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
e.g., temperature above/below zero, elevation above/below sea level, debits/credits,
positive/negative electric charge
I Can:
Examples
I can describe quantities
having opposite directions
or values.
Write a positive or negative integer that represents the situation.
1. You withdraw $42 from an account. (-$42)
2. An airplane climbs 37,500 feet. (+37,500)
3. You lose 56 points in a video game. (-56)
I can use positive and
negative numbers to
represent quantities in realworld contexts.
Write an integer to represent each situation. Plot these integers on the number line.
10 degrees above zero (+10)
a loss of 10 dollars (-10)
a gain of 5 points (+5)
8 steps backward (-8)
Vocabulary:
inequality
integers
negative numbers
positive numbers
signed numbers
I can explain the meaning of
0 in each situation.
.
Prerequisites
I know the value of
positive/negative numbers.
(integers)
On a number line, opposites are the same distance from 0 but on different sides of 0.
Zero is its own opposite. Integers are the set of all whole numbers and their opposites.
Resources
Teacher Notes:
http://www.mathplayground.com/ASB_OrbitIntegers.html
http://www.mathplayground.com/ASB_IntegerWarp.html
http://www.mathplayground.com/ASB_SpiderMatchIntegers.html
http://www.mathplayground.com/XDetectives/XDetectives.html
http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson
=m6lessonshell06.swf
http://www.youtube.com/watch?v=vK2vDSqN7is
http://www.bigideasmath.com/protected/content/srh/04/msna_srh_0401_ans.pdf
Page 4
Target Standards
•Identify most important standards
for every subject area.
•Write I can statements for each
standard. (Refer to next page)
•Identify vocabulary, resources,
etc. relevant to each power
standard. (Refer to next page)
Proficiency Scale
Example on Page 4
•Determine what proficiency looks
like for each power standard.
Break down the target into steps
needed to be get to this
proficiency level.
•Create a proficiency scale rubric
that defines the proficiency levels
of each standard.
Assessments
•Create a district level common
summative assessment for each
power standard.
•Create building level common
formative assessments for each
power standard.
•Use assessments to determine
student proficiency levels for
report cards.
Cluster: Apply and extend previous understandings of numbers to the
system of rational numbers.
Code
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, debits/credits, positive/negative electric
charge); use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation.
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.
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.
Understand ordering and absolute value of rational numbers.
6.NS.6
6.NS.7
a.
Interpret statements of inequality as statements about the relative
position of two numbers on a number line diagram.
Page 3
Content:
Standard:
Grade Level:
I can statements:
Score
4.0
In addition to Score 3.0, in-depth inferences and applications that go beyond
what was taught.
3.5
Score
3.0
Sample Activities
In addition to score 3.0 performance, in-depth inferences and applications with
partial success.
The student:


The student exhibits no major errors or omissions.
2.5
Score
2.0
No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0
content.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 recognizes or recalls specific terminology, such as:
o
 performs basic processes, such as:
o

However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
1.5
Score 1.0
Score 0.0
Partial knowledge of the 2.0 content, but major errors or omissions regarding the 3.0
content.
With help, a partial understanding of some of the simpler details and processes and some of
the more complex ideas and processes.
0.5
With help, a partial understanding of the 2.0 content, but not the 3.0 content.
Even with help, no understanding or skill demonstrated.
Page 5
This is a sample of a proficiency scale – taken from:
publicportal.lwsd.org/.../Pre-Algebra%20Proficiency%20Scales.docx
Proficiency Scales | CMP 7
Power Standard 1: Students demonstrate conceptual understanding of addition, subtraction, multiplication
and division of positive and negative integers by explaining these procedures using chip models and
number lines.
Proficiency Scale
Score Descriptor
Complex content and thinking about content (not new content), including deeper, more conceptual applications that
include in-depth inferences that go beyond what was explicitly taught in class.

4
Exceeds
Standard




Creates a multi-step word problem using integers then models the solution using a
number line or chips.
Relates integers to a real-world situation not encountered in class.
Compares and contrasts the chip and number line models.
Explains the limitations of the chip and number line models to model certain
operations with integers.
Justifies algorithms for operations with integers using fact families, chip models,
and line models.
The standard/learning target: content, concepts, and/or processes/skills (simple or complex) which were explicitly
taught in class.
Students demonstrate conceptual understanding of addition, subtraction, multiplication
and division of positive and negative integers by explaining these procedures using chip
models and number lines.
 Models addition and subtraction of integers using red and black chips.
3
At Standard


Example: -4 – 6
Start with 4 red chips. To take away 6 black chips, you
need to put “zero pairs” on the board until there are 6 black chips to take
away. End with 10 red chips.
Compares, orders, and locates integers on a number line.
Models addition and subtraction of integers using a number line.
Example: -4 – 6
Start at -4 and move left 6 to end at -10.
 Uses fact families to explain the rules for adding and subtracting integers.
Uses the chip model and/or number line to solve word problems involving operations with
integers.
Simpler content, details, procedures and processes, including foundational knowledge and vocabulary/concepts, which
were explicitly taught in class.
2
Approaching
Standard





1
Not At
Standard
Recalls that opposites (additive inverses) sum to zero.
Recalls that red chips represent negative integers and black chips represent
positive integers.
Recalls that numbers on a number line to the left of zero are negative and
numbers to the right of zero are positive.
Uses appropriate notation to indicate positive and negative numbers.
Writes down fact families for the addition and subtraction of integers.
With help, partial understanding of some of the simpler and complex details and processes.
With help, student can perform score 2.0 and 3.0 expectations.
EXCELLENT examples of proficiency scales for ALL content areas can be found at:
http://www.marzanoresearch.com/free_resources/itembank.aspx. Registration is required, but it is free and simple.
Math examples - http://www.docstoc.com/docs/109548774/Pre-Algebra-Proficiency-Scales
History examples - https://sites.google.com/a/linnmar.k12.ia.us/mrnietert/home/proficiency-scale
ELA examples - http://www.michigan.gov/documents/mde/2-ELA_Linking_Document_7.18.09.docGJMedit_335003_7.pdf
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