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Teacher:__________________________________ Course:_______________________________________________ Dates:______________________________
Class Time
Common Core
STANDARD:
Date: 2-13-12
PASS 3.1- Right Triangles
and Pythagorean Theorem
Date: 2-14-12
Date: 2-15-12
Date: 2-16-12
Date: 2-17-12
PASS 3.2- Special right
triangles.
PASS 3.2- Special right
triangles.
PASS 3.3- Right Triangle
Trigonometry
No School.
Know: How to apply the
Pythagorean Theorem to
word problems and how to
use a Pythagorean Triplet to
determine if a triangle is
acute, right, or obtuse.
Know: the properties of 4545-90 and 30-60-90 right
triangles.
Know: the properties of 4545-90 and 30-60-90 right
triangles.
Know: Sine, Cosine, and
Tangent functions and how
they apply to right triangles.
Understand: The key
qualities of acute, right and
obtuse triangles.
Understand: that there are
some special types of right
triangles which special
formulas can be used to
calculate each side. Theses
formulas apply no matter
what the length of sides.
Understand: that there are
some special types of right
triangles which special
formulas can be used to
calculate each side. Theses
formulas apply no matter
what the length of sides.
Understand: that a sideside, or side-angle pair,
when combined with a trig.
Function, is enough
information to calculate
other unknowns in right
triangles.
Be able to: Mathematically
determine if a triangle is
acute, right, or obtuse even
when not given a figure of
the triangle.
Be able to: calculate for
each side of special right
triangles, how to convert
between different answer
forms.
Be able to: calculate for
each side of special right
triangles, how to convert
between different answer
forms.
Be able to: correctly choose
which trig. Function applies
to the problem, use the trig.
Function to calculate for an
unknown side or angle.
By the end of this
lesson, students will…
Know:
Understand:
Be able to Do:
Differentiated
Instruction
Content
Process
Product
Interest
Readiness
Learning
Profile
Multiple Intelligences
Visual
Verbal
Interpersonal
Intrapersonal
Kinesthetic Natural
Logical/Mathematical
Content
Process
Product
Interest
Readiness
Learning
Profile
Visual
Verbal
Interpersonal
Intrapersonal
Kinesthetic Natural
Logical/Mathematical
Content
Process
Product
Interest
Readiness
Learning
Profile
Visual
Verbal
Interpersonal
Intrapersonal
Kinesthetic Natural
Logical/Mathematical
Content
Process
Product
Interest
Readiness
Learning
Profile
Visual
Verbal
Interpersonal
Intrapersonal
Kinesthetic Natural
Logical/Mathematical
Content
Process
Product
Interest
Readiness
Learning
Profile
Visual
Verbal
Interpersonal
Intrapersonal
Kinesthetic Natural
Logical/Mathematical
Teacher:__________________________________ Course:_______________________________________________ Dates:______________________________
Opening:
15-25
Context & KUD
BAV
Connect to prior
knowledge
Direct Instruction
Provide rubrics for
group work
Learning Exp: 30-50
Small group
exploration of new
knowledge
Active, rigorous, and
relevant
Informal Assessment
Remediation
Individual Practice
Students will review what
acute, right, and obtuse
triangles are. Teacher will
introduce modified form of
Pythagorean theorem that
will help students
determine which type of
triangle.
Do Now: Students will
solve a word problem
involving the Pythagorean
Theorem and will also
determine if a triangle is
acute, right, or obtuse
based on its Pythagorean
triplet.
Do Now: Students will
solve a word problem
involving the Pythagorean
Theorem and will also
determine if a triangle is
acute, right, or obtuse
based on its Pythagorean
triplet.
Do Now: Students will
solve for the sides of special
right triangles. Students
will be given a difficult EOI
problem that involves both
their knowledge of right
triangles and their
knowledge of radical math.
Students will be instructed
on how to apply the
Pythagorean theorem to
any Pythagorean triplet and
will determine if triangles
are acute, right, or obtuse
based simply on side
measure.
Students will review radical
math (how to multiply and
divide radicals, how to solve
for a variable using radicals,
how to simplify answers
with radicals in them).
Students will review radical
math (how to multiply and
divide radicals, how to solve
for a variable using radicals,
how to simplify answers
with radicals in them).
Students will then be
introduced to two types of
special right triangles: 4545-90 (isosceles right
triangle) and 30-60-90.
Students will learn that
sides in each of these
triangles can be solved
using special relationships.
Students will then be
introduced to two types of
special right triangles: 4545-90 (isosceles right
triangle) and 30-60-90.
Students will learn that
sides in each of these
triangles can be solved
using special relationships.
Teacher will introduce trig.
Functions and how they
apply to right triangles.
Students will understand
that while the Pythagorean
theorem deals exclusively
with sides, trig functions
can be used to also
calculate unknown angles
of right triangles.
Students will solve 45-45-90
triangles for the
hypotenuse and legs, and
then compare these
answers to what they had
done before with triangles
with congruent legs.
Students will then be
introduced to EOI problems
involving special right
triangles and will work on
eliminating answer choices
based on their knowledge
of radical math.
Students will solve 45-45-90
triangles for the
hypotenuse and legs, and
then compare these
answers to what they had
done before with triangles
with congruent legs.
Students will then be
introduced to EOI problems
involving special right
triangles and will work on
eliminating answer choices
based on their knowledge
of radical math.
Students will solve
problems involving
Pythagorean triplets and
will work to memorize
the formulas for acute
and obtuse. Obtuse
triangles have large
hypotenuses relative to
the other sides;
therefore, the greater
than symbol will be
‘eating’ the c value, or
the hypotenuse. Acute
triangles are the other
Students will be introduced
to and practice setting up
trig ratios, which involve
decision-making as to which
trig function is involved and
what goes where.
Teacher will then
demonstrate how to solve
for an unknown side when
given an angle and another
side in a right triangle.
Students will practice
making decisions about
which trig function to use
and how to solve for the
side using their calculator.
Teacher will then
demonstrate how to solve
for an unknown angle using
Teacher:__________________________________ Course:_______________________________________________ Dates:______________________________
way around.
Students will finish
homework on section 8-1
(Pythagorean theorem).
Closing:
10-20
Students share
discoveries with class
Self-Assessment:
What did I learn
today?
Review rubrics
What level of
understanding did
students reach?
Wrap-Up & lead in to
next class period
To close class, teacher will
review properties of radical
math and how it pertains to
right triangles and the
Pythagorean theorem.
Students will solve basic
problems involving radicals
and learn how to convert
between different forms.
Next, students will solve for
the legs and hypotenuse of
30-60-90 right triangles and
will then determine what
minimal amount of
information is needed to
determine all the
components of these
triangles.
Next, students will solve for
the legs and hypotenuse of
30-60-90 right triangles and
will then determine what
minimal amount of
information is needed to
determine all the
components of these
triangles.
the inverse trig function.
Finally, students will be
given time to work
homework involving these
two types of right triangles:
they will solve word
problems involving these
types of triangles.
Finally, students will be
given time to work
homework involving these
two types of right triangles:
they will solve word
problems involving these
types of triangles.
Finally, teacher will review
how trig applies to right
triangles and the decision
making process that goes in
to setting up a trig function
properly. Students will be
given time to start their
homework, with the
teacher walking around and
answering any questions
the students might have.
Students will practice
solving for unknown angles
using inverse trig functions
and their calculators.