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© 2014 Pacific Crest
5
M
odel(s)
Exemplars and representations
Learning to Multiply and Divide Fractions: Applying the Learning Process Methodology
I have always found it difficult to remember how to correctly multiply or divide fractions; I just can’t
remember which thing to “flip” and always need to be reminded. Because I’m so unsure of myself, I also
end up feeling that I need to ask others if I’ve done it correctly. I’m tired of not being able to do this and
want to learn to perform this common math task independently and with confidence.
Step
Explanation
1. Why
I am tired of not knowing how and why the calculations of fractions work,
especially when multiplying and dividing
2.
Orientat
i
on
Numbers can be represented in many ways: as whole numbers, decimals,
and fractions. Having to switch representations in order to perform
calculations is slow and limiting. I therefore need to be able to perform
calculations in all three of these forms.
3.
Prerequisites
addition, subtraction, and multiplication of whole numbers
4.
Learning
Objectives
1.
Learn to multiply fractions 2. Learn to divide fractions
3.
Learn the relationship between the multiplication and division of fractions
5.
Performance
Criteria
Perform the multiplication and division of any improper fraction, giving an
accurate, validated, and well-reasoned answer
6.
Vocabulary
numerator
—
the top portion of the fraction
denominator
—
the bottom portion of the fraction
multiplicative
identity
—
multiplying by 1 leaves a number unchanged
reciprocal
—
the fraction multiplied by its reciprocal is 1
7.
Information
× =
× =
= × =
a
a b a c ac
a d ad
b
c
b a b d bd
b c bc
d
1
8.
Plan
How will I use multiplying and dividing fractions in the future? Most likely,
when finding how I can divide things among people and how many portions
make up how many wholes.
9.
Models
Dividing a pizza among a group of people
10.
Thinking Critically
Q1. What is a half of a half of a pizza (one half divided in two)?
1/4
Q2. How do you calculate this mathematically?
÷ =
=
×
1
1 1 1
2
2
2 2 4
Q2. Assume there are three people and there
is only 2/3 of a pizza. How much does each
person get?
This is 2/3 divided in 3:
÷ =
=
×
2
2 1 2
3
3
3 3 9
1.1 The Learning Process Methodology