The students will use pictures of patty paper to partition fractions of
fractions . We found that
students seem to be able to see multiplication ideas better if they draw one
fraction using
vertical lines and then finding the fraction of this fraction using horizontal
lines. In the Kathy’s
cake example, the students are told that Kathy has three-sevenths of a cake left
over as shown in
the picture below.

Kathy’s Cake

Kathy is then going to eat two -fifths of this amount of
cake. Although you could draw in
vertical lines to find two-fifths of the three-sevenths it would be difficult to
see. Please model
and encourage your students to draw in horizontal lines when they partition the
three-sevenths
into fifths. To explain the amount of the darkly shaded part of the cake,
students will need to
extend the horizontal lines across the whole patty paper. If students folded the
patty paper first
into sevenths and then into fifths, the paper would have creases showing the
horizontal
partitions.

two-fifths of three-sevenths darkly shaded

By the end of the lesson you want students to be able to explain that the
product of the
denominators show the size of the pieces. When you take fifths of sevenths you
will get pieces
that are thirty-fifths of the unit. The product of thenumerators is more
difficult to explain. The
students should be able to explain that the total number of darkly shaded pieces
can be counted
by finding the product of the numerators.

By the end of this lesson students should be able to reason that the product of
the numerators
determine the number of pieces that you are interested in and the product of the
denominators
is the number of pieces in which the unit is partitioned.

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