Algebra 1 Pacing Guide - Wikispaceshcsresources.wikispaces.com/file/...Schools_Algebra... ·...

70
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 5 1/3 to be the cube of 5 because we want (5 1/3 ) 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

Transcript of Algebra 1 Pacing Guide - Wikispaceshcsresources.wikispaces.com/file/...Schools_Algebra... ·...

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.