Hueneme Elementary School District
Grade 6 Mathematics
Unit 1 Outline: The Number System
Chapter 1 of 4
Approximate Length:
7 days
Enduring understanding addressed in this chapter:

NUMBERS: The set of real numbers is infinite, and each real number can be associated with a unique point on the
number line.
Emphasized Mathematical Practices:
2. Reason abstractly and quantitatively.
4. Model with mathematics
5. Use appropriate tools strategically
Priority Standards

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.
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.
Hueneme Elementary School District
Grade 6 Mathematics
Unit 1 Outline: The Number System
Learning Objectives
Students will use a number line to
represent quantities with opposite
directions or values in relation to
real-world contexts.
Students will describe real-world
examples of numbers and their
opposites in relation to zero.
Criteria for Success
Given two numbers with
opposite signs, students will
plot the points on a number
line and explain a real-world
situation that represents the
numbers in relation to zero.
Students will select a pair of
opposites and generate a
real-world scenario
representing the numbers.
Relevant Essential Questions
How/why is a number line useful in showing the
relationship between numbers?
How is (-3) related to (4)?
How are positive and negative numbers related to
real life?
What is the opposite of an opposite?
Hueneme Elementary School District
Grade 6 Mathematics
Unit 1 Outline: The Number System
Chapter 2 of 4
Approximate Length: 9 days
Enduring Understanding addressed in this chapter:

COMPARISON: Numbers and measures can be compared by their relative values.
Emphasized Mathematical Practices:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics
Priority Standards

6.NS.7. 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 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC.

6.EE.8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or
mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions;
represent solutions of such inequalities on number line diagrams.
Hueneme Elementary School District
Grade 6 Mathematics
Unit 1 Outline: The Number System
Learning Objectives
Students will explain the
relationship between two
numbers based on their position
on a number line and within a
real-world context.
Criteria for Success
Given two thermometers, write two
inequality statements to describe
the relationship between the two
thermometers.
Relevant Essential Questions
How is (-10) related to (-30)?
Students will write inequalities to
represent a real-world and/or
mathematical problem.
Given a chart showing the average
depth of many of the world’s
oceans, students will write two
inequality statements to compare
oceans.
How can you use the relative values of numbers to
make comparisons?
Hueneme Elementary School District
Grade 6 Mathematics
Unit 1 Outline: The Number System
Chapter 3 of 4
.
Enduring Understanding(s) addressed in this chapter:
Approximate Length: 9 days

NUMBERS: The set of real numbers is infinite, and each real number can be associated with a unique point on the
number line.

COMPARISON: Numbers and measures can be compared by their relative values.
Emphasized Mathematical Practices:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
5. Use appropriate tools strategically
Priority Standard

6.NS.7. Understand ordering and absolute value of rational numbers.
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.
Hueneme Elementary School District
Grade 6 Mathematics
Unit 1 Outline: The Number System
Learning Objectives
Criteria for Success
Relevant Essential
Questions
Given a set of numbers,
students will identify the
absolute values and provide
proof for their answers
using a number line.
What is absolute value? How
are absolute values of positive
and negative numbers related
to each other?
Given a situation involving
negative numbers (debts,
elevations below sea
level…) students will use
absolute value to interpret
the meaning.
Students will use
Given a listing of debts (as
absolute values to make negative numbers) students
comparisons.
will use absolute value to
determine and explain
which debt is greater.
Why/when is it necessary to
rely on absolute value to
interpret positive and negative
numbers?
Explain absolute value
using a number line.
Use absolute value to
interpret meanings of
rational numbers in realworld situations.
How can absolute value be
used to compare numbers?
Type(s) of assessments
recommended (SR/SCR/PT)
and Possible Instructional
Resources
CR: On the horizontal number
line, plot 7 and -7. What is the
distance of each point from
zero? What is the distance
between 7 and -7? How does
absolute value help you find
the distance between 7 and 7?
SCR
SCR
Hueneme Elementary School District
Grade 6 Mathematics
Unit 1 Outline: The Number System
Chapter 4 of 4
Approximate Length: 10 days
Big Idea(s) addressed in this chapter:

ORIENTATION & LOCATION: Objects in space can be oriented in an infinite number of ways, and an object’s
location in space can be described quantitatively.
Emphasized Mathematical Practices:
4. Model with mathematics
5. Use appropriate tools strategically
Priority Standards

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.
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.

6.G.3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length
of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the
context of solving real-world and mathematical problems
Hueneme Elementary School District
Grade 6 Mathematics
Unit 1 Outline: The Number System
Learning Objectives
Criteria for Success
Students will identify, locate, and
place pairs of integers and rational
numbers on a coordinate plane.
Given a set of coordinates of a
town, students will place points of
interest on a coordinate plane.
Students will explain relationships
between ordered pairs and their
reflections.
Given a list of ordered pairs,
students will locate their reflections
across one or both axes.
Students will use absolute value to
determine the distance between
two points with a common
coordinate.
Students will find distance from one
point of interest to another on same
axis.
Relevant Essential Questions
Why are there four quadrants on a
coordinate plane? How do you
determine in which coordinate an
ordered pair should be placed?
How can you form a reflection with a
given ordered pair?
How can you use absolute value to find
the distance between two ordered pairs?