Got Its Eye on you—Or the
Ball
13.3 They’re A Lot More Than Just
Sparklers
Chapter 14
4 Instructional—2 Software—1 Assessment
14.3 Imagine the Possibilities
14.4 It’s Not Complex—Just Its
solutions are Complex!
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
solutions. Derive the quadratic formula from this
form.
b) CCSS.MATH.CONTENT.HSA.REI.B.4.B
Solve quadratic equations by inspection (e.g., for x2
= 49), taking square roots, completing the square,
the quadratic formula and factoring, as appropriate
to the initial form of the equation. Recognize when
the quadratic formula gives complex solutions and
write them as a ± bi for real numbers a and b.
3) HSA.SSE.B.3
Choose and produce an equivalent form of an
expression to reveal and explain properties of the
quantity represented by the expression.*
a) HSA.SSE.B.3.A
Factor a quadratic expression to reveal the zeros of
the function it defines.
1) CCSS.MATH.CONTENT.HSA.REI.B.4
Solve quadratic equations in one variable.
b) CCSS.MATH.CONTENT.HSA.REI.B.4.B
Solve quadratic equations by inspection (e.g., for x2
= 49), taking square roots, completing the square,
the quadratic formula and factoring, as appropriate
to the initial form of the equation. Recognize when
the quadratic formula gives complex solutions and
write them as a ± bi for real numbers a and b.
1) CCSS.MATH.CONTENT.HSA.CED.A.1
Create equations and inequalities in one variable and use
them to solve problems. Include equations arising from linear
and quadratic functions, and simple rational and exponential
functions.
1) CCSS.MATH.CONTENT.HSN.RN.A.2
Rewrite expressions involving radicals and rational
exponents using the properties of exponents.
2) CCSS.MATH.CONTENT.HSA.REI.B.4
Solve quadratic equations in one variable.
b) CCSS.MATH.CONTENT.HSA.REI.B.4.B
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CHAPTERS/LESSONS
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
Solve quadratic equations by inspection (e.g., for x2
= 49), taking square roots, completing the square,
the quadratic formula and factoring, as appropriate
to the initial form of the equation. Recognize when
the quadratic formula gives complex solutions and
write them as a ± bi for real numbers a and b.
6/3/2014
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Youngstown City Schools - - CURRICULUM MAP – MATH (2014-2015)
Algebra 1: Unit: # 4
Name: Quadratic Functions & Modeling
CHAPTERS/LESSONS
Chapter 15: Other Functions and Inverses
15.1 Piecewise Functions
15.2 Step Functions
Time: 14 instructional + 3 software + 2 assessments
MATH STANDARDS
N.Q.2
Define appropriate
quantities for the
purpose of
descriptive
modeling.
F.IF.4
For a function that
models a
relationship
between two
quantities,
interpret key
features of graphs
and tables in terms
of the quantities,
and sketch graphs
showing key
features given a
verbal description
of the
relationship. Key
features include:
intercepts;
intervals where
the function is
increasing,
6/3/2014
MATH PRACTICES
1. Make sense of problems
and persevere in solving
them.
2. Reason abstractly and
quantitatively.
3. Construct viable
arguments and critique the
reasoning of others.
4. Model with mathematics.
5. Use appropriate tools
strategically.
6. Attend to precision.
7. Look for and make use of
structure.
8. Look for and express
regularity in repeated
reasoning
SPECIAL
EXPLANATIONS
OMIT 15.3 & 15.4
Youngstown City Schools – Math Map – Algebra I – 2014-2015 33
CHAPTERS/LESSONS
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
decreasing,
positive, or
negative; relative
maximums and
minimums;
symmetries; end
behavior; and
periodicity.*
F.IF.5
Relate the domain
of a function to its
graph and, where
applicable, to the
quantitative
relationship it
describes. For
example, if the
function h(n) gives
the number of
person-hours it
takes to assemble
n engines in a
factory, then the
positive integers
would be an
appropriate domain
for the function.*
F.IF.7b
Graph square root,
cube root, and
piecewise-defined
6/3/2014
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CHAPTERS/LESSONS
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
functions,
including step
functions and
absolute value
functions.
Chapter 16: Mathematical Modeling+
16.1 Modeling Using Exponential Functions
16.2 Modeling Stopping Distances and Reaction Times
16.3 Using Quadratic Functions to Model Data
16.4 Choosing the Best Function to Model Data
16.5 Modeling with Piecewise Functions
F.IF.4
For a function that
models a
relationship
between two
quantities,
interpret key
features of graphs
and tables in terms
of the quantities,
and sketch graphs
showing key
features given a
verbal description
of the
relationship. Key
features include:
intercepts;
intervals where
the function is
increasing,
decreasing,
6/3/2014
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CHAPTERS/LESSONS
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
positive, or
negative; relative
maximums and
minimums;
symmetries; end
behavior; and
periodicity.*
F.IF. 5
Relate the domain
of a function to its
graph and, where
applicable, to the
quantitative
relationship it
describes. For
example, if the
function h(n) gives
the number of
person-hours it
takes to assemble
n engines in a
factory, then the
positive integers
would be an
appropriate domain
for the function.*
F.IF.7
Graph functions
expressed
6/3/2014
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CHAPTERS/LESSONS
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
symbolically and
show key features
of the graph, by
hand in simple
cases and using
technology
for more
complicated
cases.*
F.BF.1
Write a function
that describes a
relationship
between two
quantities.*
F.BF.4
Find inverse
functions.
F.LE.1
Distinguish
between
situations that
can be modeled
with linear
functions and
with exponential
functions.
F.LE.2
Construct linear
6/3/2014
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CHAPTERS/LESSONS
MATH STANDARDS
MATH PRACTICES
SPECIAL
EXPLANATIONS
and exponential
functions,
including
arithmetic and
geometric
sequences, given
a graph, a
description of a
relationship, or
two input-output
pairs (include
reading these
from a table).
6/3/2014
Youngstown City Schools – Math Map – Algebra I – 2014-2015 38
Youngstown City Schools - - CURRICULUM MAP – MATH (2014-2015)
Unit: #5
Name: Descriptive Statistics
MATH STANDARDS
Chapter 8
CCSS.MATH.CONTENT.HSS.ID.A.1
Represent data with plots on the real number
line (dot plots, histograms, and box plots).
CCSS.MATH.CONTENT.HSS.ID.A.2
Use statistics appropriate to the shape of the
data distribution to compare center (median,
mean) and spread (interquartile range, standard
deviation) of two or more different data sets.
CCSS.MATH.CONTENT.HSS.ID.A.3
Interpret differences in shape, center, and
spread in the context of the data sets,
accounting for possible effects of extreme data
points (outliers).
Time: (21 instruction days, 7 computer days, 3 testing days)
CHAPTERS/LESSONS
Chapter 8: Analyzing
Data Sets for One
Variable
8.1, 8.2, 8.3, 8.4, 8.5
Chapter 9: Correlation
and Residuals
9.1, 9.2, 9.3, 9.4, 9.5
Chapter 10: Analyzing
Data Sets for Two
Categorical Variables.
10.1, 10.2, 10.3, 10.4
MATH PRACTICES
1. Make sense of problems
and
persevere in solving them.
2. Reason
abstractly and quantitatively.
3. Construct viable
arguments and critique the
reasoning of others.
4. Model with
mathematics.
5. Use appropriate
tools strategically.
6. Attend to
precision.
7. Look for and
make use of structure.
8. Look for and
express regularity in repeated
reasoning
SPECIAL
EXPLANATIONS
Chapter 8
8.1: Graphically
Representing Data
Do Problems 1 and 3
Do the check for
understanding.
8.2: Determining the Best
Measure of Center for Data
Set
Do Problems 1 and 2.
8.3: Calculating IQR and
Identifying outliers
Do Problems 1 and 2.
8.4: Calculating and
interpreting Standard
Deviation
Chapter 9
CCSS.MATH.CONTENT.HSS.ID.B.6
Do Problems 1 and 2.
Represent data on two quantitative variables on
a scatter plot, and describe how the variables
are related.
8.5: Analyzing and
Interpreting Data
Skip
CCSS.MATH.CONTENT.HSS.ID.B.6.A
Fit a function to the data; use functions fitted to
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MATH STANDARDS
CHAPTERS/LESSONS
MATH PRACTICES
SPECIAL
EXPLANATIONS
Chapter 9
data to solve problems in the context of the
data. Use given functions or choose a function
suggested by the context. Emphasize linear,
quadratic, and exponential models.
9.1: Least Squares
Regression
Do Problems 1 and 3.
CCSS.MATH.CONTENT.HSS.ID.B.6.B
9.2: Correlation and
Residuals
Informally assess the fit of a function by
plotting and analyzing residuals.
Do problem 2 and 3.
(Google how to find r using
TI30XIIS)
CCSS.MATH.CONTENT.HSS.ID.B.6.C
Fit a linear function for a scatter plot that
suggests a linear association.
9.3: Creating Residual Plots
CCSS.MATH.CONTENT.HSS.ID.C.7
Do entire section
Interpret the slope (rate of change) and the
intercept (constant term) of a linear model in
the context of the data.
9.4: Using Residual Plots
Do problem 1.
CCSS.MATH.CONTENT.HSS.ID.C.8
9.5: Causation vs.
Correlation
Compute (using technology) and interpret the
correlation coefficient of a linear fit.
Do Problem 1 and 2.
CCSS.MATH.CONTENT.HSS.ID.C.9
Distinguish between correlation and causation.
Chapter 10
Chapter 10
10.1: Interpreting
Frequency Distributions
CCSS.MATH.CONTENT.HSS.ID.B.5
Do Problems 1 and 2.
Summarize categorical data for two categories
in two-way frequency tables. Interpret relative
frequencies in the context of the data (including
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Youngstown City Schools – Math Map – Algebra I – 2014-2015 40
MATH STANDARDS
CHAPTERS/LESSONS
MATH PRACTICES
SPECIAL
EXPLANATIONS
10.2: Relative Frequency
Distribution
joint, marginal, and conditional relative
frequencies). Recognize possible associations
and trends in the data.
Problem 1 and Check for
Students’ Understanding
(584A Teacher’s edition)
10.3: Relative Frequency
Conditional Distribution
Problem 1 and Check for
Students’ Understanding
(600A Teacher’s edition)
10.4: Drawing Conclusions
from Data
Do Problems 1 and 2.
6/3/2014
Youngstown City Schools – Math Map – Algebra I – 2014-2015 41