Vance County Schools
Pacing Guide 2016-17
Vance County Schools
GRADE 8 MATH
2015-2016 Pacing Guide
UNIT
1. Exponents & Scientific Notation
STANDARDS
8.EE.1
8.NS.1
8.NS.2
2. Rational and Irrational Numbers
3. One-Variable Linear Equations
4. Pythagorean Theorem and
8.G.6
Geometric Formulas
5. Intro to Functions
6. Linear and Nonlinear Functions
Congruence & Similarity
9. Bivariate Data & Linear Regression
10. Two-Way Tables & Relative
8.EE.4
8.EE.2
8.EE.7
8.G.7
10
8.G.8
8.G.9
Benchmark A– Week of November 7, 2016
8.EE.5
8.EE.6
8.F.1
8.F.3
Benchmark B– Week of February 6, 2017
8.G.1
8.G.2
8.G.4
8.G.5
8.SP.1
8.SP.2
8.SP.4
Frequencies
Mock EOC– Week of April 24, 2017
EOC Review
for the remainder of the year
12
10
7
8.F.2
8.F.5
18
8.F.4
16
8.EE.8
7. Systems of Linear Equations
8. Geometric Transformation,
8.EE.3
NO. OF
DAYS
12
15
8.G.3
15
8.SP.3
10
10
NINE
WEEKS
Vance County Schools
Pacing Guide 2016-17
Testing Information
Domain
Weight Distributions for 8th Grade Math
The Number System
2-7%
Expressions & Equations
27-32%
Functions
22-27%
Geometry
20-25%
Statistics and Probability
15-20%
In addition to the content standards, the CCSS includes eight Standards for Mathematical Practice that cross domains,
grade levels, and high school courses. Assessment items written for specific content standards will, as much as
possible, also link to one or more of the mathematical practices.
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Vance County Schools
Pacing Guide 2016-17
The pacing guide should be used along with the Common Core State Standards for Math and the NCDPI unpacking document
Unit 1: Exponents and Scientific Notation– 12 Days
Standards: 8.EE.1, 8.EE.3, 8.EE.4
Learning Targets
 Model and explain what positive and negative
exponents mean
 Prove and explain the laws of exponents with
positive, negative and zero exponents; especially
raising powers and zero exponents
 Explain how to write numbers in correct scientific
notation and explain why the first factor should be
between -10 and 10
 Model and explain how numbers can be written in
scientific notation, converting between standard
and scientific notation form
 Order and compare numbers in scientific form
 Give real world examples of very large and very
small quantities and use scientific notation to
describe the quantities
 Compare and contrast the size and magnitude of
amounts using different units and justify the unit
chosen in contextual situations
Vocabulary
Laws of Exponents
Power
Perfect Squares
Perfect Cubes
Root
Sample Questions
* A baby hummingbird weighed about 4.4 × 10–3 pounds. A
baby eastern bluebird weighed about 6.2 × 10–2 pounds.
About how many times heavier was the baby eastern
bluebird than the baby hummingbird? 8.EE.3
* What is the value of the expression (4 × 103)(5.6 × 105)?
8.EE.4
* What is the value of the expression (33)2 ÷ 34? 8.EE.1
–3
–3
* What is the value of (9.7 x 10 ) + (1.3 x 10 )? 8.EE.4
Square Root
Cube Root
Magnitute
Scientific Notation
Standard Form
*One of the viruses that causes the common cold measures
2.5 × 10–6 m. What is this measurement written in standard
form? 8.EE.3
* What is the product of 3.6 × 106 and 900,000,000
expressed in scientific notation? 8.EE.4
* What is the value of (32) × (2–2)2? 8.EE.1
* Lake Erie has a surface area of about 9.9 x 103 square
miles. Lake Michigan has a surface area of about 2.2 x
104 square miles. About how many times larger is the
surface area of Lake Michigan than the surface area of
Lake Erie? 8.EE.3
Vance County Schools
Pacing Guide 2016-17
Unit 2: Rational and Irrational Numbers – 10 Days
Standards: 8.NS.1, 8.NS.2, 8.EE.2
Learning Targets
 Make a graphic representation to show that
 natural numbers are a subset of whole numbers
 whole numbers are a subset of integers
 integers are a part of rational numbers
 rational and irrational numbers make up the set
of real numbers
 Divide fractions to show that all rational numbers
either repeat or terminate
 Change rational decimals to fractions
 Use long division to divide terminating decimals by
factors to prove that terminating decimals have a
prime factor of 2 or 5
 Truncate decimals to get closer approximations
and to order decimals
 Compare and order rational and irrational numbers;
identify on the number line
 Model perfect square roots; prove that non-perfect
square roots are irrational
 Explain why positive and negative numbers
squared are positive but square roots can be
positive or negative
 Recognize that squaring and taking the square
root, cubing and taking the cube root, are inverse
operations
Vocabulary
Sample Questions/Clarifications
Real Numbers
* Which letter is located at approximately
number line below? 8.NS.2
on the
Irrational Numbers
Rational Numbers
* What is the value of
Integers
*
? 8.EE.2
8.NS.1
Whole Numbers
Natural Numbers
Radical
Radicand
Terminating
Decimals
* Jackson is comparing two squares. The first square has
an area of 64 cm2. The second square has an area of 121
cm2. What is the difference in the perimeters of the two
squares? 8.EE.2
Repeating Decimals * Which fraction is equivalent to
? 8.NS.1
Truncate
* What is the value of
? 8.EE.2
*Sam stores his coin collection in a cube-shaped box that
has a volume of 27 in.3 He moves the coins into a larger
cube-shaped box that has a volume of 729 in.3 What is the
difference between the edge lengths of the two boxes?
8.EE.2
Vance County Schools
Pacing Guide 2016-17
Unit 3: One-Variable Linear Equations – 12 Days
Standards: 8.EE.7a, b
Learning Targets
 Identify terms of expressions
 Model and prove the properties of equalities and
properties of operations (e.g. distributive property)
 Write equations from word problems
 Transform an equation by utilizing the distributive
property
 Transform and simplify an equation by combining
like terms
 Transform and simplify an equation with variable
on both sides
 Solve multi-step equation and justify each step;
with rational and integer coefficients
Vocabulary
Sample Questions
* The perimeter of the rectangle below is 48 feet.
Expression
Equation
Constant
What is the value of x? 8.EE.7b
Variable
* What is the solution to the equation below? 8.EE.7a
0.5(9x + 18) = –1.5(5x) – 2(3x + 4.5)
Coefficient
Distributive
Property
* Three times the difference of a number, x, and fourteen is
six times the sum of the same number, x, and twelve. What
is the value of x? 8.EE.7b
Like Terms
* What is the solution to the equation below? 8.EE.7a
Substitution
* A moving company offers two price plans.
Solution

The first plan charges a flat rate of $39.95 plus $0.12
per mile driven.
 The second plans charges a flat rate of $19.95 plus
$0.28 per mile driven.
How many miles must the truck be driven for the two plans
to cost the same? 8.EE.7b
Vance County Schools
Pacing Guide 2016-17
Unit 4: Pythagorean Theorem & Geometric Formulas –17 days
Standards: 8.G.6, 8.G.7, 8.G.8, 8.G.9
Learning Targets
 Use the Pythagorean Theorem to find unknown
side lengths of right triangles
 Prove, model and explain the Pythagorean
Vocabulary
Sample Questions/Clarification
Right Triangle
* What is the approximate volume of
the sphere below? Area? 8.G.9
Hypotenuse
Theorem
 Identify Pythagorean triples
 Solve volume and surface area problems; apply
Legs
Pythagorean
Theorem
Pythagorean
Triple
figures on the coordinate plane
 Compare and contrast characteristics of cones,
cylinders, and spheres and their formulas
 Describe, prove and solve problems using the
* Rectangle TUVW is shown to the
right.
Pythagorean Theorem if applicable
 Find the perimeter and area or two-dimensional
* Wendy has a rectangular flower garden that measures 20ft
long and 10ft wide. She wants to construct a diagonal
walkway through her garden. What is the approximate
length of the walkway? 8.G.7
Cone
Cylinder
Sphere
What is the approximate length of the
diagonal of rectangle TUVW? 8.G.8
* In the figure shown below, one square has side lengths
of a units and the other square has side lengths
of b units. The squares are divided into two triangles with a
hypotenuse of c units. The pieces are rearranged to form a
square with side length c.
formulas for cones, cylinders and spheres
Radius
Diameter
Volume
Height
Pi
Which equation represents the relationship among the
values of a, b, and c? 8.G.6
Vance County Schools
Pacing Guide 2016-17
Unit 5: Intro to Functions –18 days
Standards: 8.EE.5, 8.EE.6, 8.F.2, 8.F.5
Learning Targets
 Model and explain how x- and y-values in a function
table are proportional
 Define unit rate, especially as it relates to a function
table and a line on a graph
Vocabulary
Sample Questions/Clarification
Unit Rate
* Company R uses the formula C = 36 + 40h to calculate the
cost, C, for doing h hours of work. Company S uses the table
below to calculate their charges.
Proportional
Relationships
Hours
1
3
7
Cost
$80
$158
$314
 Compare and contrast how proportional relationships
are shown in graphs, tables, and equations
Independent
Variable
 Given an equation of a proportional relationship,
graph the relationship and identify the unit rate
Dependent
Variable
Which company has the higher hourly rate, and by how
much? 8.F.2
 Compare and contrast two different proportional
relationships represented two different ways (i.e.
equation and table)
Slope
*The cost of a gallon of gasoline at Store M is represented by
Vertical Line
the equation y = 3.61x, where x is the number of gallons of
gasoline and y is the total cost. The costs of gallons of
gasoline at Store N are listed in the table below.
 Explain how changing the b value in an equation
written in slope-intercept form changes the
equations graph
Horizontal
Store N Gasoline Prices
Gallons
Total Cost
2
$7.16
4
$14.32
6
$21.48
Slope-intercept
 Graph lines in the forms y = mx and y = mx + b
 Model and define slope as the rate of change and the
y-intercept as the initial value of a function, and
explain how these help represent a function
 Determine the rate of change and the initial value
from a description
 Find two points (two pairs of x- and y-values) from a
table or graph and find the rate of change and initial
value
Y- Intercept
Linear
Relationship
What is the difference in the cost of a gallon of gasoline at
the two stores? 8.EE.5
Rate of Change
* Which graph shows the line of the equation
Initial Value
Function
8.EE.6
* Bill and Sue save their leftover lunch money. Sue saves $5 a
week. The equation m = 3.50w models the amount of
money, m, Bill has saved after w weeks. At the end of 36
weeks, how much more money has Sue saved than Bill? 8.F.2
Vance County Schools
Learning Targets cont.
 Model and explain how to find the y-intercept from a
table by finding what the y-value is when x = 0
Pacing Guide 2016-17
Sample Questions/Clarification cont.
* Which is an equation of the line graphed below? 8.EE.6
 Identify the initial value as the y-intercept in a real
world situation
 Identify the rate of change in a real world situation
(e.g. identify and discuss one time fees and repeated
fees)
 Write an equation of a line in slope-intercept form
from a real world situation
 Describe the shape of points or a group of connected
points on a graph using the following vocabulary:
 Increasing or decreasing
 Model and explain how the points or lines on a graph
show a relationship or action between the
independent and dependent values
 Sketch a graph that relates the action taking place
between two quantities in a scenario or situation
 Model and explain how to find slope from a table,
equation or a graph
 Model and explain how the points or lines on a graph
show a relationship or action between the
independent and dependent values
 Sketch a graph that relates the action taking place
between two quantities in a scenario or situation
* A bus drives through Washington, D.C., allowing visitors to
get off and on at various museums and monuments. Which
graph best represents this situation? 8.F.5
* Sam leaves the park to walk home, but about halfway
there he stops to talk to a friend. After talking to a friend for
5 minutes Sam continues home. Which graph represents
Sam’s walk home from the park? 8.F.5
* John was comparing the voltage of two circuits. The
voltage, V, of Circuit 1 with a constant current can be
represented by the equation V = 6R, where R represents the
amount of resistance. The table below shows the voltage of
Circuit 2 with a constant current and varying resistance 8.EE.5
Circuit 2
Resistance (R)
3
5
10
Voltage (V)
12
20
40
Which is true of the graphs comparing voltage to resistance?
A The graphs have the same slope.
BTTThe graph of Circuit 1 is steeper than the graph of Circuit 2.
C The graph of Circuit 2 is steeper than the graph of Circuit 1.
D The graph of Circuit 1 has a negative slope and the graph of Circuit 2 has a positive slope.
Vance County Schools
Pacing Guide 2016-17
Unit 6: Linear and Nonlinear Functions –16 days
Standards: 8.F.1, 8.F.3, 8.F.4
Learning Targets
 Apply properties to model linear equations in
different forms
 Model and identify functions as a set of ordered pairs
satisfying one rule
 State and model the rule for functions as having
exactly one y-value for any x-value
 Model x as input and y as output in ordered pairs,
tables, and graphs
 Model and use the vertical line test to identify
functions from graphs Identify and explain why a
graph or table is not a function
 Describe the shape of points or a group of connected
points on a graph using the following vocabulary:
 Linear or nonlinear
 Compare and contrast linear, quadratic, and
exponential functions
 Identify functions from equations, graphs, ordered
pairs, and tables
 List the properties of functions as equations and
determine whether an equation represents a
function, justifying why or why not
 Compare and contrast a linear equation in standard
and y = mx + b form
 Make a table that represents a given graph or
equation of a function
 Given a table, a graph, or a set of order pairs that is a
linear function, write an equation for the function
 Write an equation for a line that passes through a
given point and has a given slope
 Write an equation for a line that passes through two
given points in slope-intercept form
Vocabulary
Non-Linear
Function
Sample Questions/Clarification
*Which set of ordered pairs represents a linear
relationship? 8.F.3
A{({(0, 1), (2, 2), (–2, 0), (4, 3)}
Linear Function
B {(0, –2), (1, 1), (–1, –3), (2, 3)}
Input
C {(0, –1), (1, 1), (–1, –2), (2, 3)}
Output
D {(0, –2.5), (5, 2.5), (1, –2.5), (–1, –3.5)}
Rate of Change
* What is the equation of the line that passes through the
origin and the point (–1, 3)? 8.F.4
* Ryan paints the inside of houses to earn money. He
charges a flat rate for supplies and a per room charge.
 To paint 3 rooms, Ryan charges $155.
 To paint 5 rooms, Ryan charges $225.
How much does Ryan charge per room? 8.F.4
Linear
Relationship
Slope
Standard Form
* Which equation is not a function? 8.F.1
Initial Value
A
y-intercept
B
Exponential
C
Quadratic
D
* Which table of data shows a nonlinear function? 8.F.3
Vance County Schools
Pacing Guide 2016-17
Unit 7: Systems of Linear Equations –15 days
Standards: 8.EE.8
Learning Targets
 Model and explain that when two linear equations
intersect on a line, the ordered pair of the point of
intersection is a solution for both equations and that
the x-value will generate the y-value
 Graph systems of equations to give solutions
 Model and compare using graphs and equations that
systems of linear equations can have no solution, one
solution, or infinitely many solutions
 Solve systems of equations with rational numbers
 Write systems of equations from word problems and
explain the purpose of each variable, factor, and
constant
 Use substitution to solve a system of equations
 Compare and contrast scenarios that are easier to
interpret into a standard form equation with
scenarios that are easier to interpret into a slopeintercept form equation
 Solve real world problems leading to two linear
equations in two variables
 Graph two linear equations to determine whether
they will intersect
Vocabulary
Sample Questions/Clarification
Point of
Interception
* A system of equations is shown below.
Parallel Lines
Coefficient
Using the solution to the system, what is the value of x + y?
Substitution
No Solution
Solution
Infinitely Many
Solutions
* Lucas earns $7.50 per hour, and Ashley earns $8.00 per
hour. Last week, Ashley worked 10 more hours than Lucas.
The total amount Lucas and Ashley earned last week was
$266. How many hours did Lucas work last week?
* A store sells candy bars and packages of gum.

The price of a candy bar is $0.69, and a package of gum
costs $0.89.
 On Tuesday, the number of packages of gum sold was 2
less than 3 times the number of candy bars sold.
 The total amount of the sales was $82.22, before tax.
How many packages of gum were sold?
* Line m is graphed below. Line n
will be graphed below. Line n will
go through the points (1, 5) and
(–3, –3).
What will be the point of intersection of lines m and n?
Vance County Schools
Pacing Guide 2016-17
Unit 8: Geometric Transformation, Congruence & Similarity –15 days
Standards: 8.G.1, 8.G.2, 8.G.3, 8.G.4, 8.G.5
Learning Targets
 Define congruency and its symbol
 Define, describe, and perform rigid transformations
 Compare angles, side lengths, and parallel lines of
pre-images and images after transformations have
been performed
 Use appropriate tool (compass, protractor, rulers)
to construct rigid transformations and prove their
properties
 Define, describe and perform dilations, translations,
reflections, rotations
 Identify the effect of each transformation on
coordinates and state why
 Given a graph and coordinates of a reflection,
identify the line of reflection; identify clock wise
and counter-clockwise degrees of the rotation
 Construct two parallel lines with a transversal;
identify alternate interior and exterior,
corresponding, vertical, and adjacent angles;
supplementary and complementary angles
 Given a graph or coordinates of pre-image and
image, find scale factor of dilations
 Find missing angle measurements when two
parallel lines are cut by two transversals to form a
triangle
Vocabulary
Translations
Sample Questions/Clarification
* Triangle PQR has vertices at P(–5, 2), Q(–4, 5), and R(–3, 2).
The triangle will be translated 6 units to the right and 5
units down. What will be the coordinates of Q′?8.G.3
Rotations
Reflections
* In the figure below, lines j and k are parallel.
Congruence
Dilations
Supplementary
Complementary
Angles:
Exterior
Interior
Alternate Interior
Vertical
Adjacent
What is the value of m? 8.G.5
* Triangle STU will be transformed to the points S′(–2, 1), T′(0, –5), and U′(3, –1).
What type of
transformation will
occur to triangle STU?
8.G.3
A
reflection
B rotation
C dilation
D translation
Vance County Schools
Pacing Guide 2016-17
Unit 9: Bivariate Data & Linear Regression –10 days
Standards: 8.SP.1, 8.SP.2, 8.SP.3
Learning Targets
 Use tools to generate data
Vocabulary
Sample Questions/Clarification
Bivariate Data
* The scatterplot below shows the average January
temperatures for 10 cities compared to their latitude.
 Graph bivariate date on a scatterplot by hand and
with tools
Scatter Plot
 Explain why it is easier to change year dates into
values of 0, 1, 2, etc. to write linear equations
Linear Model
 Examine and analyze scatterplots to determine and
interpret and describe relationship (linear vs. nonlinear association, positive vs. negative association,
and correlation vs. no correlation and strength of
correlation)
 Identify outliers on a scatterplot and their effect on
the line of best fit; interpret and describe their
meaning in context
Line of Best Fit
Linear Association
Nonlinear
Association
Outliers
Positive
 Make predictions based on the graphed data and line Association
of best fit
Negative
Association
 Given a linear model that represents a scatter plot
(line of best fit), write an equation for that line
Correlation
 Interpret and describe the slope and intercepts of the Coefficient
equation of a linear model in the context of the
bivariate measurement data
 Solve problems in the context of bivariate data
Using a linear model, what is the predicted average January
temperature for a city located at 30° North latitude? 8.SP.3
* Cameron surveyed students about the number of hours
spent watching television each week, and the amount of
allowance they received each week from their parents. His
data is in the table below.
Hours
Watching TV
0
2
4
Allowance
$20
$15
$10 $12
6
8
10
12
14
$10
$10
$5
$5
Which statement describes the association between the
data? 8.SP.1
* The graph below shows the population of a town since
1950.
Which equation best fits the data?
8.SP.2
Vance County Schools
Pacing Guide 2016-17
Unit 10: Two-Way Tables & Relative Frequencies –10 days
Standards: 8.SP.4
Learning Targets
 Collect bivariate categorical data from the same
subjects and explain why both have to be
collected from each subject
 Construct a two-way table with categorical data
collected by displaying frequencies and relative
frequencies
Vocabulary
Sample Questions/Clarification
Categorical Data
* The table below shows the gender and grade of students
in the band at a middle school.
Two-way Table
Relative
Frequency
Bivariate Data
 Interpret a two-way table and summarize the data
 Calculate relative frequencies to describe
associations between two variables
 Solve problems by interpreting patterns of
association and relative frequencies in bivariate
categorical data from a two-way table
Approximately what percent of the female students in the
band are in the 8th grade?
* A survey was conducted of 75 members of Mr. Smith’s
class to determine if they enjoy basketball and soccer. The
results of the survey are shown in the table below.
Based on the results of the survey, which statement is true?
A Twenty-one of Mr. Smith’s students do not enjoy
basketball or soccer.
B Forty of Mr. Smith’s students enjoy basketball but do
not enjoy soccer.
C Thirty-two of Mr. Smith’s students do not enjoy soccer.
D Fifty-two of Mr. Smith’s students enjoy basketball.