Vance County Schools
GRADE 6 MATH
2016-2017 Pacing Guide
UNIT
NO. OF
DAYS
STANDARDS
6.NS.2
6.NS.1
6.NS.3
6.NS.4
10
14
Factors & Multiples
3. Integers & Absolute Value
6.NS.5
6.NS.6a, c
6.NS.7
12
4. Coordinate Graphing
6.NS.6b
6.NS.8
10
Benchmark A – Week of November 7, 2016
6.RP.1
6.RP.3a
6.RP.3d
15
1. Dividing Fractions
2. Decimal Computations/
5. Ratios
Number Line
only
6.NS.6c
6. Unit Rates & Percents
6.RP.2
7. Equivalent Expressions
6.EE.1
6.RP.3b
6.RP.3c
6.EE.2
8. Solving Equations and
6.EE.5
6.EE.6
Inequalities
6.EE.9
15
6.EE.3
6.EE.4
12
6.EE.7
6.EE.8
15
Benchmark B – Week of February, 6 2017
6.G.3
6.G.1
6.EE.2
9. Area: Coordinate Plane & 2-D
10. Volume & Surface Area
11. Understanding Statistics
12. Statistical Graphs &
6.G.2
6.SP.1
6.G.4
6.SP.2
6.SP.4
6.SP.3
6.SP.5
13
12
10
15
Distribution
Mock EOG – Week of April 24, 2017
EOG Preparations
for the rest of the year
2016-2017
Vance County Schools
Pacing Guide 2016-17
Vance County Schools
6th Grade Math
Testing Information
Domain
Weight Distributions for 6th Grade Math
Ratios & Proportional
Relationships
12-17%
The Number System
27-32%
Expressions & Equations
27-32%
Geometry
12-17%
Statistics and Probability
7-12%
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.
Standards for 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.
2016-2017
Vance County Schools
Pacing Guide 2016-17
Vance County Schools
6th Grade Math PACING GUIDE 2016-2017
The pacing guide should be used along with the Common Core State Standards for Math and the NCDPI unpacking document
To Be Addressed Throughout the Course When Appropriate
6.NS.2 Fluently divide multi-digit numbers using the standard algorithm
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation
Unit 1: Dividing Fractions– 10 Days
Standards: 6.NS.1
Learning Targets Vocabulary
 Compute
quotients of
Quotient
fractions divided
by fractions
Mixed Number
(including mixed
numbers)
Dividend
 Determine which Divisor
value in a word
problem is the
Reciprocal
dividend and the
divisor
Multiplicative Inverse
 Determining
whether or not
an answer is
reasonable
Sample Questions
* Paul has a bird feeder that holds
cups of birdseed. He
bought a bag of birdseed that contains
cups. What is
the maximum number of times Paul can completely fill his
bird feeder? 6.NS.1
* Andrew divided a pizza into sixths. How many sixths are
there in
of a pizza? 6.NS.1
* Haley had
pounds of candy.
 She put the candy into gift bags for her friends.

Each gift bag had -pound of candy.
How many gift bags did Haley make? 6.NS.1
* A pan of brownies has an area of
ft2. Each brownie has
an area of
ft2. Each brownie contains 250 calories. How
many calories are in the entire pan of brownies? 6.NS.1
2016-2017
Vance County Schools
Pacing Guide 2016-17
Unit 2: Decimal Computations & Finding Factors – 14 days
Standards: 6.NS.2, 6.NS.3, 6.NS.4
Learning Targets
 Divide multi-digit numbers using the
long-division process, with speed and
accuracy
 Add, subtract, multiply and divide multi-
Vocabulary
Sample Questions/Clarification
Place Value
* Mr. Bradley purchased 20 trays of flowers. Each tray had 3
dozen flowers. Mr. Bradley’s total for all the flowers was
$273.60. All the flowers were the same price. How much did
each flower cost? 6.NS.3
Multi-Digit
Factor
digit decimals with speed and accuracy
Multiples
 Explain and use multiply computation
algorithms
 Round decimals
 Use at least two strategies to make
estimations
 Use order of operations to write
expressions for problems in context
 Identify the factors of two whole
numbers less than or equal to 100 and
determine the GCF
 Identify the multiples of two whole
numbers less than or equal to 12 and
determine the LCM
GCF – Greatest Common
Factor
LCM – Least Common
Multiple
Prime Number
Composite Number
Prime Factorization
* Marsha bought a new car that cost $23,567, including
interest. She will make equal monthly payments for 6 years.
About how much will Marsha pay each month?
* Ms. Cave has 96 colored pencils and 36 maps.
 Each group of students will get the same number of
colored pencils.
 Each group of students will get the same number of
maps.
 All the colored pencils and maps will be given out.
What is the greatest number of groups Ms. Cave can have in
her class? 6.NS.4
* Stephen has an art lesson every 6 days and a swim lesson
every 9 days. Stephen has an art lesson and a swim lesson
on Tuesday. On which day of the week will Stephen have
both lessons again? 6.NS.4
Distributive Property
* Jasmine bought 4 notebooks at $2.79 each and 3 dividers at
$1.10 each. About how much money did she spend? 6.NS.3
* Three tickets to a show cost $69 before sales tax. The
total sales tax on the three tickets was $4.83. Each ticket
cost the same amount. What was the total price for one
ticket? 6.NS.3
2016-2017
Vance County Schools
Pacing Guide 2016-17
Unit 3: Integers & Absolute Value – 12 days
Standards: 6.NS.5 , 6.NS.7, 6.NS.6a, c (Number line only)
Learning Targets
 Identify an integer and its opposite
 Identify a rational number as a point on the
number line
 Identify the absolute value of an integer as a
distance away from 0 on the number line
 Recognize opposite signs of numbers as
locations on opposite sides of 0 on the
number line
Vocabulary
Sample Questions cont.
Rational Numbers
* Which number is between points S and T
on the number line to the right? 6.NS.6
Opposites
Absolute Value
Greater Than
Less Than
* Julie had debits of $25, $75, and $45 to
her savings account. She had credits of
$35 and $70 to her savings account. Which
integer represents the change in the
balance of Julie’s savings account? 6.NS.5
* What is the approximate location of
point E on the number line below?
 Use integers to represent quantities in real
world situations (above/below sea level, etc)
*A thermometer below shows the temperature at 6:00
a.m.
 By noon the temperature had
risen 15°.
 Then by 6:00 p.m. the
temperature had dropped 7°.
What was the temperature
at 6:00 p.m.? 6.NS.5
* Which number is greater than W but less than X on the
number line below? 6.NS.7
2016-2017
Vance County Schools
Pacing Guide 2016-17
Unit 4: Coordinate Graphing – 10 days
Standards: 6.NS.6b, 6.NS.6c, 6.NS.8
Learning Targets
 Plot x and y values that represent independent and
dependent variables on the coordinate plane in quadrant 1
 Recognize the signs of both numbers in an ordered pair
indicate which quadrant of the coordinate plane the
ordered pair will be located
 Find and position pairs of integers and other rational
numbers on a coordinate plane
 Graph points in all four quadrants of the coordinate plane
 Draw polygons in the coordinate plane
 Use coordinates (with the same x-coordinate or the same
y-coordinate) to find the length of a side of a polygon and
the distance between two points
Vocabulary
Sample Questions/Clarification
Opposites
* Evan mapped the places he traveled today on a
coordinate grid.
How many units did
Evan travel if he
went from:
 home to school,
 then from school
to the park,
 then from the park
to the library,
 then back home?
Origin
Quadrant
Coordinate plane
Ordered pairs
x-axis
y-axis
Coordinates
Distance
* Rectangle QRST has vertices at Q(–3, 1),
R(5, 1), S(5, –3), and T(–3, –3). What is the distance
between points Q and T? 6.NS.8
*Line segment RT has points at R
and
T
. What is the distance between
points R and T? 6.NS.8
*Which point is located at (2, –1)? 6.NS.6
2016-2017
Vance County Schools
Pacing Guide 2016-17
Unit 5: Ratios– 15 Days
Standards: 6.RP.1, 6.RP.3a, d
Learning Targets
 Write/read ratio notation (e.g. 3:5, 3 to 5, 3/5)
 Explain why order matters when
reading/writing ratios
Vocabulary
Sample Questions
Ratio
* A farmer owns 6 chickens, 4 pigs, 3 cows, and 1 rooster.
What is the ratio of pigs to all of the animals? 6.RP.1
Part-to-Part
 Simplify ratios
Part-to-Whole
 Use ratios to compare two quantities
Rate
 Recognize that ratios appear in a variety of
context (i.e. part-to-whole, part-to-part, rates)
Equivalent Ratios
 Make a table of equivalent ratios
 Find the missing value(s) of equivalent ratios
* What is the ratio of pens to
the total number of books
and pencils? 6.RP.1
* How much will it cost Mrs. Moore to buy 50 tiles? 6.RP.3a
Number of Tiles Cost
10
$25
20
$50
30
$75
* How much sugar would be needed for 8 cups of
strawberries? 6.RP.3a
Sample Questions cont.
* Luke needs to take 1/3 ounce of cough medicine 3
times each day. About how many milliliters of cough
medicine will Luke take after 7 days? (1 ounce ≈ 29.6
milliliters) 6.RP.3d
Sugar (cups)
12
?
3
Strawberries(cups)
16
8
4
* A professional basketball court is 94 feet long. Most high
school basketball courts are 84 feet long. About how many
meters longer is a professional court than a high school
court?
(1 foot ≈ 0.3 meter) 6.RP.3d
2016-2017
Vance County Schools
Pacing Guide 2016-17
Unit 6: Unit Rates & Percents – 15 Days
Standards: 6.RP.2, 6.RP.3b, c, 6.EE.9, 6.NS.8 (Quadrant I only)
Learning Targets
Vocabulary
Unit Rate
 Identify and calculate a unit rate
 Use appropriate terminology related to rates
Percent
 Recognize that a percent is a ratio of a number
to 100
Independent Variable
 Find a percent of a number as a rate per 100
Dependent Variable
 Plot x and y values on a coordinate plane
(Quadrant 1)
Coordinate Plane
 Interpret the rate from a graph or equation
Quadrant
Sample Questions/Clarifications
**Expectations for unit rates in this grade a limited to noncomplex fractions**
* Joseph drove 117 miles and used 5 gallons of gasoline.
Molly drove 224 miles and used 10 gallons of gasoline. Who
has the better mileage and by how much? 6.RP.2
* In Mrs. Carter’s homeroom, 25% of the students are going
to the dance. If 6 of Mrs. Carter’s students are going to the
dance, how many students are in Mrs. Carter’s homeroom?
6.RP.3c
* A recipe needs ¾ cup of sugar to make 24 cookies. How
much sugar will be needed to make 36 cookies? 6.RP.3b
* In a class of 32 students, the ratio of left-handed students
to right-handed students is 1 : 7. How many right-handed
students are in the class? 6.RP.3b
OPPORTUNITIES FOR
CONNECTIONS AMONG
DOMAINS
Students’ work with ratios and
proportional relationships (6.RP) can be
combined with their work in representing
quantitative relationships between
dependent and independent variables
(6.EE.9)
* Which equation will calculate the amount of money Alexis
will earn if she works x hours? 6.EE.9
A. y = x + 8
B. y = 8x
C. y = x + 12
D. y = 12x
2016-2017
Vance County Schools
Pacing Guide 2016-17
Unit 7: Equivalent Expressions – 12 days
Standards: 6.EE.1, 6.EE.2, 6.EE.3, 6.EE.4
Learning Targets
 Write numerical expressions involving whole
number exponents (Ex. 34 = 3x3x3x3)




Vocabulary
Exponent
Base
Expression
Evaluate numerical expressions involving
Evaluate
4
whole number exponents (Ex. 3 = 3x3x3x3 = Variables
81)
Order of Operations
Constant
Solve order of operation problems that
Equivalent Expressions
contain exponents (Ex. 3 + 22 – (2 + 3) = 2)
Distributive Property
Like Terms
Use numbers and variables to represent
Multiplicative Identity
desired operations
Commutative Property
Substitute specific values for variables
Associative Property
 Evaluate algebraic expressions including
those that arise from real-world problems
 Generate equivalent expressions using the
properties of operations (e.g. distributive
property, associative property, adding like
terms with the addition property of equality,
etc.)
 Recognize when two expressions are
equivalent
Identify parts of an
expression using
mathematical terms:
 sum
 difference
 term
 product
 factor
 quotient
 coefficient
Sample Questions/Clarification
* Which word best describes 5x2 in the expression 5x2 + 2x +
3? 6.EE.2
* What is the solution to the expression
18 ÷ 2 +
• 8 • 4? 6.EE.1
* What is the value of the expression 5x3 + 6y • 7z,
when x = 2, y = 8, and z = 4.5? 6.EE.2
* Which expression is equal to 12(2x + 3y)? 6.EE.3
* Which expression is equivalent to the quotient of 4 and a
number, n? 6.EE.2
* Which inequality is true? 6.EE.1
A 72 > 27
B 94 > 49
C
25 > 52
D 43 > 34
* Which expression is equal to 2 × w + 2 × 5? 6.EE.3
A 2(5w)
B
2(w + 5)
C 2w(w + 5)
D 2 + (w + 5)
2016-2017
Vance County Schools
Pacing Guide 2016-17
Unit 8: Solving Equations and Inequalities – 15 days
Standards: 6.EE.5, 6.EE.6, 6.EE.7, 6.EE.8, 6.EE.9
Learning Targets
 Recognize that the solutions of an equation or
inequality are the values that make the equation
or inequality true
 Use substitution to determine whether a given
number in a specified set makes an equation or
inequality true
 Use inverse operations to solve 1-step equations
 Set up an inequality using the correct symbol,
based on a real-world problem
 Recognize that inequalities of the form
x > c or x < c have infinitely many solutions
Vocabulary
Sample Questions/Clarification
Equation
Inverse operation
Variable
Substitution
Solution
Dependent variable
Independent
Discrete Data
Continuous data
Inequality
Infinitely many
solutions
Solution set
Greater than
Greater than or equal
to
Less than
Less than or equal to
Open circle
Closed circle
* What graph represents the inequality x ≥ 5? 6.EE.8
* Natalie is sending a package to
her friend. The graph below shows
the cost for Natalie to ship a
package to her friend, y, based
on the weight of the package,
x, in pounds.
Which equation would calculate the cost for Natalie to
ship a package that weighs x pounds? 6.EE.9
* What is the value of p in the equation
p + 16.4 = 78? 6.EE.5
* Sally made a deposit of $43.50 into her checking
account. After the deposit, she now has $72.85. Which
equation would calculate the amount of money in
Sally’s checking account, m, before she made the
deposit? 6.EE.7
* Judy and Steve collect baseball cards. Judy has six
less than twice the number of cards Steve has.
If n represents the number of baseball cards Steve has,
which expression represents the number of baseball
cards Judy has? 6.EE.6
* Sarah’s math grade is greater than 80%. Which
inequality represents Sarah’s math grade, g? 6.EE.8
2016-2017
Vance County Schools
Pacing Guide 2016-17
Unit 9: Area: Coordinate Plane & 2-D – 13 days
Standards: 6.G.1, 6.G.3, 6.EE.2 (revisit)
Learning Targets
 Find the area of triangles and rectangles
 Find the perimeter of polygons
 Compose and decompose special polygons into
triangles and rectangles to find area, including
trapezoids and parallelograms
 Calculate missing side lengths in a polygon, given
the area
 Calculate missing side lengths in a polygon, given
the measurements of other side lengths
 Draw polygons in the coordinate plane
 Use coordinates (with the same x-coordinate or
the same y-coordinate) to find the length of a side
of a polygon
Vocabulary
Sample Questions/Clarification
Area
Dimensions
Vertices
Height
Trapezoid
Quadrilateral
Rectangle
Square
Parallelogram
Rhombus
Kite
Polygon
Composing
Decomposing
Perimeter
Distance
* Right triangle JKL has sides that measure 20 in., 21 in.,
and 29 in. What is the area of triangle JKL? 6.G.1
* Polygon EFGHI is made up of a rectangle and two right
triangles.
What is the area of polygon EFGHI? 6.G.1
*Triangle JKL has vertices at coordinates
J(–2, 4), K(2, 4), and L(0, –2). What is the area of
triangle JKL? 6.G.3
* What is the area of the parallelogram shown below?
6.G.1
2016-2017
Vance County Schools
Pacing Guide 2016-17
Unit 10: Volume & Surface Area – 12 days
Standards: 6.G.2, 6.G.4
Learning Targets

Calculate the volume and surface area of a right
rectangular prism

Recognize and represent 3D figures using nets

Find the surface area of cubes, right rectangular
prisms, triangular prisms, triangular pyramids, and
square pyramids using nets

Calculate the volume of right rectangular prisms
using cubic units with fractional edge lengths

Describe the difference between volume and
surface area
Vocabulary
Sample Questions/Clarification
Volume
* The net of a cube is shown below.
Three dimensional
What is the surface area
of the cube? 6.G.4
Edge
Prisms
* What is the surface area of the rectangular prism
shown below? 6.G.4
Right rectangular
prism
face
Base
* What is the volume of the rectangular prism shown
below? 6.G.2
Nets
Rectangular prism
Cube
Square pyramid
Sample Questions cont.
* What is the volume of a right rectangular prism with a
length of 10 m, a width of m, and a height of 15 m?
6.G.2
* What is the surface area of the triangular prism
shown below? 6.G.4
Triangular prism
Triangular pyramid
Surface area
2016-2017
Vance County Schools
Pacing Guide 2016-17
Unit 11: Understanding Statistics – 10 days
Standards: 6.SP.1, 6.SP.2, 6.SP.3
Learning Targets
 Recognize that data can have variability and explain





Vocabulary
Statistical question
Variability
what variability means
Statistics
Data
Recognize a statistical question (examples versus
Cluster
non-examples)
Distribution
Box plots
Understand that a set of data has a distribution
Center
Peak
Describe a set of data by its center, e.g., mean and
Spread
median
Measure of center
Mean
Describe a set of data by its spread and overall shape,
Median
e.g. by identifying data clusters, peaks, gaps and
Dot plot
symmetry
Histogram
Measure of center
Find measures of central tendency for a data set, e.g.,
Range
mean, median, mode
Variation
 Find measures of variances for a data set, e.g., range,
interquartile range, mean absolute deviation
 Make judgments about which measure of central
tendency best represents my data
Sample Questions/Clarification
*In an apartment complex with 120 identical
apartments, a random sample of renters are selected
for a survey. Which question would most likely
generate data without variability? 6.SP.1
A How many pets do you have?
B How much money do you earn in a year?
C How many people live in your apartment?
D How many bedrooms are in your apartment?
*Which of the following is not a statistical question?
A How many pets are owned by my uncle?
B How many pets are adopted in a pet store each wk
C How many pets are owned by the individual teachers
in my school?
D How many pets are owned by the individual
students in a karate class?
*Rita caught 5 fish. The lengths, in inches, of each fish
are listed.
Which statement best represents the meaning of the
range for these data? 6.SP.3
A The difference between the shortest and longest fish is
12 inches.
B The length of the next fish caught will most likely be
12 inches.
C The longest fish caught is 13 inches longer than the
shortest fish.
D There are an equal number of fish that were both longer
and shorter than 13 inches.
2016-2017
Vance County Schools
Pacing Guide 2016-17
Unit 12: Statistical Graphs & Distribution – 15 days
Standards: 6.SP.4, 6.SP.5
Learning Targets

Identify the components of dot plots, histograms,
and box plots
 Find the median, quartile and interquartile range
of a set of data
 Organize and display data in tables and graphs
 Describe the data being collected, including how it
was measured and its units of measurement
 Calculate quantitative measures of center, e.g.,
mean, median, mode
 Calculate quantitative measures of variance, e.g.,
range, interquartile range, mean absolute
deviation
 Identify outliers of a set of data
Sample Questions cont.
What is the mean absolute deviation for this set of data?
6.SP.5
Vocabulary
Sample Questions/Clarification
Box plots
Dot plots
Histograms
Frequency tables
Cluster
Peak
Gap
Mean
Median
Interquartile range
Quartiles
Lower quartile (1st
quartile or Q1)
upper quartile (3rd
quartile or Q3)
Symmetrical
Skewed
Outlier
Mean Absolute
Deviation
Summary statistics
Measures of center
Variability
* Ms. Adams recorded the number of books some of
her students read during the summer. The data is
shown below.
5, 14, 20, 8, 33, 35, 25, 23, 10, 18
What is the interquartile range of the data? 6.SP.5
* The list below shows the ages of the oldest ten
presidents in United States history at the time of their
inauguration.
69, 68, 65, 64, 64, 62, 61, 61, 61, 60
Which dot plot represents this data? 6.SP.4
*A pet store owner surveyed her customers. She
recorded the age of each pet in the table below.
Pets’ Ages in Years
5
18
16
11
14
12
10
19
2
8
19
10
9
14
Which
histogram best represents the data? 6.SP.4
*Scott listed the distance he threw the shotput at each
team competition. The data below was measured in
feet.
24, 25, 27, 30, 32, 32, 33, 33, 33, 36
2016-2017
Vance County Schools
Pacing Guide 2016-17
2016-2017