Common Core Algebra CURRICULUM MAP
Units for Algebra 1A, 1B and 1C
and Proposed Lessons for Each Unit
2013-2014 BLOCK 1 CURRICULUM MAP
Course: Algebra 1A
2013-2014 BLOCK 1 CURRICULUM MAP
Course: Algebra 1A
Unit 1
Foundations of Algebra




Representing Problems
Using Variables and
Expressions
Operations with Rational
Numbers
Reasoning and
Simplifying with
Properties of Real
Numbers and
Polynomials
Introduction to Problem
Solving Methods
8 days
Common Core
Math Standard(s)
□N-Q.1, □N-Q.2, □N-Q.3
○N-RN.3
A-SSE.1a,
A-SSE.1.b,
A-SSE.2
A-APR.1
Mathematical Practice(s)
Explicitly Taught

MP.1

MP.2

MP.4

MP.6

MP.7

MP.8
Key Vocabulary: Equivalent, Expressions, Variable, Coefficient, Constant, Like Terms,
Simplifying, Distribution, Factor, Properties, Absolute Value, Polynomials, Degree, Monomials,
Binomial, Trinomial, Standard Form, Leading Terms, Modeling, Reasoning, Structures, Units,
Estimate, Translate, Represent, Strategic Problem Solving
Essential Questions:
How can a relationship between quantities be represented numerically, symbolically, or
graphically?
What procedures must be followed to manipulate expressions?
Unit 2
Linear Equations







One-step Equations
Two-step Equations
Multi-step Equations
Variables on both sides
Literal Equations &
Formulas
Ratios & Proportions
Proportion Applications
12 days
Common Core
Math Standard(s)
○N-RN.3, □N-Q.1, □N-Q.2, □N-Q.3,
A-CED.1,
A-REI.1,
A-SSE.1a,
A-CED.3,
A-SSE.1.b,
A-SSE.2
A-CED.4
A-REI.3
Mathematical Practice(s)
Explicitly Taught

MP.1

MP.2

MP.3

MP.4

MP.5

MP.6

MP.7

MP.8
Key Vocabulary: Equivalent, Variable, Coefficient, Constant, Like Terms, Simplifying,
Distribution, Factor, Properties, Modeling, Reasoning, Structures, Units, Estimate, Translate,
Represent, Strategic, Equations, Inverse Operations, Reciprocal, Identity, Formula,
Reasonable Solutions, Critique, Rearrange, Quantity of Interest
Essential Questions:
How can equations be used to solve problems in context?
How can the structure of an equation help determine a solution strategy?
Unit 3
Inequalities





10 days
Common Core
Math Standard(s)
One Variable
Inequalities
One-step Inequalities
Multistep Inequalities
Compound Inequalities
Absolute Value
Equations & Inequalities
○N-RN.3, □N-Q.1, □N-Q.2, □N-Q.3,
A-CED.1,
A-REI.1,
A-SSE.1a,
A-CED.3,
A-SSE.1.b,
A-SSE.2
A-CED.4
A-REI.3
Mathematical Practice(s)
Explicitly Taught

MP.1

MP.2

MP.3

MP.4

MP.5

MP.6

MP.7
 MP.8
Key Vocabulary: Equivalent, Variable, Coefficient, Constant, Like Terms, Simplifying,
Distribution, Factor, Properties, Absolute Value, Modeling, Reasoning, Structures, Units,
Estimate, Translate, Represent, Strategic, Equations, Inverse Operations, Reciprocal, Identity,
Reasonable Solutions, Critique, Rearrange, Quantity of Interest, Inequality, Compound
Statements, Union, Intersection, Line Graphs
Essential Questions:
How can inequalities be used to solve problems in context?
How can the structure of an inequality help determine a solution strategy?
2013-2014 BLOCK 2 CURRICULUM MAP
Course: Algebra 1B
Unit 4
Intro to Functions






Patterns
Arithmetic sequences
Interpreting Graphs
Intro to Functions
Write and Apply Linear
Functions
Graphing Functions
8 days
Common Core
Math Standard(s)
□N-Q.1, □N-Q.2, □N-Q.3,
A-REI.1,
A-SSE.1a,
A-SSE.1.b,
A-SSE.2,
Mathematical Practice(s)
Explicitly Taught
A-CED.1,
A-CED.3,
A-CED.4,
A-REI.3
A-CED.2
A-REI.10,
F-IF.1,
A-REI.11
F.-IF.2,
F-IF.3,
F-IF.4,
F-IF.5, □F-IF.7a,
b, c, e, □F-IF.9
□F-BF.1a; F-BF.2, ○F-BF.3
□F-LE.1a, b, c, □F-LE.2, □F-LE.3, □F-LE.5

MP.1

MP.2

MP.3

MP.4

MP.5

MP.6

MP.7

MP.8
Key Vocabulary: Ordered Pair, Linear Equation, Domain, Range, x-intercept, y-intercept,
Coordinate Plane, x-axis, y-axis, Quadrant, Function, Relation, Arithmetic Sequence, Solutions,
Plotting, Points, Solution Set, Intersection, Linear Graph, Quadratic Graph, Absolute Value
Graph, Piecewise Graph, Exponential Graph, Square Root Graph, Polynomial Function, Table
of Values, Translation(Shift), Dilation(Shrink, Expand), Find Structure
Essential Questions:
How can a relationship be represented graphically?
How can a recursive pattern be represented graphically?
How can a graph be interpreted in context of the situation?
Unit 5
Linear Functions









12 days
Common Core
Mathematical Practice(s)
Explicitly Taught
Math Standard(s)
Rate of Change & Slope
Direct Variation
Slope-Intercept Form
Point-Slope Form
Standard Form
Applications of
Equations
Parallel and
Perpendicular Lines
Graphing Linear
Inequalities
Application of
Inequalities
□N-Q.1, □N-Q.2, □N-Q.3,
A-REI.1,
A-REI.3
,
A-SSE.1a,
F-IF.1,
F.-IF.2,
A-SSE.1.b,
F-IF.4,
A-SSE.2,
A-CED.2
A-REI.10,
A-REI.12
F-IF.6, □F-IF.7a
□F-LE.1a, b, c, □F-LE.2, □F-LE.5
G-GPE.5
A-CED.1,
A-CED.3,
A-CED.4,

MP.1

MP.2

MP.3

MP.4

MP.5

MP.6

MP.7

MP.8
F-IF.5, □F-IF.9, □F-BF.1a, ○F-BF.3
Key Vocabulary: Ordered Pair, Linear Equation, Domain, Range, x-intercept, y-intercept,
Coordinate Plane, x-axis, y-axis, Quadrant, Function, Relation, Solutions, Plotting, Points, Solution
Set, Intersection, Linear Graph, Table of Values, Translation(Shift), Dilation(Shrink, Expand), Slope,
Slope-Intercept Form, Point-Slope Form, Standard Form, Parallel Functions, Perpendicular
Function
Essential Questions:
How do you identify key features of a graph and interpret it in terms of the context?
How can you compare functions and their relationships to each other?
Unit 6
Systems of Equations





Foundations of Linear
Systems
Solving by Substitution
Solving by Elimination
Applications of Systems
Systems of Linear
Inequalities
10 days
Common Core
Math Standard(s)
□N-Q.1, □N-Q.2, □N-Q.3,
A-REI.1,
A-REI.3
,
A-SSE.1a,
F-IF.1,
F.-IF.2,
A-SSE.1.b,
F-IF.4,
A-SSE.2,
○A-REI.5, ○ A-REI.6
A-REI.11,
A-CED.1,
A-CED.3,
A-CED.4,

MP.1

MP.2

MP.3

MP.4

MP.5

MP.6

MP.7

MP.8
F-IF.5, □F-IF.9, □F-BF.1a, ○F-BF.3
A-CED.2
A-REI.10,
Mathematical Practice(s)
Explicitly Taught
A-REI.12
F-IF.6, □F-IF.7a
□F-LE.1a, b, c, □F-LE.2, □F-LE.5
Key Vocabulary: Ordered Pair, Linear Equation, Domain, Range, x-intercept, y-intercept,
Coordinate Plane, x-axis, y-axis, Quadrant, Function, Relation, Solutions, Plotting, Points, Solution
Set, Intersection, Linear Graph, Table of Values, Translation(Shift), Dilation(Shrink, Expand), Slope,
Slope-Intercept Form, Point-Slope Form, Standard Form, Parallel Functions, Perpendicular Function,
Infinite Solutions (Dependent/Consistent), No Solution (Independent/Inconsistent), Coinciding
Lines
Essential Questions:
How can the solutions to a system be represented and interpreted?
In what ways can a system be solved?
2013-2014 BLOCK 3 CURRICULUM MAP
Course: Algebra 1C
Unit 7
Data






Data Displays
Scatter Plots
Trend Lines
Relative Frequencies
Central Tendencies
Distribution
10 days
Common Core
Math Standard(s)
A-SSE.1a,
A-CED.2,
F.-IF.2,
F-IF.4,
F-IF.5, □F-IF.9, ○F-BF.3, □F-LE.2, □F-LE.5
□N-Q.1, □N-Q.2, □N-Q.3
○S-ID.1, ○S-ID.2, ○S-ID.3, □S-ID.5, □S-ID.6a, □S-ID.6b,
S-ID.7,
S-ID.8,
S-ID.9
Mathematical Practice(s)
Explicitly Taught

MP.1

MP.2

MP.3

MP.4

MP.5

MP.6

MP.7

MP.8
Key Vocabulary: Scatter Plot, Histogram, Box Plot, Joint Relative Frequency, Marginal
Relative Frequency, Conditional Relative Frequency, Correlation Coefficient, Outliers,
Skewed Distribution, Normal Distribution, Mean, Median, Mode, Standard Deviation, Inter
Quartile Range
Essential Questions:
How do varied representations of data relate to varied interpretations of data?
How do different methods of identifying the center and the spread of data compare to one
another?
Unit 8
Exponential Functions




Introduction to
Exponential Functions
Forms of Exponential
Growth
Forms of Exponential
Decay
Modeling with
Exponential Functions
12 days
Common Core
Math Standard(s)
□N-Q.1, □N-Q.2, □N-Q.3,
IF.9, ○F-BF.3
A-SSE.1a,
A-SSE.1.b,
A-REI.10,
A-REI.11,
□ A-SSE.3c
Mathematical Practice(s)
Explicitly Taught
F.-IF.2,
F-IF.5, □F-

MP.1

MP.2

MP.3

MP.4

MP.5

MP.6

MP.7

MP.8
A-CED.2
F-IF.3,
F-IF.4, □F-IF.7e, □F-IF.8b
□F-BF.1a
□F-LE.1a, b, c, □F-LE.2, □F-LE.3, □F-LE.5
Key Vocabulary: Ordered Pair, Linear Equation, Domain, Range, x-intercept, y-intercept,
Coordinate Plane, x-axis, y-axis, Quadrant, Function, Relation, Arithmetic Sequence, Solutions,
Plotting, Points, Solution Set, Intersection, Linear Graph, Quadratic Graph, Absolute Value Graph,
Piecewise Graph, Exponential Graph, Square Root Graph, Polynomial Function, Table of Values,
Translation(Shift), Dilation(Shrink, Expand), Find Structure, Geometric Pattern, Common
Factor, Exponential Function, Asymptote, End Behaviors, Exponential Growth, Exponential
Decay
Essential Questions:
How do you identify key features of a graph and interpret it in terms of the context?
How can you compare functions and their relationships to each other?
Unit 9
Exponents and
Polynomials




Exponential Properties
with Monomials
Adding and
Subtracting
Polynomials
Multiplying Binomials
Factoring Polynomials
8 days
Common Core
Math Standard(s)
Mathematical Practice(s)
Explicitly Taught
□N-Q.1, □N-Q.2, □N-Q.3

MP.1
○N-RN.3

MP.2

MP.3

MP.6

MP.7

MP.8
A-SSE.1a,
SSE.3
A-SSE.1.b,
A-APR.1
A-SSE.2, □ A-
Key Vocabulary: Equivalent, Expressions, Variable, Coefficient, Constant, Like Terms,
Simplifying, Distribution, Factor, Properties, Absolute Value, Polynomials, Degree, Monomials,
Binomial, Trinomial, Standard Form, Leading Terms, Modeling, Reasoning, Structures, Units,
Estimate, Translate, Represent, Strategic Problem Solving
Essential Questions:
Do mathematical relationships remain true to arithmetic rules even when using algebraic
expressions?
Using the rules of algebra, how can an expression be rewritten into an equivalent form?
Common Core Algebra 1A–Unit 1– Foundations of Algebra
Lesson
Topic
Order of
Operations
Variables &
Expressions
Integer
Operations
Objective
Expectation
Common Core
Standard
A-SSE.1a
A-SSE.1
A-SSE.1a
Prepare for
N.RN.3
(7.NS.A.1d)
(7.NS.A.2c)
Possible Student
Tasks/Activities
*Create posters with their own
pneumonic device to remember
PEMDAS instead of “Please Excuse
My Dear Aunt Sally”
*Order of Operations Bingo
*Exit Slip: Write out in sentences
step by step how to evaluate an
expression. Ex:
Resources
Bingo
24 Game
http://illuminations.nctm.org/LessonDetail.aspx?id=L730
*Give each student an expression
with a single variable and have
them roll a die to practice plugging
a number in.
*Lego Sorting
*Poster (vocabulary)
*Exit Slip: Give 5 examples of Like
Terms that could be combined
when simplifying variable
expressions.
Class Activityhttp://ispeakmath.wordpress.com/2012/10/02/simplifyingalgebraic-expressions-activity/
Bingo http://edubakery.com/Bingo-Cards/SimplifyingAlgebraic-Expressions-v1-Bingo-Cards
*Hexagon Tiles
*Dice (operations)
Number lines
Hexagon Tiles
Real
Numbers
and
Properties
Common Core Algebra 1A - Unit 2- Linear Equations
Lesson Topic
1. ONE STEP
EQUATIONS
OBJECTIVE.
EXPECTATION
Common Core
Standard
Possible Student
Tasks/Activities
After this lesson is
completed, the
students will be
able to: 1) State
the inverse
operation of a
given
circumstance 2)
Use inverse
operations to
transform an
equation 3)
Compare and
contrast equations
to see if they are
equivalent
AZ-HS.A-CED.1.
Create equations and
inequalities in one
variable and use
them to solve
problems. Include
equations arising
from linear and
quadratic functions,
and simple rational
and exponential
functions. [From
cluster: Create
equations that
describe numbers or
relationships]
Scale Activity –
Students will see
balance of scales that
will represent balance
of equations. Teacher
may use any objects
that will relate to class.
Actual Scale or website
www.mathplayground.com/algebraequations.html
[This resource gives option of one step & two step equation]
Possible outside
activity can have
students use a type of
see-saw
http://www.mathx.net/students/MATHX.NET-One-step_word_problemscombined_equations.pdf
[Basic one step word problems list of 400. Addition, subtraction, multiplication & Divisio
Scale Activity –
Students will see
Actual Scale or website
www.mathplayground.com/algebraequations.html
After this lesson is
completed, the
AZ-HS.A-REI.3.
Solve linear
equations and
inequalities in one
variable, including
equations with
coefficients
represented by
letters. [From cluster:
Solve equations and
inequalities in one
variable]
AZ-HS.A-CED.1 &
AZ-HS.A-REI.3.
Resources
http://nlvm.usu.edu/en/nav/framesasid324g4t2.html?open=instructions&from=categoryg4
[Use of balance scale to solve computer generated problems or teacher generated problem
have integer solution]
2. TWO STEP
EQUATIONS
3. MULTI-STEP
EQUATIONS
students will be
able to: 1) State
the inverse
operation of a
given
circumstance 2)
Use inverse
operations to
transform an
equation 3)
Compare and
contrast equations
to see if they are
equivalent 4) Use
inverse Order of
Operations
Simplify/Solve
algebraic
equations using
the properties of
equality and
distributive
property to clear
()’s and fractions
[FROM LESSON 1]
AZ-HS.A-REI.1.
Explain each step in
solving a simple
equation as following
from the equality of
numbers asserted at
the previous step,
starting from the
assumption that the
original equation has
a solution. Construct
a viable argument to
justify a solution
method. [From
cluster: Understand
solving equations as
a process of
reasoning and
explain the
reasoning]
AZ-HS.A-CED.1 &
AZ-HS.A-REI.3 &
AZ-HS.A-REI.1
. [FROM LESSON
1&2]
balance of scales that
will represent balance
of equations. Teacher
may use any objects
that will relate to class.
Possible outside
activity can have
students use a type of
see-saw
[This resource gives option of one step & two step equation]
http://nlvm.usu.edu/en/nav/framesasid324g4t2.html?open=instructions&from=categoryg4
[Use of balance scale to solve computer generated problems or teacher generated problem
have integer solution]
http://www.funbrain.com/guess2/index.html
[students required to create equation and guess the number, example Guess the number th
when you subtract 3 and then subtract 8 is -9.]
http://www.mathx.net/students/MATHX.NET-Two-step_equations-word_problems-intege
[Basic two step word problems list of 400. With integers]
http://www.mathx.net/students/MATHX.NET-Two-step_equations-word_problemsdecimals.pdf [Basic two step word problems list of 400. With decimals]
Teacher stump –
Students asked to
create a word problem
that will require
teacher to solve the
word problem.
Magician math Choose any number
and to add 9 to it. (It's
easier to pick small
numbers to do math.)
Multiply this number
by 2. Subtract 4.
Divide the remainder
by 2. Subtract the
number first chosen.
The result will always
http://www.mathx.net/students/MATHX.NET-Multi-step_equations-integers.pdf
[multi-step problems list of 800 with integers]
http://www.mathx.net/students/MATHX.NET-Multi-step_equations-decimals.pdf
[multi-step problems list of 800 with decimals
http://www.mathx.net/students/MATHX.NET-Multi-step_equations_fractions.pdf
[multi-step problems list of 800 with fractions]
]
be 7 no matter what
number was chosen.
[Students can create
their own Magic Math
Problem]
4. SOLVE
EQUATIONS
WITH
VARIABLE ON
BOTH SIDES
5. LITERAL
EQUATIONS &
FORMULAS
AZ-HS.A-CED.1 &
AZ-HS.A-REI.3 AZHS.& A-REI.1
. [FROM LESSON 1
& 2]
AZ-HS.A-CED.1 &
AZ-HS.A-REI.3 &
AZ-HS.A-REI.1
. [FROM LESSON 1
& 2]
AZ-HS.N-Q.1.Use
units as a way to
understand problems
and to guide the
solution of multi-step
problems; choose and
interpret
units
consistently
in
formulas; choose and
interpret the scale
and the origin in
graphs and data
displays.
[From
cluster:
Reason
quantitatively
and
use units to solve
problems]
AZ-HS.A-CED.4.
Rearrange formulas
to
highlight
a
quantity of interest,
http://nlvm.usu.edu/en/nav/framesasid324g4t2.html?open=instructions&from=categoryg4
[Use of balance scale to solve computer generated problems or teacher generated problem
have integer solution]
using
the
same
reasoning
as
in
solving
equations.
For
example,
rearrange Ohm’s law
V = IR to highlight
resistance R. [From
cluster:
Create
equations
that
describe numbers or
relationships]
AZ-HS.NQ.1.[FROM
LESSON 5]
6, RATIOS &
PROPORTIONS
7. PROPORTION
APPLICATIONS
AZ-HS.N-Q.2.
Define appropriate
quantities for the
purpose of
descriptive modeling.
[From cluster:
Reason quantitatively
and use units to solve
problems]
AZ-HS.N-Q.1., AZHS.N-Q.2 , AZHS.A-REI.1, AZHS.A-REI.3., AZHS.A-CED.1. [
FROM LESSON 1, 2
& 6]
Common Core Algebra 1A– Unit 3 – INEQUALITIES
Lesson Topic
1. ONE
VARIABLE
INEQUALITES
AND GRAPHS
2. ONE-STEP
INEQUALITES
3. MULTI-STEP
INEQUALITIES
4. COMPOUND
INEQUALITIES
OBJECTIVE. EXPECTATION
Common Core Standard
AZ-HS.A-REI.3. Solve linear
equations and inequalities in one
variable, including equations
with coefficients represented by
letters. [From cluster: Solve
equations and inequalities in one
variable]
AZ-HS.A-REI.3
AZ-HS.A-CED.1. Create
equations and inequalities in one
variable and use them to solve
problems. Include equations
arising from linear and quadratic
functions, and simple rational
and exponential functions.
[From cluster: Create equations
that describe numbers or
relationships]
AZ-HS.N-Q.2. Define
appropriate quantities for the
purpose of descriptive modeling.
[From cluster: Reason
quantitatively and use units to
solve problems]
AZ-HS.A-REI.3
AZ-HS.A-CED.1
AZ-HS.A-REI.3
AZ-HS.A-CED.1
Possible Student
Tasks/Activities
Resources
AZ-HS.A-CED.1
5. ABSOLUTE
VALUE
EQUATION AND
INEQUALITIES
AZ-HS.A-SSE.1. Interpret
expressions that represent a
quantity in terms of its context.
[From cluster: Interpret the
structure of expressions]
AZ-HS.A-SSE.1.b Interpret
complicated expressions by
viewing one or more of their
parts as a single entity. For
example, interpret P(1+r)^n as
the product of P and a factor not
depending on P. [From cluster:
Interpret the structure of
expressions]
Common Core Algebra 1B- Unit 4 – Intro to Functions
Lesson Topic
Introduction to
functions


Interpreting
Graphs

Objective
Expectation
SWBAT identify a
function
SWBAT determine
the domain and
range and
differentiate
between the
dependent and
independent
variables for any
given set or
display of data.
SWBAT interpret a
graph, and create a
graph for a real
world situation,

Patterns
SWBAT identify
a pattern for in
Common Core Standard
CCSS.Math.Content.HSA-CED.A.1 Create
equations and inequalities in one variable
and use them to solve problems. Include
equations arising from linear and quadratic
functions, and simple rational and
exponential functions.
CCSS.Math.Content.HSF-IF.B.4 For a
function that models a relationship
between two quantities, interpret key
features of graphs and tables in terms of
the quantities, and sketch graphs showing
key features given a verbal description of
the relationship. Key features include:
intercepts; intervals where the function is
increasing, decreasing, positive, or
negative; relative maximums and
minimums; symmetries; end behavior; and
periodicity.★
CCSS.Math.Content.HSACED.A.2 Create equations in two or more
Possible Student
Tasks/Activities
Cups on cups on cups:
students will discover the
terms associated with
functions by observing the
relationship of cups to
height.
Interpreting and
constructing:
Students will first create a
graph for their own
situation. Blind partners,
students will pair up and
provide situations for each
other while their partner
constructs the graph.
Developing patterns:
Resources

Stacking cups.
any given
representation
(graphs, tables,
pictures, etc.)
variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.

SWBAT
determine and
apply an
arithmetic
sequence
o
CCSS.Math.Content.HSASSE.A.1 Interpret expressions that
represent a quantity in terms of its
context.★


Arithmetic
Sequences

o
CCSS.Math.Content.HSAREI.D.10 Understand that the graph of an
equation in two variables is the set of all
its solutions plotted in the coordinate
plane, often forming a curve (which could
be a line).
Students will be divided
into groups elements of
the pattern will be given to
each students in each
group. Students will create
a pattern.
Other groups will
determine an nth term or
continue the pattern.
Students will end by
creating patterns with
numbers.
Auditorium Arithmetic:
Students will be given the
example of and auditorium
CCSS.Math.Content.HSA- that has several rows of
SSE.A.1a Interpret parts of an expression, seating, the first of which
such as terms, factors, and coefficients.
starts with 20 seats. The
CCSS.Math.Content.HSA- second has 24, the third
has 28 and so on for 30
SSE.A.1b Interpret complicated
rows of seats.
expressions by viewing one or more of
their parts as a single entity. For example,
interpret P(1+r)n as the product of P and a
factor not depending on P.
o
CCSS.Math.Content.HSFIF.A.3 Recognize that sequences are
functions, sometimes defined recursively,
whose domain is a subset of the
integers. For example, the Fibonacci
sequence is defined recursively by f(0) =
f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
o
CCSS.Math.Content.HSFBF.A.1 Write a function that describes a
Auditorium Arithmetic
relationship between two quantities.★
CCSS.Math.Content.HSF-BF.A.2 Write
arithmetic and geometric sequences both
recursively and with an explicit formula,
use them to model situations, and
translate between the two forms.★
CCSS.Math.Content.HSFLE.A.2 Construct linear and exponential
functions, including arithmetic and
geometric sequences, given a graph, a
description of a relationship, or two inputoutput pairs (include reading these from a
table).
Write & Apply
Linear
Functions


SWBAT write a
linear function for
any given graph,
table, or situation.
SWBAT apply the
concepts of linear
functions to real
world situations
CCSS.Math.Content.HSAREI.D.10 Understand that the graph of an
equation in two variables is the set of all
its solutions plotted in the coordinate
plane, often forming a curve (which could
be a line).
CCSS.Math.Content.HSF-IF.B.4 For a
function that models a relationship
between two quantities, interpret key
features of graphs and tables in terms of
the quantities, and sketch graphs showing
key features given a verbal description of
the relationship. Key features include:
intercepts; intervals where the function is
increasing, decreasing, positive, or
negative; relative maximums and
minimums; symmetries; end behavior; and
periodicity.★
CCSS.Math.Content.HSN-Q.A.2 Define
appropriate quantities for the purpose of
descriptive modeling.
* without using slope (it
will be taught in Unit 5:
Linear functions)
Example: A certain football
player averages 6.8 yards
per carry. Construct a table
and equation for this
situation.

CCSS.Math.Content.HSASSE.A.1 Interpret expressions that
represent a quantity in terms of its
context.★
o
CCSS.Math.Content.HSASSE.A.1a Interpret parts of an expression,
such as terms, factors, and coefficients.
CCSS.Math.Content.HSA-CED.A.2 Create
equations in two or more variables to
represent relationships between
quantities; graph equations on coordinate
axes with labels and scales.
Graphing
Functions

SWBAT construct a
graph using the
input & output
values for a given
equation, table, or
situation.
CCSS.Math.Content.HSN-Q.A.1 Use units
as a way to understand problems and to
guide the solution of multi-step problems;
choose and interpret units consistently in
formulas; choose and interpret the scale
and the origin in graphs and data displays.
CCSS.Math.Content.HSAREI.D.10 Understand that the graph of an
equation in two variables is the set of all
its solutions plotted in the coordinate
plane, often forming a curve (which could
be a line).
CCSS.Math.Content.HSF-IF.B.5 Relate
the domain of a function to its graph and,
where applicable, to the quantitative
relationship it describes. For example, if
the function h(n) gives the number of
person-hours it takes to assemble n
engines in a factory, then the positive
integers would be an appropriate domain
Graph situation derived
from the previous day.
for the function.★
Common Core Algebra 1B– Unit 5 – Linear Functions
Lesson Topic
Rate of Change &
Slope


Direct variation



Objecive
Expectation
SWBAT identify the
slope as the
constant rate of
change and
determine the slope
given a graph, table
or two points of a
line
SWBAT interpret the
slope as a rate of
change for a real
world example
SWBAT explain the
direct variation in
terms of the
constant of
variation
SWBAT create an
equation for and
graph any given real
world situation
involving direct
variation
SWBAT relate the
constant of
Common Core Standard
CCSS.Math.Content.HSFIF.B.6 Calculate and interpret the
average rate of change of a
function (presented symbolically or
as a table) over a specified
interval. Estimate the rate of
change from a graph.★
Possible Student
Tasks/Activities

CCSS.Math.Content.HSFLE.A.1b Recognize situations in
which one quantity changes at a
constant rate per unit interval
relative to another.
CCSS.Math.Content.HSNQ.A.2 Define appropriate
quantities for the purpose of
descriptive modeling.
CCSS.Math.Content.HSACED.A.2 Create equations in two
or more variables to represent
relationships between quantities;
graph equations on coordinate
axes with labels and scales.

Resources
variation with slope
and rate of change
Slope-Intercept
Form



SWBAT write an
equation in slopeintercept form for a
given situation and
construct.
SWBAT interpret the
meaning of each
term in the slope
intercept equation
SWBAT recognize
the terms “m” and
“b” as shifts in the
line y = x
CCSS.Math.Content.HSASSE.A.1 Interpret expressions that
represent a quantity in terms of its
context.★
CCSS.Math.Content.HSASSE.A.1a Interpret parts of an
expression, such as terms, factors,
and coefficients.
CCSS.Math.Content.HSASSE.A.2 Use the structure of an
expression to identify ways to rewrite
it. For example, see x4 – y4 as (x2)2 –
(y2)2, thus recognizing it as a
difference of squares that can be
factored as (x2 – y2)(x2 + y2).
CCSS.Math.Content.HSACED.A.2 Create equations in two or
more variables to represent
relationships between quantities;
graph equations on coordinate axes
with labels and scales.
CCSS.Math.Content.HSF-IF.B.4 For a
function that models a relationship
between two quantities, interpret key
features of graphs and tables in terms
of the quantities, and sketch graphs
showing key features given a verbal
description of the relationship. Key
features include: intercepts; intervals
where the function is increasing,
decreasing, positive, or negative;
relative maximums and minimums;
symmetries; end behavior; and
periodicity.★
CCSS.Math.Content.HSFIF.C.7 Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases
and using technology for more
complicated cases.★
CCSS.Math.Content.HSFIF.C.7a Graph linear and quadratic
functions and show intercepts,
maxima, and minima.
CCSS.Math.Content.HSFBF.A.1 Write a function that describes
a relationship between two
quantities.★
CCSS.Math.Content.HSFBF.A.1a Determine an explicit
expression, a recursive process, or
steps for calculation from a context.
CCSS.Math.Content.HSFBF.B.3 Identify the effect on the graph
of replacing f(x) by f(x) + k, k f(x),f(kx),
and f(x + k) for specific values
of k (both positive and negative); find
the value of k given the graphs.
Experiment with cases and illustrate
an explanation of the effects on the
graph using technology. Include
recognizing even and odd functions
from their graphs and algebraic
expressions for them.
CCSS.Math.Content.HSFLE.A.2 Construct linear and
exponential functions, including
arithmetic and geometric sequences,
given a graph, a description of a
relationship, or two input-output pairs
(include reading these from a table).
CCSS.Math.Content.HSFLE.B.5 Interpret the parameters in a
linear or exponential function in terms
of a context.
Point-Slope Form

SWBAT write a
Same as above
linear equation in
point slope form and
construct the graph,
given the slope and
point of a line
Standard Form


Applications of
Equations
Parallel and
perpendicular lines
Graphing linear
SWBAT determine
the x and y-intercept
of an equation in
standard form and
use this information
to graph the
equation on a
coordinate plane.
SWBAT state the
interpretation of the
x and y-intercept for
a given situation

SWBAT determine
an appropriate form
of a linear equation
in order to derive a
graph, table, and
solution to
determine the
inpu/output for a
given situation.

SWBAT identify
parallel and
perpendicular lines
given a graph or
equation.

SWBAT graph linear
inequalities from a
Same as above

CCSS.Math.Content.HSNQ.A.2 Define appropriate
quantities for the purpose of
descriptive modeling.
CCSS.Math.Content.HSFIF.C.9 Compare properties of two
functions each represented in a
different way (algebraically,
graphically, numerically in tables,
or by verbal descriptions). For
example, given a graph of one
quadratic function and an
algebraic expression for another,
say which has the larger
maximum.

CCSS.Math.Content.HSGGPE.B.5 Prove the slope criteria
for parallel and perpendicular lines
and use them to solve geometric
problems (e.g., find the equation of
a line parallel or perpendicular to a
given line that passes through a
given point).
CCSS.Math.Content.HSAREI.D.12 Graph the solutions to a

inequalities
Applications of
Inequalities
given scenario
 SWBAT write an
inequality from a
graph a situation
SWBAT interpret linear
inequalities


SWBAT construct a
graph and create
and inequality for a
given situation.
SWBAT determine
an appropriate form
of a linear equation
in order to derive a
graph, table, and
solution to
determine the
input/output for a
given situation.
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.
Same as “slope-intercept form”
Section

Common Core Algebra 1B - Unit 6 - Systems of Equations
Lesson Topic
Foundations of
linear systems
Solving by
Substitution
OBJECTIVE. EXPECTATION
SWBT find solution to system
by graphing
SWBT find solution to system
by substitution
Common Core Standard
AZ-HS.A-REI.6. Solve systems
of linear equations exactly and
approximately (e.g., with
graphs), focusing on pairs of
linear equations in two variables.
[From cluster: Solve systems of
equations]
AZ-HS.A-REI.6.
AZ-HS.A-REI.6.
Solve by
Elimination
Application of
Systems
SWBT find solution to system
by elimination
SWBT find solution to real
world system problems.
AZ-HS.A-REI.5. Prove that,
given a system of two equations
in two variables, replacing one
equation by the sum of that
equation and a multiple of the
other produces a system with the
same solutions. [From cluster:
Solve systems of equations]
AZ-HS.A-REI.6.
AZ-HS.N-Q.2. Define
appropriate quantities for the
purpose of descriptive modeling.
[From cluster: Reason
quantitatively and use units to
solve problems]
AZ-HS.N-Q.3. Choose a level of
Possible Student
Tasks/Activities
Resources
http://illuminations.nctm.org/LessonDetail.aspx?ID=L641
[Everything balance outs in the end]
http://illuminations.nctm.org/LessonDetail.aspx?ID=L770
[Road Rage Movement with functions]
http://illuminations.nctm.org/LessonDetail.aspx?ID=L724
[Supply & Demand]
accuracy appropriate to
limitations on measurement
when reporting quantities. [From
cluster: Reason quantitatively
and use units to solve problems]
AZ-HS.A-CED.3. Represent
constraints by equations or
inequalities, and by systems of
equations and/or inequalities,
and interpret solutions as viable
or nonviable options in a
modeling context. For example,
represent inequalities describing
nutritional and cost constraints
on combinations of different
foods. [From cluster: Create
equations that describe numbers
or relationships]
Systems of
linear
inequalities
SWBT solve systems of linear
inequalities.
AZ-HS.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.
[From cluster: Represent and
solve equations and inequalities
graphically]
Common Core Algebra 1C– Unit 7 – Data
Lesson Topic
Scatter Plots
OBJECTIVE. EXPECTATION
Common Core Standard
AZ-HS.N-Q.1.Use units as a
way to understand problems and
to guide the solution of multistep problems; choose and
interpret units consistently in
formulas; choose and interpret
the scale and the origin in graphs
and data displays. [From cluster:
Reason quantitatively and use
units to solve problems]
AZ-HS.F-LE.5. Interpret the
parameters in a linear or
exponential function in terms of
a context. [From cluster:
Interpret expressions for
functions in terms of the
situation they model]
Trend Lines
AZ-HS.SP-ID.6. Represent data
on two quantitative variables on
a scatter plot, and describe how
the variables are related. [From
cluster: Summarize, represent,
and interpret data on two
categorical and quantitative
variables]
AZ-HS.SP-ID.6.a Fit a function
Possible Student
Tasks/Activities
Resources
to the data; use functions fitted
to data to solve problems in the
context of the data. Use given
functions or choose a function
suggested by the context.
Emphasize linear, quadratic, and
exponential models. [From
cluster: Summarize, represent,
and interpret data on two
categorical and quantitative
variables]
xAZ-HS.SP-ID.6.c Fit a linear
function for a scatter plot that
suggests a linear association.
[From cluster: Summarize,
represent, and interpret data on
two categorical and quantitative
variables]
AZ-HS.SP-ID.7. Interpret the
slope (rate of change) and the
intercept (constant term) of a
linear model in the context of the
data. [From cluster: Interpret
linear models]
AZ-HS.SP-ID.8. Compute
(using technology) and interpret
the correlation coefficient of a
linear fit. [From cluster: Interpret
linear models]
Central
Tendencies
AZ-HS.SP-ID.9. Distinguish
between correlation and
causation. [From cluster:
Interpret linear models]
AZ-HS.N-Q.2. Define
appropriate quantities for the
purpose of descriptive modeling.
[From cluster: Reason
quantitatively and use units to
solve problems]
AZ-HS.SP-ID.2. Use statistics
appropriate to the shape of the
data distribution to compare
center (median, mean) and
spread (interquartile range,
standard deviation) of two or
more different data sets. [From
cluster: Summarize, represent,
and interpret data on a single
count or measurement variable]
AZ-HS.SP-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). [From cluster:
Summarize, represent, and
interpret data on a single count
or measurement variable]
Common Core Algebra 1C–Unit 8-Exponents & Polynomial
Lesson Topic
Multiplication
with
exponents
Division with
exponents
OBJECTIVE. EXPECTATION
Common Core Standard
AZ-HS.N.RN.1. Explain how
the definition of the meaning of
rational exponents follows from
extending the properties of
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 root
of 5 because we want (5^1/3)^3
= 5(^1/3)^3 to hold, so (51/3)3
must equal 5. [From cluster:
Extend the properties of
exponents to rational exponents]
** only integer exponents **
AZ-HS.N.RN.1
** only integer exponents **
AZ-HS.N.RN.1
** only integer exponents **
Zero and
negative
exponents
AZ-HS.N.RN.2. Rewrite
expressions involving radicals
and rational exponents using the
properties of exponents. [From
cluster: Extend the properties of
exponents to rational exponents]
Adding &
Subtracting
Polynomials
AZ-HS.A-APR.1. Understand
that polynomials form a system
analogous to the integers,
namely, they are closed under
Possible Student
Tasks/Activities
Resources
Multiply
Binomials
Factoring GCF
the operations of addition,
subtraction, and multiplication;
add, subtract, and multiply
polynomials. [From cluster:
Perform arithmetic operations on
polynomials]
AZ-HS.A-APR.1
** only integer exponents **
AZ-HS.A-SSE.1.a Interpret parts
of an expression, such as terms,
factors, and coefficients. [From
cluster: Interpret the structure of
expressions]
Common Core Algebra 1C - Unit 9 - Exponential Functions
Lesson Topic
Intro to Exponential
Functions
Objectives
Expectations
Common Core Standard
Possible Student
Tasks/Activities
A-SSE 1 Interpret
Expressions in terms of their
contexts.
-Word problem like the
Rice and the king and the
checker board.
F-IF 4 Key features of Graphs
Or you have 2 money
options one is linear one is
exponential
Make a table and a graph
…answer questions
comparing the graphs for
example when is the linear
equation at a higher value?
When are they the same?
When is the exponential
higher?
F-IF 7 and 7e Graph functions
and key features
F-LE 2 construct linear and
exponential functions from
arithmetic and geometric
sequences given a graph a
description of a relationship
or two input output pairs.
When graphing remember
to describe key features of
graphs including intercepts,
increasing, and end
behavior.
Students will compare
differences between
arithmetic (y = x) and
geometric sequences which
are exponential equations
(y = b ^ x)
Resources
Given a table of values
students will identify if it’s
linear or exponential and is
it a constant rate of growth?
( A common ratio?)
Forms of
Exponential Growth
A-CED 2 create equations
between quantities and graph
F-IF 4 Key features of Graphs
Identify major parts of
exponential equations such
as the a value in y=ab^x
F-IF 5 Relate Domain of a
function to its graph
What happens if you
change the a value?
F-IF 7and 7e / F-LE 5 Graph
functions and key features
Looking at exponential
function graphs in the
form
y = ab^x what is the
domain? And end
behavior? Introduce
asymptote.
F-IF 9 compare properties of
two functions represented in a
different way.
A-SSE 1a. Interpret parts of
an expression
F-BF 1 Write a function
describing relationship
between 2 quantities
F-LE 1C recognize growth
and decay
Write exponential
equations given a verbal
description (word problem)
Given a graph of one
exponential equation and
an algebraic expression for
another, say which has the
largest value at a given
input.
If you have time:
Writing exponential growth
equations given a table of
values and the y intercept.
Forms of
Exponential Decay
F-IF 4 Key features of Graphs
F-IF 7 and 7e Graph functions
and key features
A-SSE 1a. Interpret parts of
an expression
F-LE 1C recognize growth
and decay
Causes of Growth and
Decay. Use real life
examples like population
and radioactive decay etc.)
Identify growth and decay
in an equation (if the base
is less than one or greater
than one) to AND
remember to tie it into the
properties of exponents
When graphing remember
to describe key features of
graphs including intercepts,
increasing, and end
behavior.
Modeling with
Exponential
Functions
F-IF 4 Key features of Graphs
F-IF 7and 7e Graph functions
and key features
A-SSE 1a. Interpret parts of
an expression
A-SSE 3c./F-IF 8b Use
properties of exponents to
transform exponential
Interest rate formulas and
word problems involving
simple and compounded
interest.
Use the properties of
exponents to transform
expressions for exponential
functions for example the
expression 1.15^t can be
rewritten as (1.15
function.
^1/12)^12t to reveal the
approximate equivalent
monthly interest rate if the
annual rate is 15%
Banking guest speakers
may be appropriate for this
lesson.