2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance
Algebra 1
Welcome to math curriculum design maps for ManhattanOgden USD 383, striving to produce learners who are:
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Effective Communicators who clearly express ideas and effectively
communicate with diverse audiences,
Quality Producers who create intellectual, artistic and practical products
which reflect high standards
Complex Thinkers who identify, access, integrate, and use available
resources
Collaborative Workers who use effective leadership and group skills to
develop positive relationships within diverse settings.
Community Contributors who use time, energies and talents to improve
the welfare of others
Self-Directed Learners who create a positive vision for their future, set
priorities and assume responsibility for their actions. Click here for more.
Overview of Math Standards
Teams of teachers and administrators comprised the pK-12+ Vertical
Alignment Team to draft the maps below. The full set of Kansas College and
Career Standards (KCCRS) for Math, adopted in 2010, can be found here.
To reach these standards, teachers use Holt curriculum, resources,
assessments and supplemented instructional interventions.
1
Standards of Mathematical Practice
1: Make sense of problems and persevere in solving them
2: Reason abstractly and quantitatively
3: Construct viable arguments and critique the reasoning of others
4: Model with mathematics
5: Use appropriate tools strategically
6: Attend to precision
7: Look for and make use of structure
8: Look for and express regularity in repeated reasoning. Click here for more.
Additionally, educators strive to provide math instruction centered on:
1: Focus - Teachers significantly narrow and deepen the scope of how time
and energy is spent in the math classroom. They do so in order to focus
deeply on only the concepts that are prioritized in the standards.
2: Coherence - Principals and teachers carefully connect the learning within
and across grades so that students can build new understanding onto
foundations.
3: Fluency - Students are expected to have speed and accuracy with simple
calculations; teachers structure class time and/or homework time for
students to memorize, through repetition, core functions.
4: Deep Understanding - Students deeply understand and can operate
easily within a math concept before moving on. They learn more than the
trick to get the answer right. They learn the math.
5: Application - Students are expected to use math concepts and choose the
appropriate strategy for application even when they are not prompted.
6: Dual Intensity - Students are practicing and understanding. There is
more than a balance between these two things in the classroom – both are
occurring with intensity. Click here for more.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Algebra 1
When appropriate:
• Use multiple representations to enforce concepts (graph, table, equation).
• Model real life situations that compliment the mathematical techniques.
Notes:
• Vocabulary terms are listed only in the unit they are first introduced.
Unit/Chapter
KCCRS
Standards
1. Solving Linear
Equations
1.1 Solving Simple
Equations
1.2 Solving Multi-Step
Equations
1.3 Solving Equations
with Variables on Both
Sides
1.4 Solving Absolute
Value Equations
1.5 Rewriting
Equations and
Formulas
A-CED.A.1
A-REI.A.1
A-REI.B.3
N-Q.A.1
A-CED.A.4
2. Solving Linear
Inequalities
2.1 Writing & Graphing
Inequalities
2.2 Solving Inequalities
Using + and –
2.3 Solving Inequalities
Using x and ÷
A-CED.A.1
A-REI.B.3
1
Vocabulary
Essential Questions Resources
Conjecture
Rule
Theorem
Equation (linear)
Solution
Inverse operations
Equivalent equations
Identity
Absolute value
equation
Extraneous solution
Literal equation
Formula
How can you use equations to
solve real-life problems?
Inequality
How can you use an inequality
to describe a real-life
statement?
Solution set
Equivalent inequalities
Compound inequality
How can you solve an
equation with variables on
both sides?
How can you solve an
absolute value equation?
How can you use a formula for
one measurement to write a
formula for a different
measurement?
How can you solve simple and
multi-step inequalities using
the four basic operations?
I Can…
…Solve simple
and multi-step
equations in
one variable
using the
properties of
equality.
…Solve
equations
containing an
absolute value.
…Manipulate
equations to
solve for
different
variables.
…Write, graph,
and solve single
and multi-step
linear
inequalities
using properties
of inequalities
Notes
Might be
necessary to
incorporate
some review
work including
number sense
and order of
operations.
Use inequality
notation,
ex. x < 3 but
show how to
read set
builder, and if
appropriate,
show interval
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Algebra 1
Unit/Chapter
KCCRS
Standards
2.4 Solving Multi-Step
Inequalities
2.5 Solving Compound
Inequalities
2.6 Solving Absolute
Value Inequalities
Vocabulary
Absolute value
inequality
Absolute deviation
Essential Questions Resources
How can you use inequalities
to describe intervals on the
real number line?
How can you solve an
absolute value inequality?
I Can…
…Write, graph
and solve
compound
inequalities
using properties
of inequalities
Notes
notation for
advanced
classes
…Write, graph,
and solve
absolute value
inequalities
3. Graphing Linear
Functions
3.1 Functions
3.2 Linear Functions
3.3 Function Notation
3.4 Graphing Linear
Equations in Standard
Form
3.5 Graphing Linear
Equations in SlopeIntercept Form
3.6 Transformations of
Linear Functions
3.7 Graphing Absolute
Value Functions
2
F-IF.A.1
A-CED.A.2
A-REI.C.10
F-IF.B.5
F-IF.C.7a
F-LE.A.1b
F-IF.A.2
F-IF.C.7a
F-IF.C.9
F-IF.B.4
F-LE.B.5
F-BF.B.3
A-REI.D.10
F-IF.C.7b
Relation
Function
Domain
Range
Independent variable
Dependent variable
Linear equation
Linear function
Nonlinear function
Function notation
x and y intercepts
Slope (rise and run)
Standard form
Slope-intercept form
Constant function
Family of functions
Parent function
Transformation
Translation
Reflection
What is a function?
How can you determine
whether a function is linear or
nonlinear?
How can you use function
notation to represent a
function?
How can you describe the
graph of a linear function in
both slope-intercept and
standard form?
How is an absolute value
function graphed?
How do translations and
reflections affect the parent
…Determine
whether a
relation is a
function, and if
so name its
domain and
range.
…Represent
situations using
function
notation.
…Differentiate
between linear
and nonlinear
functions.
…Graph and
interpret linear
functions when
When teaching
transformations,
include only
translations and
reflections.
Consider going
over linear and
absolute value
graphs, and then
do
transformations
on both at the
same time
(horizontal shifts
are easier to see
on absolute
value functions)
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Algebra 1
Unit/Chapter
KCCRS
Standards
Vocabulary
Absolute value
function
Vertex
Vertex form
Essential Questions Resources
graph of a linear or absolute
value function?
I Can…
Notes
presented in
both standard
and slopeintercept form.
…Graph and
interpret an
absolute value
function in
vertex form.
…Translate and
reflect linear
and absolute
value functions
to form many
other graphs all
related to the
parent graph.
4. Writing Linear
Functions
4.1 Writing Equations
in Slope-Intercept Form
4.2 Writing Equations
in Point-Slope Form
4.3 Writing Equations
of Parallel &
Perpendicular Lines
4.4 Scatter Plots &
Lines of Best Fit
4.5 Analyzing Lines of
Fit
3
A-CED.A.2
F-BF.A.1a
F-LE.A.1b
F-LE.A.2
F-LE.B.5
S-ID.B.6a
S-ID.B.6b
S-ID.B.6c
S-ID.C.7
S-ID.C.8
S.ID.C.9
Linear model
Point-slope form
Parallel lines
Perpendicular lines
Scatter plot
Correlation
Line of best fit
Piecewise function
(optional)
When given information about
a linear function, how can you
write its equation?
When are two lines parallel or
perpendicular?
…Write an
equation for a
linear function
in both pointslope and slopeintercept form.
How can you use a scatter plot
and a line of best fit to make
conclusions and predictions
about data?
…Determine
when two lines
are parallel or
perpendicular.
Stress pointslope form and
the
relationships
between the
various forms
of a line.
Students
should be able
to draw a line
of best fit, and
estimate its
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Algebra 1
Unit/Chapter
4.7 Piecewise
Functions (teacher
discretion)
5. Solving Systems of
Linear Equations
5.1-5.3, 5.5 Solving
Systems of Linear
Equations by Graphing,
Substitution, and
Elimination
4
KCCRS
Standards
Vocabulary
Essential Questions Resources
F-If.A.3
F-BF.A.1a
F-BF-A.2
A-REI.D.10
F-IF.C.7b
A-CED.A.3
A-REI.C.6
A-REI.C.5
A-REI.D.11
A-REI.D.12
System of linear
equations
Substitution
Elimination
Half-plane
How can a system of linear
equations be solved?
How many solutions can a
system of linear equations
have?
I Can…
Notes
…Draw a line of
best fit, find a
suitable
equation, and
use it to
interpret and
predict.
equation using
point-slope
techniques,
understand the
difference
between
positive,
negative, and
no correlation
and make
predictions
based on the
line of best fit.
…Solve a linear
system in two
variables using
the techniques
of graphing,
substitution, an
elimination.
4.7 could be
used to
reinforce
earlier
concepts such
as domain,
range, but
completely at
teacher’s
discretion (not
tested)
More emphasis
should be
placed on
systems of two
lines, but
absolute value
functions
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Algebra 1
Unit/Chapter
KCCRS
Standards
Vocabulary
5.4 Solving Special
Systems of Linear
Equations
5.6 Graphing Linear
Inequalities in Two
Variables
5.7 Systems of Linear
Inequalities
Essential Questions Resources
How can a linear inequality or
system of linear inequalities
be solved?
**SEMESTER BREAK**
I Can…
Notes
…Realize how
many solutions
are possible just
by looking at
the equations of
the system (ex.
two lines could
intersect once,
infinitely many
times, or not at
all.
should be used
as well.
…Interpret a
special solution
(infinite or no
solutions).
Stress multiple
ways to solve
systems;
encourage
efficiency, but
ultimately the
correct
solution (by
whichever
method) is
most
important.
…Solve a single
linear inequality
or a system of
linear
inequalities by
graphing.
6. Exponential
Functions and
Sequences
6.1 Properties of
Exponents
6.2 Radicals & Rational
Exponents
5
N-RN.A.2
N-RN.A.1
A-CED.A.2
F-If.B.4
F-IF.C.7e
F-IF.C.9
F-BF.A.1a
nth root
Radical
Index of radical
Exponential function
Exponential growth,
decay
Exponential equation
What are the basic rules of
exponents?
How are roots and powers
used to make a rational
exponent?
…Apply the
basic rules of
exponents to
expressions
containing
numbers and
variables.
May choose to
combine or
change order
of sections 5.15.5 to best suit
class
needs/teaching
style.
6.1 will require
thorough review
and time.
Students should
understand that
a rational
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Algebra 1
Unit/Chapter
6.3 Exponential
Functions
6.4 Exponential Growth
& Decay
6.5 Solving Exponential
Equations
KCCRS
Standards
F-BF.B.3
F-LE.A.1a
F-LE.A.2
A-SSE.B.3c
F-IF.C.8b
F-LE.A.1c
A-CED.A.1
A-REI.A.1
A-REI.D.11
F-IF.A.3
F-BF.A.2
Vocabulary
Essential Questions Resources
What are the characteristics of
an exponential function, and
how is it like and different
from a linear function?
What is the difference
between exponential growth
and exponential decay?
How is an exponential
equation solved?
I Can…
…Convert
between
roots/powers
and rational
exponents.
…Graph
exponential
growth and
decay functions
and transform
them using
translations and
reflections.
…Solve an
exponential
equations with
like bases.
6
Notes
exponent is
another way of
writing a root
and a power; can
limit to square
and cube roots.
Students should
recognize and
understand a
very basic
exponential
function, both
growth and
decay, with
previously
learned
transformations
applied.
Students should
be able to solve
an exponential
equation with
LIKE bases;
teachers can
experiment with
unlike bases if
applicable to
their students.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Algebra 1
Unit/Chapter
7. Polynomial
Equations and
Factoring
7.1-7.8
7
KCCRS
Standards
Algebra
A-APR. A.1:
Understand that
polynomials form a
system similar to
integers in being
closed.
A-APR.B.3: Identify
zeros of polynomials
in factored form.
A-REI.B.4b: Solve
quadratic equations
in one variable by
inspection-example
x2=49, quadratic
formula, factoring.
A-SSE.A.2: Use the
structure of an
expression to identify
ways to rewrite it.
A-REI.B.3a: Solve
linear equations and
inequalities in one
variable including
equations with
coefficients
represented by
letters.
Vocabulary
Polynomial (also
monomial, binomial,
trinomial)
Degree
Factored form
Standard form
Zero-product property
Leading coefficient
FOIL method (special
case of distribution)
Root (also repeated
root)
Closed
Essential Questions Resources
How are polynomials added,
subtracted, multiplied and
divided?
How is a polynomial equation
solved?
How is factoring used to break
a trinomial into a product of
two binomials?
How do you recognize and
factor special products?
I Can…
…Perform the
four basic
operations on
polynomial
expressions
(including long
and synthetic
division).
…Solve a
polynomial
equation
through
factoring and
application of
the zeroproduct
property and
recognize the
the solutions
are the xintercepts o the
polynomial
equation.
…Factor a
polynomial
expression
Notes
Consider
breaking the
unit into two
parts and
testing
separately
(operations
and then
factoring).
Review
factoring out a
GCF from a
polynomial.
Spend plenty
of time
factoring as it is
an important
component for
many algebra 2
skills.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Algebra 1
Unit/Chapter
8. Graphing Quadratic
Functions
8.1 Graphing Quadratic
Functions (with Vertical
Stretch/Compression)
8.2 Graphing Quadratic
Functions (with Vertical
Translations)
8.3 Graphing in
Standard Form
8.4 Graphing in Vertex
Form
8.5 Using Intercept
Form
8.6 Comparing Linear,
Exponential, and
Quadratic Functions
8
KCCRS
Standards
Algebra
A-CED.A.2: Create
equations in two or
more variables to
represent
relationships, graph
equations on
coordinate axes with
labels and scales.
F-IF.C.7a: Graph
linear and quadratic
functions and show
intercepts, maxima,
and minima.
F-BF.B.3: Identify the
effect on the graph
by replacing f(x) by
f(x) + k. kf(x), f(kx)
and f(x+k) for specific
values of k,
experiment using
technology.
F-IF.C.9: Compare
properties of two
Vocabulary
Quadratic function
Parabola
Vertex
Axis of symmetry
Vertical stretch, shrink
Maximum and
minimum value
Zero
Vertex form
Intercept form
Essential Questions Resources
What are some characteristics
of the graph of a quadratic
function?
How do transformations affect
the graph of 𝑓𝑓(𝑥𝑥) = 𝑥𝑥 2 ?
How do you graph a quadratic
function when given in
standard, vertex , or intercept
form?
How can you compare the
growth rates of linear,
exponential, and quadratic
functions?
I Can…
completely
using
appropriate
strategies.
…Graph a
quadratic
function and
transform the
parent function
to form many
other functions.
…Graph a
quadratic
function when
presented in
different forms.
…Make
connections
among the
different forms
of a quadratic
function.
…Compare and
contrast
features of the
linear,
exponential,
and quadratic
functions.
Notes
Teach
VERTICAL
stretches and
shrinks in this
unit (not
previously
taught).
Observe that
all quadratics
have
symmetry, but
no need to
even/odd
terminology.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Algebra 1
Unit/Chapter
KCCRS
Standards
functions
represented in a
different way
(algebraically,
graphically,
numerically in tables,
or by verbal
description)
F-IF.B.4: Interpret
and sketch graphs.
F-BF.A.1: Write a
function that
describes a
relationship between
two quantities.
A-SSE.B.3: Factor a
quadratic to find
zeros.
A-APR.B.3: Identify
zeros of polynomials
when factored and
use zeros to
construct a rough
graph.
A-CED.A.2: Create
equations to
represent
relationships, graph
9
Vocabulary
Essential Questions Resources
I Can…
Notes
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Algebra 1
Unit/Chapter
KCCRS
Standards
Vocabulary
Essential Questions Resources
I Can…
Notes
equations on
coordinate axes.
F-IF.C.8: Write a
function in
equivalent and
explain properties of
the function.
F-IF.B.6: Calculate
and interpret the
average rate of
change.
F-LE.A.3: Observe
using graphs and
tables increasing
functions.
9. Solving Quadratic
Equations
9.1 Properties of
Radicals
9.2 Solving Quadratic
Equations by Graphing
9.3 Solving Quadratic
Equations by Square
Roots
10
N-RN.A.2
N-RN.B.3
A-REI.D.11
F-IF.C.7a
A-CED.A.1
A-CED.A.4
A-REI.B.4b
A-SSE.B.3b
A-REI.B.4a
F-IF.C.8a
A-REI.C.7
Radical expression
Rationalize
Quadratic equation
Quadratic formula
Discriminant
How are the four basic
operations performed on
square and cube roots?
…Simplify
radical
expressions.
How are quadratic equations
solved?
…Solve
quadratic
equations using
the methods of
graphing,
square roots,
and quadratic
formula.
How can you determine the
number of real solutions to a
quadratic equation?
How many solutions are
possible when you have
Students are
expected to
rationalize
denominators,
but exclude
use of the
conjugate.
Limit radicals
to square and
cube roots
(include both
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Algebra 1
Unit/Chapter
9.5 Solving Quadratic
Equations by the
Quadratic Formula
9.6 Systems on NonLinear Equations
KCCRS
Standards
Vocabulary
Essential Questions Resources
system on non-linear
equations?
I Can…
…Determine the
number of real
solutions to a
quadratic
equation
through
graphing or
evaluating the
discriminant.
…Determine
how many
solutions exist
when given the
graph of a nonlinear system.
Notes
variables and
numbers).
Stress multiple
ways to solve
quadratic
equations;
encourage
efficiency, but
ultimately the
correct
solution (by
whichever
method) is
most
important.
Students are
not expected
to solve a
system of nonlinear
equations, only
note the
number of
possible
solutions and
understand
why; you might
discuss how to
solve, but the
expectation is
not to carry out
11
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Algebra 1
Unit/Chapter
KCCRS
Standards
Vocabulary
Essential Questions Resources
I Can…
Notes
substitution or
elimination for
specific
solution sets.
10. Radical Functions
and Equations
10.1 Graphing Square
Root Functions
10.3 Solving Square
Root Equations
A-CED.A.2
F-IF.B.4
F.IF.B.6
F-IF.C.7b
F.IF.C.9
A-CED.A.1
Square root function
What are some characteristics
of the graph of a square root
function?
How can you solve an
equation involving square
roots?
…Graph and
describe a
square root
function,
including ones
that have been
transformed.
If time allows,
introduce the
square root
function
(graphs and
equations)
…Solve an
equation
containing a
square root.
11. Data Analysis and
Displays
11.1 Measures of
Center and Variation
11.2 Box-and-Whisker
Plots
12
S-ID.A.3
S-ID.A.1
Mean
Median
Mode
Range
Interquartile range
Outlier
Quartile
Box-and-whisker plot
How can you describe the
center and variation of a data
set?
How can a box-and-whisker
plot be used to describe a
data set?
…I can choose
an appropriate
measure of
center.
If time allows
and teacher
feels there is a
need, students
should be able
to use the
…I can use a
box-and-whisker three measures
plot to interpret of center,
range as a
a data set.
measure of
variation, and
displaying onevariable data in
box-and-
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Algebra 1
Unit/Chapter
KCCRS
Standards
Vocabulary
Essential Questions Resources
I Can…
Notes
whisker (or
other) plots.
13