Title: To navigate the PowerPoint presentation place the mouse arrow inside the box containing the slide and click on the mouse to advance the program. Or, use the up and down arrows on your keyboard
1To navigate the PowerPoint presentation place
the mouse arrow inside the box containing the
slide and click on the mouse to advance the
program. Or, use the up and down arrows on your
keyboard
2Multiplying Fractions
- When teaching children how to multiply fractions,
it is important to make the process meaningful.
This may be done best by using a five-step
process that helps children to visualize fraction
multiplication, understand fraction
multiplication, be able to do fraction
multiplication, and be confident when multiplying
fractions.
3- In the first step of this instructional process,
children use a model to find answers to some
fraction-multiplication examples. - In the second step (which really happens
concurrently with step one) the children keep a
record of the results from step one.
4- After enough examples have been completed the
children move to the third step. They look for a
pattern that suggests how to do the
multiplication without the model. - In the fourth step the children hypothesize how
to do the multiplication without the model.
5- This hypothesis really a first description of the
fraction-multiplication algorithm (procedure). - The fifth step is to complete examples using the
hypothesized procedure and then redo those
examples with the model to check the correctness
of the procedure.
6- Of course, this 5-step instructional process can
only work if you have an effective (and
believable) way to model the multiplication of
fractions. - We will look at three procedures for modeling
fraction multiplication that are found in the
literature.
7There are 3 approaches for modeling fraction
multiplication
- A Fraction of a Fraction
- Length X Length Area
- Cross Shading
We will now examine each of these 3 approaches.
8We will think of multiplying fractions as finding
a fraction of another fraction.
We use a fraction square to represent the
fraction .
9Then, we shade of . We can see that it is
the same as .
But, of is the same as .
X
So,
10To find the answer to , we will use the
model to find of .
We use a fraction square to represent the
fraction .
11Then, we shade of . We can see that it is
the same as .
12In this example, of has been shaded
What is the answer to ?
X
13- Modeling multiplication of fractions using the
fraction of a fraction approach requires that the
children understand the relationship of
multiplication to the word of. - We can establish this understanding showing
whole-number examples like 6 threes is the same
as 6 X 3.
14In the second method, we will think of
multiplying fractions as multiplying a length
times a length to get an area.
15In the second method, we will think of
multiplying fractions as multiplying a length
times a length to get an area.
16We think of the rectangle having those sides.
Its area is the product of those sides.
17We can find another name for that area by seeing
what part of the square is shaded.
18We have two names for the same area. They must
be equal.
19Length X Length Area
This area is X
20What is the answer to X ?
21- Modeling multiplication of fractions using the
length times length equals area approach requires
that the children understand how to find the area
of a rectangle. - A great advantage to this approach is that the
area model is consistently used for
multiplication of whole numbers and decimals.
Its use for fractions, then is merely an
extension of previous experience.
22In the third method, we will represent both
fractions on the same square.
is
23The product of the two fractions is the part of
the square that is shaded both directions.
X
is
is
24We will look at another example using cross
shading. We shade one direction.
25Then we shade the other direction.
The answer to X is the part that is
shaded both directions.
26- Modeling multiplication of fractions using the
cross shading approach does produce correct
answers. However, to children, it is a nonsense
method. - The rationale for the answer, because it is
shaded both directions does not make sense. It
would make as much sense to say that the answer
is all the parts that are shaded only one
direction or the part that is not shaded.
27- If the rationale for the answer does not make
sense to the children--if it is not
meaningful--it is simply another rote rule. For
this reason, THE CROSS SHADING METHOD IS NOT
RECOMMENDED. Teachers should choose to use
either the fraction of a fraction method or the
length times length equals area method when
modeling multiplication of fractions.
28- With your partner, practice using the fraction of
a fraction method to model multiplication of
fractions until you are both comfortable enough
to make a presentation using the method. - Also, practice using the length times length
equals area method to model multiplication of
fractions until you are both comfortable enough
to make a presentation using this method. - When you are ready, make an appointment with your
instructor to demonstrate each method.
29The End
- Dr. Benny Tucker
- Ex. 5396