Math Grade 6
The Number System (NS)
Teacher Key
Rational Numbers Part 1
Benchmarks that are Measured in this Quizlet
Benchmark Code
Benchmark
Item #
6.SMC.NS.3.1-1.b
Show that positive and negative numbers are used together to describe
quantities having opposite directions or values
6.SMC.NS.3.1-2.b
Explain the meaning of zero when using positive and negative numbers to
represent quantities in real-world contexts
3, 4
6.SMC.NS.3.2-1.a
Express opposite signs of numbers as indicating locations on opposite sides of
0 on the number line
5, 6
6.SMP.7.c
Look for and make use of structure
1, 2, 7
7
August 2015
MATH GR6 NS QUIZLET 3
Teacher Key
NOTES TO TEACHERS
This series of Quizlets is meant to be used for classroom formative assessment. Different from tools to evaluate student learning
summatively, they are meant to be used by teachers as a part of the instructional process.
Some features of these Quizlets are:
 The Quizlets are fully aligned with the Benchmarks.
 Each Quizlet is has a variety of item types: multiple choice (MC), multiple response (MR), short response (SR) and
performance-based (PB).
 The Quizlets were created using Microsoft® Word so that they can be modified.
 Item stems and graphic organizers can be used to create additional assessments that are aligned to the benchmarks.
Quizlets can be used to identify benchmarks where students are struggling or identify individual students who need additional learning
opportunities.
Item
Teacher Key: Rational Numbers Part 1
Benchmark Code
Benchmark
Correct
Answer
Number
of Points
1.
6.SMC.NS.3.1-1.b
Show that positive and negative numbers are used together to describe
quantities having opposite directions or values
SR
4
2.
6.SMC.NS.3.1-1.b
Show that positive and negative numbers are used together to describe
quantities having opposite directions or values
SR
4
3.
6.SMC.NS.3.1-2.b
Explain the meaning of zero when using positive and negative numbers
to represent quantities in real-world contexts
SR
2
4.
6.SMC.NS.3.1-2.b
Explain the meaning of zero when using positive and negative numbers
to represent quantities in real-world contexts
SR
2
5.
6.SMC.NS.3.2-1.a
Express opposite signs of numbers as indicating locations on opposite
sides of 0 on the number line
A
1
6.
6.SMC.NS.3.2-1.a
Express opposite signs of numbers as indicating locations on opposite
sides of 0 on the number line
SR
4
6.SMC.NS.3.1-1.b
Show that positive and negative numbers are used together to describe
quantities having opposite directions or values
PB
8
7.
6.SMP.7.c
Look for and make use of structure
Page 2
MATH GR6 NS QUIZLET 3
Teacher Key
Explained Answers
SHORT RESPONSE EXPLAINED ANSWERS
ITEM 1. Positive and Negative on a Number Line (4 points)
Benchmark: 6.SMC.NS.3.1-1.b Show that positive and negative numbers are used together to describe quantities having opposite directions or values
Item Stem
Part A Using the number line below, place an X at 3. Place
another X at the point opposite of 3.
Responses
Points
2 points for correct
response
Part B What is the value of the point opposite of 3?
-3
2 points for correct
response
SHORT RESPONSE EXPLAINED ANSWERS
ITEM 2. Positive and Negative on a Number Line (4 points)
Benchmark: 6.SMC.NS.3.1-1.b Show that positive and negative numbers are used together to describe quantities having opposite directions or values
Item Stem
Part A Using the number line below, plot a point 2 units to the
right of 0. Plot another point 2 units to the left of zero. What is
the value of each point?
Responses
Points
2 points for correct
response
Part B What is the value of each point?
-2, 2
2 points for correct
response
SHORT RESPONSE EXPLAINED ANSWERS
ITEM 3. Zero on a Number Line (2 points)
Benchmark: 6.SMC.NS.3.1-2.b Explain the meaning of zero when using positive and negative numbers to represent quantities in real-world contexts
Item Stem
On the number line below, b = -a. What is the value of c?
Responses
c=0
Page 3
Points
2 points for correct
response
MATH GR6 NS QUIZLET 3
Teacher Key
SHORT RESPONSE EXPLAINED ANSWERS
ITEM 4. Fishing Boat (2 points)
Benchmark: 6.SMC.NS.3.1-2.b Explain the meaning of zero when using positive and negative numbers to represent quantities in real-world contexts
Item Stem
Responses
A boy is fishing in a boat. His fishing line is 3 feet below the
surface of the water. His hat is 3 feet above the surface of the
water. If the fishing line is at -3 feet and his hat is at 3 feet,
what could be described as at 0 feet?
The surface of the water is at 0 feet.
Points
2 points for correct
response
SHORT RESPONSE EXPLAINED ANSWERS
ITEM 6. Opposite Signs on Number Line (4 points)
Benchmark: 6.SMC.NS.3.2-1.a Express opposite signs of numbers as indicating locations on opposite sides of 0 on the number line
Item Stem
Part A On the number line below, a = 5. What is the value of
b?
Responses
Part B On the number line above, x = -10. What is the value
of y?
Page 4
Points
b = -5
2 points for correct
response
y = 10
2 points for correct
response
MATH GR6 NS QUIZLET 3
Teacher Key
PERFORMANCE-BASED RUBRIC
ITEM 7. Tractor Pull (8 points)
Benchmark: 6.SMC.NS.3.1-1.b Show that positive and negative numbers are used together to describe quantities having opposite directions or values
Benchmark: 6 SMP.7.c Look for and make use of structure
Item Stem:
Level
Criteria
Tractors often have contests called "Tractor Pulls" (pictured below) to see which
In addition to the understanding in Level 3.0, the student
4.0
tractor has the strongest engine. The tractors pull against one another until one
exhibits in-depth inferences and applications that go
(7-8
tractor is dragged 50 feet.
Points)
beyond what was taught.
3.0
(5-6
Points)
Tractor A
Tractor B
Part A Write an "A" for Tractor A on the number line that shows the beginning of the
Pull. Do the same for Tractor B.
Example:
2.0
Beginning of the Tractor Pull Example
(3-4
Points)
Your Turn:
Beginning of the Tractor Pull
(assume every mark on the line equals 10 feet)
1.0
The two tractors rev their engines and begin pulling. Describe your own Tractor Pull
contest in words including the beginning, middle, and end.
(1-2
Points)
0.0
(0
Points)
Page 5
The student exhibits no major errors or omissions at
sixth grade level by:

6.SMC.NS.3.1-1.b Showing that positive and negative
numbers are used together to describe quantities having
opposite directions or values by showing an
understanding of changing position on the number line.

6 SMP.7.c Looking for and making use of structure by
showing the relationship of the changing positions on a
number line.
The student exhibits major errors or omissions regarding
the more complex ideas and processes, but makes no
major errors or omissions regarding the simpler details
and processes at sixth grade level, including:

6.SMC.NS.3.1-1.b Show that positive and negative
numbers are used together by changing position on the
number line.

6 SMP.7.c Being unclear of the relationship of A and B on
a number line.
With help, the student demonstrates partial
understanding of some of the score 2.0 elements and
some of the score 3.0 elements at the sixth grade level.
Even with help, the student demonstrates little
understanding of skills.
MATH GR6 NS QUIZLET 3
Teacher Key
PERFORMANCE-BASED RUBRIC
ITEM 7. Tractor Pull (8 points) Continued
Benchmark: 6.SMC.NS.3.1-1.b Show that positive and negative numbers are used together to describe quantities having opposite directions or values
Benchmark: 6 SMP 4.c Model with mathematics
Item Stem: Continued
Part B Place A and B on the Halfway and End lines that correspond to your
description of your tractor pull contest.
Half way through the Tractor Pull
End of the Tractor Pull
Possible Responses:
Part A Write an "A" for Tractor A on the number line that shows the beginning of the
Pull. Do the same for Tractor B. The two tractors rev their engines and begin pulling.
Describe your own tractor pull contest in words.
Description of the Tractor Pull (answers will vary)
Tractors A and B begin the contest spinning their wheels. After a few minutes
Tractor A starts to slowly pull Tractor B to the left 20 feet. After another few minutes
of pulling, Tractor A pulls Tractor B 50 feet and wins.
Beginning of the Tractor Pull
Part B Place A and B on the Halfway and End lines that correspond to your
description of your tractor pull contest.
Half way through the Tractor Pull
End of the Tractor Pull
Page 6