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This lesson provided by:
Author: Sara Little
System:Hoover City
School:Hoover High School
Lesson Plan ID: 26361
Title:

Midpoint of a Line Segment.

Overview/Annotation:

Investigate finding the midpoint of a line segment and derive the formula for the midpoint of two points on a coordinate plane. 

This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

Content Standard(s):
MA2013(8) 7. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5]
Local/National Standards:

 

NCTM Principle's and Standards:

Problem Solving
Instructional programs from prekindergarten through grade 12
should enable all students to-

Build new mathematical knowledge through problem solving
Solve problems that arise in mathematics and in other contexts
Apply and adapt a variety of appropriate strategies to solve problems.

Reasoning and Proof
Instructional programs from prekindergarten through grade 12 should enable all students to-

Recognize reasoning and proof as fundamental aspects of mathematics
Make and investigate mathematical conjectures
Develop and evaluate mathematical arguments and proofs
Communication
Instructional programs from prekindergarten through grade 12 should enable all students to-

Organize and consolidate their mathematical thinking through communication
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others
Analyze and evaluate the mathematical thinking and strategies of others;
Use the language of mathematics to express mathematical ideas precisely. 

Primary Learning Objective(s):

The students will be able to determine the midpoint of a line segment on a coordinate plane using the midpoint formula.

Additional Learning Objective(s):  
Approximate Duration of the Lesson: 31 to 60 Minutes
Materials and Equipment:

Investigation of a Midpoint Activity sheet (attached), pencil, chart paper, meter sticks and markers.

Technology Resources Needed:

Computer with Internet access and LCD projector.

Background/Preparation:

The student should be able to graph points on the coordiante plane and find the mean of 2 or more numbers.

Procedures/Activities:

Engage:

Have students view attached dividing video clip and follow with a discussion.  Sample questions:

What is the machine doing to the dough?
What do you notice about all the pieces of dough?

Make sure students notice that all pieces of dough are of equal size.  Conclude the discussion with telling the students they are going to investigate how to divide a line segment into two equal parts by finding the midpoint.

Explore: 
Have students in groups of 4. Give each student an Investigation of Midpoint of a Line activity sheet (attached), and each group a piece of chart paper, markers and meter stick. Students will work together to complete the activity sheet and then come to a consensus on a formula for midpoint.  They should then complete the chart paper for their presentation.  Teacher should monitor groups and ask leading questions such as:

What could you use to represent the numbers so you can write a formula?
How did you find that midpoint?
Are you sure that is really the midpoint?
Can you prove your point is the midpoint?

Explain: 
Groups make presentations and teacher asks probing questions and leads the class to a consensus of the formula for midpoint.  Teacher should monitor groups and ask leading questions such as:

  1. How did you find the midpoint given two endpoints?
  2. How is the challenge problem different from the original problems where you were finding the midpoint?
  3. Can you write the formula for midpoint including the equals sign, and then substitute the information that you have and then solve for the missing parts?
  4. What is the equation of a line in slope intercept form?
  5. Can you find the slope of the line between the original two points? 
  6. What is the slope of the perpendicular line?

Extend: 

With students still in their groups, have them complete the Midpoint Formula Extra Practice and Extension activity sheet.  Encourage groups to work together on the challenge questions. 


Attachments:**Some files will display in a new window. Others will prompt you to download. InvestigationofMidpointofaLine.rtf
MidpointFormulaExtraPracticeandExtension.rtf
Midpointgrouprubric.pdf
dividingvideo.wmv
Assessment Strategies:

Evaluate:  Teacher is monitoring groups thorough out the lesson.  Activity sheets can be turned in for individual grades.  Groups can be evaluated.  See attached rubric.

Extension:

The Midpoint Extra Practice and Extension Activity sheet includes challenge problems for groups that find the midpoint formula quickly or for those groups that already know the midpoint formula.  Special needs students needing additional assistance can use the following link for a midpoint tutorial.

Use the link to use a midpoint calculator.

Remediation:

Use the following link for a tutorial for students that are absent or that are still having difficultly using the midpoint formula.

Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems.

Presentation of Material Environment
Time Demands Materials
Attention Using Groups and Peers
Assisting the Reluctant Starter Dealing with Inappropriate Behavior

Be sure to check the student's IEP for specific accommodations.
Variations Submitted by ALEX Users:
Alabama Virtual Library
Alabama Virtual Library

Hosted by Alabama Supercomputer Authority
The University of Alabama at Birmingham
The University of Alabama at Birmingham
The Malone Family Foundation
The Malone Family Foundation
Thinkfinity
Thinkfinity
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