Primary Type: Lesson Plan
Status: Published
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Resource ID#: 47311
Discovering our Addition of Integer Rules
In this lesson, students will develop the rules for adding integers by using the absolute value of integers and number lines.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Suggested Technology: Overhead Projector
Instructional Time: 1 Hour(s)
Freely Available: Yes
Keywords: adding integers, absolute value
Instructional Design Framework(s): Structured Inquiry (Level 2)
Resource Collection: CPALMS Lesson Plan Development Initiative
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will apply previous understandings of addition and subtraction to add rational numbers.
Students will:
Use a number line to show addition of positive and negative integers and rational numbers.
Represent real world situations by writing addition equations using negative and positive integers.
Prior Knowledge: What prior knowledge should students have for this lesson?
MAFS.6.NS.3.6
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.
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.
MAFS.6.NS.3.7
c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative
quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.
Students should be able to construct a number line with integers and know where 0 is on a number line.
Guiding Questions: What are the guiding questions for this lesson?
How can we define the absolute value of a number?
How can we use absolute value to create rules for adding integers and rational numbers?
page 1 of 4 How can we use the number line to prove our statement?
What do you already know about addition and subtraction that will help you find the answer?
Teaching Phase: How will the teacher present the concept or skill to students?
On a white board/communicator have students construct a number line. Have students show their answers at once. Use the responses to adapt instruction, assisting
students who do not have the prerequisite prior knowledge.
Select a correct and incorrect number line and have students contrast the difference between the two number lines. (formative assessment) let students know that 0
is in the middle of the number line and that the negatives are on the left, emphasizing the order of the negative numbers as the numbers move away from 0 and the
positives numbers are to the right of 0.
Introduction of the lesson:
Teacher: today we will discover how absolute value is used to discover the rules for adding integers
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Let students group or pair themselves.
Hand out Group Work Sheet Adding Integers.docx
(The answer key: Group Work Sheet Adding Integers Answersheet.docx)
Ask students to answer the Review questions and discuss their answers.
Next have the students identify the direction on a number line based on the sign of the number. Using the number line as a reference, have the student identify the
direction from 0 by pointing left or right. (teacher gives several examples integers as an example -3 (negative 3) students point left or +3 (positive 3) students point
right). (formative assessment).
On the whiteboards/communicator have students graph one number at a time and display their answers for understanding. Give several examples that include
fractions and decimals.
Teacher: What is the absolute value of an integer?
Student: various responses which may include a correct response, and the student could share his/her knowledge.
Teacher: Absolute value is the distance a number is from zero. Example: 2 is 2 units from zero. -3 is 3 units from zero. Show notation of absolute value.
When this lesson says "See Example" refer to the Teacher Example Answer Sheet
See Example 1
(Check for understanding by giving students several examples and asking them to display their answers on the whiteboard/communicator)
Addition of Integers with the Same Sign:
Teacher: let's graph two negative numbers on the same number line using the whiteboard/communicator. To graph integers you need 3 things: distance,
direction and location. Let's graph two negative integers together. Let's graph -3 and -1
Teacher: How would we graph -3? Distance from 0 and direction
Student response: 3 units left
Teacher: Where is this first point located on your number line?
Student response: -3
Now graph the -3 on a number line and display your answer (formative assessment).
Teacher: What is the absolute value of -3, and how do you know?
Student: 3, because it is 3 units from 0
Teacher: What is the absolute value of -1?
Student: 1
Teacher: After we do the next example, look for a relationship between the absolute values, the signs of the integers you are adding, and the answer in the
equation below.
See Example 2
Teacher: If you wanted to add -3 + -1, how far from the first point, -3, will you need to move?
Student response: 1 unit left
Teacher: On what point did you land?
Student: -4
See Example 3
*Have the students graph the movement of the numbers above the number starting at zero and have them make movements on the number line by giving them a
second number to add to it. Make sure student understands that the second movement will move from where they are not starting back at 0.
Teacher: How can we show this as an addition equation? Student responses (on whiteboards/communicators): -3 + (-1) = -4
Explain to students that where they end after their movements is the answer in their equation.
Teacher: "What rule can we create about adding integers with the same signs using their absolute value? Have students work with their partner to come up
with a rule.
Rule: Find the absolute value of the integers, add them and keep the common sign.
Teacher: Who will explain why this rule simplifies the process of adding integers with the same sign? Ask for a student to state what he/she would do, if the
rule is not remembered.
Addition of Integers with Different Signs:
The teacher graphs these integers on the same number line using their whiteboard/communicator. Check for understanding and ask students what the movement
for each number is.
+4: teacher says positive 4
The student will move 4 units to the right from 0 because that is the starting number.
-3: teacher says negative 3
Student will move 3 units to the left.
See Example 4
Teacher: Create an addition equation from this number line. (The teacher circulates the class, checking for understanding and providing guiding questions and
feedback to students.
Student response: answer: +4 + (-3)= 1)
Teacher: Look at the number line answer, then look at the absolute values of the two integers, and the answer in the equation. What rule can we create about
adding integers with the different signs using their absolute value?
page 2 of 4 If students do not respond appropriately, ask guiding questions to assist their concept development.
*Teacher elicits from students that when adding integers with different signs, you find the absolute value of each integer, find their difference, and take the sign of
the larger absolute value.
Ask a volunteer to explain why this rule works (making the connection between the movement on the number line and absolute values).
Ask students to complete the remaining problems on the Group Work Sheet. Circulate, monitor, and ask guiding questions to assist students with the task. When the
students have finished, ask students to share their answers and use their responses to ask questions to guide their understanding, when needed.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
This independent practice is an independent summative assessment, not group work.
Adding Integers-Rational Numbers Worksheet
Adding Integers-Rational Number Answersheet
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
As a class, depending on the number of groups you have, have two of the groups state each of the rules (from the Group Worksheet). These should be two groups that
you have reviewed their rules when circulating the room making sure that each student got the general rules for adding integers and can explain why the rule works.
You can then have different groups restate the reasoning, give an example, and restate the rule for the example.
The teacher should restate that there are two ways to add integers, but that applying the rule for adding integers is more efficient. and emphasize that adding rational
numbers have the same rules as integers.
adding integers and rational numbers with the same signs using absolute value: find the absolute value of the integers add them and keep the common sign
adding integers and rational numbers with different signs using absolute value: find the absolute value of each integer find their differences and take the sign of the
larger absolute value
The teacher asks, if the students knows of a situation where adding positive and negative numbers is used. Some answers might be the money in a checking account,
the temperature after changes during the day, football yards (gains and losses).
Summative Assessment
The Independent Practice worksheet is the Summative Assessment.
Adding Integers and Rational Numbers Worksheet with answers and rubric
Formative Assessment
As the students complete the Group Worksheet, the teacher will assess their performance. See the Teaching Phase of this lesson for the attachment and further
instructions.
Feedback to Students
As students work in their groups, circulate among the groups.
Review the prior section to ensure that students understood the prior section, ask guiding questions to correct any misunderstandings as needed.
Offer any feedback to the groups about the current section as needed.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations: While circulating and checking for understanding give one-on-one help to students who are not grasping the concept, before moving to a new
concept.
Extensions: Have each group create a real world problem that represents each of the 2 rules that was created.
Suggested Technology: Overhead Projector
Special Materials Needed:
Whiteboards/Communicators
Dry erase markers
Erasers
Further Recommendations: If you don't have whiteboards or communicators, a sheet protector with a sheet of paper in it will also work. Have students write on
the sheet protector with the dry erase marker
Additional Information/Instructions
By Author/Submitter
This lesson addresses the Mathematical Practice Standard:
MAFS.K12.MP.4.1, Model with mathematics, because the students will represent their answers on a number line.
SOURCE AND ACCESS INFORMATION
Contributed by: Soraya Burke
Name of Author/Source: Soraya Burke
District/Organization of Contributor(s): Volusia
Is this Resource freely Available? Yes
Access Privileges: Public
page 3 of 4 License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.7.NS.1.1:
Description
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent
addition and subtraction on a horizontal or vertical number line diagram.
a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge
because its two constituents are oppositely charged.
b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on
whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses).
Interpret sums of rational numbers by describing real-world contexts.
c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the
distance between two rational numbers on the number line is the absolute value of their difference, and apply this
principle in real-world contexts.
d. Apply properties of operations as strategies to add and subtract rational numbers.
Remarks/Examples:
Fluency Expectations or Examples of Culminating Standards
Adding, subtracting, multiplying, and dividing rational numbers is the culmination of numerical work with the four
basic operations. The number system will continue to develop in grade 8, expanding to become the real numbers
by the introduction of irrational numbers, and will develop further in high school, expanding to become the complex
numbers with the introduction of imaginary numbers. Because there are no specific standards for rational number
arithmetic in later grades and because so much other work in grade 7 depends on rational number arithmetic,
fluency with rational number arithmetic should be the goal in grade 7.
page 4 of 4