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Unit 4 – Operations with Integers – 6th grade
5E Lesson Plan Math 
	Grade Level:  6th grade
	Subject Area: Math
	Lesson Title: Unit 4 – Operations with Integers
	Lesson Length: 10 days
	THE TEACHING PROCESS
	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… 
examine number relationships involving identifying a number, its opposite, and absolute value
represent absolute value on a number line as the distance a number is from zero.
develop integer operations with concrete and pictorial models
develop and connect integer operations to standardized algorithms
add, subtract, multiply, and divide integers fluently
	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 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:
ELPS.c.5B - write using newly acquired basic vocabulary and content-based grade-level vocabulary
ELPS.c.4F - use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language
	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.
Related Vocabulary:
Addend, Ascend, Compare, Credit, Debit, Deposit, Dividend, Divisor, Factor, Gain, Like signs, Loss, Opposite, Positive, Product, Profit, Quotient, Sum
	List of Materials:
Day 1 
PowerPoint
Day 1 Notes
Task Cards
Integers at Sea
Day 2
Red and yellow construction paper
Video “Number Line Dance”
Two color counters or red and yellow squares cut from construction paper
Handout – Adding Integers with Models 
Handout – Adding Integers with Number Lines
Day 3
PowerPoint – Adding Integers
Integer Foldable
Handout - Integer practice without models
Handout - Homework – Magic Sum and Word Problems
Exit ticket
Day 4
Video “Khan Academy” Subtracting integers
Handout – Subtracting Integers with a Number Line and counters
Video – You tube – how to teach subtracting models
Day 5
Video – You tube – Subtracting integers song
Video – “Khan Academy part 2” Why subtracting a negative is a positive 
Handout - Subtracting Integers
Handout - Homework – Subtracting Integers practice and word problems
Exit Ticket
Day 6
Video – Modeling Multiplying Integers
Handout for the video 
Handout – Discovery Activity
Video – Multiplying Integers
Video – Why negative times a negative is a positive?
Handout – Homework Multiplication Magic and word problems
Exit Ticket
Day 7
Counters, red and yellow pencils or red and yellow construction paper (choose one)
Handout – Division of Integers
Handout – Discovery rules for dividing integers
Video – “Dividing Integers” by The Khan Academy
Handout - Homework – Dividing Integers with word problems
Exit Ticket
Day 8
Handout – Extending Integers
Day 9 
Handout – Integer Practice
Day 10 
Performance Indicators
	INSTRUCTIONAL SEQUENCE
	Phase 1 – Engage the Learner
	Integers – Opposites – Absolute Value
	Day 1 Activity 1: 
Have two students stand back to back. Tell the students to take 5 steps forward. Illustrate this situation with a number line on the board starting with zero.
	What’s the teacher doing?
The teacher is directing the students to illustrate a human number line and questioning the class. 
Questions:
What integer is represented by student A and student B? (5, -5)
Are the integers the same on the number line? (No, these are called opposites)
What integers would be represented if the students took ten steps? (-10, 10)
How far from zero is Student Aand Student B? The students are the same distance from zero if they both took five steps or if they both had taken ten steps. This is called Absolute Value. Absolute value is the distance from zero. 
	What are the students doing?
 
The students are answering questions and thinking about the human number line. 
	Phase 2 Explain/Explore
	Integers – Opposites – Absolute Value
	Day 1 Activity 2: 
Show the power point explaining integers, opposites and absolute value.
After showing the PowerPoint have students complete the notes for integers. Then have students create 5 real-life situations where integers are used. After students have had a chance to create examples they will share their situations with a partner and trade examples to figure out what integer is represented by the situations. 
Day 1 Activity 3: 
Task card activity: Depending on the amount of time left, you can have the task cards posted around the room and have students complete all twenty cards or you can have students choose 4, 8, or 10 etc. to complete. This activity could be completed with partners or independently. (See Handout)
Day 1 Activity 4:
Exit Ticket: What was important in today’s lesson? Why?
Homework or Classwork Activity: Students will complete Integers at Sea for homework or classwork, if time allows. 
	What’s the teacher doing?
The teacher is going over the PowerPoint slides with students to define integers and absolute value. 
Questions:
How would you interpret the word “loss”? (positive or negative)
How would you interpret the word “deposit”? (positive or negative)
How would you interpret the word “withdrawal”? (positive or negative)
Is the number “0” positive or negative? (neither)
What is the relationship between a number, its opposite and its absolute value? 
How can positive and negative numbers be represented in real-world problem situations? (temperature, money, etc.)
 Activity 3: The teacher is walking around the room and helping students as needed. 
	What are the student’s doing?
Students are listening and reading the slides from the PowerPoint. Then students are creating examples and interpreting situations. 
Activity3: Students are working problems found on task cards. 
Activity 4: Students will complete a number line activity by drawing examples using real-life situations. (Integers at Sea)
	Phase 3 Engage the Learner
	Adding Integers
	Day 2 Activity 1: 
Give ½ the students a sheet of red construction paper and the rest of the class a yellow sheet. Tell the students that red means negative and yellow means positive. 
Have the students model -4 + 2 by facing each other, red on one side and yellow on the other. One red cancels out one yellow so how many are left? What color is left? Based on this example what is the sum of -4 + 2? 
Day 2 Activity 2:
Teach your students the Integer RAP – watch the video on the teaching channel to learn the dance moves (http://www.alexkajitani.com/videos.html) or (https://www.teachingchannel.org/videos/math-teaching-techniques)
Student part:
Negative to the left, 
Positive to the right. 
It’s the number line dance. 
I could dance all night. 
	What’s the teacher doing?
The teacher is facilitating the integer model with students and asking questions. 
The teacher is asking questions about the video and having the students describe how integers are used in everyday situations. 
	What are the students doing? 
Students are modeling positive and negative numbers. 
Students are learning the number line dance and discussing how integers are used in real-life situations. 
 
	Phase 4 Explain/Explore 
	Adding Integers
	Day 2 Activity 3: 
(See Handout) Have the students complete examples of adding integers with two color counters or red and yellow squares and then discuss what happens when you add two integers together. Does adding a positive plus a positive result in a negative or positive answer? Does adding a positive plus a negative give you a positive or negative answer? (it depends) Does adding a negative plus a negative result in a positive or negative solution? In the solution 3 plus -1 the sum is +2 but 3 plus -5 the sum is -2 why is one sum positive and the other sum negative? In order to answer this question use models to illustrate the relationship between positives and negatives. 
(See Handout) Have students complete examples using a number line. What do you notice about the number line when you add a negative and a negative number? What happens when you add two opposites on the number? What happens when you add 9 + -3 on the number line? 
	What’s the teacher doing?
Questions: 
Does adding a positive plus a positive result in a negative or positive answer? (positive)
Does adding a positive plus a negative give you a positive or negative answer? (it depends)
Does adding a negative plus a negative result in a positive or negative solution? (negative)
In the solution 3 plus -1 the sum is +2 but 3 plus -5 the sum is -2 why is one sum positive and the other sum negative? 
What do you notice about the number line when you add a negative and a negative number? (it moves to the left)
What happens when you add two opposites on the number line? (always equals 0)
What happens when you add 9 + -3 on the number line? (positive 6)
How are concrete and pictorial models used with integer operations (e.g., number lines, two-color counters, etc.)?
	What are the students doing? 
Students will complete examples with the counters. 
Students will complete examples using a number line. 
	Phase 5 Explain/Explore/Elaborate 
	Adding Integers
	Day 3 Activity 1:
 
Explore:
 
Show the PowerPoint with adding integers. Have a class discussion about adding integers and create a foldable for integer operations. Complete only the adding integers portion today. http://everybodyisageniusblog.blogspot.com/2012/07/integer-foldable.html
(See handout) 
After students have practiced adding integers with models have them try a few problems with larger numbers such as -97 + -36, -97 + 36, and 100 + -24. How do you solve problems that are too large to use a model? Simply ask yourself: Do you have more positives or negatives? How many more positives or negatives do you have? By having the students asking these two questions, students will not need a model to determine the answer. 
Explain: Exit Ticket: What generalization can be made about the sum of two integers with the same sign? When adding integers, if a pair of addends has the same sign, then the sum will ………………….. What generalization can be made about the sum of two integers with opposite signs? When adding integers, if a pair of addends has the opposite signs, then the sum will ……………………
Elaborate: Homework: Students will practice adding integers “Magic Sum” and word problems. (See Handout)
	What’s the teacher doing? 
What generalization can be made about the sum of two integers with the same sign? (pos. + pos. = pos., neg. + neg. = neg.) 
What generalization can be made about the sum of two integers with opposite signs? (the sign will be same as the number with the largest absolute value)
Does the problem have more positives or negatives? How many more positives or negatives does it have?
	What are the students doing? 
Students will complete adding integers with and without models. 
After solving several problems with and without models students will make generalizations about adding integers. 
	Phase 6 Engage and Explore 
	Subtracting Integers
	Day 4 Activity 1:
Engage:
Watch the video on subtracting integers and discuss. Students may question that subtracting a negative is the same as adding a positive and that is where the second video from “Khan Academy” has a great explanation. SeeDay 5’s lesson for the other video.
https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-pre-alg/add-subtract-negatives-pre-alg/v/adding-and-subtracting-negative-number-examples
Day 4 Activity 2:
Explore: 
(See Handout) Students will practice solving subtraction problems using a number line and make generalizations at the conclusion of this activity. 
Students will model subtraction of integers using counters. See this video for help on showing students how to model subtraction of integers. The counter example starts 4 minutes into the video. https://www.youtube.com/watch?v=Va_CiPK49vU
	What’s the teacher doing? 
The teacher is having a class discussion after watching the video and answering student questions. The teacher goes over examples of subtracting integers on a number line and with models (counters).
How is subtraction related to addition? (they are opposites)
What generalization can be made about the difference of two integer numbers with opposite signs? 
	
	What are the students doing?
Students are watching the video and then solving subtraction of integers with models. (number lines and counters)
	Phase 7 Engage, Explore, Explain, Elaborate and Evaluate
	Subtracting Integers
	Day 5 Activity 1:
Engage: 
Watch the videos and discuss.
https://www.youtube.com/watch?v=5f0rF4m9TGY
https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-pre-alg/add-subtract-negatives-pre-alg/v/why-subtracting-a-negative-equivalent-to-adding-a-positive 
Use the foldable from yesterday to complete only the subtracting integers portion. http://everybodyisageniusblog.blogspot.com/2012/07/integer-foldable.html
Day 5 Activity 2:
Explain/Explore: 
(See Handout) Students will complete the engage problems by solving as many problems as they can in three minutes and look for a pattern between problems. As they complete the problems they should notice a pattern to help solve the remaining problems. Once students have completed the problems have a class discussion about the type of problems they see and how to solve them. Some students may be able to create rules for subtracting integers based on the examples. After the brief discussion, go over the examples by rewriting them as addition problems and adding the opposite integer following the subtraction symbol, and then applying the rules for adding integers. Students will then select equivalent problems. 
Elaborate:
Homework: Students will practice subtracting integers with and without models. Students will also incorporate word problems involving integers.
 
Evaluate:
Exit Ticket: How is subtracting integers related to adding integers? 
	What’s the teacher doing? 
The teacher is playing the videos and answering student questions. The teachers will facilitate the lesson and guide students to rewrite integer problems as addition problems. 
How can you change a subtraction problem to an addition problem? (by adding the opposite)
How is subtracting integers related to adding integers? (it is the same as adding once you add the opposite) 
What generalizations can you make about subtracting integers? 
	What are the students doing? 
Students are watching the video and asking questions. 
Students will complete a pattern of problems and practice rewriting subtraction problems as addition problems. Students will compare expressions to find equivalent problems. Students will practice subtracting integers with and without models for homework. Students will explain in written form how subtracting integers and adding integers are related. 
 
	Phase 8 Engage, Explore, Explain etc. 
	Multiplying Integers
	Day 6 Activity:
Engage:
Students will watch the video of modeling multiplication with integers. While they are watching the video have them follow along by setting up the models on their paper and coloring the models. Pause the video as the students work. (See Handout) https://www.youtube.com/watch?v=Gk4QhK3KMq4
Explain/Explore:
Once students have practiced with models they will complete the handout with experimental practice and discover the rules for multiplying integers. After students have drawn conclusions for multiplying integers show the video. https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-pre-alg/mult-div-negatives-pre-alg/v/multiplying-positive-and-negative-numbers
Then show “Why a negative times a negative is a positive”.
https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-pre-alg/mult-div-negatives-pre-alg/v/why-a-negative-times-a-negative-makes-intuitive-sense
Students should complete the multiplying integers part of their foldable.
Elaborate: Homework: Students will practice multiplying integers with word problems. (See Handout)
Evaluate:
Exit Ticket: What generalization can be made about the product or quotient of two or more integers with no negative signs or an even number of negative signs? What generalization can be made about the product or quotient of two or more integers with one negative sign or an odd number of negative signs?
	What’s the teacher doing? 
Engage Activity 
The teachers is walking around the room watching the students create models from the video and pausing the video as necessary. 
How do you model -5 x 2?
How do you model -2 x -5?
How do you model -2 x 5?
How do you model 5 x 2?
Explain/Explore Activity
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.
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.
	What are the students doing? 
Engage Activity
The student are following the video and creating models from the video and coloring them onto their paper. 
Explain/Explore Activity
Students will complete the handout with experimental practice and discover the rules for multiplying integers. After the conclusions have been made show students the video for multiplying integers. 
Evaluate:
Students will complete an exit ticket and work on homework. 
	Phase 9 Engage, Explore, Explain etc. 
	Dividing Integers
	Day 7 Activity:
Engage/Explore:
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 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 in 4 groups with 2 positive counters in each group.)
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 equation 8 ÷ 2 = 4? (I would separate 8 positive counters equally into 2 groups with 4 positive counters in each group.)
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 8 negative counters equally in 4 groups with 2 negative counters in each group.)
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 negative counters equally into 2 groups with 4 negative counters in each group.)
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 would separate 8 positive counters equally into 4 groups with 2 positive counters in each group and then flip the counters over to the negative 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)? ((−4) • (−2) = 8)
How would you model the expression 8 ÷ (−2)? (I would separate 8 positive counters equally into 2 groups with 4 positive 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? ((−4) • 2 = (−8))
How would you model the expression (−8) ÷ (−2)? (I would separate 8 negative counters equally into 2 groups with 4 negative 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))
Explain/Explore #1: 
Instruct student pairs to complete problems on the Division of Integers handout. 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.
Explain/Explore #2: 
Once students have practiced with models they will complete the handout with experimental practice and discover the rules for dividing integers. After the conclusions have been made show students the video for dividing integers. 
https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-pre-alg/mult-div-negatives-pre-alg/v/dividing-positive-and-negative-numbers
Students should complete the final part of their foldable.
Elaborate: Homework: Students will practice dividing integers with word problems. 
Evaluate:
Exit Ticket: What generalization can be made about the product or quotient of two or more integers with no negative signs or an even number of negative signs? What generalization can be made about the product or quotient of two or more integers with one negative sign or an odd number of negative signs?
	What’s the teacher doing? 
Engage Activity 
Facilitate a class discussion about using two-color counters to model division problems. 
Explain/Explore Activity
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.
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 are the students doing? 
Engage Activity
Students will replicate the model with two-color counters, create a sketch of the model with pictures of the two color counters or (–) and (+), and record an equation to represent the model in their math journal.
Explain/Explore Activity
Student will complete the discovery worksheet to create rules for dividing integers. 
Evaluate:
Students will complete an exit ticket and work on homework. 
	Phase 10 Elaborate
	Integers Operations
	Day 8 Activity 1:
Elaborate 1: 
Students apply integer rules to solve equations with more than 2 numbers and real-life problem situations.
Place students in pairs and distribute handout: Extending Integers to each student. Instruct student pairs to complete the handout. 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.
Day 9 Activity 1:
Elaborate 2: 
Handout (optional): Integer Practice may be used as additional practice, as needed.
	What’s the teacher doing? 
Monitor and assess student pairs to check for understanding. Facilitate a class discussion to debrief student solutions. 
	What are the students doing? 
 Students apply integer rules to solve equations. 
	Phase 11 Evaluate
	Integers Operations
	Day 10 Activity:
Assess student understanding of related concepts and processes by using the Performance
Indicator(s) aligned to this lesson.
	What’s the teacher doing?
The teacher monitors students and walks the room to ensure students are on task.
	What are the students doing? 
Students are demonstrating their knowledge by completing the performance indicator. 
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_1471944482/thMathIntegersandAbsolutValuesPowerpoint.ppt
*
Integers and Absolute Values 
*
Here is a number line. 
*
An integer is a positive or negative number. 
*
0
+1
+2
+3
+4
+5
-5
-4
-3
-2
-1
Positive integers are integers greater than 0. They can be written without + sign.
*
0
+1
+2
+3
+4
+5
-5
-4
-3
-2
-1
Negative integers are integers less than 0. They are written with a 
- sign.
*
0
+1
+2
+3
+4
+5
-5
-4
-3
-2
-1
Zero is neither negative nor positive.
*
Here are some real-world examples…
*
Let’s write an integer for each situation.
Weather: 5 degrees below
Because this weather is below normal, the integer is written as -5.
*
Let’s write an integer for each situation.
Rainfall: 5 inches above normal
Because this rainfall is above normal, the integer is written as +5 or just 5.
*
Let’s write an integer for each situation.
Banking: a deposit of $23
Because deposit is adding an amount to your bank account, it is +23 or just 23.
*
You can also graph integers on a number line.
*
0
+1
+2
+3
+4
+5
-5
-4
-3
-2
-1
Graph this set on a number line.
(-4, -2, 0, 5)
.
.
.
.
Just draw a point (or a dot) on the location of the integer. That’s all!
*
0
+1
+2
+3
+4
+5
-5
-4
-3
-2
-1
Graph this set on a number line.
(-5, -1, 3)
.
.
.
You get the point, right? Pun totally intended.
*
Hey, have you noticed that -5 and 5 are each 5 units (spaces) from 0?
*
-5 and 5 are both 5 spaces away from 0. They have the same absolute value.
*
Absolute value of a number is the distance between the number and 0 on a number line.
*
And it’s written like this…
*
5 units
5 units
*
This means that the absolute value of both -5 and 5 are 5 (distance from 0).
*
4
Let’s try this one…
*
So…basically…
*
OK…I get it, I get it!
*
Now, you can even do this…
*
= 
= 
= 
= 
*
Good job!
_1472318891/AddingIntegersTutorial.pptx
Adding
integers
1
When adding integers and the signs are the SAME:
	ADD THE NUMBERS TOGETHERKEEP THE SIGN
EXAMPLE
	
1
9 + 11=
20
EXAMPLE
	
2
-9 + -11=
-20
Think: I owe you $9 and I owe you $11,
So I owe you $20 altogether.
EXAMPLE
	
3
98 + 13=
111
EXAMPLE
	
4
-98 + -13=
-111
Think: I owe you $98 and I owe you $13,
So I owe you $111 altogether.
When adding integers and the signs are DIFFERENT:
	SUBTRACT THE NUMBERS 
	USE THE SIGN OF THE LARGER 	NUMBER
EXAMPLE
	
1
-9 + 11=
2
Think: I owe you $9 and I HAVE $11,
So I pay you $9 and have $2 left.
LET’S 
TRY IT 
WITH
PICTURES!
-9 + 11=
-
-
-
-
-
-
-
-
-
+
+
+
+
+
+
+
+
+
+
+
This represents -9
Add
11
Now, remove the matches: 
1 + and 1 - = 0
-9 + 11=
2
EXAMPLE
	
2
9 + -11=
-2
Think: I have $9 and I OWE $11,
So I pay you $9 and still OWE $2.
LET’S 
TRY IT 
WITH
PICTURES!
9 + -11=
-
-
-
-
-
-
-
-
-
+
+
+
+
+
+
+
+
+
This represents 9
Add
-11
Now, remove the matches: 
1 + and 1 - = 0
-
-
9 + -11=
-2
EXAMPLE
	
3
-98 + 13=
-85
EXAMPLE
	
4
98 + -13=
85