algebra 1 pacing guide - wikispaceshcsresources.wikispaces.com/file/...schools_algebra... ·...
TRANSCRIPT
1
Algebra 1 Pacing Guide 90-minute Block Schedule
Glencoe Text (Copyright 2004)
Revised (June 2011)
The textbook should be considered one of many resources. Manipulative should be used as teaching and learning tools to enhance students’
understanding.
Note: The current SCOS will continue to be taught and tested in the 2011-12 school year.
The Common Core Standards will be fully implemented in the 2012-13 school year.
The graphing calculator is used throughout the entire course.
Day Days Section Objectives by NCSCOS Common Core Optional 1-1
1-2
1-3
1-1 Write
mathematical
expressions for verbal
expressions and vice
versa.
1-2 Evaluate
numerical and
algebraic expressions
by using the order
rule.
1-3 Solve open
sentence equations and
inequalities.
1.01
Write equivalent
forms of algebraic
expressions to solve
problems
a. Apply the laws of
exponents.
b. Operate with
polynomials
c. Factor polynomials.
N.RN.1 (SCoS 1.01)
Extend the properties of exponents to rational exponents
Explain how the definition of the meaning of rational
exponents follows from extending the properties fo integer
exponents to those values, allowing for a notation for radicals
in terms of rational exponents. For example, we define 51/3
to
be the cube of 5 because we want (51/3
)3 must equal 5
N.RN.2 (SCoS 1.01)
Extend the properties of exponents to rational exponents.
Rewrite expressions involving radicals and rational exponents
using the properties of exponents.
N.RN.3 (SCoS 1.01)
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.
A.APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations no polynomials
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
2
1.02
Use formulas and
algebraic expressions,
including iterative and
recursive forms, to
model ad solve
problems
multiply polynomials
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers.
For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
3
Optional 1-4
1-5
1-6
1-4 Recognize and use
the properties of
identity and equality.
1-5 Use the
Distributive Property
to evaluate and
simplify expressions.
1-6 Recognize and use
the Commutative and
Associative Properties
to simplify
expressions.
1.01
Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02
Use formulas and
algebraic expressions,
including iterative and
recursive forms, to
model ad solve
problems
A.APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations no polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers.
For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
1,2,3
3
1-8
1-9
1-8 Interpret and
draw graphs of
functions.
1-9 Analyze data
given in tables and
1.02
Use formulas and
algebraic expressions,
including iterative and
recursive forms, to
model ad solve
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
4
graphs. problems
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers.
For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
4,5 2 13-2 13-2 Solve problems
by adding or
subtracting matrices
or multiplying,
multiplying by a
scalar.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers.
For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
5
Organize and read
data in matrices.
3.01 Use of matrices
to display and
interpret data.
3.03 Create linear
models, for sets of
data, to solve
problems.
a) Interpret contents
and coefficients in the
context of the data.
b) Check the model
for goodness of fit
and use the model,
where appropriate, to
draw conclusions or
make predictions.
SCoS (3.01, 3.02) Moved to a fourth course to follow
Algebra II.
S.ID.6 (SCoS 3.03)
Summarize, represent, and interpret data on two
categorical and quantitative variables
Represent data on two quantitative variables on a scatter plot,
and describe how the variables are related.
a) Fit a function to the data; use functions fitted to data to
solve problems in the context of the data. Use given
functions or choose function suggested by the context,
Emphasize linear and exponential models.
b) Informally assess the fit of a function by plotting and
analyzing residuals.
c) Fit a linear function for a scatter plot that suggested a
linear association.
S.ID.7 (SCoS 3.03)
Interpret the slope (rate of change) and the intercept
(constant term) of a linear model in the context of the data.
6 1 Assessment/EOC
Practice Goal
Specific
Optional 2-1
2-2
2-3
2-4
2-7
Graph rational
numbers on a number
line. Find absolute
values of rational
numbers.
Add and subtract
integers and rational
numbers.
Multiply integers.
1.01
Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
A.APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations no polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
6
Multiply rational
numbers.
(Calculator )
Divide integers.
Divide rational
numbers.
Find square roots.
Classify and order real
numbers. (Calculator
)
1.02
Use formulas and
algebraic expressions,
including iterative and
recursive forms, to
model ad solve
problems
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers.
For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
7 1 Assessment/EOC
Practice Goal
Specific
8,9 2 3-1
3-2
3-3
Translate verbal
sentences into
equations and vice
versa.
Solve equations by
using addition and
subtraction.
Solve equations by
using multiplication
and division.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02Use formulas and
A.APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations no polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
Rearrange formulas to highlight a quantity of interest using the
7
algebraic expressions,
including iterative and
recursive forms, to
model ad solve
problems
same reasoning as in solving equations. For example,
rearrange Ohm’s law V=IR to highlight resistance R.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
10,11
2
3-4
3-5
Solve equations
involving more than
one operation.
Solve equations with
the variable on each
side. Solve equations
involving grouping
symbols.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations no polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
8
solve problems
1.03 Model and solve
problems using direct
variation.
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
Moved to 7th
grade CCSS
12 1 3-6
3-7 Determine whether
two ratios form a
proportion. Solve
proportions.
Find percents of
increase and decrease.
Solve problems
involving percents of
change.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
9
forms, to model ad
solve problems
1.03 Model and solve
problems using direct
variation.
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
13,14 2 3-8
3-9 Solve equations for
given variables. Use
formulas to solve
real-world problems.
Solve mixture
problems. Solve
uniform motion
problems
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
10
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
15 1 Assessment/EOC
Practice Goal
Specific
16,17
2
8-1
Multiply monomials.
Simplify expressions
involving powers of
monomials.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
11
18,19 2 8-2
8-3 Simplify expressions
involving the
quotient of
monomials and
containing negative
exponents.
Find products and
quotients of numbers
expressed in
scientific notation.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
20,21 2 8-4
8-5 Find the degree of a
polynomial. Arrange
the terms of a
polynomial in
ascending or
descending order.
Add and subtract
polynomials.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
12
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
22,23 2 8-6
8-7 Find the product of a
monomial and a
polynomial. Solve
equations involving
polynomials.
Multiply 2 binomials
by using the FOIL
method. Multiply 2
polynomials by using
the Distributive
Property.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
13
iterative and recursive
forms, to model ad
solve problems
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
24,25 2 8-8 Find the squares of
sums and differences.
Find the product of a
sum and a difference.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
14
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
26 1 Assessment/EOC
Practice Goal
Specific
27 1 4-1
4-3 Locate and graph
points on the
coordinate plane.
Represent relations
as sets of ordered
pairs, tables,
mappings, and
graphs. Find the
inverse of a relation.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems
2.01 Find the lengths
and the midpoints of
segments to solve
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
SCoS 2.01 Move to Geometry Common Core
State Standards
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
15
problems
4.01 Use linear
functions or
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
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 that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
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
Analyze functions using different representations
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.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
16
quantities.
a) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
of a context.
28,29 2 4-4
4-5 Use an equation to
determine the range
for a given domain.
Graph the solution
set for a given
domain.
Determine whether
an equation is linear.
Change equations
into “y =” form.
(Calculator)
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
3.03 Create linear
models, for sets of
data, to solve
problems.
a) Interpret contents
and coefficients n the
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
S.ID.6(SCoS 3.03)
Summarize, represent, and interpret data on two categorical and
quantitative variables
Represent data two quantitative variables on a scatter plot, and
describe how the variables are related.
a) Fit a functions to the data; use functions fitted to data to
solve problems in the context of the data.
b) Informally asses the fit of a function by plotting and
analyzing residuals
c) Fit a linear function for a scatter plot that suggests a linear
association.
17
context of the data.
b) Check the model
for goodness of fit
and use the model for
goodness of fit and
use the model, where
appropriate, to draw
conclusions or make
predictions.
4.01 Use linear
S.ID.7 (SCoS 3.03)
Interpret linear models
Interpret slope (rate of change) and the intercept (constant term) of a
linear model in the context of the data.
S.ID.1 (SCoS 3.03)
Summarize, represent, and interpret data on a single count or
measurement variable
Represent data with plots on the real number line (dot plots,
hstograms, and box plots).
S.ID2
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.
S.ID.3
Interpret differences in shape, center, and spread in the context of the
data sets, accounting for possible effects of extreme data points.
(outliers)
S.ID.5
Summarize, represent, and interpret data on two categorical and
quantitative variables.
Summarize categorical data for two categories in two-way frequency
tables. Interpret relative frequencies in the context of the data
(including joint, marginal, and conditional relative frequencies).
Recognize possible associations and trends in the data.
S.ID.8
Compute ( using technology) and interpret the correlation coefficient
of a linear fit.
S.ID.9
Interpret linear models
Distinguish between correlation and causation.
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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 that describe numbers or relationships
18
functions or
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
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
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
b) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
b) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
Interpret expressions for functions in terms of the situation they
19
model
Interpret the parameters in a linear or exponential function in terms
of a context.
30,31 2 4-5 Graph linear
equations.
( Calculator)
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
3.03 Create linear
models, for sets of
data, to solve
problems.
a) Interpret contents
and coefficients n the
context of the data.
b) Check the model
for goodness of fit
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
S.ID.6(SCoS 3.03)
Summarize, represent, and interpret data on two categorical and
quantitative variables
Represent data two quantitative variables on a scatter plot, and
describe how the variables are related.
d) Fit a functions to the data; use functions fitted to data to
solve problems in the context of the data.
e) Informally asses the fit of a function by plotting and
analyzing residuals
f) Fit a linear function for a scatter plot that suggests a linear
association.
S.ID.7 (SCoS 3.03)
Interpret linear models
Interpret slope (rate of change) and the intercept (constant term) of a
linear model in the context of the data.
20
and use the model for
goodness of fit and
use the model, where
appropriate, to draw
conclusions or make
predictions.
4.01 Use linear
functions or
inequalities to model
and solve problems;
justify results.
S.ID.1 (SCoS 3.03)
Summarize, represent, and interpret data on a single count or
measurement variable
Represent data with plots on the real number line (dot plots,
hstograms, and box plots).
S.ID2
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.
S.ID.3
Interpret differences in shape, center, and spread in the context of the
data sets, accounting for possible effects of extreme data points.
(outliers)
S.ID.5
Summarize, represent, and interpret data on two categorical and
quantitative variables.
Summarize categorical data for two categories in two-way frequency
tables. Interpret relative frequencies in the context of the data
(including joint, marginal, and conditional relative frequencies).
Recognize possible associations and trends in the data.
S.ID.8
Compute ( using technology) and interpret the correlation coefficient
of a linear fit.
S.ID.9
Interpret linear models
Distinguish between correlation and causation.
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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 that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
21
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
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
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
c) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
c) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
of a context.
32,33 2 4-6 Determine whether a
relation is a function.
1.02 Use formulas
and algebraic A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
22
Find functional
values.
expressions, including
iterative and recursive
forms, to model ad
solve problems.
3.03 Create linear
models, for sets of
data, to solve
problems.
a) Interpret contents
and coefficients n the
context of the data.
b) Check the model
for goodness of fit
and use the model for
goodness of fit and
use the model, where
appropriate, to draw
conclusions or make
predictions.
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
S.ID.6(SCoS 3.03)
Summarize, represent, and interpret data on two categorical and
quantitative variables
Represent data two quantitative variables on a scatter plot, and
describe how the variables are related.
g) Fit a functions to the data; use functions fitted to data to
solve problems in the context of the data.
h) Informally asses the fit of a function by plotting and
analyzing residuals
i) Fit a linear function for a scatter plot that suggests a linear
association.
S.ID.7 (SCoS 3.03)
Interpret linear models
Interpret slope (rate of change) and the intercept (constant term) of a
linear model in the context of the data.
S.ID.1 (SCoS 3.03)
Summarize, represent, and interpret data on a single count or
measurement variable
Represent data with plots on the real number line (dot plots,
hstograms, and box plots).
S.ID2
Use statistics appropriate to the shape of the data distribution to
23
4.01 Use linear
functions or
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
compare center (median, mean) and spread (interquartile range,
standard deviation) of two or more different data sets.
S.ID.3
Interpret differences in shape, center, and spread in the context of the
data sets, accounting for possible effects of extreme data points.
(outliers)
S.ID.5
Summarize, represent, and interpret data on two categorical and
quantitative variables.
Summarize categorical data for two categories in two-way frequency
tables. Interpret relative frequencies in the context of the data
(including joint, marginal, and conditional relative frequencies).
Recognize possible associations and trends in the data.
S.ID.8
Compute ( using technology) and interpret the correlation coefficient
of a linear fit.
S.ID.9
Interpret linear models
Distinguish between correlation and causation.
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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 that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two quantities, and
sketch graphs showing key features given a verbal description of the
relationship.
24
Key features include: intercepts; intervals where the function is
increasing, decreasing, positive, or negative; relative maximums and
minimums; symmetries; end behavior; and periodicity.
F.FIF
Interpret functions that arise in applications in terms
of the context
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
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
d) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
d) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
of a context.
Optional 4-7
Use iterative and
recursive formulas to
model and solve
problems.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
A.APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations no polynomials
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
25
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems
multiply polynomials
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers.
For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
34,35 2 4-8 Write an equation
(using the calculator)
given some of the
solutions.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
26
3.03 Create linear
models, for sets of
data, to solve
problems.
a) Interpret contents
and coefficients n the
context of the data.
b) Check the model
for goodness of fit
and use the model for
goodness of fit and
use the model, where
appropriate, to draw
conclusions or make
predictions.
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
S.ID.6(SCoS 3.03)
Summarize, represent, and interpret data on two categorical and
quantitative variables
Represent data two quantitative variables on a scatter plot, and
describe how the variables are related.
j) Fit a functions to the data; use functions fitted to data to
solve problems in the context of the data.
k) Informally asses the fit of a function by plotting and
analyzing residuals
l) Fit a linear function for a scatter plot that suggests a linear
association.
S.ID.7 (SCoS 3.03)
Interpret linear models
Interpret slope (rate of change) and the intercept (constant term) of a
linear model in the context of the data.
S.ID.1 (SCoS 3.03)
Summarize, represent, and interpret data on a single count or
measurement variable
Represent data with plots on the real number line (dot plots,
hstograms, and box plots).
S.ID2
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.
S.ID.3
Interpret differences in shape, center, and spread in the context of the
data sets, accounting for possible effects of extreme data points.
(outliers)
S.ID.5
Summarize, represent, and interpret data on two categorical and
quantitative variables.
Summarize categorical data for two categories in two-way frequency
tables. Interpret relative frequencies in the context of the data
27
4.01 Use linear
functions or
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
(including joint, marginal, and conditional relative frequencies).
Recognize possible associations and trends in the data.
S.ID.8
Compute ( using technology) and interpret the correlation coefficient
of a linear fit.
S.ID.9
Interpret linear models
Distinguish between correlation and causation.
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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 that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
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
28
F.IF.7
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
e) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
e) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
of a context.
36 1 Assessment/EOC
Practice Goal
Specific
37
1
5-1
5-2
Find the slope of a
line. Use rate of
change to solve
problems.
Solve problems
involving direct
variation. Include
writing and graphing
direct variation
equations.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
29
3.03 Create linear
models, for sets of
data, to solve
problems.
a) Interpret contents
and coefficients n the
context of the data.
b) Check the model
for goodness of fit
and use the model for
goodness of fit and
use the model, where
appropriate, to draw
conclusions or make
predictions.
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
S.ID.6(SCoS 3.03)
Summarize, represent, and interpret data on two categorical and
quantitative variables
Represent data two quantitative variables on a scatter plot, and
describe how the variables are related.
m) Fit a functions to the data; use functions fitted to data to
solve problems in the context of the data.
n) Informally asses the fit of a function by plotting and
analyzing residuals
o) Fit a linear function for a scatter plot that suggests a linear
association.
S.ID.7 (SCoS 3.03)
Interpret linear models
Interpret slope (rate of change) and the intercept (constant term) of a
linear model in the context of the data.
S.ID.1 (SCoS 3.03)
Summarize, represent, and interpret data on a single count or
measurement variable
Represent data with plots on the real number line (dot plots,
hstograms, and box plots).
S.ID2
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.
S.ID.3
Interpret differences in shape, center, and spread in the context of the
data sets, accounting for possible effects of extreme data points.
(outliers)
S.ID.5
Summarize, represent, and interpret data on two categorical and
quantitative variables.
Summarize categorical data for two categories in two-way frequency
tables. Interpret relative frequencies in the context of the data
30
4.01 Use linear
functions or
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
(including joint, marginal, and conditional relative frequencies).
Recognize possible associations and trends in the data.
S.ID.8
Compute ( using technology) and interpret the correlation coefficient
of a linear fit.
S.ID.9
Interpret linear models
Distinguish between correlation and causation.
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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 that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
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
31
F.IF.7
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
f) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
f) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
of a context.
38,39,40 3 5-3 Write and graph linear
equations in slope-
intercept form. Model
real-world data with
a linear equation.
(Calculator)
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
32
3.03 Create linear
models, for sets of
data, to solve
problems.
a) Interpret contents
and coefficients n the
context of the data.
b) Check the model
for goodness of fit
and use the model for
goodness of fit and
use the model, where
appropriate, to draw
conclusions or make
predictions.
S.ID.6(SCoS 3.03)
Summarize, represent, and interpret data on two categorical and
quantitative variables
Represent data two quantitative variables on a scatter plot, and
describe how the variables are related.
p) Fit a functions to the data; use functions fitted to data to
solve problems in the context of the data.
q) Informally asses the fit of a function by plotting and
analyzing residuals
r) Fit a linear function for a scatter plot that suggests a linear
association.
S.ID.7 (SCoS 3.03)
Interpret linear models
Interpret slope (rate of change) and the intercept (constant term) of a
linear model in the context of the data.
S.ID.1 (SCoS 3.03)
Summarize, represent, and interpret data on a single count or
measurement variable
Represent data with plots on the real number line (dot plots,
hstograms, and box plots).
S.ID2
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.
S.ID.3
Interpret differences in shape, center, and spread in the context of the
data sets, accounting for possible effects of extreme data points.
(outliers)
S.ID.5
Summarize, represent, and interpret data on two categorical and
quantitative variables.
Summarize categorical data for two categories in two-way frequency
tables. Interpret relative frequencies in the context of the data
(including joint, marginal, and conditional relative frequencies).
Recognize possible associations and trends in the data.
S.ID.8
Compute ( using technology) and interpret the correlation coefficient
of a linear fit.
S.ID.9
Interpret linear models
33
4.01 Use linear
functions or
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
Distinguish between correlation and causation.
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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 that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
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
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
g) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
34
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
g) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
of a context.
41,42 2 5-4 Write an equation of
a line given a) the
slope & one point on
a line b) two points
on the line
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
3.03 Create linear
models, for sets of
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
S.ID.6(SCoS 3.03)
Summarize, represent, and interpret data on two categorical and
quantitative variables
Represent data two quantitative variables on a scatter plot, and
describe how the variables are related.
s) Fit a functions to the data; use functions fitted to data to
solve problems in the context of the data.
35
data, to solve
problems.
a) Interpret contents
and coefficients n the
context of the data.
b) Check the model
for goodness of fit
and use the model for
goodness of fit and
use the model, where
appropriate, to draw
conclusions or make
predictions.
t) Informally asses the fit of a function by plotting and
analyzing residuals
u) Fit a linear function for a scatter plot that suggests a linear
association.
S.ID.7 (SCoS 3.03)
Interpret linear models
Interpret slope (rate of change) and the intercept (constant term) of a
linear model in the context of the data.
S.ID.1 (SCoS 3.03)
Summarize, represent, and interpret data on a single count or
measurement variable
Represent data with plots on the real number line (dot plots,
hstograms, and box plots).
S.ID2
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.
S.ID.3
Interpret differences in shape, center, and spread in the context of the
data sets, accounting for possible effects of extreme data points.
(outliers)
S.ID.5
Summarize, represent, and interpret data on two categorical and
quantitative variables.
Summarize categorical data for two categories in two-way frequency
tables. Interpret relative frequencies in the context of the data
(including joint, marginal, and conditional relative frequencies).
Recognize possible associations and trends in the data.
S.ID.8
Compute ( using technology) and interpret the correlation coefficient
of a linear fit.
S.ID.9
Interpret linear models
Distinguish between correlation and causation.
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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.
36
4.01 Use linear
functions or
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
A.CED.2
Create equations that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
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
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
h) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
h) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
37
F.lE.5
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
of a context.
43,44 2 5-5
5-6
Write the equation of a
line in point-slope
form. Write linear
equations in different
forms.
Write an equation of
the line that passes
through a given
point,
parallel/perpendicula
r to a given line.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
3.03 Create linear
models, for sets of
data, to solve
problems.
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
2.02 Moved to Geometry
S.ID.6(SCoS 3.03)
Summarize, represent, and interpret data on two categorical and
quantitative variables
Represent data two quantitative variables on a scatter plot, and
describe how the variables are related.
v) Fit a functions to the data; use functions fitted to data to
solve problems in the context of the data.
w) Informally asses the fit of a function by plotting and
analyzing residuals
38
a) Interpret contents
and coefficients n the
context of the data.
b) Check the model
for goodness of fit
and use the model for
goodness of fit and
use the model, where
appropriate, to draw
conclusions or make
predictions.
x) Fit a linear function for a scatter plot that suggests a linear
association.
S.ID.7 (SCoS 3.03)
Interpret linear models
Interpret slope (rate of change) and the intercept (constant term) of a
linear model in the context of the data.
S.ID.1 (SCoS 3.03)
Summarize, represent, and interpret data on a single count or
measurement variable
Represent data with plots on the real number line (dot plots,
hstograms, and box plots).
S.ID2
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.
S.ID.3
Interpret differences in shape, center, and spread in the context of the
data sets, accounting for possible effects of extreme data points.
(outliers)
S.ID.5
Summarize, represent, and interpret data on two categorical and
quantitative variables.
Summarize categorical data for two categories in two-way frequency
tables. Interpret relative frequencies in the context of the data
(including joint, marginal, and conditional relative frequencies).
Recognize possible associations and trends in the data.
S.ID.8
Compute ( using technology) and interpret the correlation coefficient
of a linear fit.
S.ID.9
Interpret linear models
Distinguish between correlation and causation.
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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 that describe numbers or relationships
39
4.01 Use linear
functions or
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
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
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
i) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
i) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
Interpret expressions for functions in terms of the situation they
40
model
Interpret the parameters in a linear or exponential function in terms
of a context.
45,46,47 3 5-7 Interpret points on a
scatter plot. Write
equations for lines of
fit.
3.03 Create linear
models, for sets of
data, to solve
problems.
a) Interpret contents
and coefficients n the
context of the data.
b) Check the model
for goodness of fit
and use the model for
goodness of fit and
use the model, where
appropriate, to draw
conclusions or make
predictions.
S.ID.6(SCoS 3.03)
Summarize, represent, and interpret data on two categorical and
quantitative variables
Represent data two quantitative variables on a scatter plot, and
describe how the variables are related.
y) Fit a functions to the data; use functions fitted to data to
solve problems in the context of the data.
z) Informally asses the fit of a function by plotting and
analyzing residuals
aa) Fit a linear function for a scatter plot that suggests a linear
association.
S.ID.7 (SCoS 3.03)
Interpret linear models
Interpret slope (rate of change) and the intercept (constant term) of a
linear model in the context of the data.
S.ID.1 (SCoS 3.03)
Summarize, represent, and interpret data on a single count or
measurement variable
Represent data with plots on the real number line (dot plots,
hstograms, and box plots).
S.ID2
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.
S.ID.3
Interpret differences in shape, center, and spread in the context of the
data sets, accounting for possible effects of extreme data points.
(outliers)
S.ID.5
Summarize, represent, and interpret data on two categorical and
quantitative variables.
Summarize categorical data for two categories in two-way frequency
tables. Interpret relative frequencies in the context of the data
(including joint, marginal, and conditional relative frequencies).
Recognize possible associations and trends in the data.
S.ID.8
41
4.01 Use linear
functions or
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
Compute ( using technology) and interpret the correlation coefficient
of a linear fit.
S.ID.9
Interpret linear models
Distinguish between correlation and causation.
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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 that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
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
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
42
graph, by hand in simple cases and using technology for more
complicated cases.
j) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
j) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
of a context.
48 1 Assessment/EOC
Practice Goal
Specific
49,50 2 6-1
6-2 Solve linear
inequalities by using
addition and
subtraction.
Solve linear
inequalities by using
multiplication and
division. (
Calculator)
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
4.01 Use linear
functions or
inequalities to model
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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
43
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
Create equations that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
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
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
k) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
k) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
44
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
of a context.
51,52 2 6-3 Solve linear
inequalities involving
more than one
operation; involving
the Distributive
Property.
(Calculator)
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
45
4.01 Use linear
functions or
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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 that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
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
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
46
l) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
l) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
of a context.
53,54 2 6-4
6-5 Solve conjunction
and disjunction
inequalities and
graph their solution
sets.
Solve absolute value
equations.
(Calculator)
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
4.01 Use linear
functions or
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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 that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
47
b) Interpret constants
and coefficients in the
context of the
problem.
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
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
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
m) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
m) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
of a context.
48
55,56 2 6-6
7-5 Graph inequalities
on the coordinate
plane. Solve real-
world problems
involving linear
inequalities.
Solve systems of
inequalities by
graphing. Solve real-
world problems
involving systems of
inequalities.
(Calculator)
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
4.01 Use linear
functions or
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
4.03
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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 that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
Relate the domain of a function to its graph and, where applicable, to
49
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
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
n) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
n) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
of a context.
57 1 Assessment/EOC
Practice Goal
Specific
58,59 2 7-1 Determine the
number of solutions
for a system of linear
equations. Solve
systems of equations
by graphing.
2.02
3.03
4.01
4.03
4.01 Use linear
functions or
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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 that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
50
b) Interpret constants
and coefficients in the
context of the
problem.
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
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
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
o) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
o) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
51
of a context.
60,61 2 7-2 Solve systems of
equations by using
substitution. Solve
real-world problems
involving systems.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
4.01 4.03
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
4.03
4.01 Use linear
functions or
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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.
52
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
A.CED.2
Create equations that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two 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.FIF
Interpret functions that arise in applications in terms of the
context
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
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
p) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
p) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
53
F.lE.5
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
of a context.
62,63,64 3 7-3
7-4 Solve systems of
equations by using
elimination with
addition and
subtraction.
Solve systems of
equations by using
elimination and by
Matrices.
Determine the best
method for solving.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
4.01 Use linear
functions or
inequalities to model
and solve problems;
justify results.
a) Solve using tables,
graphs, and algebraic
properties.
b) Interpret constants
and coefficients in the
context of the
problem.
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED.1 (SCoS 4.01)
Create equations that describe numbers or relationships
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 that describe numbers or relationships
Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels
and scales.
F.FIF.2
Understand the concept of a function and use function notation
Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context.
F.FIF.4
Interpret functions tat arise in applications I terms of the context
For a function that models a relationship between two quantities, and
sketch graphs showing key features given a verbal description of the
54
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.FIF
Interpret functions that arise in applications in terms of the
context
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
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases.
q) Graph linear and quadratic functions and show intercepts,
maxima, and minima.
F.BF.1
Build a function that models a relationship between two
quantities
Write a function that describes a relationship between two a
quantities.
q) Determine an explicit expression, a recursive process, or
steps for calculation from a context.
F.lE.5
Interpret expressions for functions in terms of the situation they
model
Interpret the parameters in a linear or exponential function in terms
of a context.
A.CED.3 (SCoS 4.03) Create Equations that describe numbers or
relationships
Represent constraints by equations or inequalities, and by systems of
equations and/or inequalities, and interpret solutions as viable or non-
viable ooptions in a modeling context.
For example, represent inequalities describing nutritional and cost
constraints on combinations of different foods.
A.REI.5 Solve systems of equations
55
4.03 Use systems of
linear equations or
inequalities in two
variables to model
and solve problems.
Solve using tables,
graphs, and algebraic
properties; justify
results.
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
A.REI.6
Solve systems of linear equations exactly and approximately (with
graphs), focusing on pairs of linear equations in two variables.
A.REI.7
Represent and solve equations and inequalities graphically
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.
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.REI.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.
A.REI.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.
65 1 Assessment/EOC
Practice Goal
Specific
66 1 9-1
9-2 Find prime
factorizations and
the greatest common
factors of integers
and monomials.
Use the Distributive
Property to factor
polynomials. Solve
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
56
quadratic equations
of the form ax² + bx
= 0.
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2)
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
67 1 9-3
9-4 Factor trinomials
and solve equations
of the form x² + bx +
c.
Factor trinomials
and solve equations
of the form ax² + bx +
c.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
Rearrange formulas to highlight a quantity of interest using the
57
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
same reasoning as in solving equations. For example,
rearrange Ohm’s law V=IR to highlight resistance R.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
68
1
9-5
9-6
Factor binomials that
are the differences of
squares. Solve
equations involving
the differences of
squares.
Factor perfect square
trinomials
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
58
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
69 1 Assessment/EOC
Practice Specific
Optional 11-1 Simplify radical
expressions using the
Product Property and
the Quotient Property
of Square Roots.
1.02
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
59
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
70 1 11-2 Add, subtract, and
multiply radical
expressions.
(Calculator)
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
60
71 1 11-3
11-4 Solve radical
equations.
(Calculator)
Solve problems by
using the Pythagorean
Theorem.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
72
1
11-5
4-1
Solve problems
finding the length of
a segment.
Solve problems
finding the midpoint
of a segment.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
61
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
73 1 Assessment/EOC
Practice Specific
74,75 2 10-1
10-2 Graph quadratic
functions. Find the
equation of the axis
of symmetry & the
vertex coordinates of
a parabola.
Solve quadratic
equations by
graphing.
(Calculator)
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
62
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
4.02 Graph, factor,
and evaluate quadratic
functions to solve
problems.
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3 Understand the concept of a function and use
function notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
A.REI.4 (SCoS 4.02)
Solve equations and inequalities in one variable
Solve quadratic equations in one variable.
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.
b) Solve quadratic equations by inspection (e.g., 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 and a-bi for real numbers a and b.
F.IF.7 Analyze functions using different representations
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.
63
Analyze functions using different representations
Write a function defined by an expression in different but
equivalent forms to reveal and explain different properties.\
a) Use the process of factoring and completing the square in
a quadratic function to show zeros, extreme values, and
symmetry of the graph, and interpret these terms of a context.
76,77
2
9-6
Solve quadratic
equations by
factoring and with
calculator use.
(Calculator)
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor polynomials.
1.02 Use formulas
and algebraic
expressions, including
iterative and recursive
forms, to model ad
solve problems.
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
78,79 2 10-5 Graph exponential 1.01 Write equivalent APR.1 (SCoS 1.01b, 1.01c)
64
functions. Identify
data that displays
exponential behavior.
(Calculator)
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor
polynomials.
1.02 Use formulas
and algebraic
expressions,
including iterative
and recursive forms,
to model ad solve
problems.
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
F.FIF.7 (SCoS 4.04)
Analyze functions using different representations
Graph functions expressed symbolically and show key featurrs
of the graph, by hand in simple cases and using technology for
more complicated cases.
e) Graph exponential and logarithmic functions,
showing intercepts and end behavior, and trigonometric
65
4.04 Graph and
evaluate exponential
functions to solve
problems.
functions, showing period, midline, and amplitude.
F.L.E.1 Construct and compare linear and exponential
models and solve problems Distinguish between situations that can be modeled with linear
functions and with exponential functions
a) Prove that linear functions grow by equal
differences over equal intervals, and that exponential
functions grow by equal factors over equal intervals.
b) Recognize situations in which one quantity changes at a
constant rate per unit interval relative to another.
c) Recognize situations which a quantity grows or decays by a
constant percent rate per unit interval relative to another.
FLE.2 Construct and compare linear and exponential
models and solve problems 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)
80 1 10-6 Solve problems using
formulas for
exponential growth
and decay.
(Calculator)
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor
polynomials.
1.02 Use formulas
and algebraic
expressions,
including iterative
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
66
and recursive forms,
to model ad solve
problems.
4.04 Graph and
evaluate exponential
functions to solve
problems.
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
F.FIF.7 (SCoS 4.04)
Analyze functions using different representations
Graph functions expressed symbolically and show key featurrs
of the graph, by hand in simple cases and using technology for
more complicated cases.
f) Graph exponential and logarithmic functions,
showing intercepts and end behavior, and trigonometric
functions, showing period, midline, and amplitude.
F.L.E.1 Construct and compare linear and exponential
models and solve problems Distinguish between situations that can be modeled with linear
functions and with exponential functions
b) Prove that linear functions grow by equal
differences over equal intervals, and that exponential
functions grow by equal factors over equal intervals.
b) Recognize situations in which one quantity changes at a
constant rate per unit interval relative to another.
c) Recognize situations which a quantity grows or decays by a
constant percent rate per unit interval relative to another.
FLE.2 Construct and compare linear and exponential
models and solve problems 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)
67
81 1 Assessment/ EOC
Practice Specific
Optional 12-2 Simplify rational
expressions.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor
polynomials.
1.02 Use formulas
and algebraic
expressions,
including iterative
and recursive forms,
to model ad solve
problems.
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
Optional 12-3
12-4
Multiply rational
expressions.
Divide rational
expressions.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
68
exponents.
b) Operate with
polynomials
c) Factor
polynomials.
1.02 Use formulas
and algebraic
expressions,
including iterative
and recursive forms,
to model ad solve
problems.
multiply polynomials
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write artithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers.
For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
Optional 12-5
12-6
Divide a polynomial
by a monomial.
Divide a polynomial
by a binomial.
Add and subtract
rational expressions
with like
denominators.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor
polynomials.
A.APR.1 Perform arithmetic operations on polynomials.
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.
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
69
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
Optional 12-8
12-9
Simplify complex
fractions.
Solve rational
equations that are
proportions.
1.01 Write equivalent
forms of algebraic
expressions to solve
problems
a) Apply the laws of
exponents.
b) Operate with
polynomials
c) Factor
polynomials.
1.02 Use formulas
and algebraic
expressions,
including iterative
and recursive forms,
to model ad solve
problems.
APR.1 (SCoS 1.01b, 1.01c)
Perform arithmetic operations on polynomials
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
A.SSE2
Interpret the structure of expressions
Use the structure of an expression to identify ways to rewrite it.
For example, see x4
– x4 as (x
2)2 –(y
2)2, thus recognizing it as a
difference of squares that can be factored as ( x2 – y
2)(x
2 +y
2).
A.CED4 (SCoS 1.02)
Create equations that describe numbers or relationships
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.
F.BF.2
Build a function that models a relationship between two
quantities
Write arithmetic and geometric sequences both recursively and
with an explicit formula, use them to model situations, and
translate between the two forms.
F.IF.3
Understand the concept of a function and use function
notation
Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, Fibonacci sequence is defined recursively by
f(0)=f(1)=1, f(n+1)=f(n)+f(n-1) for n≥1
70
82-90 9 Review
***** Please note that optional means that you may weave that objective in with another topic.
Algebra 1 Percent of
Questions
Days based on
80 days of
Instructional time
Goal 1--The learner will perform operations with numbers
and expressions to solve problems. 20%-25% About 16-20 days
Goal 2---The learner will describe geometric figures in the
coordinate plane algebraically. 10%-15% About 8-12 days
Goal 3—The learner will collect, organize, and interpret data
with matrices and linear models to solve problems. 30%-35% About 24-28 days
Goal 4---The learner will use relations and functions to solve
problems. 35%-40% About 28-32days
Focus heavily on Goal 3 and Goal 4. Those goals account for 65%-75% of the End-of-Course Test.