UNIT PLAN
Subject/Grade Level:
Grade
Unit #:
Unit Name:
Geometry
10-12
5
Right Triangles
Big Idea/Theme:
Right triangles have many real world applications.
Culminating Assessment:
See attached : “Pythagorean Spiral”
Unit Understanding(s)
Unit Essential Question(s):
Students will understand…
What are the different parts of a
right triangle and where are they
The different parts of a right
triangle.
located?
The use of the Pythagorean
When is the Pythagorean Theorem
Theorem.
used?
The relationships between the sides
How are the relationships between
of 45-45-90 right triangles and 30the sides of a 45-45-90 right triangle
60-90 right triangles.
and a 30-60-90 right triangle used
to solve for missing sides?
The use of trigonometric ratios of
right triangle.
How do you use trigonometric ratios
to solve problems with right
triangles?
Students will know… / Students will be able to…
Name the parts of a right triangle.
Use the Pythagorean Theorem and its converse to solve problems.
Find missing sides of a special right triangle.
Use trigonometric ratios to solve problems involving right triangles.
South Carolina Academic Standards:
G-1.1 Formulate and demonstrate an understanding of the axiomatic structure of
geometry by using undefined terms, definitions, postulates, theorems, and
corollaries.
G-1.2 Communicate knowledge of geometric relationships by using
mathematical terminology appropriately.
G-1.8 Connect geometry with other branches of mathematics.
G-1.9 Demonstrate an understanding of how geometry applies to real world
contexts (including architecture, construction, farming, and astronomy).
G-1.10 Demonstrate an understanding of geometric relationships (including
constructions through investigations by using a variety of tools such as
straightedge, compass, Patty Paper, dynamic geometry software, and
handheld computing devices).
G-3.10 Use the Pythagorean theorem and its converse to solve problems.
G-3.11 Use the properties of 45-45-90 and 30-60-90 triangles to solve
problems.
G-3.12 Use trigonometric ratios to solve problems involving right triangles.
Interim Assessment (formative)
Board work
Class discussion
Group activities
Journals
Observations
Question and answer
Quizzes/Tests
Key Criteria (to meet the standard/rubric)
See attached rubric.
Unit #5 Culminating Activity
The Pythagorean Spiral Project
http://www.fcps.edu/AnnandaleHS/GeometryProjects/pythagorean.htm
You will use compass constructions to create a poster of the Pythagorean spiral. The result
needs to be colored and may be creatively decorated. You will need to turn in your poster and a
separate piece of paper with all calculations.
Materials: + poster board + ruler + compass + pencil, colored pencils or markers
Step 1: Place the poster board in landscape orientation. Measure from the top left hand corner
27.5 cm right and 20.5 cm down. This will be the starting point for your diagram. It will assure
that your diagram stays on the page.
Step 2: Using your ruler create a segment that is 10 cm across starting from the starting point
and heading towards the center of the poster. Make this segment perpendicular to the side of the
poster. Use your compass and ruler (without measuring) to construct a congruent segment that is
perpendicular to the original. Connect the endpoints of the two segments to create a right
isosceles triangle.
Step 3: On a separate piece of paper, use the Pythagorean Theorem to calculate the length of the
hypotenuse. Show all work and write your answer in reduced radical form.
Step 4: Using the hypotenuse of the first triangle, create another right triangle on top of the
previous hypotenuse. The old hypotenuse will be the new base and construct a perpendicular
segment to this, with a length of 10. Then connect the two segments to form a new hypotenuse.
Step 5: On your separate piece of paper, show the calculations to find the length of the new
hypotenuse.
Step 6: Continue to repeat this process of connecting and constructing new triangles with a side
length of 10, using the previous hypotenuse as the other side. Continue to show your
calculations on your separate piece of paper. Construct triangles until you have formed a full
spiral.
Step 7: Detail your Pythagorean Spiral with a design. Use color and a pattern to make a creative
picture.
TO TURN IN:
Your poster with light pencil lines shown for constructions and color used to decorate the
pattern. Your work for each hypotenuse length on a separate sheet of paper.
Grading Rubric for Pythagorean Spiral Project
Number of Use of Compass Calculations for
Points
Constructions
each hypotenuse
4
Evidence of each All work is
compass
shown using the
construction
Pythagorean
shown
Theorem and
each answer is
simplified
3
Evidence of most
compass
constructions
shown
2
Partial or
incorrect
constructions
shown
1
Construction
markings are not
visible
Poster Result
The result shows
17 right triangles
that rotate
around to the
right and the last
triangle overlaps
the original
All work is
The result shows
shown using the an error in
Pythagorean
construction
Theorem but
resulting in one
some answers are fewer or one
not properly
more triangle
simplified
All work is
The result goes
shown but with
the wrong
errors in
direction and/or
calculation
is off by more
and/or
than one
simplification
triangle
Only partial
The result does
work is shown
not appear to
and/or no
have followed
evidence of the
the proper
Pythagorean
requirements
Theorem
A: 15 - 16 B+: 13 – 14 B: 11 – 12 C: 9 – 10 C: 7 – 8 D+: 6 D: 5 F: 0 – 4
Click on the image to see a larger view.
Creativity
The poster is
creatively
colored and
decorated
The poster is
colored but
the results
are not neat.
The poster is
partially
colored or
incomplete.
The poster is
not colored
or decorated