2015-16 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 8
Grade 8A
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 Math in Focus curriculum, resources,
assessments and supplemented instructional interventions from additional
websites and app for specific skills.
Standards of Mathematical Practice
1
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.
2015-16 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 8
KCCRS Standards
Math 8 Book A
1. Exponents –
Exponential
Notation, The
Product and the
Quotient of
Powers, The
Power of a
Power, The
Power of a
Product and the
Power of a
Quotient, Zero
and Negative
Exponents, RealWorld Problems:
Squares and
Cubes
This should be a
review to start
the year.
1
The Number System
8.NS.1: Know that numbers
that are not rational are called
irrational. Understand
informally that every number
has a decimal expansion; for
rational numbers show that the
decimal expansion repeats
eventually, and convert a
decimal expansion which
repeats eventually into a
rational number.
8.NS.2: Use rational
approximations of irrational
numbers to compare the size of
irrational numbers, locate them
approximately on a number
line diagram, and estimate the
value of expressions.
Expressions and Equations
8.EE.1: Know and apply the
properties of integer exponents
to generate equivalent
numerical expressions.
8.EE.2: Use square root and
cube root symbols to represent
solutions to equations.
Evaluate square roots of small
perfect squares and cube roots
of small perfect cubes. Know
that √2 is irrational.
Vocabulary
exponential
notation
base
power
terminating
decimal
repeating
decimal
irrational
number
integer
exponent
square root
cube root
radical
Essential
Questions
How do radicals
and exponents
influence one’s
understanding of
other content, such
as geometry and
science?
When are radicals
and integer
exponents used in
expressions and
equations to tell a
story or represent
an authentic
situation in life?
How can you use
exponential
notation to
represent repeated
multiplication of
the same factor?
Resources
8.NS.1
KCCRS flipbook
grade 8 additional
tools/resources
listed on page 16.
Transition Guide
Skill 1 & 2
I Can Learning Target
Samples
8.NS.1
I can understand that rational and
irrational numbers have decimal
expansions.
I can convert a repeating decimal into a
rational number.
Purple Textbook A
pages 3 & 98
8.NS.2
I can approximate the location of
irrational numbers on a number line.
8.NS.2
KCCRS flipbook
grade 8 additional
tools/resources
listed on page 19.
8.EE.1
I can understand and apply the
properties of integer exponents to
generate equivalent numerical
expressions.
Transition Guide
Skill 3
8.EE.2
I can solve problems using square root
and cube roots symbols and know that
the √2 is irrational.
8.EE.1
KCCRS flipbook
grade 8
tools/resources page
22.
8.EE.2
KCCRS flipbook
grade 8
tools/resources page
26.
2015-16 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 8
Math 8 Book A
2. Scientific
Notation –
Understanding
Scientific
Notation, Adding
and Subtracting
in Scientific
Notation,
Multiplying and
Dividing in
Scientific
Notation
Math 8 Book A
3. Algebraic
Linear Equations
– Solving Linear
Equations with
One Variable,
Identifying the
Number of
Solutions to a
Linear Equation,
Understanding
Linear Equations
with Two
Variables,
2
Expressions and Equations
8.EE.1: Know and apply the
properties of integer exponents
to generate equivalent
numerical expressions.
8.EE.3: Use numbers expressed
in the form of a single digit
times an integer power of 10 to
estimate very large or very
small quantities, and to express
how many times as much one is
than the other.
8.EE.4: Perform operations
with numbers expressed in
scientific notation, including
problems where both decimal
and scientific notation are
used. Use scientific notation
and choose units of
appropriate size for
measurements. Interpret
scientific notation that has
been generated by technology.
Expressions and Equations
8.EE.7: Solve linear equations
in one variable.
8.EE.7a: Give examples of
linear equations in one variable
with one solution, infinitely
many solutions, or no
solutions. Show which of these
possibilities is the case by
successively transforming the
given equation into simpler
forms.
8.EE.7b: Solve linear equations
with rational number
scientific
notation
coefficient
How can we
measure, model,
and calculate using
extremely large and
small numbers?
Textbook 8A page 3
8.EE.1
KCCRS flipbook
grade 8
tools/resources page
22.
8.EE.3
KCCRS flipbook
grade 8
tools/resources page
28
8.EE.1
I can apply the properties of integer
exponents to generate equivalent
numerical expressions.
8.EE.3
I can use scientific notation to estimate
very large or very small quantities.
8.EE.4
I can perform operations with numbers
expressed in scientific notation.
8.EE.4
KCCRS flipbook
grade 8
tools/resources page
30
coefficient
like terms
equations
Why do we utilize
algebraic linear
equations to solve
real-world math
problems?
8.EE.7
KCCRS flipbook
grade 8
tools/resources page
42.
How do we solve
the equations and
check for
reasonableness?
Purple Textbook A
pages 96-108, pages
118 – 123.
8.EE.7
I can give examples of linear equations
in one variable with one solution, no
solution, and infinite many solutions.
I can use properties to transform
equations into simpler forms.
I can solve linear equations with
rational coefficients including
expanding expressions.
8.EE.5
2015-16 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 8
Solving for a
Variable in a
Two-variable
Linear Equation
coefficients, including
equations whose solutions
require expanding expressions
using the distributive property
and collecting like terms.
8.EE.5: Graph proportional
relationships, interpreting the
unit rate as the slope of the
graph. Compare two different
proportional relationships.
Math 8 Book A
Expressions and Equations
8.EE.5: Graph proportional
4. Lines and
Linear Equations relationships, interpreting the
unit rate as the slope of the
– Finding and
graph. Compare two different
Interpreting
proportional relationships
Slopes of Lines,
represented in different ways.
Understanding
8.EE.6: Use similar triangles to
explain why the slope m is the
Slope-Intercept
same between any two distinct
Form, Writing
Linear Equations, points on a non-vertical line in
the coordinate plane; derive
Sketching Graphs
the equation y= mx for a line.
of Linear
Equations, RealWorld Problems:
Linear Equations
3
8.EE.5
KCCRS flipbook
grade 8
tools/resources page
33.
slope
y-intercept
slope-intercept
form
x-intercept
linear equation
linear
relationship
What types of real
world information
can be modeled by
linear
relationships?
How is the graph of
a linear equation in
two variables a
line?
Purple Textbook A
pages 109 – 117,
pages 165 - 181.
8.EE.5
KCCRS flipbook
grade 8
tools/resources page
33
8.EE.6
KCCRS flipbook
grade 8
tools/resources page
36.
Purple Textbook A
pages 130 – 164.
I can compare two different
proportional relationships in different
ways.
8.EE.5
I can graph proportional relationships
interpreting the unit rate as the slope
of the graph.
I can compare two different
proportional relationships represented
in different ways.
8.EE.6
I can derive the equation y = mx + b
from a graph.
I can explain the slope and y-intercept
of the context of real-world problems.
2015-16 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 8
Math 8 Book A
5. Systems of
Linear Equations
– Introduction to
Systems of
Linear Equations,
Solving Systems
of Linear
Equations Using
Algebraic
Methods, RealWorld Problems:
Systems of
Linear Equations,
Solving Systems
of Linear
Equations by
Graphing,
Inconsistent and
Dependent
Systems of
Linear Equations
Expressions and Equations
8.EE.8: Analyze and solve pairs
of simultaneous linear
equations.
8.EE.8a: Understand that
solutions to a system of two
linear equations in two
variables correspond to points
of intersection of their graphs,
because points of intersection
satisfy both equations
simultaneously.
8.EE.8b: Solve systems of two
linear equations in two
variables algebraically, and
estimate solutions by graphing
the equations. Solve simple
cases by inspection.
8.EE.8c: Solve real-world and
mathematical problems leading
to two linear equations in two
variables.
simultaneous
linear equations
(system of
linear
equations)
elimination
method
substitution
method
standard form
graphical
method
Math 8 Book A
6. Functions –
Understanding
Relations and
Functions,
Representing
Functions,
Understanding
Linear and
Nonlinear
Functions,
Functions
8.F.1: Understand that a
function is a rule that assigns to
each input exactly one output.
The graph of a function is the
set of ordered pairs consisting
of an input and the
corresponding output.
8.F.2: Compare properties of
two functions each
represented in a different way.
output
function
input
vertical line test
linear function
rate of change
nonlinear
function
4
How can systems of
equations be used
to represent
authentic scenarios
and solve problems
in life?
8.EE.8
KCCRS flipbook
grade 8
tools/resources page
47
What does the
number of
solutions (none,
one, or infinite) of a
system of linear
equations
represent?
Describe what this
would look like.
I can understand that solutions to a
system correspond to points of
intersection of their graphs.
I can demonstrate that solutions to a
system satisfy both equations
simultaneously.
I can determine if a system of
equations has one solution, no
solution, or infinitely many solutions.
What methods can
be used to solve
systems of
equations? Why do
we have different
methods for solving
systems of
equations?
How can functional
relationships be
used to represent
authentic situations
in life and solve
actual problems?
8.EE.8
I can analyze and solve pairs of
simultaneous linear equations.
I can solve a system of equations by
graphing, elimination and substitution.
I can solve real-world problems leading
to two linear equations in two
variables.
8.F.1
KCCRS flipbook
grade 8
tools/resources page
50.
8.F.2
KCCRS flipbook
grade 8
tools/resources page
52
8.F.1
I can understand that a function is a
rule that assigns exactly one output to
each input.
I can see that a graph is made up of a
set of ordered pairs.
8.F.2
I can compare properties of two
functions represented either
2015-16 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 8
Comparing Two
Functions
Algebra I book
7. Polynomial
Equations and
Factoring
7.1-7.8
5
8.F3: Interpret the equation y=
mx+ b as defining a linear
function, whose graph is a
straight line; give examples of
functions that are not linear.
8.F.4: Construct a function to
model a linear relationship
between two quantities.
Determine the rate of change
and initial value of the function.
8.F.5: Describe qualitatively
the functional relationship
between two quantities by
analyzing a graph. Sketch a
graph that exhibits the
qualitative features of a
function that has been
described verbally.
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
algebraically, graphically, numerically
in tables, or by verbal description.
8.F.3
KCCRS flipbook
grade 8
tools/resources page
54
8.F.4
KCCRS flipbook
grade 8
tools/resources page
58
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)
How are
polynomials added,
subtracted,
multiplied and
divided?
8.F.5
KCCRS flipbook
grade 8 additional
tools/resources page
62
8.F.3
I can recognize a linear function and
nonlinear function.
8.F.4
I can construct a function to model a
linear relationship between two
quantities.
I can determine the rate of change and
y intercept from two (x,y) values or
from a table or graph.
I can interpret the rate of change from
the situation.
8.F.5
I can describe whether the function is
increasing, decreasing, linear or
nonlinear.
I can sketch a graph that has been
described verbally.
…Perform the four basic operations on
polynomial expressions (including long
and synthetic division).
How is a
polynomial
equation solved?
…Solve a polynomial equation through
factoring and application of the zeroproduct property and recognize the the
solutions are the x-intercepts o the
polynomial equation.
How is factoring
used to break a
trinomial into a
…Factor a polynomial expression
completely using appropriate
strategies.
2015-16 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 8
Math 8 Book B
8. Geometric
Transformations
– Translations,
Reflections,
Rotations,
Dilations,
Comparing
Transformations
Algebra I Book
8. Graphing
Quadratic
Functions
8.1 Graphing
Quadratic
Functions (with
Vertical
Stretch/Compres
sion)
8.2 Graphing
Quadratic
Functions (with
Vertical
Translations)
8.3 Graphing in
Standard Form
6
equations with coefficients
represented by letters.
Closed
product of two
binomials?
Geometry
8.G.1: Verify experimentally
the properties of rotations,
reflections, and translations:
8.G.1a: Lines are taken to lines,
and line segments to line
segments of the same length.
8.G.1b: Angles are taken to
angles of the same measure.
8.G.1c: Parallel lines are taken
to parallel lines.
8.G.3: Describe the effect of
dilations, translations,
rotations, and reflections on
two-dimensional figures using
coordinates.
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.
translation
image
transformation
reflection
line of
reflection
rotation
angle of
rotation
center of
rotation
dilation
scale factor
center of
dilation
How does one
recognize and apply
transformations of
shapes to solve
problems?
Quadratic
function
Parabola
Vertex
Axis of
symmetry
Vertical stretch,
shrink
Maximum and
minimum value
Zero
Vertex form
Intercept form
What are some
characteristics of
the graph of a
quadratic function?
8.G.1
KCCRS flipbook
grade 8 additional
tools/resources page
66.
8.G.3
KCCRS flipbook
grade 8 additional
tools/resources page
73.
How do
transformations
affect the graph of
𝑓𝑓(𝑥𝑥) = 𝑥𝑥 2 ?
…Graph a quadratic
function and
transform the parent
function to form
many other
functions.
…Graph a quadratic
function when
presented in
How do you graph a different forms.
quadratic function
…Make connections
when given in
among the different
standard, vertex ,
forms of a quadratic
or intercept form?
function.
How can you
compare the
8.G.1
I can verify experimentally the
properties of rotations, reflections, and
translations.
8.G.3
I can describe the effect of dilations,
translations, rotations, and reflections
on two-dimensional figures using
coordinates.
A-CED.A.2: I can identify and graph
quadratic equations on coordinate axes
F-IF.C.7a: I can write quadratic
functions in the form of y = a𝑥𝑥 2 + bx +
c and identify a, b, c.
I can identify the vertex, the minimum
or maximum, the domain, and the
range for each function.
F-BF.B.3: I can explain how the graphs
1
of y = 5𝑥𝑥 2 and y = 5 𝑥𝑥 2 compare with
the parent graph, y = 𝑥𝑥 2 .
F-IF.C.9: I can compare properties of
two functions represented in a
different way (algebraically,
2015-16 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 8
8.4 Graphing in
Vertex Form
8.5 Using
Intercept Form
8.6 Comparing
Linear,
Exponential, and
Quadratic
Functions
Algebra I Book
9. Solving
Quadratic
Equations
9.1 Properties of
Radicals
9.2 Solving
Quadratic
7
F-IF.C.9: Compare properties
of two 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 graph.
A-CED.A.2: Create equations to
represent relationships, graph
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.
N-RN.1: Rewrite expressions
involving radicals and rational
exponents using the properties
of exponents.
F-IF7A: Graph quadratic
functions and show intercepts,
maxima, and minima.
growth rates of
linear, exponential,
and quadratic
functions?
…Compare and
contrast features of
the linear,
exponential, and
quadratic functions.
graphically, numerically in tables, or by
verbal description)
F-IF.B.4: I can interpret and sketch
graphs
F-BF.A.1: I can write a function that
describes a relationship between two
quantities.
A-SSE.B.3: I can factor a quadratic
equation to find the roots or the
solutions.
A-APR.B.3: I can use the factored form
of a quadratic equation to find the
zeroes and sketch a graph.
F-IF.C.8: I can write the equation in
a𝑥𝑥 2 + bx + c form and determine if the
graph opens upward or downward.
F-IF.B.6: I can use my slope formula to
check the rate of change at different
intervals.
F-LE.A.3: I can determine an increasing
function by looking at a table or graph.
Radical
expression
Rationalize
Quadratic
equation
Quadratic
formula
Discriminant
How are the four
basic operations
performed on
square and cube
roots?
I can simplify radical expressions.
How are quadratic
equations solved?
I can determine the number of real
solutions to a quadratic equation
I can solve quadratic equations using
the methods of graphing, square roots,
and quadratic formula.
2015-16 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 8
Equations by
Graphing
9.3 Solving
Quadratic
Equations by
Square Roots
9.5 Solving
Quadratic
Equations by the
Quadratic
Formula
9.6 Systems on
Non-Linear
Equations
Algebra I Book
10. Radical
Functions and
Equations
10.1 Graphing
Square Root
Functions
10.3 Solving
Square Root
Equations
Math 8 Book B
10. Statistics –
Scatter Plots,
Modeling Linear
Associations,
Two-Way Tables,
8
F-IF7B: Graph square roots and
cube roots.
How can you
determine the
number of real
solutions to a
quadratic
equation?
through graphing or evaluating the
discriminant.
I can determine how many solutions
exist when given the graph of a nonlinear system.
How many
solutions are
possible when you
have system on
non-linear
equations?
Square root
function
What are some
characteristics of
the graph of a
square root
function?
I can graph and describe a square root
function,
including ones that have been
transformed.
I can solve an equation containing a
square root.
How can you solve
an equation
involving square
roots?
Statistics and Probability
8.SP.1: Construct and interpret
scatter plots for bivariate
measurement data to
investigate patterns of
association between two
quantities. Describe patterns.
8.SP.2: Know that straight lines
are widely used to model
relationships between two
quantitative variables. For
scatter plot
positive
association
negative
association
clustering
bivariate
measurement
data
line of best fit
outlier
What mathematical
processes and skills
are used to
investigate patterns
of association in
bivariate data?
How can we gather,
organize, and
display bivariate
data to
8.SP.1
KCCRS flipbook
grade 8 additional
tools/resources page
90.
8.SP.2
KCCRS flipbook
grade 8 additional
tools/resources page
94.
8.SP.1
I can construct and interpret scatter
plots.
8.SP.2
I can utilize lines of best fit.
8.SP.3
2015-16 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 8
11. Probability –
Compound
Events,
Probability of
Compound
Events,
Independent
Events,
Dependent
Events
KCCRS Math
Standards not
emphasized in
Math in Focus
8th Grade MIF:
scatter plots that suggest a
linear association.
8.SP.3: Use the equation of a
linear model to solve problems
in the context of bivariate
measurement data,
interpreting the slope and
intercept.
8.SP.4: Understand that
patterns of association can also
be seen in bivariate categorical
data by displaying frequencies
and relative frequencies in a
two-way table. Construct and
interpret a two-way table.
Probability is not emphasized in
the 8th grade KCCRS.
communicate and
justify results in
authentic
situations?
How can we
analyze bivariate
data to make
inferences and/or
predictions based
on surveys,
experiments,
probability, and
observations?
8.SP.3
KCCRS flipbook
grade 8 additional
tools/resources page
96.
8.SP.4
I can construct and interpret a twoway table.
8.SP.4
KCCRS flipbook
grade 8 additional
tools/resources page
99.
8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel
lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
8.G.5. Has very little emphasis in MIF. Need to add more with supplemental materials.
8.G.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
8.G.9. Has very little emphasis in MIF. Need to add more with supplemental materials.
High School – currently using Holt for Alg. I, Geom., Adv. Alg. II
Adopting for next year either Glencoe or Big Ideas Math
9
I can use the line of best fit to find the
slope and y intercept.