Download Common Core Algebra – Unit 3 – INEQUALITIES

Common Core Algebra CURRICULUM MAP
Units for Algebra 1A, 1B and 1C
and Proposed Lessons for Each Unit
Algebra 1A
Unit 1
Foundations
of algebra
Common Core
Math Standard(s)
A.SSE.1; A.SSE.1.a; N.RN.3
Mathematical Practice(s)
Explicitly Taught

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

Variables and expressions
Order of operations
Real numbers
Properties of real numbers
Adding, subtracting
Multiply, divide
Distributive
Key Vocabulary
Real-World Context
Unit 2
Solving
equations
Common Core
Math Standard(s)
A.CED.1; A.REI.3; N.Q.1; A.CED.4; A.REI.1;
N.Q.2; N.Q.3
Mathematical Practice(s)
Explicitly Taught








One-step
Two-step
Multi-step
Equations with variables on both sides
Linear equations and formulas
Ratios
Solving proportions
Proportion applications
o Percent (?)
Key Vocabulary
Real-World Context
Unit 3
Inequalities
Common Core
Mathematical Practice(s)
Explicitly Taught
Math Standard(s)
A.CED.1; A.REI.3; N.Q.2; A.REI.3; A.SSE.1;
A.SSE.1.b




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Key Vocabulary
Real-World Context
Inequalities and graphs
Solving inequalities using addition or subtraction
Solving inequalities using multiplication or
division
Solving multi-step inequalities
Compound inequalities
Absolute value equations and inequalities
Algebra 1B
Unit 4
Intro to
Functions
Common Core
Math Standard(s)
A.REI.10; F.IF.4; N.Q.1; F.IF.5; A.REI.11; N.Q.2;
A.SSE.1; A.SSE.1.a; A.CED.2; F.IF.1; F.IF.2; F.IF.3;
F.BF.1; F.BF.1.a; F.BF.2; F.LE.2; A.REI.1
Mathematical Practice(s)
Explicitly Taught






Intro to functions
Patterns of equations, graphs
Interpreting graphs
Patterns and linear functions
Applications of linear functions (writing and
graphing a function)
Arithmetic sequences
Key Vocabulary
Real-World Context
Unit 5
Linear
Functions
Common Core
Mathematical Practice(s)
Explicitly Taught
Math Standard(s)
F.IF.6; F.LE.1.b; N.Q.2; A.CED.2; F.BF.3; A.SSE.1;
A.SSE.1.a; A.SSE.2; A.CED.2; F.IF.4; F.IF.7; F.IF.7.a;
F.BF.1; F.BF.1.a; F.BF.3; F.LE.2; F.LE.5; A.CED.3;
A.REI.12; G.GPE.5
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
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Rate of change and slope
Direct variation
Slope-intercept form
Point-slope form
Standard form
Parallel and perpendicular lines
Graphing linear inequalities
Applications
Key Vocabulary
Real-World Context
Unit 6
Systems of
equations
Common Core
Math Standard(s)
A.REI.6; A.REI.5; N.Q.2; N.Q.3; A.CED.3; A.REI.12
Key Vocabulary
Real-World Context
Mathematical Practice(s)
Explicitly Taught
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



Foundations of linear systems and graphing
Solving systems by substitution
Solving systems by elimination
Applications of systems
Systems of linear inequalities
Algebra 1C
Unit 7
Exponents
and
polynomials
Common Core
Math Standard(s)
N.RN.1; N.RN.2; A.APR.1
Mathematical Practice(s)
Explicitly Taught

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

Multiplication with exponents
Division with exponents
Zero and negative exponents
Adding and subtracting polynomials
Multiplying binomials
Factoring out the GCF
Key Vocabulary
Real-World Context
Unit 8
Data
Common Core
Math Standard(s)
N.Q.1; F.LE.5; S.ID.6; S.ID.6.a; S.ID.6.c; S.ID.7;
S.ID.8; S.ID.9; N.Q.2; S.ID.2; S.ID.3
Mathematical Practice(s)
Explicitly Taught



Scatterplots
Trend lines
Central tendencies
Key Vocabulary
Real-World Context
Unit 9
Exponential
functions
Common Core
Math Standard(s)
A.SSE.1; A.CED.2; A.REI.11; F.IF.4; F.IF.5; F.IF.7;
F.IF.7.e; F.IF.9; F.LE.2; A.SSE.1.a; A.SSE.1.b;
A.SSE.3.c; F.IF.8; F.IF.8.b; F.BF.1; F.BF.3;
F.LE.1.c; F.LE.5
Key Vocabulary
Real-World Context
Mathematical Practice(s)
Explicitly Taught



Intro to exponential functions
Exponential growth and decay
Applications of exponential functions
Common Core Algebra – Unit 1 – Foundations of Algebra
Lesson
Topic
Order of
Operations
Evaluating
Variable
Expressions
Simplifying
Variable
Expressions
Variables &
Expressions
Common Core
Standard
A-SSE.1a
A-SSE.1a
A-SSE.1a
A.SSE.1
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
*Worksheet for Individual Practice
*Exit Slip: Write out step by step how to
evaluate 5 + 3(9 − 42 ) + 12 ÷ 3 + 2
Resources
Kutasoftware.com
Bingo
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.
Exit Slip: Evaluate an expression for
*Exit Slip: Give 5 examples of Like Terms
that could be combined when simplifying
variable expressions.
*Power Point/Notes
*Lego Sorting
*Poster (vocabulary)
*Supplemental WS
*Exit Slip – vocab
Class Activityhttp://ispeakmath.wordpress.com/2012/10/02/simplifyingalgebraic-expressions-activity/
Bingo http://edubakery.com/Bingo-Cards/SimplifyingAlgebraic-Expressions-v1-Bingo-Cards
PP/notes
HM Practice 2
Integer
Operations
Real
Numbers
and
PRoperties
Prepare for N.RN.3
(7.NS.A.1d)
(7.NS.A.2c)
*Hexagon Tiles
*Notes
*Dice (operations)
Number lines
Hexagon Tiles
Common Core Algebra - Unit 2- Linear Equations
Lesson Topic
1. SOLVE ONE
STEP
EQUATIONS
2. SOLVE TWO
STEP
OBJECTIVE.
EXPECTATION
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
After this lesson is
completed, the
students will be
able to: 1) State
Common Core
Standard
Possible Student
Tasks/Activities
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
balance of scales that
will represent balance
Actual Scale or website
www.mathplayground.com/algebraequations.html
[This resource gives option of one step & two step equation]
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.
[FROM LESSON 1]
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]
EQUATIONS
3. SOLVE
MULTI-STEP
EQUATIONS
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
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]
of equations. Teacher
may use any objects
that will relate to class.
Possible outside
activity can have
students use a type of
see-saw
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
be 7 no matter what
number was chosen.
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]
]
[Students can create
their own Magic Math
Problem]
4. SOLVE
EQUATIONS
WITH
VARIABLE ON
BOTH SIDES
5. LITERAL
EQUATIONS
AND 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,
using
the
same
reasoning
as
in
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]
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 &
SOLVING
PROPORTIONS
7. PROPORTION
APPLICATION
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 – Unit 3 – INEQUALITIES
Lesson Topic
1. ONE
VARIABLE
INEQUALITES
AND GRAPHS
2. SOLVE ONESTEP
INEQUALITES
3. SOLVE
MULTI-STEP
INEQUALITIES
4. COMPOUND
INEQUALITIES
5. ABSOLUTE
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
AZ-HS.A-CED.1
Possible Student
Tasks/Activities
Resources
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 - Unit 4 – Intro to Functions
Lesson Topic
Common Core Standard
Introduction to
functions
CCSS.Math.Content.HSACED.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.
Interpret Graphs

Patterns
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 variables to represent
relationships between quantities; graph
equations on coordinate axes with


Possible Student
Tasks/Activities
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.
Cups on cups on cups: students will
discover the terms associated with
functions by observing the
relationship of cups to height.
 SWBAT interpret a graph, and
create a graph for a real world
situation,
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.

SWBAT identify a pattern for in
any given representation
(graphs, tables, pictures, etc.)
Developing patterns:
Resources

Stacking cups.
labels and scales.
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).

Arithmetic
Sequences
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.
o
CCSS.Math.Content.HSASSE.A.1b 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.
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.HSF-BF.A.1 Write
a function that describes a relationship
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.
 SWBAT determine and apply an
arithmetic sequence
Auditorium Arithmetic: Students
will be given the example of and
auditorium that has several rows of
seating, the first of which starts
with 20 seats. The second has 24,
the third has 28 and so on for 30
rows of seats.
Auditorium Arithmetic
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
input-output pairs (include reading
these from a table).
Writing &
Application of
Linear Functions
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


SWBAT write a linear function
for any given graph, table, or
situation.
SWBAT apply the concepts of
linear functions to real world
situations
* 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.
descriptive modeling.

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.HSACED.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
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

SWBAT construct a graph using
the input & output values for a
given equation, table, or
situation.
Graph situation derived from the
previous day.
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.★
Common Core Algebra – Unit 5 – Linear Functions
Lesson Topic
Rate of change & Slope
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.★


CCSS.Math.Content.HSFLE.A.1b Recognize situations in which
one quantity changes at a constant rate
per unit interval relative to another.
Direct variation
CCSS.Math.Content.HSN-Q.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.
Slope intercept From
(two days)
CCSS.Math.Content.HSA-SSE.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.HSA-SSE.A.2 Use the
structure of an expression to identify ways
to rewrite it. For example, see x4 – y4 as





Possible Student
Tasks/Activities
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 variation with slope and
rate of change
SWBAT write an equation in
slope-intercept form for a
given situation and
construct.
SWBAT interpret the
meaning of each term in the
slope intercept equation
Resources
(x2)2 – (y2)2, thus recognizing it as a
difference of squares that can be factored
as (x2 – y2)(x2 + y2).
CCSS.Math.Content.HSA-CED.A.2 Create
equations in two or more variables to
represent relationships between quantities;
graph equations on coordinate axes with
labels and scales.
CCSS.Math.Content.HSF-IF.B.4 For a
function that models a relationship between
two quantities, interpret key features of
graphs and tables in terms of the quantities,
and sketch graphs showing key features
given a verbal description of the
relationship. Key features include:
intercepts; intervals where the function is
increasing, decreasing, positive, or
negative; relative maximums and
minimums; symmetries; end behavior; and
periodicity.★
CCSS.Math.Content.HSF-IF.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.HSF-IF.C.7a Graph
linear and quadratic functions and show
intercepts, maxima, and minima.
CCSS.Math.Content.HSF-BF.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.HSF-BF.B.3 Identify
the effect on the graph of replacing f(x)
by f(x) + k, k f(x),f(kx), and f(x + k) for
specific values of k (both positive and
negative); find the value of k given the
graphs. Experiment with cases and illustrate
an explanation of the effects on the graph
using technology. Include recognizing even
and odd functions from their graphs and

SWBAT recognize the terms
“m” and “b” as shifts in the
line y = x
algebraic expressions for them.
CCSS.Math.Content.HSF-LE.A.2 Construct
linear and exponential functions, including
arithmetic and geometric sequences, given
a graph, a description of a relationship, or
two input-output pairs (include reading
these from a table).
CCSS.Math.Content.HSF-LE.B.5 Interpret
the parameters in a linear or exponential
function in terms of a context.
Same as above

SWBAT write a linear
equation in point slope form
and construct the graph,
given the slope and point of
a line
Same as above

CCSS.Math.Content.HSN-Q.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.

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 yintercept for a given
situation
Point-slope form
Standard form
Applications #1

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.
Parallel and
perpendicular lines
Graphing linear
inequalities
Applications #2
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
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

SWBAT identify parallel and
perpendicular lines given a
graph or equation.

SWBAT graph linear
inequalities from a 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.
Common Core Algebra - Unit 6 - Systems of Equations
Lesson Topic
OBJECTIVE. EXPECTATION
1. Foundations
of linear
systems &
Graphing
SWBT find solution to system
by graphing
2. Solving
Systems by
Substitution
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.
3. Solve
Systems by
Elimination
4. 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
accuracy appropriate to
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]
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]
5. 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 – Unit 7 - Exponents & Polynomials
Lesson Topic
1.
Multiplication
with
exponents
2. 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 **
3. 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]
4. 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
5. Multiply
Binomials
6. Factor 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 – Unit 8 – Data
Lesson Topic
1. 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]
2. 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
to the data; use functions fitted
to data to solve problems in the
context of the data. Use given
functions or choose a function
Possible Student
Tasks/Activities
Resources
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]
3. 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 - Unit 9 : Exponential Functions
Note: The following standards were taken out (with Steve’s approval) A-REI 11, A-SSE1B, F-BF 3
Lesson Topic
Common Core Standard
Possible Student
Tasks/Activities
Intro to Exponential
Functions
A-SSE 1 Interpret Expressions in
terms of their contexts.
-Word problem like the Rice and
the king and the checker board.
(2 days)
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)
Given a table of values students
will identify if it’s linear or
exponential and is it a constant
rate of growth? ( A common
Resources
ratio?)
Different 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
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.
Modeling: Interest Rate
F-IF 4 Key features of Graphs
F-IF 7and 7e Graph functions and key
Interest rate formulas and word
problems involving simple and
compounded interest.
features
A-SSE 1a. Interpret parts of an
expression
A-SSE 3c./F-IF 8b Use properties of
exponents to transform exponential
function.
Exponential growth and
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
Use the properties of exponents
to transform expressions for
exponential functions for
example the expression 1.15^t
can be rewritten as (1.15
^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.
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.