Unit 4 Operations with Integers, 6th Grade
5E Lesson Plan Math
Grade Level: 6
Lesson Title: Operations with Integers
Subject Area: Math
Unit Number: 4
Lesson Length:10 days
Lesson Overview
This unit bundles student expectations that address identifying a number, its opposite, and its
absolute value, and representing and modeling integer operations fluently, including
standardized algorithms. According to the Texas Education Agency, mathematical process
standards including application, a problem-solving model, tools and techniques,
communication, representations, relationships, and justifications should be integrated (when
applicable) with content knowledge and skills so that students are prepared to use
mathematics in everyday life, society, and the workplace.
During this unit, students examine number relationships involving identifying a number, its
opposite, and absolute value. Previous work with number lines transitions to the understanding
that absolute value can be represented on a number line as the distance a number is from
zero. This builds to the relationship that since distance is always a positive value or zero, then
absolute value is always a positive value or zero. Although students have been introduced to
the concept of integers, this is the first time students are exposed to operations with negative
whole numbers, which is a subset of integers. The development of integer operations with
concrete and pictorial models is foundational to student understanding of operations with
integers. Forgoing the use of concrete and pictorial models as a development of integer
operations could be detrimental to future success with computations involving negative
quantities, such as negative fractions and decimals. The use of concrete and pictorial models
for integer operations is intended to be a bridge between the abstract concept of operations
with integers and their standardized algorithms. It is expected that once the concept of integer
operations has been sufficiently developed and connected to the standardized algorithms,
students should add, subtract, multiply, and divide integers fluently.
Unit Objectives:
Students will…
 Be able to identify a number, its opposite, and its absolute value
 Be able to represent and model integer operations fluently, including standard
algorithms
Standards addressed:
TEKS:
6.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
6.1B Use a problem-solving model that incorporates analyzing given information, formulating
a plan or strategy, determining a solution, justifying the solution, and evaluating the
problem-solving process and the reasonableness of the solution.
6.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems.
6.1D Communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate.
6.1E Create and use representations to organize, record, and communicate mathematical
1
Unit 4 Operations with Integers, 6th Grade
ideas.
6.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
6.1G Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
6.2B Identify a number, its opposite, and its absolute value.
6.3C Represent integer operations with concrete models and connect the actions with the
models to standardized algorithms.
6.3D Add, subtract, multiply, and divide integers fluently.
ELPS
c.1E internalize new basic and academic language by using and reusing it in meaningful
ways in speaking and writing activities that build concept and language attainment
c.3B expand and internalize initial English vocabulary by learning and using high-frequency
English words necessary for identifying and describing people, places, and objects, by
retelling simple stories and basic information represented or supported by pictures, and
by learning and using routine language needed for classroom communication
c.5F write using a variety of grade-appropriate sentence lengths, patterns, and connecting
words to combine phrases, clauses, and sentences in increasingly accurate ways as
more English is acquired
Misconceptions:
 Some students may think the absolute value is the opposite of a number rather than the
distance of the number away from zero (e.g. A student may think that the absolute
value for 5 is -5, but -5 is actually the opposite.)
 Some students may forget to attach the sign of the integers to the sum or difference
when adding or subtracting integers.
 Some students may have difficulty rewriting subtraction problems involving integers as
the addition of an opposite.
 Some students may think that subtracting a negative integer from a negative integer
always results in a difference of a negative integer.
 Some students may think that multiplying a negative integer by a negative integer
results in a product that is negative.
 Some students may think that dividing a negative integer by a negative integer results
in a quotient that is negative.
Vocabulary:
 Absolute value – the distance of a value from zero on a number line
 Fluency– efficient application of procedures with accuracy
 Integers- the set of counting (natural numbers), their opposites, and zero
{-n, …, -3, -2, -1, 0, 1, 2, 3, ..., n}. The set of integers is denoted by the symbol Z.
List of Materials:
Day 1
 Example of Fahrenheit thermometer
 Handout: Whose Side Are You On?
 Post-it notes
 Large Number Line
2

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
Day 2

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

Unit 4 Operations with Integers, 6th Grade
Quart Plastic Bags
Video: http://studyjams.scholastic.com/studyjams/jams/math/numbers/integers.htm
Frayer Model
I Have Who Has Cards
Handout: Identifying Integers and Absolute Value
Display: How Cold Is It?
Handouts: Line Dance 1-4
http://blog.aimsedu.org/conferences/?conf=CAMTEricksonIntegers
Small Number Lines

Day 3
 Two Color Counters
 Handout: Adding Integers Two Color Counters
 Handout: Subtracting Integers Two Color Counters
Day 4
 Handout: Adding Integers Number Line
 Handout: Subtracting Integers Number Line
Day 5
 http://everybodyisageniusblog.blogspot.com/2012/07/integer-foldable.html
Day 5/6
 Handout: Adding and Subtracting Integers Practice
 Grab A Charge Activity
 Zip, Zilch, Zero Recording Sheet & Rules
Day 7
 Two Color Counters
 Handout: Multiplying and Dividing Integers
Day 8
 Video: https://www.youtube.com/watch?v=QMst5BcgHhQ
 Handout: Multiplying and Dividing Integers Problem Solving
 Speed Integer Set (set 1) PowerPoint
Day 9
 Handout: Student Recording & Integer Unit Review Scavenger Hunt Questions
http://campuses.fortbendisd.com/campuses/documents/Teacher/2012%5Cteacher_201
21107_1438.pdf
INSTRUCTIONAL SEQUENCE
Phase One: Engage the Learner
Identifying Integers & Absolute Value
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Unit 4 Operations with Integers, 6th Grade
Day 1 Materials:
 Example of Fahrenheit thermometer
 Handout: Whose Side Are You On?
 Post-it notes
 Large Number Line
 Quart Plastic Bags
 Video: http://studyjams.scholastic.com/studyjams/jams/math/numbers/integers.htm
 Frayer Model
Day 1 Activity #1:
Look up today’s temperature and locate it on a Fahrenheit thermometer. Hold a class
discussion about how to locate numbers on the thermometer.
What’s the teacher doing?
Development/Procedures:
The teacher begins by presenting a
Fahrenheit thermometer to the class
and asking a question:
“What is the temperature today?
How many degrees above zero is
that? What is the temperature on
a hot, sunny day?”
Have the student point out the degree
on the thermometer.
“What might the temperature be
on a snowy day? Have you ever
experienced a temperature that is
below zero?”
Next, ask them what it means for the
temperature to be 10 degrees below
zero and show where this is on the
thermometer. Explain that you would
use a negative sign to write this number
since it is below zero. Next, ask them
where 15 degrees below zero would be
on the thermometer, and then ask them
whether it is hotter or colder than 10
degrees below zero. Since 15 degrees
below zero is colder (or has less
temperature) than 10 degrees below
zero, negative 15 is less than negative
10. Show students how to write
negative numbers (ex: -10,-15).
What are the students doing?
Students are participating in class discussion.
4
Unit 4 Operations with Integers, 6th Grade
Phase Two: Explore the Concept
Identifying Integers & Absolute Value
Day 1 Activity #2:
Divide students into partners. Give each group a baggie of sentence strips. Direct the
students to look through their bag and make a pile of situations that would represent positive
numbers and a separate pile that would represent negative values.
The teacher will then facilitate a class discussion and get each group to explain why they put
their sentence strips in the column that they placed them in. Some focus questions may be:
What words were key words in the situation in making your decisions? (increasing,
below, etc) What characteristics are found in the positive column? (gain, above, etc)
What characteristics are found in the negative column? (decreasing, loss, etc)
The teacher will then read aloud the situations from the sentence strips. For each situation the
teacher will select a group to identify the integer that would represent the situation (for
example a loss of 2 yards = -2). The teacher will then ask that group to write the integer for
each situation on a post-it note and then graph on a number line in front of the class. Some
questions may be: How did you know that number went to the left of zero? (it was
negative) How far away is that number from zero? (answers will vary)
What’s the teacher doing?
What are the student’s doing?
The teacher will cut apart each
sentence from “Whose Side Are You
On?” and place into baggies ahead of
time.
The teacher will pass out baggies to
each group of students.
The students are working with their partner to sort
the sentence strips into two piles. The students
listen as each group writes an integer to represent
each situation and graph the integer on a class
number line.
The teacher will create a T-table with
the headings “positive numbers” and
“negative numbers”. The teacher will
ask each group to identify the words
from each sentence that helped them
determine whether it went into the
positive pile or negative pile. The
teacher will record these words (ex:
loss, deduction, above) into the
appropriate column in the table.
Then the teacher will ask students to
write an integer to represent each
situation on sticky notes. Students will
graph the sticky notes on a large
number line in the displayed in the
class.
The teacher will ask guiding questions.
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Unit 4 Operations with Integers, 6th Grade
Phase Three: Explain the Concept
Identifying Integers & Absolute Value
and Define Key Terms.
Day 1 Activity #3:
Watch http://studyjams.scholastic.com/studyjams/jams/math/numbers/integers.htm and define
the vocabulary words: integer and absolute value on the Frayer model.
To close the activity, ask students to turn to their partner and answer the following questions:
What makes an integer positive or negative? (if it is more or less than zero) How are
positive and negative integers used in real life situations? (represent gains, losses of
yards in football, withdraws or deposits in money, etc)
What’s the teacher doing?
What are the students doing?
The teacher monitors students to make
sure they are actively listening to the
video.
The students watch the video and complete the
Frayer models for two vocabulary words: integer
and absolute value.
Absolute value distance of a value from
zero on a number line
Integers- counting numbers (natural
numbers), their opposites, and zero.
The set of integers is denoted by the
symbol Z.
Phase Four: Elaborate on the
Identifying Integers & Absolute Value
Concept
Day 2 Materials:
 I Have Who Has Cards
 Handout: Identifying Integers and Absolute Value
 Display: How Cold Is It?
 Handouts: Line Dance 1-4
http://blog.aimsedu.org/conferences/?conf=CAMTEricksonIntegers
 Small Number Lines
Day 2 Activity #1:
Play a round of I Have, Who Has with the class to practice concepts from Day 1. Instruct
students to complete the Handout: Identifying Integers and Absolute Value.
6
Unit 4 Operations with Integers, 6th Grade
What’s the teacher doing?
What are the students doing?
The teacher will cut out the I Have Who
Has cards before class. Pass out one
card to each student. The student who
is holding a card with an asterisk (*) will
begin by reading the Who has… from
their card. The teacher will monitor the
card activity to make sure students are
answering correctly.
Students will participate in I Have Who Has activity.
They will also complete the handout.
The teacher will pass out the handout:
Identifying Integers and Absolute
Value for students to complete.
Phase One: Engage the Learner
Adding& Subtracting Integers
Day 2 Activity #2:
Display How Cold Is It? to the class.
What’s the teacher doing?
What are the students doing?
Display the problem How Cold Is It?
Ask students to answer the question.
Ask students to share their solution
strategies.
Guiding Questions:
How did you solve this problem?
Did you use a tool to help you solve
this problem? Or, is there a tool you
could have used to help you with this
problem? (number line, thermometer)
Students work the problem displayed and actively
participate in the discussion of the problem.
Phase Two: Explore the Concept
Adding and Subtracting Integers
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Unit 4 Operations with Integers, 6th Grade
Day 2 Activity #3:
Instruct students to participate in the Line Dance Activity. (see directions)
What’s the teacher doing?
What are the students doing?
The teacher has created a large number
line on the floor. The teacher has also
created smaller number lines for
students to place on their desks or in
their math journals (see Line Dance
Resource)http://blog.aimsedu.org/confer
ences/?conf=CAMTEricksonIntegers
Students listen to the directions called out by the
teacher and move the corresponding number of
steps forward and backwards. They record their
moves and solutions on their handouts.
Phase Three: Explain the Concept
and Define Key Terms
Adding and Subtracting Integers
Day 3 Materials:
 Two Color Counters
 Handout: Adding Integers Two Color Counters
 Handout: Subtracting Integers Two Color Counters
Day 3 Activity #1:
Handouts: Adding Integers Two Color Counters and Subtracting Integers Two Color
Counters
What is the teacher doing?
What are the students doing?
Instructional Procedures:
Students use two-color counters to explore the
1. Place students in pairs and distribute relationship of adding and subtracting integers.
20 two-color counters to each
student.
2. Display the expression 1 + (−1) for
the class to see. Instruct students to
lay 1 two-color counter on yellow
and another two-color counter on
red. Explain to students that the
yellow side of the two-color counters
will be used to represent the integer
1, while the red side of the two-color
counters will be used to represent
the integer (−1). Facilitate a class
8
Unit 4 Operations with Integers, 6th Grade
discussion to define the term “zero
pairs”.
Ask:
 How would you model 1 + (−1)
using two-color counters?(use
1 yellow and 1 red)
 What would be a real life
example of 1 + (−1)?Answers
may vary. I made 1 point and I
lost 1 point, so, I have 0 points;
etc.
Explain to students that 1 + (−1)
is called a “zero pair.”
 Why do you think 1 + (−1) is
called a zero pair? Answers
may vary. A number and its
opposite that combine to a value
of zero; etc.
 What is the sum of the counter
set of 1 and (−1)? (1 + (−1) = 0)
1
+
–1
=
0
3. Distribute handout: Adding Integers
Two-Color Counters to each
student. Instruct student pairs to
model the addition problems with
two-color counters, create a sketch
of the model with pictures of the twocolor counters or ( –) and (+), and
record each solution process in their
handout. Allow time for student pairs
to complete the addition problems.
Monitor and assess student pairs to
check for understanding. Facilitate a
class discussion to debrief student
solutions.
4. Display the expression (−4) + (−3)
for the class to see.
Ask:
 How would you model the
expression (−4) + (−3) with
two-color counters?(I would
place 4 negative counters and 3
negative counters on the integer
mat for a total of 7 negative
counters.)
9
Unit 4 Operations with Integers, 6th Grade
(−4) + (−3) = (−7)

How is the expression 8 – 4
different from the problems
you have been modeling?
Answers may vary. I am now
subtracting instead of adding;
etc.
 How would you model the
expression 8 – 4 with two-color
counters?(I would place 8
positive counters on the integer
mat and then remove 4 positive
counters leaving 4 positive
counters.)
5. Display the expression 7 – 8 for the
class to see. Facilitate a class
discussion about subtracting
integers.
Ask:
 How would you begin to model
the expression 7 ─ 8 with twocolor counters? (Place 7
positive counters on the integer
mat.)
 What does “subtract 8”
mean?(remove 8 positive
counters)
 How do you model removing 8
positive counters when you
only have 7 positive counters?
Explain. Answers may vary. I will
have to create a zero pair and
then I will have 8 positive
counters to remove; etc.
10
Unit 4 Operations with Integers, 6th Grade
7 − 8 = (−1)

What remains when the 8
positive counters are removed
from the integer mat? (1
negative counter)
 What integer value is
remaining on the integer mat?
((−1))
6. Distribute handout: Subtracting
Integers Two-Color Counters to
each student.
7. Display the expression (−6) ─ (−4)
for the class to see. Facilitate a class
discussion about subtracting
negative integers. Instruct students
to model the subtraction problems
with two-color counters, create a
sketch of the model with pictures of
the two-color counters or ( – ) and
(+), and record each solution
process on their handout:
Subtracting Integers Two-Color
Counters throughout the discussion.
Ask:
 How would you begin to model
the expression (−6) ─ (−4) with
two-color counters? (Place 6
negative counters on the integer
mat.)
Explain to students that “subtract
negative 4” means “the opposite of
removing negative 4” and that the
opposite of removing negative 4 is
adding positive 4.
Ask:
 If you have 6 negative
counters and you add 4
positive counters, how many
zero pairs are created? (4 zero
pairs)
 What remains when the zero
pairs are removed from the
integer mat? (2 negative
counters)
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Unit 4 Operations with Integers, 6th Grade
 What integer value is
remaining on the integer mat?
((−2))
 What addition equation can be
created using 6 negatives that
would yield the same solution
as (−6) ─ (−4)? ((−6) + 4 =(−2))
 How are these problems
similar? Different? Answers
may vary. Both have negative 6.
The second integers in each
problem are opposites, and one
problem has a subtraction
symbol and the other problem
has an addition symbol; etc.
 Why do both (−6) – (−4) and
(−6) + 4 equal (−2)? Answers
may vary. Both expressions
equal (−2) because subtracting
negative 4 from negative 6 is
read as the opposite of removing
negative 4 from negative 6. The
opposite of removing negative 4
is adding positive 4; etc.
8. Display the expression (−7) ─ (−4)
for the class to see.
Ask:
 How would you begin to model
the expression (−7) ─ (−4) with
two-color counters? (Place 7
negative counters on the integer
mat.)
 What does “subtract negative
4” mean?(the opposite of
removing 4 negative counters)
 What is the opposite of
removing 4 negative counters?
(adding 4 positive counters)
 If you have 7 negative
counters and you add 4
positive counters, how many
zero pairs are created? (4 zero
pairs)
 What remains when the zero
pairs are removed from the
integer mat? (3 negative
counters)
 What integer value is
12
Unit 4 Operations with Integers, 6th Grade
remaining on the integer mat?
((−3))
 What addition equation can be
created using 7 negatives that
would yield the same solution
as (−7) ─ (−4)? ((−7) + 4 = (−3))
 How are these problems
similar? Different? Answers
may vary. Both have negative 7.
The second integers in each
problem are opposites, and one
problem has a subtraction
symbol and the other problem
has an addition symbol; etc.
 Why do both (−7) – (−4) and
(−7) + 4 equal (−2)? Answers
may vary. Both expressions
equal (−2) because subtracting
negative 4 from negative 7 is
read as the opposite of removing
negative 4 from negative 7. The
opposite of removing negative 4
is adding positive 4; etc.
9. Display the expression 7 ─ (−4) for
the class to see.
Ask:
 How is this problem different
from the expression you just
modeled? (The first number is
positive 7 instead of (−7).)
 How would you begin to model
the expression 7 ─ (−4) with
two-color counters? (Place 7
positive counters on the integer
mat.)
 What does “subtract negative
4” mean?(the opposite of
removing 4 negative counters)
 What is the opposite of
removing 4 negative counters?
(adding 4 positive counters)
 If you have 7 positive counters
and you add 4 positive
counters, how many zero pairs
are created? (0 zero pairs)
 What is on the integer mat
when you add 4 positive
counters to the 7 positive
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Unit 4 Operations with Integers, 6th Grade
counters? (11 positive counters)
 What integer value is
remaining on the integer mat?
(11)
 What addition equation can be
created using 7 positives that
would yield the same solution
as 7 ─ (−4)? (7 + 4 = 11)
 How are these problems
similar? Different? Answers
may vary. Both have positive 7.
The second integers in each
problem are opposites, and one
problem has a subtraction
symbol and the other problem
has an addition symbol; etc.
 Why do both 7 ─ (−4) and 7 + 4
equal 11? Answers may vary.
Both expressions equal 11
because subtracting the opposite
of negative 4 from positive 7 is
read as the opposite of removing
negative 4 from positive 7. The
opposite of removing negative 4
is adding positive 4; etc.
10. Display the expression (−8) ─ 2 for
the class to see.
11. Instruct students to individually
evaluate the expression by modeling
the solution process with two-color
counters, creating a pictorial record
of the process, and recording the
symbolic mathematical
representation for each step in the
process in their math journal.
Monitor and assess students to
check for understanding. Facilitate a
class discussion to summarize
subtracting integers with two-color
counters using the problem (−8) ─ 2.
Ask:
 How would you begin to model
the expression (−8) ─ 2 with
two-color counters? (Place
8negative counters on the integer
mat.)
 What does “subtract 2”
mean?(remove2positive
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Unit 4 Operations with Integers, 6th Grade



counters)
How would you model
removing 2 positive counters
when you only have 8negative
counters? Explain. Answers
may vary. I will have to create 2
zero pairs, and then I will have 2
positive counters to remove; etc.
What remains when the 2
positive counters are removed
from the integer mat? (10
negative counters)
What integer value is
remaining on the integer mat?
((−10))
Phase Three: Explain the Concept
Adding and Subtracting Integers
Day 4 Materials:
 Handout: Adding Integers Number Line
 Handout: Subtracting Integers Number Line
Day 4 Activity #1:
Handouts: Adding Integers Number Line and Subtracting Integers Number Line
What’s the teacher doing?
What are the students doing?
Ask:
 How would you model the
expression (−4) + (−3) using a
number line?(Begin at 0 and
move in the direction of the sign
of the integer in front of the
addition symbol, (−4), then move
in the direction of the sign of the
integer following the addition
symbol, (−3).)
(–3)
Students use a number line to explore the
relationship of adding and subtracting integers.
(– 4)
– 7 – 6 – 5 – 4 – 3 – 2 –1
0
1
2
3
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Unit 4 Operations with Integers, 6th Grade
1. Facilitate a class discussion about
the generalization for adding
integers on a number line.
Ask:
 When adding integers on a
number line, which direction
would you move? (Begin at 0
and move in the direction of the
sign of the integer in front of the
addition symbol, then move in
the direction of the sign of the
integer following the addition
symbol.)
2. Distribute handout: Subtracting
Integers Number Line to each
student. Demonstrate the solution
process for the first 2 problems.
Instruct students to replicate the
model throughout the demonstration.
Facilitate a class discussion about
the solution process.
Ask:
 What relationship exists
between addition and
subtraction? (They are opposite
operations.)
 When you encountered the
addition symbol to model
adding integers on a number
line, you began at 0 and first
moved in the direction of the
integer in front of the addition
symbol and then moved in the
direction of the integer
following the addition symbol.
What do you think you would
do when you encounter the
subtraction symbol to model
subtracting integers on a
number line? (I will begin at 0
and move in the direction of the
sign of the integer before the
subtraction symbol, and then I
will move in the opposite
direction of the sign of the integer
following the subtraction symbol.)
 How would you model the
expression (−5) ─ (−3) using a
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Unit 4 Operations with Integers, 6th Grade
number line?(Step 1: Begin at 0
and move in the direction of the
sign of the integer that is in front
of the subtraction symbol, (−5).
(–5)
–7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6
7
5
6
7
6
7
Step 2: Begin at (−5) and
move in the opposite direction
of the sign of the integer
following the subtraction
symbol, (−3) move in a
positive direction 3 units.
Move in the opposite
direction of (–3) .
(–5)
– 7 – 6 – 5 – 4 – 3 – 2 –1
0
1
2
3
4
Step 3: The non-overlapping
section of the rays is the
difference between both
integers. The number line
model for the expression (−5)
─ (−3) is the same as the
number line model for the
expression (−5) + 3.)
The non-overlapping
section is (– 2) .
– 7 – 6 – 5 – 4 – 3 – 2 –1
0
1
2
3
4
5

What addition equation can be
created using 5 negatives that
would yield the same solution
as (−5) ─ (−3) = (−2)? ((−5) + 3 =
(−2))
3. Display the expression 4 ─ 7 for the
class to see.
Ask:
 How would you model the
expression 4 ─7 using a
number line? (Step 1: Begin at 0
and move in the direction of the
17
Unit 4 Operations with Integers, 6th Grade
sign of the integer that is in front
of the subtraction symbol, 4.
4
–7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6
7
Step 2: Begin at 4 and move
in the opposite direction of the
sign of the integer following
the subtraction symbol, 7
move in a negative direction 7
units.
Move in the opposite
direction of positive 7.
4
–7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6
7
Step 3: The non-overlapping
section of the rays is the
difference between both
integers. The number line
model for the expression 4 ─
7 is the same as the number
line model for the expression
4 + (−7).)
The non-overlapping
section is (–3) .
–7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6
7

What addition equation can be
created using 4 positive that
would yield the same solution
as4 ─ 7 = (−3)? (4 + (−7) = (−3))
4. Instruct student pairs to complete
the remainder of handout:
Subtracting Integers Number
Lines. Allow time for students to
complete the number lines. Monitor
and assess student pairs to check
for understanding. Facilitate a class
discussion to debrief student
solutions.
5. Facilitate a class discussion about
the generalization for subtracting
18
Unit 4 Operations with Integers, 6th Grade
integers on a number line.
Ask:
When subtracting integers on a
number line, which direction would
you move?(Begin at 0 and move in the
direction of the sign of the integer in
front of the subtraction symbol, then
move in the opposite direction of the
sign of the integer following the
subtraction symbol.)
Phase Four: Elaborate on the
Adding and Subtracting Integers
Concept
Day 5 Materials:
 http://everybodyisageniusblog.blogspot.com/2012/07/integer-foldable.html
Day 5 Activity #1:
Folding Notes activity to summarize the discoveries of rules for adding and subtracting
integers.
http://everybodyisageniusblog.blogspot.com/2012/07/integer-foldable.html
What is the teacher doing?
Ask:
 When integers with the same
sign are added, what
inferences can you make?
Answers may vary. I ended up
combining sets, so the sum has
the same sign as the integers;
etc.
 Does this pattern always
work? Explain your reasoning.
(Yes) Answers may vary. There
will be no zero pairs if the signs
are the same; on the number
line, if the directions from zero
are the same the sum will be the
same direction from zero; etc.
 When integers with different
What are the students doing?
Creating folding notes over adding and subtracting
integers.
19
Unit 4 Operations with Integers, 6th Grade
signs are added, what
inferences can you make?
Answers may vary. When
integers having different signs
are added, sets of zero pairs are
produced. The sign of the sum
depends on which integer has
more two-color counters; when
integers having different signs
are added on the number line,
there will always be portions of
the number line that show both
directions, (−) and (+). This
corresponds to the same
distance from zero in a positive
and negative direction; the sign
of the sum depends on which
integer is the farthest from zero,
and in which direction; etc.
 When a number and its
opposite are added, what do
you notice? Why do you think
this happens? What did you
call these numbers? (The sum
is 0.) Answers may vary. Both
numbers are equal distances
from 0 and have opposite signs;
these numbers are opposites and
form a set of zero pairs; etc.
1. Facilitate a class discussion about
the patterns for subtracting integers.
Ask:
 When integers with the same
sign are subtracted, what
inferences can you make?
Answers may vary. When
integers having the same signs
are subtracted, add the opposite
and then follow the addition
rules; etc.
 When integers with different
signs are subtracted, what
inferences can you make?
Answers may vary. When
integers having different signs
are subtracted, add the opposite
of the second number and follow
the addition rules; etc.
20
Unit 4 Operations with Integers, 6th Grade
Phase Four: Elaborate on the
Adding and Subtracting Integers
Concept
Day 5/6 Materials:
 Handout: Adding and Subtracting Integers Practice
 Grab A Charge Activity
 Zip, Zilch, Zero Recording Sheet & Rules
Day 5 Activity #2/ Continue on Day 6:
Station A: Addition and Subtraction Integer Practice
Station B: Zip, Zilch, Zero Activity
Station C: Grab A Charge Activity
What’s the teacher doing?
What are the student’s doing?
The teacher prepares stations ahead of
time. Students will rotate through the
stations completing the tasks assigned.
The teacher will monitor students and
provide corrective feedback.
Phase One: Engage the Learner
Completing Station Activities.
Multiplying and Dividing Integers
Day 7 Materials:
 Two Color Counters
 Handout: Multiplying and Dividing Integers
Day 7 Activity #1:
Class discussion using two color counters.
21
Unit 4 Operations with Integers, 6th Grade
What is the teacher doing?
1.
What are the students doing?
Distribute 20 two-color counters to
each student and display the
following model for the class to see.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Using two color counters to model expressions.
Students will also participate in class discussion.
OR
Facilitate a class discussion about
using two-color counters to model
multiplication problems.Instruct
students to replicate the model with
two-color counters, create a sketch
of the model with pictures of the twocolor counters or (–) and (+), and
record an equation to represent the
model in their math journal.
Ask:
 What equation(s)would you
record to represent this
model? (2 + 2 + 2 + 2 = 8 or 4(2)
= 8)
 What does the equation 4(2) =
8 mean? (There are 4 groups
with 2 positive counters in each
group and the product is 8. If I
count the counters by groups,
there would be 2, 4, 6, 8.)
3. Display the following model for the
class to see:
2.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
OR
Ask:
 What equation(s) would you
record to represent this
model? (4 + 4 = 8 or 2(4) = 8)
22
Unit 4 Operations with Integers, 6th Grade
 What does the equation2(4) = 8
mean? (There are 2 groups with
4positive counters in each group
and the product is 8. If I count the
counters by groups, there would
be 4, 8.)
4. Display the following expressions for
the class to see: 4(2) and 2(4).
Ask:
 How are the expressions 4(2)
and 2(4) related? Answers may
vary. Both have the same factors
and the same product; the
factors switched positions, and
due to commutative property of
multiplication the products are
the same; etc.
5. Display the following model for the
class to see:
– –
– –
– –
OR
–
–
–
–
–
–
–
–
– –
Ask:
 What equation(s)would you
record to represent this
model? ((−2) + (−2) + (−2) + (−2)
= (−8) or 4(−2) = (−8)).
 What does the equation 4(−2) =
(−8) mean? (There are 4 groups
with 2 negative counters in each
group and the product is (−8). If I
count the counters by groups,
there would be (−2), (−4), (−6),
(−8).)
6. Display the following model for the
class to see:
– –
– –
– –
OR
–
–
–
–
–
–
–
–
– –
23
Unit 4 Operations with Integers, 6th Grade
Ask:
 What equation(s) would you
record to represent this
model? ((−4) + (−4) = (−8) or
2(−4) = (−8))
 What does the equation2(−4) =
(−8) mean? (There are 2 groups
with 4 negative counters in each
group and the product is (−8). If I
count the counters by groups,
there would be (−4), (−8).)
7. Display the following expressions for
the class to see: 4(−2) and 2(−4).
Explain to students that although
one factor is positive and one factor
is negative, the commutative
property of multiplication still applies
because the expressions 4(−2) and
2(−4) both equal (−8).
8. Display the following model for the
class to see:
+
+
– –
+
+
– –
+
+
– –
+
+
– –
Explain to students that this model
represents taking the opposite of 4
groups with 2 positive counters in
each group and can be represented
with the expression (−4)2. Remind
students that the opposite of a
positive is a negative.
( − 4 )( 2 )
The opposite of
4 groups of positive 2.
Ask:
 What equation represents the
opposite of 4 groups with 2
positive counters in each
24
Unit 4 Operations with Integers, 6th Grade
group? ((−4)2 = (−8))
9. Display the following model for the
class to see:
+
+
– –
+
+
– –
+
+
– –
+
+
– –
Explain to students that this model
represents the opposite of 2 groups
with 4 positive counters in each
group, which becomes 2 groups with
4 negative counters in each.
Ask:
 What equation(s) would you
record to represent this
model? ((−2)4 = (−8))
10. Display the following expressions for
the class to see: (−4)2 and (−2)4.
Ask:
 How are the expressions (−4)2
and (−2)4 related? Answers may
vary. Both have the same the
same product; etc.
11. Facilitate a class discussion about
multiplying two negative integers.
Ask:
 How would you model the
opposite of 4 groups with 2
negative counters in each
group? (I would place 2 negative
counters in 4 groups and then flip
the counters over to the positive
side.)

– –
+
+
– –
+
+
– –
+
+
– –
+
+
What equation would you
record to represent this
model? ((−4)(−2) = 8)
25

Unit 4 Operations with Integers, 6th Grade
How would you model the
opposite of 2 groups with 4
negative counters in each
group? (I would place4negative
counters in 2 groups and then flip
the counters over to the positive
side.)
– –
+
+
– –
+
+
– –
+
+
– –
+
+

What equation would you
record to represent this
model? ((−2)(−4) = 8)
12. Display the following expressions for
the class to see: (−4)(−2) and
(−2)(−4).
Ask:
 How are the expressions
(−4)(−2) and (−2)(−4) related?
Answers may vary. Both have
the same factors and the same
product; the factors switched
positions, and due to
commutative property of
multiplication the products are
the same; etc.
Phase Two: Explore the Concept
Multiplying and Dividing Integers
Day 7 Activity #2
Place students in pairs and distribute handout: Multiplication and Division of Integers to
each student.
What’s the teacher doing?
What are the student’s doing?
Instruct student pairs to complete
problems 1 – 5. Allow time for students
to complete the activity. Monitor and
assess student pairs to check for
understanding. Facilitate a class
discussion to debrief student solutions.
Ask:
Working in pairs to complete problems as prompted
by teacher.
26
Unit 4 Operations with Integers, 6th Grade
 What generalizations can be
made about multiplying
integers? Answers may vary.
The product of two positive
integers is always positive; the
product of two negative integers
is always positive; the product of
a positive integer and a negative
integer is always negative; etc.
Facilitate a class discussion on the
relationship between multiplication and
division.
Ask:
 How are multiplication and
division related? Answers may
vary. They are inverse
operations; a multiplication
problem involves factor x factor =
product. A division problem
involves the product from a
multiplication problem (dividend)
divided by 1 of the factors
(divisor) which will equal the
other factor (quotient); etc.
 What multiplication equation
would you use to verify the
quotient for the equation 24 ÷ 3
= 8? (3 • 8 = 24)
 How would you model the
equation 3 • 8 = 24 in terms of
groups and number of objects
per group? (I would create 3
groups with 8 positive counters in
each group for a total of 24
positive counters.)
 How would you model the
equation 24 ÷ 3 = 8 in terms of
groups and number of objects
per group? (I would separate 24
positive counters equally in 3
groups with 8 positive counters in
each group.)
Facilitate a class discussion about
using two-color counters to model
division problems. Instruct students
to replicate the model with two-color
counters, create a sketch of the
model with pictures of the two-color
counters or (–) and (+), and record
27
Unit 4 Operations with Integers, 6th Grade
an equation to represent the model
in their math journal.
Ask:
 How would you model 8
positive counters in 4 groups?
(I would separate 8 positive
counters equally in4 groups with2
positive counters in each group.)


+
+
+
+
+
+
+
+
+
+
+
+
+
+

+
+

OR
What equation would you
record to represent this
model? (8 ÷ 4 = 2)
What multiplication equation
would you use to verify the
quotient for 8 ÷ 4 = 2? (4 • 2 =
8)
How would you model the
equation8 ÷ 2 = 4? (I would
separate8 positive counters
equally into 2 groups with
4positive counters in each
group.)


+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
OR
What multiplication equation
would you use to verify the
quotient for 8 ÷ 2 = 4? (2 • 4 =
8)
How would you model 8
negative counters in 4 groups?
(I would separate 8negative
counters equally in4 groups
with2negative counters in each
group.)
What equation would you
28
Unit 4 Operations with Integers, 6th Grade
record to represent this
model?((−8) ÷ 4 = (−2))
– –
– –
OR
– –
–
–
–
–
–
–
–
–
– –


What multiplication equation
would you use to verify the
quotient for (−8) ÷ 4 = (−2)? (4 •
(−2) = (−8))
How would you model the
expression (−8) ÷ 2? (I would
separate8 negative counters
equally into 2 groups with
4negative counters in each
group.)
– –
– –
OR
– –
–
–
–
–
–
–
–
–
– –


What multiplication equation
would you use to verify the
quotient for (−8) ÷ 2 = (−4)? (2 •
(−4) = (−8))
How would you model the
opposite of 8 positive counters
in 4 groups? (I wouldseparate8
positive counters equally into 4
groups with 2 positive counters in
each group and then flip the
counters over to the negative
side.)
+
+
– –
+
+
– –
+
+
– –
+
+
– –
29







Unit 4 Operations with Integers, 6th Grade
What equation would you
record to represent this
model?(8 ÷ (−4) = (−2))
What multiplication equation
would you use to verify the
quotient for 8 ÷ (−4) = (−2)?
((−4) • (−2) = 8)
How would you model the
expression 8 ÷ (−2)? (I would
separate 8 positive counters
equally into 2 groups with
4positive counters in each group
and then flip the counters over to
the negative side.)
+
+
– –
+
+
– –
+
+
– –
+
+
– –
What multiplication equation
would you use to verify the
quotient for 8 ÷ (−2) = (−4)?
((−2) • (−4) = 8)
How would you model the
opposite of 8 negative
counters in 4 groups? (I would
separate 8 negative counters
equally into 4 groups with 2
negative counters in each group
and then flip the counters over to
the positive side.)
– –
+
+
– –
+
+
– –
+
+
– –
+
+
What equation would you
record to represent this
model? ((−8) ÷ (−4)= 2)
What multiplication equation
would you use to verify the
quotient for (−8) ÷ (−4)= 2?
30
Unit 4 Operations with Integers, 6th Grade


((−4) • 2 = (−8))
How would you model the
expression (−8) ÷ (−2)? (I would
separate 8 negative counters
equally into 2 groups with
4negative counters in each group
and then flip the counters over to
the positive side.)
– –
+
+
– –
+
+
– –
+
+
– –
+
+
What multiplication equation
would you use to verify the
quotient for (−8) ÷ (−2) = 4?
((−2) • 4 = (−8))
Instruct student pairs to complete
problems 6 – 10 on handout:
Multiplication and Division of
Integers. Allow time for students to
complete the activity. Monitor and
assess student pairs to check for
understanding. Facilitate a class
discussion to debrief student solutions.
Ask:
 What generalizations can be
made about dividing integers?
Answers may vary. The quotient
of two positive integers is always
positive; the quotient of two
negative integers is always
positive; the quotient of a positive
integer and a negative integer is
always negative; etc.
Phase Three: Explain the Concept
Multiplying and Dividing Integers
and Define Key terms
Day 8 Materials:
 Video: https://www.youtube.com/watch?v=QMst5BcgHhQ
 Handout: Multiplying and Dividing Integers Problem Solving
 Speed Integer Set (set 1) PowerPoint
Day 8 Activity #1:
31
Unit 4 Operations with Integers, 6th Grade
Multiplying and Dividing Integers Song and Folding Notes(continued from Day 5).
What is the teacher doing?
Ask:
 What patterns did you notice
when multiplying and dividing
the integers yesterday?
Answers may vary. When both
factors are positive, the product
is positive. When both factors are
negative, the product is positive.
If multiplying a pair of factors and
one of the factors is negative, the
product is negative; etc.
https://www.youtube.com/watch?v=
QMst5BcgHhQ
 Instruct students to write the
rules on the appropriate
section of the folding notes
activity from Day 5.
What are the student’s doing?
Phase Four: Elaborate on the
Concept
Day 8 Activity #2:
Multiplying & Dividing Integers
Students will participate in class discussion. They
will learn the song for Multiplying and Dividing
Integers and complete the folding notes activity that
was started on Day 5.
Handout: Multiplying and Dividing Integers Problem Solving
What’s the teacher doing?
What are the student’s doing?
The teacher will monitor students
working and will provide corrective
feedback.
Day 8 Activity #3:
Students are solving integer problems.
Speed Integer Set 1 (Power Point)
What is the teacher doing?
What are the students doing?
The teacher facilitates the speed integer
drill on the powerpoint. Students will
chart the number of problems they get
correct.
Phase Four: Elaborate on the
Concept
Students try to work each problem correctly before
the next problem flashes on the screen. They will
self-asses their fluency.
Review of Integer Concepts
32
Unit 4 Operations with Integers, 6th Grade
Day 9 Materials:
 Handout: Student Recording & Integer Unit Review Scavenger Hunt Questions
http://campuses.fortbendisd.com/campuses/documents/Teacher/2012%5Cteacher_201
21107_1438.pdf
Day 9 Activity:
Integer Unit Review Scavenger Hunt
What’s the teacher doing?
Prior to class post the scavenger
hunt questions on colored paper
around the room. Divide students
into groups of students (see
directions). Hand out the Student
Recording Sheet to each student.
What are the student’s doing?
Students will complete the scavenger hunt activity.
http://campuses.fortbendisd.com/campu
ses/documents/Teacher/2012%5Cteach
er_20121107_1438.pdf
Phase Five: Evaluate students’
Understanding of Concept
Day 10 Activity:
Performance Assessment
Performance Assessment 1:
Analyze the situation(s) described below. Organize and record your work for each of the
following tasks. Using precise mathematical language, justify and explain each mathematical
process.
1) Vance collects toy model cars. The table below shows how many toy model cars Vance
bought or sold in various months. The number of cars in his collection changes each month as
he buys and sells model cars.
a) Identify each of the given amounts of toy model cars bought and sold each month as
33
Unit 4 Operations with Integers, 6th Grade
positive or negative.
2) Consider the following numbers: -25.50 and 12.67
a) Identify the opposite of each number.
b) Identify the absolute value of each number.
c) Use a number line to describe the relationship between each number, its opposite, and its
absolute value.
Standard(s): 6.1A, 6.1D, 6.1E, 6.1F, 6.1G, 6.2B
Performance Assessment 2:
Provide concrete and/or pictorial models for students to select.
Analyze the problem situation(s) described below. Organize and record your work for each of
the following tasks. Using precise mathematical language, justify and explain each solution
process.
Mark and Peter are starting a lawn care service to make extra money during their summer
vacation. The two boys have an old lawn mower that they will be using for their company.
1) During the first week, Mark and Peter spend $23 on gasoline for the mower and $12 to
make flyers for advertisement purposes. They also purchase lawn fertilizer for $19. The two
boys mow two lawns and earn a total of $40 during the first week. Mark and Peter split the
earnings for their first week of work.
a) Use concrete and/or pictorial models to determine the amount of profit or loss for the
company after the first week of business and connect the model to the standardized
algorithms for integer operations.
2) Mark and Peter begin their second week of work with the profit or loss obtained during week
one. They purchase 3 containers of weed killer priced at $16 each and two rakes, each priced
at $8. They mow and care for several lawns during week two and earn a total of $286 during
the second week.
a) Use the standardized algorithms for integer operations to determine the amount of profit or
loss for the company after the second week of business.
3) Mark and Peter begin their third week of work with the profit or loss obtained during week
two. The boys purchase a new lawn mower for $115 and two additional containers of lawn
fertilizer at $19 per container. They mow 26 lawns during week three and earn a total of $436
during the third week. The boys decide to split the profit or loss, evenly, after the third week of
business.
a) Use the standardized algorithms for integer operations to determine the amount of profit or
34
Unit 4 Operations with Integers, 6th Grade
loss for each boy after the third week of business.
Standard(s): 6.1A, 6.1B, 6.1C, 6.1D, 6.1F, 6.1G, 6.3C, 6.3D
What’s the teacher doing?
What are the students doing?
Monitor students as they work on the
performance indicator to determine if
any re-teaching is necessary prior to the
unit assessments.
Demonstrating understanding of the topics and
skills taught in this unit by completing the
performance indicator.
35