Delta Math and Science
Partnership Initiative
M3 Summer Institutes
(Math, Middle School, MS Common Core)
Multiplication of Fractions
Materials Needed
•
•
•
•
•
Kit Kats
Copy Paper
Grid Paper
Adding Machine Tape
Colored pencils
Consider the following Problem
Jeya brings a Kit Kat to school. She decides to eat ¼ of it. Her
best friend Bailey asks for a piece, so Jeya gives her ½ of the
piece that she intends to eat. How much of the Kit Kat does
Bailey receive?
Use your
bar to find the solution.
Let’s Look at the Model
Jeya has…
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
of Jeya’s Kit Kat she intends to eat
4
If Jeya gives Bailey ½ of the piece that
she intends to eat, how much of the Kit
Kat does Bailey receive?
1 Kit Kat
Jeya’s half
Bailey’s half
Consider the following Problem
You have ¾ of a pizza left. If you give ⅓ of the leftover
pizza to your friend, how much of a whole pizza will
your friend get?
Consider the following Problem
Kierra and Danielle climb a rock wall. Kierra climbs ½
of a rock wall’s height. Danielle climbs ⅔ of Kierra’s
distance. What fraction of the total height does
Danielle climb? Use a model.
So…
Danielle climbs
2
of the total
6 height.
Another Example
The Cleveland Park Commission offers a rock-climbing
class for children ages 8-17. In one session, ⅘ of the
students are 12 years old. Of the 12-year-old
students, ¼ are from Merigold. What fraction of the
students are 12 years old and from Merigold?
Look at the two factors and the product in each
problem. Compare the numerator and denominator
of the product with the numerators and
denominators of the factors. What relationship do
you see?
1 1 1
of is
2 4 8
1 3 3
of is
3 4 12
factor
2 1 1
of is
3 2 3
factor
1 4 4
of is
4 5 20
product
Problems Involving Mixed Numbers
A student skis 3 ½ miles in an hour. An instructor can
ski 1 ⅓ times as far in an hour. How far does the
instructor ski in an hour?
More
A painting is 1 ¾ feet by feet. What will a copy of the
painting be if its length and width are 1 ⅝ the size of
the original?
Homework
Heather is helping out at Sunshine Preschool. At
noon, she notices that ½ of the children are missing.
When she calls for them, ½ of the missing children
return to the room. But as soon as Heather turned
her back, ½ of the children in the room left again. Of
those who remain in the room, ½ are playing with
blocks, ⅓ play with the dress-up clothes, and the rest
looked at books. If just one child is looking at a book,
how many children were in the room before noon?