This PullOut provides realworld
settings that guide students through
matrix addition and subtraction, and
scalar and matrix multiplication. In
Activity 1, students store prices of
pizzas, salads, and soft drinks from
three pizza houses into a matrix.
Matrix addition is used to revise the
prices to reflect the cost of additional
toppings and choices of salad dressings.
After organizing information on
coupons into a matrix, matrix subtraction
is used to apply the coupons
and reduce the costs. At the end of
Activity 1, students learn how to
store matrices in TI84 graphing calculators.
Then they use their calculators
to determine sums and differences
of two matrices. (Instructions
on using Excel are included in the
Lesson Notes.) In Activity 2, students
use scalar multiplication to compare
the prices of ordering k pizzas and k
salads from each of the pizza houses.
Matrix multiplication is introduced
in three steps: (1) multiplying a row
matrix and a column matrix, (2) multiplying
a row matrix and a multicolumn
matrix, and finally, (3) multiplying
a multirow matrix and a
multicolumn matrix. Then matrix
multiplication is used to compare
three possible options for the purchases
of pizzas and salads at the
three pizza houses. At the end of
Activity 2, students use their calculators
to investigate whether the
Associative and Commutative Laws
for Addition and Multiplication,
which students have learned in their
algebra classes, also hold for matrices. Activity 3 focuses on use of matrices
to investigate a population growth
model called the Leslie model. Students
use their calculators (or Excel) to
approximate the age distribution of a
population and the size of the total population
into the future.
The activities in this PullOut address
standard NVM(69) from the Common
Core State Standards for High School
Mathematics –Perform operations on
matrices and use matrices in applications.
Here are the details of Items 6 – 9:
6. Use matrices to represent and
manipulate data.
7. Multiply matrices by scalars to
produce new matrices.
8. Add, subtract, and multiply
matrices of appropriate dimensions.
9. Understand that, unlike multiplication
of numbers, matrix multiplication
for square matrices in not a
commutative operation but still satisfies
the associative and distributive
properties.
Mathematics prerequisites and
discussion:
Students need to be able to add, subtract,
and multiply numbers. They
should be familiar with the Associative
and Commutative Laws of Addition and
Multiplication. The mathematics in this
PullOut focuses on matrices but students
do not need to have any prior
experience with matrices. After completing
this unit, students should be able to
add and subtract matrices, perform
scalar multiplication, multiply two
matrices, and raise a square matrix to a
power. Along the way, students will discover
that the Associative Laws of
Addition and Multiplication and the
Commutative Law of Addition hold for
matrices. However, the Commutative
Law of Multiplication does not hold for
matrices.
