Step 1: Inquiry Approaches to Learning
Teach 1
Names of student(s) teaching:
Teach date:
Teach time:
Teach length:
Title of lesson: matrix multiplication
Concept statement/Main idea:
The big idea is to reach an understanding of matrix multiplication beyond the memorized routine
most learners have. This will be accomplished through an investigation of the dot product of vectors
and ISBN13 and UPC barcodes, and extended to small and large matrices.
Standards for the lesson:
HS.Modeling ; & beyond the NVACS
Objectives. Write objectives in LWBAT form.
Evaluation
LWBAT:
Write at least one question to match the
objective you listed or describe what you will look
at to be sure that students can do this.
Learners will be able to use dot product to verify
UPC and ISBN13 barcodes and practice matrix
multiplication on 2x2, 3x3, and (axn)(nxb) matrix.
How is matrix multiplication and scalar
multiplication of matrix related?
How can you scale the multiplication of vectors
to the multiplication of matrix?
Step 1: Inquiry Approaches to Learning
Engagement
Estimated time: 5 minutes
Description of activity: A conversation about the meaning of UPC and ISBN13 BarCodes. Some
history, and connection to the topic of vectors.
What the teacher does
What the student does
Possible questions to ask
students — think like a
student and consider
possible student responses
Asks; “How many bar codes do you Looks for all the barcodes they “Why do you think are there
have in your possession right
have in their wallet/ purse/
some common numbers?”
now?”
backpack.
“Why do you think are some
Displays all the barcodes on
numbers different?”
table.
“Have you ever wondered
what those numbers mean?”
“There is a pattern, a
connection between all those
numbers. Would you like to
know what it is?”
Resources needed:
Paper, Pencils/pens
Safety considerations:
None
2
Step 1: Inquiry Approaches to Learning
Exploration
Estimated time: 15 minutes
Description of activity: Practice with the vector dot product with varying materials learners
brought to class
What the teacher does
What the student does
BRIEFLY show the math for dot
product of two vectors (also called
scalar multiplication.)
Explores the dot products of
varying ISBN13’s and UPC
codes.
Depending on how deep you want
to go with the exploration, some
of the questions on the right may
be beyond the class you are
teaching.
Possible questions to ask
students — think like a
student and consider possible
student responses
Why is it called scalar
multiplication?
Why does the scalar always
end in a zero?
What does it mean if it does
not end in a zero?
Why did the designers CHOOSE
a vector of repeating [3,1…]
Why did the designers choose
to have a “1” multiplying the
check digit?
When could numbers be
transposed and the scalar still
ends in a zero? (yes, it is
possible)
Resources needed:
Paper, pencils/pens, several ISNB13’s and UPC codes.
Safety considerations:
None
3
Step 1: Inquiry Approaches to Learning
Explanation
Estimated time: 10 minutes
Description of activity: Teachers asks questions to set up the explanation of
What the teacher does
What the student does
Asks questions
Thinks and discusses in
groups, whole class.
Possible questions to ask
students — think like a
student and consider possible
student responses
Are there any other definitions
of the process that will lead to
a scalar answer? What would
they be?
Or
What other methods could we
use to calculate a single
number from the two vectors?
Explain?
Why is the method we used,
multiplication and addition, the
method that is preferred?
What are the advantages of
this method over the methods
you came up with?
We multiplied (1x12)(12x1)
vector and ended up with a
(1x1) vector; a scalar number.
What would happen if we
multiplied vectors that are
(2x12)(12x2)? Why? What
would such a vector represent?
Resources needed: same
Paper, pencils/pens
Safety considerations:
4
Step 1: Inquiry Approaches to Learning
Elaboration
Estimated time: 10 minutes
Description of activity:
What the teacher does
What the student does
Asks questions
Works problems, discusses in
groups and whole class
Possible questions to ask
students — think like a
student and consider possible
student responses
Since we predicted the
multiplication of (2x12)(12x2)
would give us a (2x2) matrix,
let’s see if we can explain why
it works? Multiply a (2x3)(3x2)
matrix. Explain how it works,
by referring back to the scalar
multiplication.
What about a (2x2)(2x2),
(3x3)(3x3)?
What about a (2x3)(2x3)? Will
it work? Why not? Refer back
to scalar multiplication in your
explanation.
Given what you know,
generalize the definition of
Matrix Multiplication to the
general form of matrix
multiplication; 𝛿𝑖𝑗 .
Resources needed:
Paper, pencils/pens
Safety considerations:
None
5
Step 1: Inquiry Approaches to Learning
Evaluations
Estimated time: 5 minutes
Description of activity: knowledge check to see if learners mastered the material. Learner must
have 100% accuracy on 1 problem.
What the teacher does
What the student does
Possible questions to ask
students — think like a
student and consider
possible student responses
Throughout lesson, teacher will
observe and correct
misconceptions.
Make mistakes and fixes
them.
Are you confident you did that
correctly?
Teacher will give 1 problem at end
of class that is a 2x3 matrix
multiplication problem.
Did you check your answer
with a classmate?
Multiplies the matrices
together.
Teacher asks for numbers from
the class to represent shear
and fracture values for
materials in a 2x3 and 3x2
matrix. Learners multiply them
and check for correct answer.
Resources needed:
Paper, pencils/pens
Safety considerations:
None
6