Matrices and Zombies
An Instructional Plan
Andria Campbell (Wiseman)
Purdue University: EDCI 566
04/12/2014
AN INSTRUCTIONAL PLAN 2
Description of Topic and Target Audience
Description of Topic
The overall focus of this unit is to introduce matrices to Algebra 2 students and how to perform
operations with them (addition, subtraction, and multiplication), find their determinants, and ultimately
solve systems of equations using Cramer’s Rule using the determinants of matrices. The specific job aid
created for this lesson will entail teaching students how to utilize graphing calculator functions to edit and
complete these operations. The point of this is to offer students a tool for checking for mistakes, which
are easy to make with the many calculations involved with matrices, not only this, but to show when it is
appropriate to utilize a calculator to save time and when it is not.
The job aid itself is a website that is organized into tabs for entering a matrix, adding matrices,
subtracting matrices, scalar multiplication on a matrix, multiplying matrices, determinants, and Cramer’s
Rule. Students will click on the area they are wishing to learn where they will be presented with a video
(narration with correlating graphing calculator images) that instructs them how to complete that task. As
you will read below, there will be a Guided Handout that they will use to organize their learning with a
quick practice problem for each area all to the theme of saving the world during the zombie apocalypse.
Target Audience
Audience Grade Level:
Audience Characteristics:
Lesson Groupings:
High School Students
(Grades 9-12)
This will be completed in a
general education setting with
mixed-ability learners.
Some work will be completed
individually, some in pairs, and
twith a beginning and ending
whole class discussion for
reflection.
Objectives and Scope and Sequence
Objectives
After completion of this chapter students will be able to:
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Correctly name matrices and identify them via the number of columns and rows.
Write matrices from problem situations.
Perform operations with matrices (addition, subtraction, and multiplication).
Find the determinants of 2x2 and 3x3 matrices.
Utilize Cramer’s Rule to solve systems of equations in both two and three variables.
AN INSTRUCTIONAL PLAN 3
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Use a graphing calculator to input a matrix, perform operations on matrices, find determinants,
and utilize Cramer’s Rule to solve systems of equations.
Decide when it is most efficient to rely on the graphing calculator to do calculations and when not
to, and to recognize possible errors that may occur when solving problems by hand versus in a
calculator and vice versa.
Scope and Sequence
It is necessary to understand that for the specific lesson utilizing the job aid involving graphing calculators
students will have already learned the material necessary to complete the objectives by hand, and will
have already been assessed on their mastery of doing so. The following lists the scope and sequence for
the specific lesson involving the job aid, where students will learn how to do on the graphing calculators
what they already have mastered by hand for the purpose of faster application and a reflection of when
calculators are efficient, when they are not, and what human errors could still occur. This job aid is all to
the theme of saving humanity from the zombie apocalypse.
1) Pre-Instruction Preparation
Before coming to class students should have written down reflections for the following questions:
a) What matrix operations (addition, subtraction, scalar multiplication, multiplication,
determinants, and Cramer’s Rule) do you find easiest to do and why?
b) What matrix operations (addition, subtraction, scalar multiplication, multiplication,
determinants, and Cramer’s Rule) do you find most difficult to do and why?
c) What are the most common errors you have caught yourself making when working with
matrices? What have you done to try to correct these mistakes?
2) Pre-Instruction Question Sharing (5-10 minutes)
The instructor will spend 5-10 minutes on getting students’ responses to the pre-instruction
questions and creating a class list of answers on the whiteboard for each question.
3) Pair Work in Computer Lab (40 minutes)
a) The instructor will hand out the Guided Handout and direct students to the job aid and tell
them to follow the directions on the Guided Handout.
b) The students will use the Guided Handout and the job aid to use graphing calculators to
answer a series of problems on the Guided Handout (from addition to solving using Cramer’s
Rule). Though this task is done individually on a computer, pairs of students will work
together on the problems after each video presentation.
c) Once completed, the students will get the guided handout checked by the instructor, and
should pick up the reflection questions for homework.
1) What matrix operations (addition, subtraction, scalar multiplication, multiplication,
determinants, and Cramer’s Rule) do you feel are more efficient to do on the graphing
calculator and why?
2) What matrix operations (addition, subtraction, scalar multiplication, multiplication,
determinants, and Cramer’s Rule) do you feel you should do by hand because you are
more efficient and why?
3) What errors are possible when working with a graphing calculator? What can you do to
make sure these errors do not occur?
4) Post-Instruction Reflection (5-10 minutes)
AN INSTRUCTIONAL PLAN 4
a) The instructor will spend 5-10 minutes on getting students’ responses to the questions and
making a list next to the previous list.
b) The instructor will then ask the students to look at the two list that they have created and
come to a conclusion about what operations are most efficient done by hand (perceived as
easy) and which are most efficient to do on a graphing calculator (perceived as difficult).
5) Learner Assessment (40 minutes)
After the post-instruction reflection an assessment will be handed out where students will apply
what they have learned about when to utilize the graphing calculator, as well as how to perform
operations and the other mentioned tasks with matrices.
Time, Materials, and Supplementary Materials
Time
This lesson will take all of one class period (50 minutes), the assessment of the learners will take an
additional class period (50 minutes) the following day.
Materials/Supplementary Materials
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Pre-instruction questions (to get students to thinking about what calculations are quick versus
daunting from this unit by hand)
Guided handout (an assignment to be completed during utilizing the job aid to apply what they
are learning to actual problems on paper)
Pencil, dry erase markers, and whiteboard
Computer, headphones, and internet access (computer lab)
Graphing calculator
Reflection questions (to get students to reflect on when they feel they should/should not spend
time using the graphing calculator when calculating with matrices)
Learner assessment (a test of application questions for learners to see if they apply the efficiency
of the calculator appropriately)
Evaluation of Learners and Lesson
Evaluation of Learners
Students will be evaluated on their responses to the pre- and post- reflection questions, their
participation in the class discussion, the completion of their Guided Handout, and their test on the
material. The test will be a typical chapter test on the material that will be graded for accuracy and follow
the school’s grading scale. The completion of their Guided Handout will be graded on just that; 5 points
for completing it, and participation in the class discussion will be the same. The evaluation of the
reflection questions will be graded based on the quality of their responses, based on what I as their
instructor know of their capabilities.
AN INSTRUCTIONAL PLAN 5
Evaluation of the Lesson
The evaluation for the specific use of the job aid will relate to only the last two of the objectives
listed above. The assessment will give students the choice to show their work for solving a problem by
hand, or check a box if they chose to solve the problem using a graphing calculator. If the student
chooses to use a graphing calculator for a problem and gets that problem correct then it is clear the job
aid was a success in teaching them how to use the graphing calculator for specific matrix operations. As
for the final objective listed above, if students choose to use the graphing calculator on problems where it
is the most efficient avenue (as discovered through the activity and discussion), then it is obvious they
have developed an understanding of when it is more efficient versus their own ability by hand. For this
last objective, responses to the post-instruction reflection questions will also assess whether a student
individual could decide when it was more efficient to use a graphing calculator, and will offer a second
indicator about the job aid’s ability to complete the final objective listed prior to the group discussion.
Multimedia Principles
Signaling Principle
There will be cues present that show the organization of the job aid by having the job aid broken down
itself into distinct pieces.
Redundancy Principle
There will only be animation and narration, except for the back-story explanation and labeling of the job
aid organization for signaling purposes.
Temporal Contiguity Principle
The narration will align with each image simultaneously for clarity in understanding for the learner.
Segmenting Principle
The job aid itself is segmented so that the students can work at their own pace on each aspect/topic
being discussed. There is also the option for students to review videos at any point.
Pretraining Principle
This lesson will simply show how to use a graphing calculator to accomplish the tasks they already know
how to do by hand (in some cases more efficiently). Thus, students will already be familiar with all
vocabulary and understanding, except how to use the graphing calculator matrix functions.
AN INSTRUCTIONAL PLAN 6
Multimedia Principle
There will be images to accompany the narration to help visually guide students to the correct buttons on
the graphing calculator.
Generation Principle
Students will be required to do pre- and post-instruction reflection questions to help them decide when
they are more efficient than a graphing calculator on these calculations.
Personalization Principle
I will be doing the narration in a conversational style, exactly how I speak during class.
Voice Principle
Since I will be doing the narration it will be in a friendly human, not machine, voice.