Unit Title: Multiplying and Dividing Fractions (intended for 8th grade Pre-Algebra—week 13)
By conducting a lesson which features an exploratory activity and some basic principles, I
will be able to draw on students’ prior knowledge regarding properties of fractions and
addition/subtraction of fractions to aid in their understanding of a new aspect to fractions. This
learning experience connects to Illinois State Goal 6, Objective 6.A. 1a, Objective 6.B. 2,
Objective 6.C. 2a, and Objective 6.C.3a.
Students will multiply proper fractions using the grid representation and then will solve
problems on a worksheet after working through examples as a class with the instructor. In
addition, students will begin to extend their new knowledge to multiplying fractions in
Materials and Lesson Aids
Grid representation website:
Computer (to show students the program)
Projector—if needed to project computer screen on board
Supplemental Grid Worksheet for each student
Supplemental Fraction Worksheet for each student
Markers or highlighters
Cut-out shapes (various fractions shaded)
Accommodations for Exceptional Learners
Students who have difficulty with their multiplication tables can be given a
supplemental times table to work with
Students with visual disabilities could receive an grid paper with larger rectangles to
make it easier to see
Conveying the multiplication of fractions in a graphic form may be helpful for visual
learners and may make the concept more concrete
Time Estimate Core Components and Method Markers
7-9 min. Hook
*Pass out shapes with various areas shaded representing different fractions
What do you notice about these shapes? (Possible answer: there is a portion
that is shaded)
What do we call this portion? (A fraction)
How do we represent it? What is the notation?
Go back to the shapes and the fractions students identified for each shape
Why does this picture represent _(insert fraction)_? (The shape is divided into
___ parts and there are ___ parts shaded.)
After students give proper answer:
How do we solve this? (write a problem on the board i.e. ½ x ¾ )
Students should know the answer is 1/6, they may spit it out. (If this doesn’t happen, or
their answer is incorrect, this will lead nicely into lesson also because we will be
covering how to multiply fractions in lesson.)Follow with:
Why is the answer 1/6?
Let students struggle for a moment or two and then move on to lesson.
We’ve already worked with adding and subtracting fractions, today we’re going to work
on multiplying fractions.
What do you think happens when we multiply fractions? Why?
25-30 min. Development
*Pass out grid paper with blank rectangles/squares on it and pull up website on
computer or draw on board
OK class; let’s say we want to multiply 1/3 by 3/4. Another way of saying this 1/3 of 3/4.
How can we represent 1/3 on the rectangle? (Divide into three equal parts and
Is there a way to represent 3/4, but in a slightly different way? (Yes, if divided
using rows the first time, use columns this time or vice versa, divide into 4 and
What does this show us? What does this picture represent? **Show on board
Let’s try another.
How would we solve 2/3 x 3/5?
First, how would we construct our rectangle?
Where would be shade?
What does this show?**Show on board
What do you notice about the answers? How does it relate to the fractions we start
with? (The final answer’s numerator is the # of squares shaded with both colors and the
final answer’s denominator is the total # of squares in the rectangle after we’ve divided
it up properly)
Hence, final answer = # square with both colors/total # squares
Now, for our first example, do you notice anything interesting about the fractions we
multiply and the answer (before we simplify)? (Students should notice that if you
multiply the numbers in the numerators, the answer is the number in the numerator of
the final answer. Also, they should notice that if you multiply the numbers in the
denominators, the answer is the number in the denominator in the final answer)
*Pass out supplemental fraction worksheet and have them solve a few—the rest is
6-8 min. Applying the concept
Write some harder fractions on the board and ask them to solve them
After, write some equations on the board that have fractions in them and ask
them to solve these. Examples: 2/3x = 5/8 and 1/4 ÷ y = 6/7. My intention with
these problems is to challenge the students to think further—this would serve
as a problem solving activity and could potentially lead into lesson taught later
in the week.
2-3 min. Culmination: Wrap Up
Today we discovered how to multiply fractions and we were able to show, using a
diagram how it works. Then, we discovered a trick to multiplying fractions to make it a
little easier. If you didn’t get the problems I just presented to you, don’t fret! We’ll be
working with more problems like these in the next few days
For tomorrow’s class, I would like you to work on those problems I gave you towards the
end of class and see if you can solve them. Can you find any tricks?
The next day, I would look at their supplemental worksheet and use that as a formative
assessment to see if the students understood the concepts we discussed in class.