MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
Unit Description
Unit: 4
Title: Rational Numbers (Ordering, Comparing & Graphing)
Suggested Length: 4 weeks
Big Idea(s)
What enduring
understandings are
essential for application to
new situations within or
beyond this content?
Enduring Understandings
Develop fluency of operations of positive rational numbers and order of the
full system of rational numbers.
Enduring Skills Rubric measures competency of the following skills:
Numbers
 The distance between any two consecutive counting numbers on a
given number line is the same.
 Zero can be associated with a unique point on the number line.
 Integers are the whole numbers and their opposites on the number
line, where zero is its own opposite.
 Each integer can be associated with a unique point on the number
line, but there are many points on the number line.
 An integer and its opposite are the same distance from zero on the
number line.
 There is no greatest or least integer on the number line.
 Each fraction can be associated with a unique point on the number
line, but not all of the points between integers can be named by
fractions.
 There are an infinite number of fractions between any two fractions on
the number line.
 A decimal is another name for a fraction and thus can be associated
with the corresponding point on the number line.
Comparison
 A number to the right of another on the number line is the greater
number.
 Integers can be compared using greater than, less than, or equal.
Orientation & Location
 The Cartesian Coordinate System is a scheme that uses two
perpendicular number lines intersection at 0 on each to name the
location of points in the plane; the system can be extended to name
points in space.
 Every point in the plane can be described uniquely by an ordered pair
of numbers; the first number tells the distance to the left or right of zero
on the horizontal number line; the second tells the distance above or
below zero on the vertical number line.
Curriculum and Instruction
2015-2016
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
Essential Question(s)
• When are negative numbers used and why are they important?
• Why is it useful for me to know the absolute value of a number?
• When is graphing on the coordinate plane helpful?
• How do I use positive and negative numbers in everyday life?
• Where do I place positive and negative rational numbers on the number
line?
How do I use positive and negative numbers to represent quantities in realworld contexts?
• What are opposites, and how are opposites shown on a number line?
• How do statements of inequality help me place numbers on a number line?
• How can I use coordinates to find the distances between points?
• How can I use number lines to find the distances between points?
• How can I use absolute value to find the lengths of the sides of polygons on
the coordinate plane?
What questions will
provoke and sustain
student engagement
while focusing learning?
•
Standards
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them. Students make
sense of problems involving points and polygons in the coordinate plane.
2. Reason abstractly and quantitatively. Students demonstrate abstract
reasoning about rational numbers with their visual representations. Students
consider the values of these numbers in relation to distance (number lines).
3. Construct viable arguments and critique the reasoning of others. Students
construct and critique arguments regarding number line representations and
the use of inequalities to represent real-world contexts.
4. Model with mathematics. Students use number lines to compare numbers
and represent inequalities in mathematical and real-world contexts.
5. Use appropriate tools strategically. Students select and use tools such as
two-color counters, number line models and the coordinate plane to
represent situations involving positive and negative numbers.
6. Attend to precision. Students attend to the language of real-world
situations to determine if positive or negative quantities/distances are being
represented.
7. Look for and make use of structure. Students relate the structure of number
lines to values of rational numbers as they use the coordinate plane.
8. Look for and express regularity in repeated reasoning. Students relate new
experiences to experiences with similar contexts when studying positive and
negative representations of distance and quantity. In the study of absolute
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
value, students demonstrate repeated reasoning by showing that both
positive and negative quantities represent the same distance from zero.
Standards for Mathematical Content
6.NS.5
Understand that positive and negative numbers are used together
to describe quantities having opposite directions or values (e.g.,
temperature above/below zero, elevation above/below sea level,
credits/debits, positive/negative electric charge); use positive and
negative numbers to represent quantities in real-world contexts,
explaining the meaning of 0 in each situation.
6.NS.6
Understand a rational number as a point on the number line.
Extend number line diagrams and coordinate axes familiar from
previous grades to represent points on the line and in the plane
with negative number coordinates.
a. Recognize opposite signs of numbers as indicating locations on
opposite sides of 0 on the number line; recognize that the
opposite of the opposite of a number is the number itself, e.g., –
(–3) = 3, and that 0 is its own opposite.
b. Understand signs of numbers in ordered pairs as indicating
locations in quadrants of the coordinate plane; recognize that
when two ordered pairs differ only by signs, the locations of the
points are related by reflections across one or both axes.
c. Find and position integers and other rational numbers on a
horizontal or vertical number line diagram; find and position
pairs of integers and other rational numbers on a coordinate
plane.
6.NS.7
Understand ordering and absolute value of rational numbers.
a. Interpret statements of inequality as statements about the
relative position of two numbers on a number line diagram. For
example, interpret –3 > –7 as a statement that –3 is located to
the right of –7 on a number line oriented from left to right.
b. Write, interpret, and explain statements of order for rational
numbers in real-world contexts. For example, write –3 oC > –7 oC
to express the fact that –3 oC is warmer than –7 oC.
c. Understand the absolute value of a rational number as its
distance from 0 on the number line; interpret absolute value as
magnitude for a positive or negative quantity in a real-world
situation. For example, for an account balance of –30 dollars,
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
write |–30| = 30 to describe the size of the debt in dollars.
d. Distinguish comparisons of absolute value from statements
about order. For example, recognize that an account balance
less than –30 dollars represents a debt greater than 30 dollars.
Supporting
Standard(s)
Which related standards
will be incorporated to
support and enhance the
enduring standards?
6.NS.8
Solve real-world and mathematical problems by graphing points in
all four quadrants of the coordinate plane. Include use of
coordinates and absolute value to find distances between points
with the same first coordinate or the same second coordinate.
6.G.3
Draw polygons in the coordinate plane given coordinates for the
vertices; use coordinates to find the length of a side joining points
with the same first coordinate or the same second coordinate.
Apply these techniques in the context of solving real-world and
mathematical problems.
6.RP.3
Use ratio and rate reasoning to solve real-world and mathematical
problems, e.g., by reasoning about tables of equivalent ratios,
tape diagrams, double number line diagrams, or equations.
a. Make tables of equivalent ratios relating quantities with whole
number measurements, find missing values in the tables, and
plot the pairs of values on the coordinate plane. Use tables to
compare ratios.
5th grade Standards:
5.OA.3 Generate two numerical patterns using two given rules. Identify
apparent relationships between corresponding terms. Form ordered pairs
consisting of corresponding terms for two patterns, and graph the ordered
pairs on a coordinate plane.
5.G.1 Use a pair of perpendicular number lines, called axes, to define a
coordinate system, with the intersection of the lines (the origin) arranged to
coincide with the 0 on each line and a given point in the plane located by
using an ordered pair of numbers, called its coordinates. Understand that the
first number indicates how far to travel from the origin in the direction of one
axis, and the second number indicates how far to travel in the direction of
the second axis, with the convention that the names of the two axes and the
coordinates correspond (e.g., x-axis and x-coordinate, y-axis and ycoordinate).
5.G.2 Represent real world and mathematical problems by graphing points in
the first quadrant of the coordinate plane, and interpret coordinate values of
points in the context of the situation.
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
Instructional
Outcomes
What must students learn
and be able to do by the
end of the unit?
I am learning to….
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Curriculum and Instruction
Identify an integer and its opposite.
Use integers to represent quantities in real world situations
(above/below sea level, temperatures above/below zero,
credits/debits etc).
Explain where zero fits into a situation represented by integers (sea
level, no debt, etc).
Identify a rational number as a point on the number line.
Identify the location of zero on a number line in relation to positive and
negative numbers.
Recognize opposite signs of numbers as locations on opposite sides of
0 on the number line.
Determine which quadrant an ordered pair is located based on the
signs of the x and y coordinates.
Find and plot integers and other rational numbers on a horizontal or
vertical number line diagram.
Find and plot pairs of integers and other rational numbers on a
coordinate plane.
Reason that the opposite of the opposite of a number is the number
itself (e.g., the opposite of 3 is -3, so the opposite of -3 is 3).
Reason that when only the x value in a set of ordered pairs are
opposites, it creates a reflection over the y axis.
Recognize that when only the y value in a set of ordered pairs are
opposites, it creates a reflection over the x axis.
Reason that when two ordered pairs differ only by signs, the locations
of the points are related by reflections across both axes.
Order rational numbers on a number line.
Identify absolute value of rational numbers.
Interpret statements of inequality as statements about relative position
of two numbers on a number line diagram. (Ex. -4 is less than -2
because it is farther to the left on a number line)
Write, interpret, and explain statements of order for rational numbers in
real-world contexts.
Describe a number’s absolute value as its distance from zero on a
number line.
Represent magnitude using absolute value (ex., -$30 means I owe
$30).
Distinguish comparisons of absolute value from statements about
order and apply to real world contexts.
Calculate absolute value.
Graph points in all four quadrants of the coordinate plane.
Given only coordinates, calculate the distances between two points
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6

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Essential Vocabulary
What vocabulary must
students know to
understand and
communicate effectively
about this content?
Resources/Activities
What resources could we
use to best teach this unit?
with the same first coordinate or the same second coordinate using
absolute value.
Draw polygons in the coordinate plane.
Use coordinates to find the length of a side of a polygon.
Essential Vocabulary
Absolute Value
Axis (plural – axes)
Coordinate Grid
Coordinate Pair
Coordinate Plane
Coordinate System
Coordinates
Inequality
Integer
Ordered pair
Origin
Polygon
Quadrants
Vertex (Vertices)
x-axis
x-coordinate
y-axis
y-coordinate
Supporting Vocabulary
Greater than
Less than
Number line
Resources/Activities
https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_6_6thGrade_Unit7.pdf
The following website is a website with lessons to address CCSS:
https://www.engageny.org/resource/grade-6-mathematics
Khan Academy – www.khanacademy.org
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 6
IXL – www.ixl.com
http://www.insidemathematics.org/common-core-resources/mathematicalcontent-standards/standards-by-grade/6th-grade
http://www.mathchimp.com/6th-grade-math-resources
Remember there are other sources in your school that may not be listed on
this resources list due to variation in each individual school. If you have a
good resource that you would be willing to share, please let Mendy Mills
know so that she can share with other math teachers. Please include the unit
number for the resource. Mendy.Mills@madison.kyschools.us
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