Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 48320
Understanding Integers
This lesson is an introduction to integers. Students will compare, order, and describe real-life situations using positive and negative whole numbers.
The concepts of opposites and vertical as well as horizontal number lines are addressed.
Subject(s): Mathematics
Grade Level(s): 6
Intended Audience: Educators
Suggested Technology: Computer for Presenter,
Computers for Students, Internet Connection,
Interactive Whiteboard, LCD Projector, Java Plugin
Instructional Time: 3 Hour(s)
Freely Available: Yes
Keywords: Integers, Positive Numbers, Negative Numbers, Opposites, Integer, Rational Number, Number Line
Instructional Design Framework(s): Structured Inquiry (Level 2)
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
Integer Investigation.doc
Integer Investigation Answer Key.doc
Understanding Integers Enrichment.doc
Understanding Integers Assessment.doc
Understanding Integers Opening Activity.doc
Understanding Integers Assessment Answer Key.doc
Understanding Integers Mathematical Practices sample questions.doc
Understanding Integers Opening Activity Answer Key.doc
LESSON CONTENT
Lesson Plan Template: Confirmatory or Structured Inquiry
Learning Objectives: What will students know and be able to do as a result of this lesson?
Students will describe and give examples of how positive or negative numbers are used to describe quantities having opposite directions or opposite values.
Students will recognize that positive and negative signs represent opposite values and/or directions. Students will use positive and negative numbers along with zero
to represent real world situations.
Students will be able to order and compare integers using words and symbols.
Prior Knowledge: What prior knowledge should students have for this lesson?
Understand number lines and placement of whole number on the number line
Understand that larger numbers are further right on a horizontal number line
Use of symbols to compare and contrast numbers
Understand operations with positive numbers
Guiding Questions: What are the guiding questions for this lesson?
page 1 of 4 How can rational numbers be represented in multiple ways?
How can integers be represented by models and real world situations?
How can a number line help in comparing integers?
How can students recognize integers and their opposites with and without the number line?
In what ways can rational numbers be useful?
Introduction: How will the teacher introduce the lesson to the students?
Ask students to give real life examples of integers. Discuss the meaning of the symbols This is a good point to connect integers and the inequalities greater than or
equal to, less than or equal to by asking what does the sign at the theme park mean when it says "You must be at least 42" to ride this ride". Can you be 41" and ride
the ride? How about 45 inches?
Broadly discuss the concept of opposite - what does it mean to them?
Have students complete the Opening Activity (attached).
Understanding Integers Opening Activity.doc
Investigate: What question(s) will students be investigating? What process will students follow to collect information that can be
used to answer the question(s)?
Opening Activity – Understanding Integers Opening Activity
For students who struggle with the activity, break out into small group for direct instruction by teacher. For students who understood the activity, the teacher can give
them the enrichment activity where they add to a mountain picture and give reasonable estimates of the integer which represents the position of each item after they
determine the placement of 0.
Understanding Integers Investigation:
Have students work in pairs or small groups.
Teacher can debrief class after each section or after every two sections.Teacher should be circulating around the room during activity asking guiding questions and
clarifying student understanding. How are integers used in the real world? How can integers be represented by models and real world situations? How can a number
line help in comparing integers? In what ways can rational numbers be useful? Students who do not have the background experience to understand the Real-life
Situation on the worksheet will need assistance in order to complete the worksheet.
Project - Understanding Integers Investigation section Understanding Integers Assessment
Analyze: How will students organize and interpret the data collected during the investigation?
Students will use the Integer Investigation unit to work through and organize their work on integers.
Teacher has the option to debrief after each section, or to combine sections. Debriefing will ensure that all students understand the material and are able to explain
their thinking to the large group.
Encourage students to share different strategies they used.
Teacher should use guiding questions and learning objectives to guide discussion.
Questions to students should include:
How does knowing the sign of a number help us determine which way to go on the number line?
How do we know if a number is positive or negative if it does not have a sign?
How does knowing what "zero" represents in different situations help us to begin solving a problem?
How do number lines help us "see" integer movement?
How do inequality signs help us order integers?
How do you know if a vertical or horizontal number line would be more useful in a specific problem?
Is there another way to think about this problem?
If I came up with a "rule", do I have multiple examples to support it? Remind students that just because it worked once, that doesn't make it true for all
situations.
Can you define "zero"?
Closure: What will the teacher do to bring the lesson to a close? How will the students make sense of the investigation?
Have students present their final project (section H of the Integer Investigation) is a great way to bring closure to this unit. As a result of this activity:
Students will describe and give examples of how positive or negative numbers are used to describe quantities having opposite directions or opposite values.
Students will recognize that positive and negative signs represent opposite values and/or directions.
Students will use positive and negative numbers along with zero to represent real world situations.
Students will be able to order and compare integers using words and symbols.
As a result of this activity, students should be able to articulate, give examples, and justify:
How can rational numbers be represented in multiple ways?
How can integers be represented by models and real world situations?
How can a number line help in comparing integers?
How can students recognize integers and their opposites with and without the number line?
In what ways can rational numbers be useful?
Summative Assessment
Use the Understanding Integers assessment (attached).
Use the Understanding Integer enrichment (attached).
Integer Investigation.doc
Understanding Integers Assessment.doc
Understanding Integers Enrichment.doc
page 2 of 4 Formative Assessment
Ask students to provide examples of positive and negative numbers in the real world. Examples include temperature, speed limit signs, spending and saving money,
gaining or losing yards in a football game.
Use the Understanding Integers Opening Activity (attached) to assess prior knowledge.
For students who need additional help understanding integer placement on the number line, teacher can use direct instruction or small group instruction.
For students ready to move on, there is an enrichment activity (attached) where students would create their own mountain picture placing and appropriately
placing the position of objects as integers.
The Integer Investigation is a guided inquiry to integers and is best used when students are working with partners or in small groups to encourage student dialogue.
The teacher may use sections of the Integer Investigation for a formative assessment and use the results to adapt future instruction. Teacher has the option to
debrief after each section or after a designated group of sections is done to assess student understanding. Teacher should circulate during the investigation to
check for student understanding and ask guiding questions.
Understanding Integers Opening Activity.doc
Integer Investigation.doc
Understanding Integers Enrichment.doc
Feedback to Students
As students are working, either individually or with partners, teacher should circulate among students checking for understanding.
Teacher should ask guiding questions.
During Investigation Activity, the teacher will bring class together after one or two sections are complete to debrief.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Provide integer chips to students who need more visualization of the integers.
Provide small group or direct instruction for struggling students.
Create diverse partnerships for this unit.
Allow students to come up with an Integer project of their own choosing (with teacher permission).
Allow students time to play online computer games to assist in understanding.
National Library of Virtual Manipulatives, Number Line Bounce:
http://nlvm.usu.edu/en/nav/frames_asid_107_g_3_t_1.html
Extensions:
Ask students to research the history of negative numbers
Allow students to complete more than one project
Have students create a game for understanding integers and their opposites
Suggested Technology: Computer for Presenter, Computers for Students, Internet Connection, Interactive Whiteboard, LCD Projector, Java Plugin
Special Materials Needed:
Pencil
Paper
Colored pencils
rulers (to draw number lines)
Playing Cards - one set for every 2 students. All face cards (kings, queens, jacks, and jokers) should be removed prior to giving to students.
All handouts
Further Recommendations: I have found that my "Florida" students have no trouble visualizing integer distance from the top of a dive board to the bottom of a
pool, but really struggle with the idea of elevators going underground. To help them develop understanding, I have found that showing pictures of the Mall of America
really allows them to see that there can be buildings, stores, and even amusement parks underground. We also discuss mountains and why Denver is called the Mile
High City.
Additional Information/Instructions
By Author/Submitter
This lesson incorporates the following Standards for Mathematical Practice:
MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them;
MAFS.K12.MP.2.1 Reason abstractly and quantitatively;
MAFS.K12.MP.3.1: Construct viable arguments and critique the reasoning of others. Sample questions for each are attached as a Word document under Attachments. Pay
close attention to vocabulary during this lesson. For many students, the concepts of ascend, descend, withdrawal, and deposit are new. This is a great opportunity to develop
some rich vocabulary.
SOURCE AND ACCESS INFORMATION
Contributed by: Laura Bamberger
Name of Author/Source: Laura Bamberger
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.6.NS.3.5:
Description
Understand that positive and negative numbers are used together to describe quantities having opposite directions or
values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric
charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0
in each situation.
page 4 of 4