Outcome: SS8.1
Demonstrate understanding of the Pythagorean Theorem concretely or pictorially and symbolically and by solving
problems. [CN, PS, R, T, V]
Indicators:
a) Generalize the results of an investigation of the expression a² + b² = c² (where a, b, and c are the lengths of the
sides of a right triangle, c being the longest):
 concretely (by cutting up areas represented by a² and b² and fitting the two areas onto c²)
 pictorially (by using technology)
 symbolically (by confirming that a² + b² = c² for a right triangle).
b) Explore right and non-right triangles, using technology, and generalize the relationship between the type of
triangle and the Pythagorean Theorem (i.e., if the sides of a triangle satisfy the Pythagorean equation, then the
triangle is a right triangle which is known as the Converse of the Pythagorean Theorem)
c) Explore right triangles, using technology, using the Pythagorean Theorem to identify Pythagorean triples (e.g., 3,
4, 5 or 5, 12, 13), hypothesize about the nature of triangles with side lengths that are multiples of the
Pythagorean triples, and verify the hypothesis.
d) Create and solve problems involving the Pythagorean Theorem, Pythagorean triples, or the Converse of the
Pythagorean Theorem.
e) Give a presentation that explains a historical or personal use or story of the Pythagorean Theorem (e.g.,
Pythagoras and his denial of irrational numbers, the use of the 3:4:5 right triangle ratio in the Pyramids, squaring
off the corner of a sandbox being built for a sibling, or determining the straight line distance between two towns
to be travelled on a snowmobile).
Level
Scale
Pre-Requisite
Knowledge
1
B - Beginning
There is a partial
understanding of
some of the simpler
details and
processes.
Prior knowledge is
understood.
2
A – Approaching
No major errors or
omissions regarding
the simpler details or
processes, but
assistance may be
required with the
complex processes.
Descriptor





Indicators
Student-Friendly
Language
Students who are
not able to be
independently
successful with
level 1 questions
will be given an E.

Knowledge and
Comprehension
Students who are
successful with
level 1 questions or
those who are
successful with
level 1 or 2
questions with
assistance will be
given a B.
a) Generalize the results of
an investigation of the
expression a² + b² = c²
(where a, b, and c are
the lengths of the sides
of a right triangle, c
being the longest):
 concretely (by cutting up
areas represented by a²
and b² and fitting the
two areas onto c²)
 pictorially (by using
technology)
 symbolically (by
confirming that a² + b² =
c² for a right triangle).

I know that, in a right
triangle, where c is the
hypotenuse and a and b
are the other two sides,
that a² + b² = c². I can
show that is true using
paper-cutting, pictures,
and math.
Applying and
Analysing
Students who are
able to be
successful with
level 1 and level 2
questions, or those
who are successful
with higher-level
questions with
assistance, will be
given an A.
b) Explore right and nonright triangles, using
technology, and
generalize the
relationship between the
type of triangle and the
Pythagorean Theorem
(i.e., if the sides of a
triangle satisfy the
Pythagorean equation,
then the triangle is a
right triangle which is
known as the Converse
of the Pythagorean
Theorem)
c) Explore right triangles,
using technology, using
the Pythagorean
Theorem to identify
Pythagorean triples (e.g.,
3, 4, 5 or 5, 12, 13),
hypothesize about the
nature of triangles with
side lengths that are
multiples of the
Pythagorean triples, and

I can use computer
programs to explore the
Pythagorean Theorem
and I can use the
Pythagorean Theorem to
find out whether a
triangle is right or not.
I know what a
Pythagorean Triple is
and I can use technology
to find some examples.


Classify triangles as right
triangles
Identify the hypotenuse
of a right triangle
Squares and square
roots

verify the hypothesis.
3
M – Meeting
No major errors or
omissions regarding
any of the
information and/or
processes that were
explicitly taught.
This is the target
level for proficiency.
4
In addition to level 3
performance, indepth inferences and
applications go
beyond what was
explicitly taught.



Evaluating and
Creating
Students who are
independently
successful with
level 3 or level 4
questions are given
an M.
Students successful
at level 4 will
receive
supplementary
comments specific
to their
achievement in
addition to the M.


Create and solve
problems involving the
Pythagorean Theorem,
Pythagorean triples, or
the Converse of the
Pythagorean Theorem.
Give a presentation that
explains a historical or
personal use or story of
the Pythagorean
Theorem (e.g.,
Pythagoras and his
denial of irrational
numbers, the use of the
3:4:5 right triangle ratio
in the Pyramids,
squaring off the corner
of a sandbox being built
for a sibling, or
determining the straight
line distance between
two towns to be
travelled on a
snowmobile).



I can use the
Pythagorean Theorem to
solve problems and I can
even make up problems
for others to solve.
I know where the
Pythagorean Theorem
came from and where it
can be used outside of
school. I can explain my
knowledge in a
presentation to other
people.
I can develop problems
based on real-life uses of
the Pythagorean
Theorem and I can solve
my own problems.
Student-Friendly Rubric
Outcome:

Meeting

Approaching

Beginning

I know that, in a right
triangle, where c is the
hypotenuse and a and b
are the other two sides,
that a² + b² = c². I can
show that is true using
paper-cutting, pictures,
and math.

I can use computer
programs to explore the
Pythagorean Theorem
and I can use the
Pythagorean Theorem
to find out whether a
triangle is right or not.
I know what a
Pythagorean Triple is
and I can use
technology to find some
examples.

I can use the
Pythagorean Theorem
to solve problems and I
can even make up
problems for others to
solve.
I know where the
Pythagorean Theorem
came from and where it
can be used outside of
school. I can explain my
knowledge in a
presentation to other
people.
I can develop problems
based on real-life uses
of the Pythagorean
Theorem and I can solve
my own problems.