Grade 6
UNIT 3: Rational Numbers
Essential Question
How are negative rational numbers used in real
life?
Unit Vocabulary
 Absolute Value
 Charge , Credit, Debit, Deposit
 Elevation
 Integers
 Magnitude
 Negative Number & Positive Number
 Opposite
 Quadrants
 Rational Number
 Withdraw
 Coordinate Pair, Coordinate Plane
 Fraction
 Line of Symmetry
 Ordered Pair
 Origin
 Quadrant
 Symmetry
 Whole Numbers

-Axis, -Coordinate

-Axis, -Coordinate
Unit Outcome (Focus)
Key Concepts



Understanding Positive and Negative
Numbers on the Number Line
Order and Absolute Value
Rational Numbers and the Coordinate
Plane
*Assessments
Mid-Module Assessment: After Section B
(3 days -1 day for assessment, 1 day for
assessment return, & 1 day for remediation)
End-of-Module Assessment: after Section C (3
days- 1, day for assessment, 1 day for
assessment return, & 1 day for remediation).
http://www.engageny.org/resource/grade-6mathematics-module-3
Suggested Number of Days for Entire UNIT: 25
Cross Curricular Connections
Art: Have students draw a tree with leaves
representing the continued growth of the
Fibonacci sequence. Instruct students to label
the leaves with the numerical value.
Social Studies: Allow students to choose one of
the countries studied (Egypt, Rome, China,
Israel). Instruct them to outline with country on
a coordinate plane. Once they have done this
students should create a list of coordinate pairs
for the outline of their country. Have students
exchange their points and graph another
students’ country.
Science: Explore the Earth’s history by creating a
timeline of epochs and eras. Use the birth of
Christ as zero. Have students display the epoch
and eras as positive and negative integers on the
timeline.
Students extend the number line (both horizontally and vertically) in Unit 3 to include the opposites of whole numbers In this unit plan, the final topic,
the number line model is extended to two-dimensions, as students use the coordinate plane to model and solve real-world problems involving rational
numbers.
Archdiocese of New York
Page 1
2014 – 2015
UNIT 3
SECTION A: Understanding Positive and Negative Numbers on the Number Line
Essential Question
How are negative rational
numbers used in real life?
Comments
Section A focuses on the
development of the
number line in the opposite
direction (to the left or
below zero). Students use
positive integers to locate
negative integers,
understanding that a
number and its opposite
will be on opposite sides of
zero and that both lie the
same distance from zero.
Students represent the
opposite of a positive
number as a negative
number and vice-versa.
Students realize that zero is
its own opposite and that
the opposite of the
opposite of a number is
actually the number itself.
Archdiocese of New York
Key Concept
Standards for Mathematical Practice

Positive and Negative Numbers on the Number Line—
Opposite Direction and Value

Real-World Positive and Negative Numbers and Zero

The Opposite of a Number

The Opposite of a Number’s Opposite

Rational Numbers on the Number Line
Standard
No.
6.NS.5
(DOK 2)
6.NS.6
(DOK 1)
Number of Days for SECTION:6
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically
7. Look for and make use of structure
Standard
 Supporting Standard
 Major Standard
 Additional Standard
 Standard ends at this grade
 Fluency Standard
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.
Priority

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.
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.
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UNIT 3
SECTION B: Order and Absolute Value
Essential Question
How are negative rational
numbers used in real life?
Comments
Students apply their
understanding of a rational
number’s position on the
number line (6.NS.C.6c) to
order rational numbers.
Students understand that
when using a conventional
horizontal number line, the
numbers increase as you
move along the line to the
right and decrease as you
move to the left. Students
compare rational numbers
using inequality symbols
and words to state the
relationship between two
or more rational numbers.
They describe the
relationship between
rational numbers in realworld situations.
Archdiocese of New York
Key Concept
Standards for Mathematical Practice
 Ordering Integers and Other Rational Number
 Comparing Integers and Other Rational Numbers
 Writing and Interpreting Inequality Statements Involving
Rational Numbers
 Absolute Value—Magnitude and Distance
 The Relationship Between Absolute Value and Order
 Statements of Order in the Real World
Standard
No.
6.NS.6c
(DOK 1)
Suggested Number of Days for SECTION :7
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically
7. Look for and make use of structure
Standard
 Supporting Standard
 Major Standard
 Additional Standard
 Standard ends at this grade
 Fluency Standard
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.
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
Priority


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°C > –7°C to express the fact that –3°C is warmer than –7°C.
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, 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
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UNIT 3
SECTION C: Rational Numbers and the Coordinate Plane
Essential Question
How are negative rational
numbers used in real life?
Comments
Students extend their
understanding of the
ordering of rational
numbers in one dimension
(on a number line) to the
two-dimensional space of
the coordinate plane. They
construct the plane’s
vertical and horizontal
axes, discovering the
relationship between the
four quadrants and the
signs of the coordinates of
points that lie in each
quadrant (6.NS.C.6b,
6.NS.C.6c).
.
Archdiocese of New York
Key Concept
Number of Days for SECTION:6
Standards for Mathematical Practice

Ordered Pairs

Locating Ordered Pairs on the Coordinate Plane

Symmetry in the Coordinate Plane

Drawing the Coordinate Plane and Points on the Plane


Distance on the Coordinate Plane
Problem-Solving and the Coordinate Plane
Standard
 Supporting Standard
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically
7. Look for and make use of structure
Standard
No.
 Major Standard
 Standard ends at this grade
6.NS.6
(DOK 1)
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.
 Additional Standard
 Fluency Standard
Priority

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.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.
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Possible Activities
INTEGER STORIES: Create a real world situation that could be represented by integer expressions such as 20 + (-10) + (-4) and have students solve it
using a number line. Ex: Scuba Sam is on a hill 20 feet above sea level and walks 10 feet down towards the water and stops to talk to a friend. Then he
moves 4 feet further down to the water. Where is Scuba Sam?
RATIONAL NUMBER LINE: Create a number line resembling a clothes-line and hang it across the classroom from -5 to 5. Write various rational numbers
on index card and have students come up one by one and place the cards on the number line.
HUMAN NUMBER LINE: (whole class or group activity) Give students a rational number written on an index card to tape to their chest or hold where it is
visible. Ask students to put themselves in order from largest to smallest without talking. Once they are in order, write the numbers on a number line on
the board. Have students discuss and verify they are in the correct order.
INTEGER COMPARISON: Write a different number on large poster boards and place the boards in each corner of the room. Give students a note card
containing an integer. Instruct students to go to the corner of the room that has a number that is larger than their integer. Then ask students to find a
number that is smaller than their number. As the students move around the room ask them to justify their positions. Additional ordering practice can be
done online at www.aaastudy.com. Select 6th grade from the top menu. Select Comparing and Ordering and one of three levels for Ordering Integers.
Resources
PRACTICE ORDERING INTEGERS: www.sheppardsoftware.com. Click on Math Games, scroll down to the Integers category, and choose Compare
or Order Integer Games.
BATTERY PACK ACTIVITY: This reproducible activity, from an Illuminations lesson, features directions and questions that guide students to place
batteries end to end and calculate the sum of the batteries' voltages. http://illuminations.nctm.org/Lessons/PowerUp/PowerUp-AS-Voltmeter.pdf
ELEVATOR INTEGERS: Students will use vertical movement of an elevator to evaluate signed number expressions. The idea behind the method of adding
and subtracting signed integers offered in this lesson and the next is that the number of rules that students have to memorize and the amount of
understanding are minimal, while the underlying concepts are not trivialized. http://illuminations.nctm.org/LessonDetail.aspx?ID=L733
Engage NY Grade 6 Module 3 Link: http://www.engageny.org/resource/grade-6-mathematics-module-3
Archdiocese of New York
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Possible Activities
FINDING YOUR WAY AROUND: GRAPHING ON THE COORDINATE PLANE: In this lesson, from Illuminations, students make their way around twodimensional space in conceptually rich activities. The teaching activities are organized around two major conceptual categories: finding one s way
around in the plane and using the plane to represent variables in two dimensions by traditionally graphing equations.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L280
COORDINATE GRAPHING ACTIVITY: Show the class a coordinate plane with letters and shapes located on it. Ask students to see how many ordered pairs
they can write down that correspond with a letter or shape on the graph. Award students a point for each correct coordinate plane.
Premade coordinate planes are available online at www.math-play.com. Choose Algebra Games from the left.
COORDINATE GRAPHING IN REAL LIFE: There are many situations in life that involve two sets of numbers that are related to each other. For example: If
the price of one ticket for a show is known, the cost for any number of people to attend can be calculated. Similarly, if the cost of one gallon of gas is
known, the amount of gas that can be purchases with a given amount of money can be determined. Challenge students to create a chart of ordered
pairs representing a real life situation and chart the pairs on a coordinate plane to create a line graph. Extend: Introduce students to function tables and
challenge them to create one using their data.
DESCRIBE THE GRAPH ACTIVITY: Instruct students to plot nine random ordered pairs on a coordinate plane. Have student record any trends or
observations. Lesson plans that expand on this activity can be found online at www.illuminations.nctm.org. Select lessons, 6-8 Algebra, click on Search,
and scroll down until you find describe the graph
.
Resources
COORDINATE GRAPHING WORKSHEETS: Find worksheets at www.superteacherworksheets.com and choose Graphing from the left menu bar, select
Ordered Pair Worksheets or Ordered Pairs Graph Art.
FINDING THE INTERSECTION: In this Cyberchase video, Inez and Digit identify the location of the transformatron using their knowledge of parallel and
intersecting lines. http://www.teachersdomain.org/resource/vtl07.math.geometry.pla.findinters/
Engage NY Grade 6 Module 3 Link: http://www.engageny.org/resource/grade-6-mathematics-module-3
Archdiocese of New York
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Archdiocese of New York
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