Download ALGEBRA 1 , ALGEBRA 2 , AND GEOMETRY COMMON CORE

ALGEBRA 1
Teacher:
Year: 2011-12
CORE Algebra I
Course: Algebra I
Month: All Months
Students will solve one variable equations
How can you represent quantities, patterns, and relationships?
One Variable Equations ~ How are properties related to algebra?
What kinds of relationships can proportions represent?
How can you solve equations?
Standards
Content
A-REI.1-Explain each Order of
step in solving a
operations of
simple equation as
expressions
following from the
verbal models
equality of numbers
asserted at the
previous step, starting
from the assumption
that the original
equation has a
solution. Construct a
viable argument to
justify a solution
method.
A-SSE.2-Use the
structure of an
expression to identify
ways to rewrite it.
A-SSE.3-Choose and
produce an equivalent
form of an expression
to reveal and explain
properties of the
quantity represented
by the expression.
A-SSE.1a-Interpret
parts of an expression,
such as terms, factors,
and coefficients.
A-CED.1-Create
Unit analysis
equations and
Proportions
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-SSE.1-Interpret
expressions that
represent a quantity in
terms of its context.
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
Skills
Vocabulary
Simplify expressions
Evaluate expressions
Translate verbal models
to algebraic
equations/expressions
PEMDAS
Objectives
Resources
Students will simplify Worksheet Website
and evaluate an algebraic
algebraic expression expression using order of
operations
exponent
Students will translate
base
verbal models to
algebraic
simplify
expressions/equations
evaluate
variable
term
coefficient
constant
Converting units in a
measurement system
Solve proportions for
an unknown.
conversion factor
cross products
proportion
rate
ratio
scale
unit analysis
Students will convert units
within and
between measurement
systems using unit analysis
and data displays.
A-REI.3-Solve linear
equations and
inequalities in one
variable, including
equations with
coefficients
represented by letters.
A-REI.1-Explain
One-variable equations
each step in solving a
Formulas
simple equation as
following from the
equality of numbers
asserted at the previous
step, starting from the
assumption that the
original equation has a
solution. Construct a
viable argument to justify
a solution method.
A-REI.3-Solve linear
equations and
inequalities in one
variable, including
equations with
coefficients represented
by letters.
Show or explain
algebraic reasoning
used to solve a onevariable equation
Solve for a single
variable with a multivariable formula
equivalent equations
formula
inverse operations
Students will show
or explain algebraic
reasoning to solve onevariable equations
Students will analyze linear functions
Linear Functions ~
How can you solve equations?
How can you represent and describe a linear relationship?
What information does the equation of a line give you?
Can functions describe real-world situations?
How can you make predictions based on a scatter plot?
How can arithmetic sequences be used to model situations?
Standards
Content
Skills
Vocabulary
A-CED.1-Create
equations and
inequalities in one
variable and use them to
solve problems. Include
equations arising from
linear and quadratic
functions, and simple
rational and exponential
functions.
A-CED.2-Create
equations in two or more
variables to represent
relationships between
quantities; graph
equations on coordinate
axes with labels and
scales.
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).
1.2-Reason abstractly
and quantitatively
1.7-Look for and make
use of structure.
F-IF.6-Calculate and
interpret the average
slope-intercept form
point-slope form
standard form of a
line
graph each form x-intercept
of linear
y-intercept
equations
slope
write linear
equations in
different forms
Objectives
Students will graph and
write linear equations
using different forms
(slope-intercept, pointslope, and standard).
Resources
rate of change of a
function (presented
symbolically or as a
table) over a specified
interval. Estimate the
rate of change from a
graph.
F-LE.1b-Recognize
situations in which one
quantity changes at a
constant rate per unit
interval relative to
another.
F-BF.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.
F-IF.7a-Graph linear and
quadratic functions and
show intercepts,
maxima, and minima.
F-BF.1-Write a function
Functions
that describes a
Domain and range
relationship between two Linear functions
quantities.
F-IF.1-Understand that a
function from one set
(called the domain) to
another set (called the
range) assigns to each
element of the domain
exactly one element of the
range. If f is a function and
x is an element of its
domain, then f(x) denotes
the output of f
corresponding to the input
x. The graph of f is the
graph of the equation y =
f(x).
F-IF.2-Use function
notation, evaluate
functions for inputs in their
domains, and interpret
statements that use
function notation in terms
of a context.
F-IF.7a-Graph linear and
quadratic functions and
show intercepts, maxima,
and minima.
1.2-Reason abstractly and
quantitatively
F-IF.4-For a function that
models a relationship
between two quantities,
interpret key features of
graphs and tables in terms
of the quantities, and
sketch graphs showing
key features given a
Define function
Analyze domain and
range
Graph linear functions
continuous graph
dependent variable
discrete graph
domain
function
independent variable
range
relation
Students will define and
analyze a function
(domain and range) and
graph linear functions.
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.
A-REI.10-Understand that
the graph of an equation
in two variables is the set
of all its solutions plotted
in the coordinate plane,
often forming a curve
(which could be a line).
F-IF.5-Relate the domain
of a function to its graph
and, where applicable, to
the quantitative
relationship it describes.
N-Q.2-Define appropriate
quantities for the purpose
of descriptive modeling.
S-ID.6a-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 suggested by
the context. Emphasize
linear, quadratic, and
exponential models.
S-ID.6b-Informally
assess the fit of a
function by plotting and
analyzing residuals.
S-ID.6c-Fit a linear
function for a scatter plot
that suggests a linear
association.
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.
Scatter plot
Correlation and
causation
Linear model
F-IF.3-Recognize that
Arithmetic sequences
sequences are functions,
sometimes defined
recursively, whose
domain is a subset of the
integers.
F-BF.2-Write arithmetic
and geometric sequences
both recursively and with
an explicit formula, use
them to model situations,
and translate between the
two forms.
F-BF.1a-Determine an
explicit expression, a
recursive process, or
steps for calculation from
a context.
F-LE.2-Construct linear
Create scatter plot
Determine correlation
Distinguish between
correlation and
causation
Create linear models to
represent data
Intepret linear model to
make predictions
Write explicit and
recursive formulas
Model situations using
arithmetic sequences
Translate between
recursive and explicit
forms
scatter plot
positive correlation
negative correlation
no correlation
trend line
interpolation
extrapolation
line of best fit
correlation coefficient
causation
residual
sequence
term of sequence
arithmetic sequence
commond difference
recursive formula
explicit formula
Students will create a
scatter plot and
determine correlation.
Students will distinguish
between correlation and
causation
Students will create and
interpret a linear model
to represent data and
use it to make
predictions.
Students will write
arithmetic sequences
both explicitly and
recursively and use
them to model situations
and translate between
the forms.
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).
1.2-Reason abstractly
and quantitatively
1.7-Look for and make
use of structure.
Students will solve systems of linear equations using a variety of methods
Systems of Linear Equations ~ How can you solve a system of equations?
How can systems of equations model real-world situations?
What does the solution to a system of equations mean?
Standards
Content
Skills
Vocabulary
A-REI.5-Prove that,
Graphing method
Solve a linear
system of linear
given a system of two
equations
Numeric (tabular) system
equations in two
solution
variables, replacing one method
equation by the sum of
Algebraic method
that equation and a
- substitution
multiple of the other
Algebraic method
produces a system with
- elimination
the same solutions.
A-REI.6-Solve systems
of linear equations
exactly and
approximately (e.g., with
graphs), focusing on
pairs of linear equations
in two variables.
1.6-Attend to precision.
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.5-Prove that, given a
Real world systems
system of two equations in of linear equations
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 (e.g.,
with graphs), focusing on
pairs of linear equations in
two variables.
Model a real world
problems using a linear
system
Solve and interpret a
real world linear system
Objectives
Resources
Students will solve a
system of linear
equations graphically,
numerically, and
algebraically
(substitution, elimination)
Students will model
and solve real-world
problems with systems of
linear equations
A-CED.2-Create equations
in two or more variables to
represent relationships
between quantities; graph
equations on coordinate
axes with labels and
scales.
A-CED.3-Represent
constraints by equations or
inequalities, and by
systems of equations
and/or inequalities, and
interpret solutions as viable
or nonviable options in a
modeling context.
1.4-Model with
mathematics.
1.6-Attend to precision.
A-CED.3-Represent
Types of linear
constraints by equations system solutions
or inequalities, and by
systems of equations
and/or inequalities, and
interpret solutions as
viable or nonviable
options in a modeling
context.
1.6-Attend to precision.
Analyze the 3
types of solution for
systems
consistent
Students will
analyze the solution of
the system of
equations.
independent
dependent
inconsistent
Students will solve and graph one variable inequalities and graph two variable inequalities.
Inequalities ~ How do you represent relationships between quantities that are not equal?
Can inequalities that appear to be different be equivalent?
How can you solve inequalities?
Standards
Content
A-REI.3-Solve linear
One-variable
equations and
inequalities
inequalities in one
Two variable
variable, including
inequalities
equations with
coefficients represented
Systems of two
by letters.
linear inequalities
A-CED.1-Create
equations and
inequalities in one
variable and use them to
solve problems. Include
equations arising from
linear and quadratic
functions, and simple
rational and exponential
functions.
A-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 halfplanes.
Skills
Vocabulary
Solving and
graphing simple
one-variable
inequalities
Disjoint sets
Graphing two
variable
inequalities
union
Graphing
systems of two
linear inequalities
Semester Review/Final ~ Semester Review/Final
interval notation
set builder notation
empty set
Objectives
Students will be able
to solve and graph onevariable inequalities.
Students will be able
to graph two variable
inequalities.
Students will be able
to graph systems of two
linear inequalities.
Resources
Standards
Content
Skills
Vocabulary
Objectives
Resources
Students will use probability and statistics to solve theoretical and real-life
problems
Probability and Statistics
How can collecting and analyzing data help you make decisions or predictions?
How can you make and interpret different representations of data?
How is probability related to real-world events?
~
Standards
Content
S-ID.1-Represent data
Data Distribution
with plots on the real
Display data via
number line (dot plots,
graphs
histograms, and box
plots).
S-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.
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).
Skills
Analyze
shape of data
distribution,
utilizing
statistics, to
compare center
and spread of two
or more different
data sets.
Vocabulary
Quartile
Objectives
Resources
Students will 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.
Displaying
data with an
appropriate graph
(dot plots,
histograms, box
plots).
Students will display
data with an appropriate
graph (dot plots,
histograms, and box
plots).
Students will analyze quadratic functions
Quadratic Functions
~
Standards
How can I simplify radical expressions using multiplication and division properties of
square roots?
How can I recognize and graph a quadratic function?
How can I use properties of multiplying binomials to factor perfect square trinomials?
How can I factor and graph quadratic functions?
By using various methods, how can I solve quadratic equations?
How can I solve a system of linear and quadratic equations?
Content
F-IF.7a-Graph linear and
Properties of
quadratic functions and rational and irrational
show intercepts,
numbers
maxima, and minima.
A-REI.2-Solve simple
rational and radical
equations in one
variable, and give
examples showing how
extraneous solutions
may arise.
Skills
Utilizing
properties of
rational or
irrational
numbers
Vocabulary
radical expression
rationalize the
denominator
F-IF.7a-Graph linear
Graphs of quadratic
Analyzing the graph
and quadratic functions functions
of a quadratic function
and show intercepts,
maxima, and minima.
A-SSE.2-Use the
structure of an
expression to identify
ways to rewrite it.
Quadratic
expressions
Factoring quadratic
expressions
Objectives
Resources
Students will use
properties of rational or
irrational numbers to
simplify expressions
(simplest radical form).
parabola
axis of symmetry
vertex
perfect-square
trinomial
difference of two
Students will analyze
the graph of a quadratic
function relative to the
vertex, the 'x' and 'y'
intercepts, and the axis
of symmetry.
Students will factor
quadratic expressions
(difference of two
A-SSE.1a-Interpret parts
of an expression, such
as terms, factors, and
coefficients.
A-SSE.1b-Interpret
complicated expressions
by viewing one or more
of their parts as a single
entity.
squares
F-IF.7a-Graph linear
Quadratic functions
Graphing and
and quadratic functions with a = 1
writing quadratic
and show intercepts,
functions with a = 1
maxima, and minima.
A-REI.4a-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.
zero-product property
Students will graph
completing the square and write quadratic
functions with a=1 using
quadratic formula
different forms (vertex
form by completing the
discriminant
square, using the
quadratic formula, and
factoring).
A-REI.4b-Solve
Quadratic equations
Solving quadratic
quadratic equations by with a = 1
equations with a = 1
inspection (e.g., for x2 =
49), taking square roots,
completing the square,
the quadratic formula
and factoring, as
appropriate to the initial
form of the equation.
Recognize when the
quadratic formula gives
complex solutions and
write them as a ± bi for
real numbers a and b.
A-REI.7-Solve a simple
Systems of
system consisting of a
equations involving
linear equation and a
linear and quadratic
quadratic equation in two equations
variables algebraically
and graphically. For
example, find the points
of intersection between
the line y = –3x and the
circle x2 + y2 = 3.
A-REI.6-Solve systems of
linear equations exactly
and approximately (e.g.,
with graphs), focusing on
pairs of linear equations
in two variables.
squares, perfect square
trinomial, trinomial with a
= 1).
Solving systems of
equations involving
linear and quadratic
equations
standard form of a
quadratic equation
Students will solve a
quadratic equation with
root of an equation a=1 by graphing, using
square roots, completing
zero of a function
the square, using the
quadratic formula, and
factoring.
consistent
independent
dependent
Students will solve
systems of equations
involving linear and
quadratic equations.
inconsistent
Students will simplify polynomial and exponential expressions and analyze
basic exponential growth and decay functions.
Polynomial and Exponential
Expressions ~
Standards
N-RN.1-Explain how the
Content
Scientific and
How can I convert numbers from standard form to scientific notation, and vice
versa?
How are properties of real numbers related to polynomials?
By using the correct properties and procedures, how can I add or subtract
polynomials?
How can I model and use an exponential function to determine exponential
growth or decay?
How can I write and use geometric sequences using recursive and explicit
forms?
Skills
Restating
Vocabulary
scientific notation
Objectives
Students will restate
Resources
definition of the meaning standard Notation
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.
N-RN.2-Rewrite
expressions involving
radicals and rational
exponents using the
properties of exponents.
numbers in
scientific or
standard
notation
standard notation
A-APR.1-Understand that
Properties of
polynomials form a
exponents
system analogous to the
integers, namely, they
are closed under the
operations of addition,
subtraction, and
multiplication; add,
subtract, and multiply
polynomials.
Simplifying
expressions
A-APR.1-Understand
Polynomials
that polynomials form a
Polynomial
system analogous to the
expressions
integers, namely, they
are closed under the
operations of addition,
subtraction, and
multiplication; add,
subtract, and multiply
polynomials.
Defining polynomial
(informally) with
differentiating between
'terms' and 'factors'.
monomial
Adding, subtracting,
and multiplying
polynomial expressions
trinomial
numbers in scientific or
standard notation.
monomial
polynomial
binomial
trinomial
degree of a
monomial
polynomial
binomial
degree of a
monomial
Students will use
properties of exponents
to simplify expressions
(including rational
exponents and
applications to scientific
notation).
Students will
informally define
polynomial and
emphasize differences
between 'terms' and
'factors'. Students will
define degree of
polynomial, degree of
term, coeffecient, and
constant term.
Students will add,
subtract, and multiply
polynomial expressions
F-IF.8b-Use the
Exponential growth
properties of exponents to and decay
interpret expressions for
Percent of change
exponential functions. For
example, identify percent
rate of change in
functions such as y =
(1.02)t, y = (0.97)t, y =
(1.01)12t, y = (1.2)t/10,
and classify them as
representing exponential
growth or decay.
N-Q.3-Choose a level of
accuracy appropriate to
limitations on
measurement when
reporting quantities.
F-BF.2-Write arithmetic
Geometric
and geometric
sequences
sequences both
recursively and with an
explicit formula, use
them to model
situations, and translate
between the two forms.
Defining exponential
growth and decay
functions and comparing
to linear and quadratic
functions using tables
and graphs
growth factor
decay factor
Utilizing percent of
change to describe
growth and decay rates
Students will define
exponential growth and
decay functions and
compare to linear and
quadratic functions
using tables and graphs
(calculate and compare
average rates of
change).
Students will use
percent of change and
use the concept to
describe growth and
decay rates.
Writing geometric
sequences explicitly and
recursively
geometric sequence
recursive
explicit
Students will write
geometric sequences
both explicitly and
recursively and use
them to model situations
and translate between
the forms.
Students will use transformations to build new functions from existing
functions.
Transformations of Functions
~
By anlayzing graphs, how can I classify special functions?
How can I transform parent functions?
Can I recognize and identify the domain and range of a function?
How can I find the inverse of a function?
Standards
Content
F-BF.3-Identify the effect
Functions and
on the graph of
their graphs
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.
F-IF.7-Graph functions
expressed symbolically
and show key features of
the graph, by hand in
simple cases and using
technology for more
complicated cases.
F-BF.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.
Skills
Vocabulary
Classifying
translation
functions
absolute value
according to their function
graphs
piecewise function
Parent functions
F-IF.1-Understand that a Domain and range
function from one set
(called the domain) to
another set (called the
range) assigns to each
element of the domain
exactly one element of the
range. If f is a function and
x is an element of its
domain, then f(x) denotes
the output of f
corresponding to the input
x. The graph of f is the
graph of the equation y =
f(x).
F-BF.4a-Solve an
Functions and their
equation of the form f(x) inverses
= c for a simple function
f that has an inverse
and write an expression
for the inverse. For
example, f(x) =2 x3 or
f(x) = (x+1)/(x–1) for x ?
1.
Transforming parent
functions
Analyzing domain
and range for specific
functions
Objectives
Resources
Students will classify
these functions
according to their graphs:
f(x) = x, f(x) = x^2, f(x) =
|x|, and f (x)= sqrt (x).
translation
relation
domain
range
Students will
transform parent
functions using the
following: f(x-h), f(x) +k,
-f(x), f(-x), af(x), f(x/b)
Students will
analyze domain and
range of a function.
vertical line test
function notation
Comparing a function
and its inverse
graphically, numerically,
and algebraically
(emphasize that it is a
reflection about the line y
= x)
Semester Review/Final ~ Semester Review/Final
inverse functions
Students will
compare a function and
its inverse graphically,
numerically, and
algebraically (emphasize
that it is a reflection
about the line y = x).
http://sublette1-wy.perfplusk12.com/Curric/Published_LandScapeMap.aspx?Publishkey=5af85311-4cdc49cd-86c6-df60d0a3f970
GEOMETRY
https://sites.google.com/site/geometrywithmosteller/standards-5
Teacher:
CORE Geometry
Year: 2011-12
Course: Geometry
Month: September
Review linear equations and inequalities though a study of
systems
Introduce matrices and apply matrices to solving linear systems
How do variables help you model real-world situations?
Introduction to Geometry Vocabulary &
Definitions ~
Standards
G-CO.1-Know precise
definitions of angle,
circle, perpendicular line,
parallel line, and line
segment, based on the
undefined notions of
point, line, distance
along a line, and
distance around a
circular arc.
Content
Undefined terms
What are the undefined terms (building blocks) of geometry?
What is a good definition?
How do points, lines and planes work together to form the other
objects in geometry?
Why do we have to use the same symbols and definitions?
What is a good definition?
How do points, lines and planes work together to form the other
objects in geometry?
What is a polygon? What shapes are NOT polygons?
What does it mean to be a regular polygon?
What is the definition of a circle?
What is an isometric drawing?
What are some strategies for sketching 3D shapes?
How are 2D nets related to 3D solids?
What is geomtric probability?
Skills
Describe the
undefined
terms
Good definitions
Define
geometric terms
Vocabulary
point
Objectives
Resources
Students will be able
to describe the undefined
terms of geometry.
line
plane
Students will be able
to use geometry
language to define new
geometric objects.
definition
collinear
coplanar
Students will be able
to use appropriate
symbols and language to
refer to or define
geometric objects.
congruent
midpoint
bisects
ray
counterexample
G-GPE.4-Use
Line segments
Measure segment
coordinates to prove
length with a ruler
Angles
simple geometric
Meaure angles in
theorems algebraically.
Midpoint on
degrees with a protractor
For example, prove or coordinate plane
disprove that a figure
Classify angles
Angle classifications
defined by four given
Use definitions to
points in the coordinate
Angle pairs
solve
angle problems
plane is a rectangle;
line segment
end points
angle
vertex
sides
reflex measure of an
angle
Students will be
able to measure line
segments with a ruler.
With a protractor,
students will be able to
draw angles of a given
measure in degrees.
Students will be
prove or disprove that
the point (1, ?3) lies on
the circle centered at the
origin and containing the
point (0, 2).
G-CO.1-Know precise
definitions of angle,
circle, perpendicular
line, parallel line, and
line segment, based on
the undefined notions of
point, line, distance
along a line, and
distance around a
circular arc.
G-CO.1-Know precise
definitions of angle,
circle, perpendicular line,
parallel line, and line
segment, based on the
undefined notions of
point, line, distance along
a line, and distance
around a circular arc.
Analyze the midpoint
formula on the coordinate
plane
Calculate the
midpoint of a segment on
the coordinate plane
able to use the
Midpoint Formula to
complementary angles calculate the midpoint
supplementary angles of a line segment in
the coordinate plane.
vertical angles
Students will be
linear pair of angles
able to use appropriate
symbols and language
to refer to or define
geometric objects.
angle bisector
Students will be
able to use geometry
language to define
new geometric
objects.
Polygons
Triangles
Quadrilaterals
Classify polygons
polygon names (1based on side lengths, 12 sides and n sides)
angle measures,
consecutive angles,
and/or parallel sides
vertices, and sides
Use definitions to
diagonal
solve problems
convex
concave
perimeter
equilateral,
equiangular, regular
acute, right, obtuse
scalene, isosceles,
equilateral
G-CO.1-Know precise
definitions of angle, circle,
perpendicular line, parallel
line, and line segment,
based on the undefined
notions of point, line,
distance along a line, and
distance around a circular
arc.
Circles
Define parts of
circles
circle
Identify parts of
circles
radius
center
diameter
Use definitions to
solve problems
chord
tangent, point of
tangency
Students will be
able to use geometry
language to define new
geometric objects.
Students will be
able to use appropriate
symbols and language
to refer to or define
geometric objects.
Students will be
able to classify
polygons based on side
lengths, angle
measures, and/or
parallel sides.
Students will be able
to use geometry
language to define new
geometric objects.
Students will be able
to use appropriate
symbols and language to
refer to or define
geometric objects.
congruent circles
concentric circles
arc, endpoints,
minor arc, major arc
semicircle
arc measure
central angle
G-CO.1-Know precise
Isometric drawings
Draw 3D shapes on
definitions of angle, circle,
isometric dot paper
Sketches of 3D
perpendicular line,
shapes
Sketch 3D shapes on
parallel line, and line
paper
segment, based on the
Nets
undefined notions of
Identify appropriate
point, line, distance along
nets by visualization
a line, and distance
around a circular arc.
Isometric drawings
Students will be able
to use geometry
language to define new
geometric objects.
Students will be able
to use appropriate
symbols and language
to refer to or define
geometric objects.
Students will be able
to copy isometric
drawings on isometric
dot paper.
Students will be able
to sketch 3D shapes
including pyramids and
prisms with polygon
bases that have more
than 4 sides.
Geometric
Analyze word
S.MD.6, S.MD.7
Students will be able
probability
problems
to analyze word problems
to calculate geometric
probability.
Draw pictures to
model probability
Calculate probabilities
ALGEBRA 2
Teacher:
CORE Algebra II
Year: 2011-12
Course: Algebra II
Month: All Months
Review linear equations and inequalities though a study of systems
Introduce matrices and apply matrices to solving linear systems
Solving Systems of Linear Equations
& Inequalities ~
How do variables help you model real-world situations?
How does representing functions graphically help you solve a
system of equations?
How does writing equivalent forms of an equation help you to solve a
system of equations?
How can linear programming be used to find the optimal solution of a
system of inequalities?
How is operations of matrices the same as operations of real
numbers?
How does operations of matrices differ from operations of real
numbers?
How are properties of equality used in the matrix solution of a
system of equations?
Standards
Content
Skills
Vocabulary
Objectives
Resources
1.4-Model with
mathematics.
Verbal models
Translate to
algebraic
expressions
Translate into
algebraic
equations
Translate into
algebraic
inequalities
algebraic models of real
world situations
Students will translate
verbal models into
algebraic expressions
and equations
Story Problems
Worksheets
A-CED.1-Create
System of linear
equations and
equations
inequalities in one
variable and use them to
solve problems. Include
equations arising from
linear and quadratic
functions, and simple
rational and exponential
functions.
A-CED.2-Create
equations in two or more
variables to represent
relationships between
quantities; graph
equations on coordinate
axes with labels and
scales.
A-CED.3-Represent
constraints by equations
or inequalities, and by
systems of equations
Solve a linear system by solution(s) of a system
graphing
Solve a linear system
using elimination
Solve a linear system
using substitution
Students will solve
systems of linear
equations
and/or inequalities, and
interpret solutions as
viable or nonviable
options in a modeling
context.
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.
A-CED.1-Create
System of linear
equations and
inequations
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.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.
A-REI.3-Solve linear
equations and
inequalities in one
variable, including
equations with
coefficients
represented by letters.
Graph and solve
Union of sets
compund inequalities
Intersection of sets
Solve and graph
Optimized values
absolute value
inequalities
Use linear programming
to find optimized values
in a system of
inequalities
N-VM.7-(+) Multiply
Matrix Operations
matrices by scalars to
produce new matrices,
e.g., as when all of the
payoffs in a game are
doubled.
N-VM.8-(+) Add,
subtract, and multiply
matrices of appropriate
dimensions.
N-VM.9-(+) Understand
that, unlike multiplication
of numbers, matrix
multiplication for square
matrices is not a
commutative operation,
but still satisfies the
associative and
distributive properties.
A-REI.8-(+) Represent a
system of linear equations as
a single matrix equation in a
vector variable.
A-REI.9-(+) Find the inverse of
a matrix if it exists and use it to
solve systems of linear
equations
(using technology for matrices
of dimension 3 × 3 or greater).
Identity matrix
Inverse matrix
Systems of multivariable linear
equations
Add and subtract
matrices
Multiply a matrix by a
scale factor
Multiply two matrices
Students will solve
systems of linear
inequalities
Matrix
Rows & columns
Dimensions
Identity matrix
Invere matirx
scalar multiplication vs.
matirx multiplication
Solve a multi-variable Matrix equations
linear system using
an identity matrix and
an inverse matrix
Analyze simple families of functions
Linear Programming
Worksheets
Students will preform
matrix operations
Students will use
matrix algebra to solve
multi-variable linear
systems
Families of Functions ~ Transform familes of functions into more complex functions
Standards
Content
F-BF.1-Write a function Algebraic parent
that describes a
functions
relationship between
Translations
two quantities.
Operations of
F-BF.3-Identify the
functions
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.
F-BF.1b-Combine
standard function types
using arithmetic
operations.
F-BF.1c-(+) Compose
functions.
F-IF.1-Understand that
a function from one set
(called the domain) to
another set (called the
range) assigns to each
element of the domain
exactly one element of
the range. If f is a
function and x is an
element of its domain,
then f(x) denotes the
output of f
corresponding to the
input x. The graph of f is
the graph of the
equation y = f(x).
F-IF.2-Use function
notation, evaluate
functions for inputs in
their domains, and
interpret statements that
use function notation in
terms of a context.
F-IF.7-Graph functions
expressed symbolically
and show key features
of the graph, by hand in
simple cases and using
technology for more
complicated cases.
F-IF.7a-Graph linear
and quadratic functions
and show intercepts,
maxima, and minima.
F-IF.7b-Graph square
root, cube root, and
piecewise-defined
functions, including step
functions and absolute
value functions.
Skills
Vocabulary
Objectives
Identify, compare
and contrast the
following parent
functions:
y=x
y=x2
y=sqrt(x) &
y=cuberoot(x)
y=abs(x)
y=sqrt(1-x2) unit
semi-cirlce
Use the following
transformations to
build new functions
from the parent
functions:
f(x-h)
f(x)+k
-f(x)
f(-x)
a f(x)
f(x/b)
Combine functions
using the following
arithmetic
operations:
f(x) + g(x)
f(x) - g(x)
f(x)*g(x)
f(x)/g(x)
f(g(x))
Solve equations
involving square
roots
Solve equations
involving absolute
value expressions
Parent functions
Translations
Reflections
Dilations
Composition of functions
Students will analyze
and develop transformed
functions from parent
functions
Polynomial Functions Review analysis of linear and quadratic functions
~
Analyze 3rd degree & higher polynomial functions
Resources
What are the advantages of a quadratic in general form? In vertex form? In factored
form?
For a polynomial equations, how are factors, roots and x-intercepts related?
What does the degree of the polynomial tell you about the graph of the polynomial
function?
Standards
Content
N-CN.1-Know there is a Quadratic functions
complex number i such
that i2 = –1, and every
complex number has the
form a + bi with a and b
real.
N-CN.2-Use the relation
i2 = –1 and the
commutative,
associative, and
distributive properties to
add, subtract, and
multiply complex
numbers.
N-CN.3-(+) Find the
conjugate of a complex
number; use conjugates
to find moduli and
quotients of complex
numbers.
N-CN.7-Solve quadratic
equations with real
coefficients that have
complex solutions.
A-APR.1-Understand
that polynomials form a
system analogous to the
integers, namely, they
are closed under the
operations of addition,
subtraction, and
multiplication; add,
subtract, and multiply
polynomials.
A-APR.2-Know and
apply the Remainder
Theorem: For a
polynomial p(x) and a
number a, the remainder
on division by x – a is
p(a), so p(a) = 0 if and
only if (x – a) is a factor
of p(x).
A-APR.3-Identify zeros
of polynomials when
suitable factorizations
are available, and use
the zeros to construct a
rough graph of the
function defined by the
polynomial.
A-REI.3-Solve linear
equations and
inequalities in one
variable, including
equations with
coefficients represented
by letters.
A-REI.4-Solve quadratic
equations in one
variable.
A-SSE.2-Use the
structure of an
expression to identify
Skills
Vocabulary
Objectives
Analyze quadratic
functions within
and between the
following forms in
order to graph:
General form
Vertex form
Factored form
Solve quadratic
equations using
the following
methods:
Extracting the
square root
Completing the
square
Quadratic
Formula
Factoring
Define the
Complex Number
System to cover
all solutions of a
quadratic
equation and
perfrom
operations of
complex
numbers.
Graph & analyze
quadratic
inequlities
General form
Vertex from
Factored from
Complete the square
Imaginary unit
Complex number system
Students will sketch
graphs of quadratic
functions
Students will apply
algebraic and graphical
techniques to find all
complex solutions of
quadratic equations
Students will analyze
quadratic inequalities
Resources
ways to rewrite it.
A-SSE.3-Choose and
produce an equivalent
form of an expression to
reveal and explain
properties of the quantity
represented by the
expression.
A-SSE.3a-Factor a
quadratic expression to
reveal the zeros of the
function it defines.
A-SSE.3b-Complete the
square in a quadratic
expression to reveal the
maximum or minimum
value of the function it
defines.
A-APR.1-Understand
Polynomial functions that polynomials form a algebraic manipulation
system analogous to the
integers, namely, they
are closed under the
operations of addition,
subtraction, and
multiplication; add,
subtract, and multiply
polynomials.
A-APR.2-Know and
apply the Remainder
Theorem: For a
polynomial p(x) and a
number a, the remainder
on division by x – a is
p(a), so p(a) = 0 if and
only if (x – a) is a factor
of p(x).
A-APR.3-Identify zeros of
polynomials when
suitable factorizations
are available, and use
the zeros to construct a
rough graph of the
function defined by the
polynomial.
A-SSE.1a-Interpret parts
of an expression, such
as terms, factors, and
coefficients.
A-SSE.3c-Use the
properties of exponents
to transform expressions
for exponential functions.
N-CN.8-(+) Extend
polynomial identities to
the complex numbers.
For example, rewrite x2
+ 4 as (x + 2i)(x – 2i).
N-CN.9-(+) Know the
Fundamental Theorem of
Algebra; show that it is
true for quadratic
polynomials.
Simplify polynomial
expressions using
properites of rational
exponents
Simplify polynomial
expression by factoring
Add, subtract, multiply
and divide polynomial
functions
- state domain and
range
- divide using long
division and synthetic
division techniques
Simpliest radical form
Polynomial long division
Synthetic division
Remainder Theorem
Factor Theorem
Fundamental Theorem
of Algebra
Students will simplify
and perform operations
involving polynomial
expressions
F-IF.7a-Graph linear and Polynomial functions quadratic functions and graphical analysis
show intercepts, maxima,
and minima.
F-IF.7c-Graph polynomial
functions, identifying
zeros when suitable
factorizations are
available, and showing
end behavior.
Describe end behavior
Find real and imaginary
zeros
Produce additional
points using
- direct substitution
- synthetic substitution
Sketch a polynomial
function noting the
domain and range of the
function
End behavior
Zeros / roots
Intercepts
Extrema
Best fit regression
model
Students will sketch
graphs of polynomial
functions
Students will use
technology to analyze
the following:
- relative extrema
- regression models of
best fit
Using technology, find
relative extrema
Using regression
capabilites of
technology, produce a
polynomial of best fit
Students will analyze exponential functions graphically and solve exponential &
logaritmic equations
Exponential
Functions ~
How are exponents and logarithms related?
How do you model a quantity that changes regularly over time by the same
percentage?
What similar techniques can be used when solving exponential and logarithmic
equations?
Standards
Content
Skills
Vocabulary
Objectives
A-CED.1-Create
equations and
inequalities in one
variable and use them to
solve problems. Include
equations arising from
linear and quadratic
functions, and simple
rational and exponential
functions.
A-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.?
F-BF.4-Find inverse
functions.
F-IF.7-Graph functions
expressed symbolically
and show key features
of the graph, by hand in
simple cases and using
technology for more
complicated cases.
F-LE.4-For exponential
models, express as a
logarithm the solution to
abct = d where a, c, and
d are numbers and the
base b is 2, 10, or e;
evaluate the logarithm
using technology.
1.5-Use appropriate
tools strategically.
Exponential
functions and
logarithmic
equations
Write the equation
of an exponential
function in the
form y=abx
Graphically
analyze and
sketch a graph of
exponential growth
and decay
functions
Develop inverse
functions
algebraically and
gaphically
Solve exponential
and logarithmic
equations
exponential growth
exponential decay
horizontal asymptotes
inverse vs functional
inverse
logarithms
Students will analyze
exponential functions
Students will graph
exponential functions
Students will create
inverse relations from
functions
Students will solve
exponential and
logarithmic equations
Resources
Rational Functions Students will analyze reducible and irreducible rational functions
~
Do two quantities vary inversely if an increase in one corresponds to a decrease in the
other?
What kind of asymptotes are possible for a rational function?
Are a rational expression/function and its simplified form equivalent?
What citeria must be met to be able to simplify rational expressions?
Standards
Content
1.2-Reason abstractly Rational function
and quantitatively
1.5-Use appropriate
tools strategically.
1.7-Look for and make
use of structure.
A-APR.6-Rewrite simple
rational expressions in
different forms; write
a(x)/b(x) in the form q(x)
+ r(x)/b(x), where a(x),
b(x), q(x), and r(x) are
polynomials with the
degree of r(x) less than
the degree of b(x),
using inspection, long
division, or, for the more
complicated examples,
a computer algebra
system.
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.?
F-IF.5-Relate the
domain of a function to
its graph and, where
applicable, to the
quantitative relationship
it describes.
Skills
Vocabulary
Objectives
Write and graph the
parent inverse
variation function: y
= 1/x
Describe the
following
characteristics of a
inverse variation /
rational function:
- domain of a
rational function
- end behavior
(horizontal vs
oblique asymptotes)
- discontinuity:
vertical asymptotes
- discontinuity:
points of
discontinuity (holes)
Inverse variation
asymptote
discontinuity
cross-product theorem
Students will analyze
rational functions
Students will solve
equations involving
rational expressions
Resources
Perform the
following
transformations to
parent inverse
variation function:
f(x)+k
f(x-h)
af(x)
Solve rational
equations using the
following methods:
- cross-product
theorem (when
appropriate)
- multiplying the
equation by the least
common
denominator
A-APR.7-(+) Understand Operations of rational
that rational expressions expressions
form a system analogous
to the rational numbers,
closed under addition,
subtraction,
multiplication, and
division by a nonzero
rational expression; add,
subtract, multiply, and
divide rational
expressions.
A-REI.2-Solve simple
rational and radical
equations in one
variable, and give
examples showing how
Add, subtract, multiply
and divide rational
expressions
Simplify rational
expressions
reducible rational
expressions
irreducible rational
expressions
Students will simplify
rational expressions
extraneous solutions
may arise.
Appropriately describe a one variable data set.
Analyze binoimial & normal distributions.
Descriptive Statistics - One
Variable ~
Standards
Content
S-CP.2-(+) Calculate the Measures of center
expected value of a
Measures of spread
random variable;
Shape of frequency
interpret it as the mean distribution
of the probability
Binomial
distribution.
distributions
S-CP.3-(+) Develop a
Normal distributions
probability distribution
for a random variable
defined for a sample
space in which
theoretical probabilities
can be calculated; find
the expected value.
S-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.
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.4-Use the mean
and standard deviation
of a data set to fit it to a
normal distribution and
to estimate population
percentages. Recognize
that there are data sets
for which such a
procedure is not
appropriate. Use
calculators,
spreadsheets, and
tables to estimate areas
under the normal curve.
What are the distinguishing factors when deciding the approriate measures to
descibe a data set?
How do mean and standard deviation relate to binomial and normal
distributions?
Skills
Calculate mean
and median
Vocabulary
categorical / qualitative
data
quantitative data
mean
Calculate range, median
inter-quartile
range
range, and
inter-quartile range
standard deviation standard deviation
Describe the
unimodal, bi-modal, multishape of a data's modal
frequency
skew
distribution
outliers
Choose
discrete vs continuous
appropraite
data
measure of center binomial probability
& spread based
binomial distribution
on type & shape normal distribution
of data set
Find binomial
probabilities and
use binomial
distributions
Use normal
distribution
Objectives
Resources
Students will produce a
frequency distibution and
decribe the distribution
relative to its shape,
center, and spread.
Students will select the
appropriate measure of
center and spread based
on the shape and type of
data.
Analyze and evaluate randomness.
Use probability to evaluate outcomes of decisions.
Make inferences and justify conclusions from sample surveys,
experiements, and observational studies.
Probability and Inferential Statistics
- One Variable ~
What is the difference between theoretical and empirical (experimental)
probability?
What are the purposes of and differences between sample surveys,
experiments, and observational studies?
How is margin of error used to decribe a population parameter?
When is a false positive test result detrimental and when is it allowable?
When is a false negative test result detrimental and when is it
allowable?
Standards
Content
S-IC.1-Understand
Statistical
statistics as a process inferencing
for making inferences
Theortical vs.
about population
parameters based on a empirical probability
random sample from
that population.
S-IC.2-Decide if a
specified model is
consistent with results
from a given datagenerating process,
e.g., using simulation.
Skills
Vocabulary
Objectives
Describe the
use of randomness
in the process of
making inferences
about a population
based on a random
sample
randomness
statisitcal inferencing
population vs sample
theoretical probability
empirical (experimental)
probability
Students will
describe the role of
randomness in statistical
inferencing.
Compare
statistical model vs.
theortical and
simulation
empirical
(experimental)
probability to decide
if a specific model is
consistent with
reuslts of a
simulation
S-IC.3-Recognize the
Data collection
purposes of and
Estimate of
differences among
population parameter
sample surveys,
(mean & proportion)
experiments, and
observational studies;
Margin of error
explain how
Statistical
randomization relates to
significance
each.
S-IC.4-Use data from a
sample survey to
estimate a population
mean or proportion;
develop a margin of error
through the use of
simulation models for
random sampling.
S-IC.5-Use data from a
randomized experiment
to compare two
treatments; use
simulations to decide if
differences between
parameters are
significant.
S-IC.6-Evaluate reports
based on data.
Analyze within and
between the following
data collecting methods:
- sample survey
- experiment
- observational study
S-MD.6-(+) Use
probabilities to make fair
decisions (e.g., drawing
by lots, using a random
number generator).
S-MD.7-(+) Analyze
decisions and strategies
using probability
concepts (e.g., product
testing, medical testing,
pulling a hockey goalie at
the end of a game).
Use probabilites to
make fair decisions
Decision outcomes
Radian Measure and Unit
Circle Trigonometry ~
Students will
compare and contrast
theoretical and empirical
probabilities in order to
evaluate if a specific
model is consistent with
the results of a datagathering process /
simulation.
sample survey
experiment
observational study
paramenter
statistic
margin of error
Estimate population sampling variability
parameters mean and/or statistical significance
proportion from sample
survey
Use the variability
between samples to
develop the concept of
margin of error
Students will
compare and contrast
the following data
collecting methods:
- sample survey
- experiment
- observational study
Students will use a
sample statistic and
margin of error to
describe a populaton
parameter.
Students will
compare the results of
an experiment and
informally decide if
differences between
parameters is
significant.
Evaluate the results
of a randomized
experiements with two
groups to decide if the
difference in the
outcomes is significant
Describe a false
positive and a false
negative result from a
diagnostic test
Resources
false positive
false negative
Students will use
probabilites to evaluate
outcomes of decisions.
Develop radian measure of an angle using arc lengths on a unit circle.
Define trigonometric functions as a pairing of real number angle measures and xand y- coordinates of points on the unit circle showing an example of a periodic
function.
What is the key characteristic of a periodic function?
Standards
F-TF.1-Understand
radian measure of an
angle as the length of
the arc on the unit circle
subtended by the angle.
F-TF.2-Explain how the
unit circle in the
coordinate plane
enables the extension of
trigonometric functions
to all real numbers,
interpreted as radian
measures of angles
traversed
counterclockwise
around the unit circle.
F-TF.5-Choose
trigonometric functions
to model periodic
phenomena with
specified amplitude,
frequency, and midline.
F-TF.8-Prove the
Pythagorean identity
sin2(?) + cos2(?) = 1
and use it to calculate
trigonometric ratios.
Content
Radian measure
Unit circle and
arc lengths
Sin(x)
Cos(x)
Tan(x)
Pythagorean
Identity
Skills
Develop the
radian measure of
an angle
Define the
following
trigonometric
functions:
sin(x)
cos(x)
tan(x)
Prove the
Pythagorean
Identity
Vocabulary
radian measure
unit circle
Objectives
Resources
Students will find the
radian measure of an
angle.
Sine
Cosine
Tangent
Students will derive
f(x)=sin(x), f(x)=cos(x),
and f(x)=tan(x) using a
trigonometric identities unit circle.
pyhtagorean identity
Students will use the
Pythagorean Identities to
evaluate sine, cosine,
and tangent of all real
numbers.
Use
Pythagorean
Identlty to find the
trigonometric
values for all real
numbers
http://sublette1-wy.perfplusk12.com/Curric/Published_LandScapeMap.aspx?Publishkey=9c7cdd05-4e0f44d2-abe3-ce19a72d1212
http://sublette1-wy.perfplusk12.com/Curric/Published_LandScapeMap.aspx?Publishkey=7e3f43ee-9b6c41eb-a470-a82aca269cc7
http://sublette1-wy.perfplusk12.com/Curric/Published_LandScapeMap.aspx?Publishkey=c110b7f1-e6d44bb0-9884-92aaabcc87d1
http://sublette1-wy.perfplusk12.com/Curric/Published_LandScapeMap.aspx?Publishkey=2c44755e-63dc4e3b-a11b-5d723cb0242b
http://sublette1-wy.perfplusk12.com/Curric/Published_LandScapeMap.aspx?Publishkey=c8edbada-429b4790-afac-04055fa5a638(algebra 2)
http://sublette1-wy.perfplusk12.com/Curric/Published_LandScapeMap.aspx?Publishkey=5af85311-4cdc49cd-86c6-df60d0a3f970(algebra 1
http://prod.perfplusk12.com/default_select_lea.asp
http://new.sd148.org/wp-content/uploads../district/curriculum/