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Grade 6 Mathematics Module 3, Topic A: Understanding Positive and Negative Numbers on the Number Line

Classroom Resource Information

Title:

Grade 6 Mathematics Module 3, Topic A: Understanding Positive and Negative Numbers on the Number Line

URL:

https://www.engageny.org/resource/grade-6-mathematics-module-3-topic-overview

Content Source:

EngageNY

Type:

Lesson/Unit Plan

Overview:

Module 3, Topic 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 a number is actually the number itself (6.NS.C.6a). They use positive and negative numbers to represent real-world quantities such as -50 to represent a $50 debt or 50 to represent a $50 deposit into a savings account (6.NS.C.5). Topic A concludes with students furthering their understanding of signed numbers to include the rational numbers. Students recognize that finding the opposite of any rational number is the same as finding an integer’s opposite (6.NS.C.6c) and that two rational numbers that lie on the same side of zero will have the same sign, while those that lie on opposites sides of zero will have opposite signs.

Content Standard(s):

Mathematics
MA2015 (2016)
Grade: 6

9 ) 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-NS6]

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. [6-NS6a]

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. [6-NS6b]

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-NS6c]

NAEP Framework

NAEP Statement::
8A2c: Graph or interpret points represented by ordered pairs of numbers on a rectangular coordinate system.

NAEP Statement::
8NPO1d: Write or rename rational numbers.

NAEP Statement::
8NPO1e: Recognize, translate or apply multiple representations of rational numbers (fractions, decimals, and percents) in meaningful contexts.

NAEP Statement::
8NPO1g: Find or model absolute value or apply to problem situations.

NAEP Statement::
8NPO1h: Order or compare rational numbers (fractions, decimals, percents, or integers) using various models and representations (e.g., number line).

NAEP Statement::
8NPO5e: Apply basic properties of operations.

Alabama Alternate Achievement Standards

AAS Standard:
M.AAS.6.9a- Identify positive and negative numbers on a number line.
M.AAS.6.9b- Locate or plot positive and negative numbers on a number line.
M.AAS.6.9c - Find given points between -10 and 10 on both axes of a coordinate plane.

Mathematics
MA2019 (2019)
Grade: 6

10. Locate integers and other rational numbers on a horizontal or vertical line diagram.

a. Define opposites as numbers located on opposite sides of 0 and the same distance from 0 on a number line.

b. Use rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.

Unpacked Content

Evidence Of Student Attainment:

Students:

Create and interpret number line diagram.
Given any rational number (positive or negative).
Locate the number on a number line.
Identify opposite signs of numbers as indicating the same distance from zero on the opposite side of zero, the opposite of the opposite, or a representation of its opposite as the point itself [-(-3) = 3], and zero as its own opposite.

Teacher Vocabulary:

Integers
Rational numbers
Horizontal line diagram
Vertical line diagram

Knowledge:

Students know:

Strategies for creating number line models of rational numbers (marking off equal lengths by estimation or recursive halving).
Strategies for locating numbers on a number line.
Notation for positive and negative numbers and zero.

Skills:

Students are able to:

Represent rational numbers and their opposites on a number line including both positive and negative quantities.
Explain and justify the creation of number lines and placement of rational numbers on a number line.
Explain the meaning of 0 in a variety of real-world contexts.

Understanding:

Students understand that:

Representing rational numbers on number lines requires using both a distance and a direction,
Locating numbers on a number line provides a representation of a mathematical context which aids in visualizing ideas and solving problems.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
M.6.10.1: Define integers, positive and negative numbers.
M.6.10.2: Demonstrate the location of positive and negative numbers on a vertical and horizontal number line.
M.6.10.3: Give examples of positive and negative numbers to represent quantities having opposite directions in real-world contexts.
M.6.10.4: Discuss the measure of centering of 0 in relationship to positive and negative numbers.
M.6.10.5: Discover that the opposite of the opposite of a number is the number itself.
M.6.10.6: Show on a number line that numbers that are equal distance from 0 and on opposite sides of 0 have opposite signs.
M.6.10.7: Define rational number.
M.6.10.8: Plot pairs of integers and/or rational numbers on a coordinate plane.
M.6.10.9: Arrange integers and /or rational numbers on a horizontal or vertical number line.
M.6.10.10: Locate the position of integers and/or rational numbers on a horizontal or vertical number line.
M.6.10.11: Identify a rational number as a point on the number line.
M.6.10.12: Name the pairs of integers and /or rational numbers of a point on a coordinate plane.

Prior Knowledge Skills:

Model writing ordered pairs.
Identify the x- and y- values in ordered pairs.
Label the vertical axis (y).
Label the horizontal axis (x).
Define ordered pair of numbers, quadrant one, coordinate plane, and plot points.
Locate positive numbers on a vertical number line.
Examples: thermometer, map.
Locate positive numbers on a horizontal number line.
Locate negative numbers on a horizontal number line.
Label x- and y-axis and zero on a coordinate.
Illustrate vertical and horizontal number lines.
Specify locations on the coordinate system.
Define x-axis, y-axis, and zero on a coordinate.
Define ordered pair of numbers.
Define parentheses, braces, and brackets.

Alabama Alternate Achievement Standards

AAS Standard:
M.AAS.6.9 Describe quantities with positive and negative numbers (e.g. temperature, sea level, etc.).

Tags:

integers, negative, number line, opposite, positive, rational number, sign

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Comments

There are six lessons in this topic.

This resource is free for teachers to access and use. All resources required for the lessons are available to print from the site.

This resource provided by:

Author:

Hannah Bradley

ALEX Classroom Resource

Grade 6 Mathematics Module 3, Topic A: Understanding Positive and Negative Numbers on the Number Line