New York State Common Core
6
Mathematics Curriculum
GRADE
GRADE 6 • MODULE 3
Topic A
Understanding Positive and Negative
Numbers on the Number Line
6.NS.C.5, 6.NS.C.6a, 6.NS.C.6c
Focus Standards:
6.NS.C.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.C.6a
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.C.6c
Instructional Days:
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.
6
Lesson 1: Positive and Negative Numbers on the Number Line—Opposite Direction and Value (E)1
Lessons 2–3: Real-World Positive and Negative Numbers and Zero (P, E)
Lesson 4: The Opposite of a Number (P)
Lesson 5: The Opposite of a Number’s Opposite (P)
Lesson 6: Rational Numbers on the Number Line (S)
1Lesson
Structure Key: P-Problem Set Lesson, M-Modeling Cycle Lesson, E-Exploration Lesson, S-Socratic Lesson
Topic A:
Understanding Positive and Negative Numbers on the Number Line
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G6-M3-TE-1.3.0-08.2015
10
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Topic A
NYS COMMON CORE MATHEMATICS CURRICULUM
6•3
In Topic A, students apply their understanding of the ordering of whole numbers, positive fractions, and
decimals to extend the number line in the opposite direction (6.NS.C.6 stem). In Lessons 1–3, students use
positive integers to locate negative integers on the number line, moving in the opposite direction from zero,
realizing that zero is its own opposite. They represent real-world situations with integers (6.NS.C.5) and
understand the vocabulary and context related to opposite quantities (e.g., deposit/withdraw, elevation
above/below sea level, debit/credit). Students use precise vocabulary to state, for instance, that −10 would
describe an elevation that is 10 feet below sea level. In Lessons 4 and 5, students focus on locating the
opposite of a number and the opposite of an opposite, using zero and the symmetry of the number line to
build a conceptual understanding (6.NS.C.6a). In Lesson 6, students extend their understanding of integers to
locate signed non-integer rational numbers on the number line (6.NS.C.6c), realizing that finding the opposite
of any rational number is the same as finding an integer’s opposite.
Topic A:
Understanding Positive and Negative Numbers on the Number Line
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G6-M3-TE-1.3.0-08.2015
11
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.