Grade 6 Mathematics Curriculum
North Jersey Arts & Science Charter Schools
2014-2015
Unit 3 Summary: Rational Numbers
Essential Questions
1. When are negative numbers used and why are they
2.
3.
4.
5.
6.
important?
How do I use positive and negative numbers in real life?
Where are positive and negative numbers located on the
number line?
How does the coordinate plane and number lines help
me to determine the distance between points.
What do algebraic inequalities represent?
How are inequalities represented on a number line?
Big Ideas
1. Negative numbers are used to represent quantities that
are less than zero.
2. Absolute value is useful in ordering and graphing positive
and negative numbers.
3. Rational numbers are points on a number line.
4. Numbers in ordered pairs indicate locations in quadrants
of the coordinate plane.
Learning Outcomes (CCSS)
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.
6.NS.6a- 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.
6.NS.6b- 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.
6.NS.6c- 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.
Grade 6 Curriculum
Unit 3: Rational Numbers
Unit 3 Summary: Rational Numbers
6.NS.7- Understand ordering and absolute value of rational numbers.
6.NS.7a- 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.
6.NS.7b- 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.
6.NS.7c- 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.
6.NS.7d- 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.
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.
Local Standards (LS) #17-32 are taught in this unit.
Prior Knowledge Expected
• Mastery: understanding the place value system
• Basic Understanding: graphing points on a coordinate plane, fractions, decimals
• Familiarity: symmetry, negative numbers
Assessment Summary
1. Mid-Unit Assessment (LS #17-25)
2. End-of-Unit Assessment (LS #17-32)
(Scope and Sequence on the next page)
Grade 6 Curriculum
Unit 3: Rational Numbers
Unit 3 Scope and Sequence: Rational Numbers
Periods*
CCSS
LS
6.NS.5
17
6.NS.5
6.NS.6a
6.NS.6a
Grade 6 Curriculum
18
19
20
Student Friendly Language
Understand that positive and negative numbers
describe quantities having opposite directions or
values.
Use positive and negative numbers to show that
amounts in real-world situations and explain what
the number 0 means in those situations.
Recognize opposite signs of a number as
indicating locations on opposite sides of 0 on a
number line.
Recognize that the opposite of the opposite of a
number is the number itself.
Resources
Textbook
Lesson 8-1; 9-1
Links
Pos & Neg Battery Voltage
Application of Integers
Other
EngageNY lessons 1-6
Georgia Unit 7
Assessment
Close & Check 8-1; 9-1
Textbook
Lesson 8-1; 9-1
Links
Pos & Neg Battery Voltage
Application of Integers
Other
EngageNY lessons 1-6
Georgia Unit 7
Assessment
Close & Check 8-1; 9-1
Textbook
Lesson 8-1; 9-1
Links
Rational Numbers on Number
Line pg 36-38
Application of Integers
Other
EngageNY lessons 1-19
Georgia Unit 7
Assessment
Close & Check 8-1; 9-1
Textbook
Lesson 8-1; 9-1
Links
Pos & Neg Battery Voltage
Application of Integers
Other
EngageNY lessons 1-19
Georgia Unit 7
Assessment
Close & Check 8-1; 9-1
Unit 3: Rational Numbers
Unit 3 Scope and Sequence: Rational Numbers
Periods
CCSS
6.NS.6a
6.NS.6b
6.NS.6b
6.NS.6c
Grade 6 Curriculum
LS
21
22
23
24
Student Friendly Language
Resources
Textbook
Lesson 8-1; 9-1
Links
Pos & Neg Battery Voltage
Application of Integers
Other
EngageNY lessons 1-19
Georgia Unit 7
Assessment
Close & Check 8-1; 9-1
Textbook
Lesson 8-4; 9-4
Links
Activitypgs 39-48
Coordinate Game
Other
EngageNY lessons 1-19
Georgia Unit 7
Assessment
Close & Check 8-4; 9-4
Textbook
Lesson 8-4; 9-4
Links
Coordinate Plane
Coordinate Game
Graphing Ordered Pairs
Other
EngageNY lessons 1-19
Georgia Unit 7
Assessment
Close & Check 8-4; 9-4
Textbook
Lesson 8-4; 9-4
Links
Graphing on Coordinate Plane pg
49-59
Graphing Ordered Pairs
Other
EngageNY lessons 1-19
Georgia Unit 7
Assessment
Close & Check 8-4; 9-4
Recognize that zero is its own opposite
Understand signs of coordinates indicate
locations in quadrants on the coordinate plane.
Recognize that when ordered pairs differ only by
their signs, they indicate points of reflection
across the axes.
Graph integers and rational numbers on a
horizontal or vertical number line.
Unit 3: Rational Numbers
Unit 3 Scope and Sequence: Rational Numbers
Periods
CCSS
6.NS.6c
LS
25
Student Friendly Language
Graph integers and rational numbers on a
coordinate plane.
Resources
Textbook
Lesson 8-4; 9-4
Links
Coordinate Game
Graphing Ordered Pairs
Other
EngageNY lessons 1-19
Georgia Unit 7
Assessment
Close & Check 8-4; 9-4
Textbook
Lesson 8-2; 9-2
Comparing and Ordering integers
6.NS.7a
26
Compare two rational numbers on a number line
using an inequality symbol
Links
Making a Number line
Number line activity
Placing rational Numbers
Other
EngageNY lessons 7-13
Georgia Unit 7
Assessment
Close & Check 8-2; 9-2
Textbook
Lesson9-9
Ordering Decimals on the
Number Line
Making a Number line
6.NS.7b
Grade 6 Curriculum
27
Write, interpret, and explain inequalities (including
negative numbers) in real-world contexts.
Links
Number line activity
Placing rational Numbers on a
Number Line
Other
EngageNY lessons 7-13
Georgia Unit 7
Assessment
Close & Check 9-3
Unit 3: Rational Numbers
6.NS.7c
6.NS.7c
6.NS.7d
6.NS.8
6.NS.8
Grade 6 Curriculum
28
Understand absolute value as the distance
from 0 on a number line.
Textbook
Lesson 8-3
Links
Absolute Value Number Balls Game
Other
EngageNY lessons 7-13
Georgia Unit 7
Assessment
Close & Check 8-3
Textbook
Lesson 8-3
Links
Absolute Value Number Balls Game
Other
EngageNY lessons 7-13
Georgia Unit 7
Assessment
Close & Check 8-3
Textbook
Lesson 8-3
29 Interpret absolute value in real-world contexts.
Use inequalities to compare numbers with their
30 absolute values in real world contexts.
Graph points in all four quadrants to solve real31 world problems.
Use absolute value to find distances between
32 coordinates which have one common coordinate.
Links
Absolute Value Number Balls Game
Abs Value and Order p 85-89
Other
EngageNY lessons 7-13
Georgia Unit 7
Assessment
Close & Check 8-3
Textbook
Lesson 8-4; 9-4
Links
Graphing Ordered Pairs
Other
EngageNY lessons 14-19
Georgia Unit 7
Assessment
Close & Check 8-4; 9-4
Textbook
Lesson 8-5
Links
Abs. Value & Order 2 p 90-95
Other
EngageNY lessons 14-19
Georgia Unit 7
Assessment
Close & Check 8-5
Unit 3: Rational Numbers
Grade 6 Curriculum
Unit 3: Rational Numbers