We are confronted with problems involving
proportionality every day. Whether we compare prices in
the grocery store, enlarge a photograph to fit in a frame
or change the size of a recipe, the basic math concepts
are the same. The following lessons introduce students
to the concept of proportionality with a variety of techniques
to enlarge and reduce figures. Students compare the original
drawings with their reproduced images, examining both
size and area to learn what "similar" means and to draw
conclusions about scale factor. By working with specific
figures, students become comfortable with the ideas of
proportions and ratios and can use these concepts to solve
complex problems. More important, they will know when
this type of reasoning is most effective in problem-solving.
... discover what makes similar figures similar. They
are introduced to the concept of scale factor, and they
use scale factors to enlarge and shrink figures. Through
continued investigations, teachers determine how scale
factor affects side lengths, angles, perimeters and
areas when figures are enlarged or shrunk.
In Workshop 2: In
Practice, Learner Teachers ...
... discuss how their students approached
the Proportionality & Similar Figures lessons from
Workshop 1. Scoring guides for student work are introduced,
and the teachers learn how to sort student work into
two categories meets standards and does not meet standards.
Finally, they create new problems to deepen their students'
On the following pages, we offer agendas for two different
levels of professional development: