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This lesson provided by:
Author: Kenneth Webb
System:Tuscaloosa City
School:Tuscaloosa City Board Of Education
Lesson Plan ID: 33241
Title:

Matrices, We Don't Die, We Multipy!

Overview/Annotation:

This lesson allows students to Multiply Matrices by scalars and Multiply Square 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 Trigonometry8. (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. [N-VM7]
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 multiplying square matrices.  Students will be given Multiplication Matrix problems with step by step work with solutions.  Students will use steps and 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 multiplying square 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, exit slips, 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 may be needed.

Background/Preparation:

Teachers

  • Have graphing calculator ready to be assigned.
  • Have Matrices with step by step work and solutions for Multiplying
  • Have all poster paper, markers, etc. ready for student use

Students:

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

ENGAGE

As students enter the classroom, they should be given a group indicator that tells where to sit.  Students will watch clips as a class: Scalar Multiplication, Scalar Matrix Multiplication, Multiply a Matrix by a Matrix from this websites 

https://www.khanacademy.org/math/algebra/algebra-matrices/Basic_matrix_operations/e/scalar_matrix_multiplication

https://www.khanacademy.org/math/algebra/algebra-matrices/matrix_multiplication/e/multiplying_a_matrix_by_a_matrix

Students will listen and jot down important ideas.  Inform the students that their mission will be to determine the process for multiplying Matrices.  

EXPLORE

Student groups will receive scalar and matrix multiplication problems with step-by-step work and solutions.  Students should develop strategies for solving these matrices.  Student groups will have matrix problems and solutions of square and different size matrices.  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 if needed). 

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. 

If students are unable to understand Matrices and dimensions, provide necessary feedback to move them forward with their thinking.  Refer to the previous clips again for review. 

EXPLAIN

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

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

Allow students time to prepare attractive posters to share with class to begin discussions about multiplying matrices, along with having the groups share their findings using the Smartview function of the calculator. Student Groups will receive exit slip the last 10 minutes of class.  This should be turned in to the teacher as the groups exit the class.


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

Use the exit slip provided in the last 10 minutes of class to assess student work individually and as a group. Students should justify all reasoning.  Exit slips are to be shared with the class the next day at the beginning of class.  The assessment process is on-going. The teacher should visit each group while students are preparing posters for justified reasoning and ask questions to make sure students understand the process for multiplying matrices.  Post the posters in the classroom and have students present conclusions.  As students present posters, they should compare posters for other information not listed on their group's poster.

Extension:

Extensions can begin with a Computer Animation Activity: 

http://illuminations.nctm.org/Lesson.aspx?id=3141

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:
Alabama Virtual Library
Alabama Virtual Library

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The University of Alabama at Birmingham
The University of Alabama at Birmingham
The Malone Family Foundation
The Malone Family Foundation
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Thinkfinity
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