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Course: Sixth Grade Math
Unit: Don’t Be Irrational
Unit Length: 6 lessons and a capstone performance task—Fourteen 45-minute class periods
Next Generation Content Standards and Objectives:
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M.6.NS.5 (CCSS.MATH.CONTENT.6.NS.5) Understand that positive and negative numbers are used
together to describe quantities having opposite directions or values; use positive and negative numbers to
represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
M.6.NS.6 (CCSS.MATH.CONTENT.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, 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.
M.6.NS.7 (CCSS.MATH.CONTENT.6.NS.7) Understand ordering and absolute value of a rational number.
a. Interpret statements of inequality as statements about the relative position of two numbers on a number line
diagram.
b. Write, interpret, and explain statements of order for rational numbers in real-world contexts.
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.
d. Distinguish comparisons of absolute value from statements about order.
M.6.NS.8 (CCSS.MATH.CONTENT.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.
Standards for Mathematical Practices:
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Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Driving question: What are rational numbers, and how are they represented in mathematical and real-world
contexts?
Overview
Welcome to the world of rational numbers! Throughout the next six lessons in unit 2, you will be
immersed in the world of rational numbers, opposites, and the coordinate plane. The driving
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questions in this unit are:
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How are positive and negative rational numbers used in everyday scenarios, and what exactly do those
numbers mean?
What are opposite numbers, and how are they plotted on a number line?
How do you know which number is greater on a number line?
How do greater than and less than symbols relate to the position of numbers on a number line?
What does the term absolute value mean?
How do you compare integers using absolute value?
How do you graph points on a coordinate plane?
Can you determine the location of a point based upon the signs of the ordered pair?
How can you compare non-similar coordinates on a coordinate plane to find the distance between points when
one of the coordinates is the same?
How can you recognize the use of absolute value when determining distance between two points?
How are rational numbers used in different mathematical concepts including absolute value, graphing, and
ordering?
What are ways rational numbers are used in everyday scenarios?
In this unit you will learn how to:
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Represent scenarios using rational numbers
Give meaning to those rational numbers
Compare rational numbers with inequalities
Order integers in ascending and descending order
Describe the meaning of zero in a variety of situations
Identify the opposites of rational numbers
Write multiple representations of inequalities
What absolute value is and its relation to distance
Plot points in the coordinate plane
Use the defining characteristics of the four quadrants in a coordinate plane to determine coordinate pair locations
Find distance between points using absolute value
You may be asking yourself, “Why do I need to learn this?” You will use rational numbers almost every day in
your life! The temperature outside, the balance in your bank account, your debt to lenders, when you travel, and
when you fly or climb a mountain are examples of when you’ll use rational numbers!
For example, if you were a pilot you would need to use the coordinate plane and altitude (elevation). When you
fly a plane you start at a specific elevation and must get to your cruising altitude. The pilot will use rational
numbers to determine what this latitude is. They must also successfully get you to your final destination on the
flight. Pilots use coordinate planes in the form of longitude and latitude to find the exact position.
At the end of the unit, you will complete a culminating performance task. During this task, you will apply the
various concepts learned in this unit to find a treasure. Now, your adventure awaits!
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The students will know:
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Vocabulary (noted in individual lessons)
Represent scenarios using rational numbers
Compare rational numbers with inequalities
Order integers in ascending and descending order
Give meaning to rational numbers
The meaning of zero in a variety of situations
Characteristics of opposites
Multiple representations of inequalities
Absolute value and its relation to distance
How to plot points in the coordinate plane
Characteristics of the four quadrants in a coordinate plane
How to find distance between points using absolute value
The students will do:
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Create inequalities that describe relationships
Identify opposites and plot them on a number line
Use rational numbers to represent real-world scenarios
Determine the absolute value of rational numbers
Graph in all four quadrants
Identify reflections across quadrants
Identify locations in a coordinate plane based on signs of ordered pair
Graph numbers on a number line
Use graphing calculators to plot points on a coordinate plane
Organize rational numbers according to their values
Find the distances between two points using absolute value
WVU K12 Partnerships Unit Overview Construction Tool