Congruent Figures � Congru-
ent figures have corresponding
angles that are equal and cor-
responding sides the same
length
Corresponds, Co rrespond-
ing � Corresponding sides or
angles have the same relati ve
position in similar fi gures.
Ratio � A ratio is a comparison
of two quantities that te lls the
scale between them
Scale Factor � The scale fac-
tor shows the ratio of the
lengths of similar figures. If
the scale factor is 3, all the
lengt h measures in the image
are three times the corre-
sponding measures in the
original Similar � Similar figures have t he same shape. Two figures
are mathematically similar if
and only if their corresponding
angles are equal and t he ratios
of all pairs of corresponding
sides are equal
Stretchi ng and Shrinking
Glossary
Connected Mathematics
Project
Everett Public Schools
Mathematics Program
Proposed Time Frame:
Approximately 6 weeks
Stretching and Shrinking
Geometry
Similarity
Unit Goals:
Enlarge and shrink plane
figures
Identify the corres ponding
parts of s imilar figures
Describe and produce
transformation of plan e figures
Analyze scale factors between
figures Apply properties of simil ar figures
Web Resources
You will find the Factor
Game and the Product Game
at:
www.illuminations.nctm.org
Paper Pool
Using Transformations
and Interactive Figures
Tips for Helping at Home
Good questions and good listening w ill
help children make se nse of mathemat-
ics an d build self-confidence. A good
question opens up a problem and su p-
ports different ways of thinking about it.
Here are some questions you might try,
notice that none of them can be an-
swered with a simple �yes � or �no�.
Getting Started
What do you need to find ou t?
What do you need to know?
What terms do you understan d or
not understand?
While Working
How can you organize the inf orma-
tion?
Do you see any patterns or relation-
ships that w ill help solve this?
What would happen if�?
Reflecting about the Solution
How do you know your answer is
reasonable?
Has the question been answ ered?
Can you explain it another w ay?
At Home:
1 Talk with your child about
what�s going on in mathem atics
class.
2 Look for ways to link mathe-
matical learning to daily activi-
ties. Encourag e your child to
figu re out the amounts for halv-
ing a recipe, estimating gas
mileage, or figuring a restau-
rant tip.
3 Encourage y our child to sched-
ule a regular time for home-
work and provide a comfortable
place for their study , free from
distractions.
4 Monitor y our child�s home-
work on a regular basis by
looking at one problem or ask-
ing your child to briefly de-
scribe the focus of the home-
work. When your child asks
for help, work with them in-
stead of doing the problem for
them.
At School
1 Attend Open House, Back to
School Nigh t, and after school
ev ents.
2 Join the parent-teacher organi-
zation
Investigation 1 Enlarging Figures
Make enlargements of similar fi gures with a rubber
band stretcher
Describe in an intuitive way w hat the word similar
means
Consider relationships between l engths and between
angles in simp le, similar figures
Investigation 2 Similar Figures
Locate points in a coordinate system
Graph figures using algebraic rules
Predict how figures on a coordi nate system are af-
fected by a gi ven rule
Experiment with exampl es and counterexamples of
simila r shapes
Investigation 3 Patterns of Similar Figures
Recognize similar figures and be abl e to tell why they
are similar
Build a larger similar shape from copies of a basic
shape
Understand that the sides and perim eters of similar
figures grow by a scale factor and that the areas
grow by the square of the scale factor
Find a missing measurement in a pai r of similar
figures
Recognize that triangles with equal corresponding
angles are simila r
Investigation 4 Using Similarity
Use definition of similarity to recognize when figures
are si milar
Find the missing measurement in pai rs of similar
figures
Solve problems that involve scali ng up and down
Investigation 5 Similar Triangles
Recognize similar figures in the real worl d
Find a missing measurement in a pair of sim ilar
figures
Apply what has been learned about simila r figures to
solve real-world problems
Connected Mathematics Project
Mathematics in
Investigations
Phone: 425-385-4062
Fax: 425-385-4092
Email: mstine@everett.wednet.edu