id: 06439671
dt: j
an: 2015d.00718
au: Davis, Marsha
ti: Modeling with matrices.
so: Consortium 107, 16 p., pull-out section (2014).
py: 2014
pu: COMAP (Consortium for Mathematics and Its Applications), Bedford, MA
la: EN
cc: H64 D84 U64 M14
ut: linear algebra; matrices; student activities; matrix calculations; matrix
addition; matrix subtraction; scalar multiplication; matrix
multiplication; graphing calculators; spreadsheets; population growth;
worksheets; mathematical applications; everyday mathematics
ci:
li:
ab: From the text: This Pull-Out provides real-world 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 TI-84 graphing calculators. Then they use their calculators
to determine sums and differences of two matrices. 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 multi-row matrix and
a multi-column 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.
rv: