Hypotenuse The side of a right
triangle that is opposite the right
angle. The hypotenuse is the long-
est side of a ri ght triangle
Irrational Number � A number that
cannot be wri tten as a fraction with
a numerator and a denominator that
are integers.
Pythagorean Theorem � The theo-
rem states that if a and b are the
lengths of the legs of a right tri angle
and c is the length of the hypote-
nuse, then a
2 +
b
2
= c
2
Rational Number� A number that
can be written as a fraction with a
numerator and a denominator that
are integers, for example 1/2.
Repeat ing Decimal� A decimal
with a pattern of digits that r epeats
forever, such as 0.333333�. Re-
peating decimals are rational num-
bers.
Square Root � If A = s
2
, then s is
the square root of A. The positive
square root of a number is the side
length of a squar e that has that
number as i ts area.
Terminating Decimal� A decimal
that ends, or termi nates, such as
0.5 or 0.125. Terminating decimals
are rational numbers
Looking for Pythagoras
Glossary
Connected Mathematics
Project
Everett Public Schools Mathematics P rogram
Proposed Time Fram e:
Approximately 6 weeks
Looking for Py thagoras
The Pyth agorean Theorem
Unit Goals:
Calculate the distance
between two points in the
plane Understanding square root s as lengths as sides of squares Understand the Pythagorea n Theorem Use the Pythagorean Theo rem to solve problems
Web Resources
You will find the Factor
Game and the Product Game
at:
www.illuminations.nctm.org
Pythagorean Theorem
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 Locating Points
To review the use of coordi nates for specifying locations
To use coordinates to specify di rection and distance
To connect properties of geometri c shapes, such as parallel
si des, to coordinate representations
Investigation 2 Finding Areas and Leng ths
To find areas of polygons draw n on a dot grid using various
strategies
To find the length of a line segm ent drawn on a grid by
thinki ng of it as the side of a square
To begin to develop an understandi ng of the concept of
square root
Investigation 3 The Pythagor ean Theorem
To deduce the Pythagorean Theorem through exploration
To use the Pythagorean Theorem to fi nd areas of squares
draw n on a dot grid
To use the Pythagorean Theorem to fi nd the distance be-
tween two poi nts on a grid
To determine whether a triangle is a right triangle
To relate areas of squares to the l engths of the sides
Investig ation 4 Using the Pythagorean Theorem
To apply the Pythagorean Theorem in several problem
situ ations
To investigate the special properti es of a 30-60-90 triangle
and an isosceles right triangle
To use properties of special ri ght triangles to solve problems
Investigation 5 Irrational Numbers
To connect decimal and fractional representations of rational
num bers
To estimate l engths of hypotenuse of right triangles
To explore patterns in terminati ng and repeating decimals
Investigation 6 Rational and Irration al Slopes
To review the concept of slope of a line
To connect the concept of sl ope to the idea of irrational
num bers
To use slopes to test whether li nes are parallel or perpen-
dicula r
Connected Mathematics Project
Mathematics in
Looking for
Pythagoras
Phone: 425-385-4062
Fax: 425-385-4092
Email: mstine@everett.wednet.edu