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This lesson provided by:
Author: Kenneth Webb
System:Tuscaloosa City
School:Tuscaloosa City Board Of Education
Lesson Plan ID: 33217
Title:

Does Size Matter?

Overview/Annotation:

This lesson allows students to add and to subtract Matrices.  Students can use graphing calculators to input Matrices.  Students will work cooperatively to develop and justify ideas/conjectures.

This is a College- and Career-Ready Standards showcase lesson plan.

Content Standard(s):
MA2013(9-12) Algebra II with Trigonometry9. (+) Add, subtract, and multiply matrices of appropriate dimensions. [N-VM8]
Local/National Standards:

  • Standard 1: Make sense of problems and persevere in solving them
  • Standard 2: Reason abstractly and quantitatively
  • Standard 3: Construct viable arguments and critique the reasoning of others
  • Standard 4: Model with mathematics
  • Standard 5: Use appropriate tools strategically
  • Standard 6: Attend to precision
  • Standard 7: Look for and make use of structure
  • Standard 8: Look for and express regularity in repeated reasoning
Primary Learning Objective(s):

Students will discover and use the process for adding and subtracting matrices.  Students will be given addition and subtraction Matrix problems with solutions.  Students will use solutions to derive strategies for the problems.  Students will eventually solve problems and justify reasoning for developed discoveries.

Additional Learning Objective(s):

Students will work cooperatively to discover patterns or strategies for adding and subtracting matrices.  Students will verify conclusions by showing relationships of matrix entries with rows and columns.  Students will document strategies and support with evidence/reasoning. 

Approximate Duration of the Lesson: 31 to 60 Minutes
Materials and Equipment:

Poster Paper or Poster with grid lines, sticky notes of different types, straight edge, markers, student may use their own devices or teacher issued graphing calculators.

Technology Resources Needed:

Computer with Internet access, LCD Projector and Document camera to share student work (helpful but not necessary.) Smartview with calculator is needed.

Background/Preparation:

Teachers

  • Have graphing calculator ready to be assigned.
  • Have Matrix solutions for Adding and Subtracting
  • Have all poster paper, markers, etc., ready for student use.

Students:

  • Algebra students should be able to Add and Subtract Real Numbers.  
  • Students should be familiar with identifying dimensions of Matrices and have some knowledge of using the graphing calculators.
Procedures/Activities:

ENGAGE

1.  As students enter the classroom, they should be given a group indicator that tells where to sit to begin working with assigned matrix investigation. Inform the students that their mission will be to determine the process for adding and subtracting Matrices.  

EXPLORE

2.  Student groups should develop strategies for adding and subtracting matrices.  Student groups will have matrix problems and solutions of square and different size matrices.  

3.  They should record these findings on their own paper (this information is to be placed on poster paper and problems can be keyed into their graphing calculators). 

4.  The students should determine if their strategies are reputable and mathematically sound.  They should look for patterns and list them on chart paper.  The groups must agree on findings and be able to justify. 

5.  If students are unable to understand Matrices and dimensions, provide necessary feedback to move them forward with their thinking.  Refer to:  http://www.purplemath.com/modules/mtrxadd.htm

EXPLAIN

6.  The teacher should be sure that students are using Matrices and dimensions correctly.  

7.  Groups will discuss strategies discovered and begin justifying their ideas; Groups can use graphing calculators to input matrices for further justification.

8.  Allow students time to prepare attractive posters to share with class to begin discussions about adding and subtracting matrices, along with having the groups share their findings using the Smartview function of the calculator.


Attachments:**Some files will display in a new window. Others will prompt you to download. RubricMatrix.docx
Assessment Strategies:

EVALUATE

Use the rubric provided to assess student work individually and as a group. Students should justify all reasoning stated on poster.  The Assessment Process is on-going. The teacher should visit each group and ask questions to make sure students understand the process for adding and subtracting matrices.  Post the posters in the classroom and have students present conclusions.  As students present posters and graphing calculator findings, they should compare posters for other information not listed on their group's poster.

Extension:

Extensions can be to develop strategies for adding and subtracting any size matrix.  Also, how is multiplying matrices similar to adding and subtracting.  Have students justify their reasoning. 

Remediation:
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:
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Alabama Virtual Library

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The University of Alabama at Birmingham
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The Malone Family Foundation
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Thinkfinity
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