Download Lesson Plans Geometry John Kallis and Janet Niemann Day 1

Lesson Plans
Geometry
John Kallis and Janet Niemann
Day 1
Parallel Lines with a transversal
From formal lesson in textbook cover alternate interior, corresponding angles, and vertical angles.
Amber puzzle from handout could also be used.
Students may discover the triangle congruency theorems during the day 2 and 3. Formal instruction will
begin on the forth day.
Day 2 and 3
Perform basic constructions with a straightedge and compass.
1) Give each student a ruler, compass, pencil, and a piece of printer paper.
2) Draw a angle on the board with only a ruler and have students do the same and not worry
about everybody having the same angles or length of sides.
3) Construct a congruent angle using the compass and straight edge.( congruent sides and angle)
4) Construct a line connecting the last side of the triangle and measure the length of the
constructed side. (Check each student so they constructed what is expected.)
5) Are the length the same? Why are they the same length
6) Construct ASA, SSA, AAS, AAA, SSS, and HL. Have students work in groups of two and
construct each example. (Students need to hand in a copy of each that they have completed)
7) Have students draw and explain if triangles are congruent. Have each group explain one on the
board.
Day 4
Introduce: Explain SAS theorem.
Use proof from your geometry book.
Day 5
Puzzle on other triangle congruency theorems.
(Attached)
In class complete a SAS proof using 2 parallel lines and vertical angles. Preparation: Cut up pieces of
statements and reasons and put in envelopes – one for each group.
The students need to put the statements and reasons in order to prove the theorem.
In small groups, students will unscramble the steps and reasons for a similar proof using AAS or
ASA. When complete, groups will post solutions on the board using magnets. (or written by a member
of the group.)
Day 6
Introduce sketch pad
Cover these points with students:
Point
Line
Intersection
Perpendicular
parallel
Construct polygons
Construct midpoints
Measuring tools angles and length
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Day 7
Have students show all theorems on sketch pad are true.
Construct a triangle. Measure all sides and all angles of the triangle with the measuring tools.
Have students grab a point and move the point around.
Day 8
Real world application.
The class is now going to setup the footing for a regular four sided house. There will not be a
basement on the house. Follow the worksheet attached.
Day 9
Assess student knowledge.
1) Students will receive a blank sheet of paper, a straightedge, compass, and protractor.
2) Students need to reconstruct yesterdays real world application on a piece of paper using
theorems and terms from yesterday to show what they know about congruence in geometry.
3) The instructor will assign the n-gon and length of side for the house for each pair of students.
Day 10 Layout of footings
The students will use day 9 information to lay out footing for a n-gon house.
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PERFORMANCE PACKAGE TASK 1
(Title of Package)
Content Standard:
Level:Partial
Specific Statement(s) from the Standard:
Grades 9-11
V. SPATIAL SENSE, GEOMETRY AND MEASUREMENT
A. Spatial Sense
Standard: Use models to represent and understand two- and three-dimensional shapes and
how various motions affect them. Recognize the relationship between different
representations of the same shape.
The student will:
1. Use models and visualization to understand and represent three-dimensional objects
and their cross sections from different perspectives.
B. Geometry
Standard: Apply basic theorems of plane geometry, right triangle trigonometry, coordinate
geometry and a variety of visualization tools to solve real-world and mathematical problems.
The student will:
1. Know and use theorems about triangles and parallel lines in elementary geometry to
justify facts about various geometrical figures and solve real-world and mathematical
problems. These theorems include criteria for two triangles to be congruent or similar
and facts about parallel lines cut by a transversal.
2. Know and use theorems about circles to justify geometrical facts and solve real-world
and mathematical problems. These theorems include the relationships involving
tangent lines and radii, the relationship between inscribed and central angles and the
relationship between the measure of a central angle and arc length.
3. Know and use properties of two- and three-dimensional figures to solve real-world
and mathematical problems such as: finding area, perimeter, volume and surface area;
applying direct or indirect methods of measurement; the Pythagorean theorem and its
converse; and properties of 45o-45o-90o and 30o-60o-90o triangles.
4. Apply the basic concepts of right triangle trigonometry including sine, cosine and
tangent to solve real-world and mathematical problems.
5. Use coordinate geometry to represent and examine geometric concepts such as the
distance between two points, the midpoint of a line segment, the slope of a line and
the slopes of parallel and perpendicular lines.
6. Use numeric, graphic and symbolic representations of transformations such as
reflections, translations and change of scale in one, two and three dimensions to solve
real-world and mathematical problems.
7. Perform basic constructions with a straightedge and compass.
8. Draw accurate representations of planar figures using a variety of tools.
C. Measurement
Standard: Use the interconnectedness of geometry, algebra and measurement to explore real world
and mathematical problems.
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Grade 11-12
TRIGONOMETRY & GEOMETRY
Standard: Understand the properties of the standard trigonometric functions and apply them
to real-world and mathematical problems, especially geometrical problems. Develop
increased mastery of geometric proof methodology.
The student will:
1. Know the six trigonometric functions defined for an angle in a right triangle.
2. Given the coordinates of a point on the terminal side of an angle in standard position
in the xy-plane, find the values of the trigonometric functions.
3. Convert between degrees and radian measures.
4. Solve applied problems about triangles using the law of sines including the
ambiguous case.
5. Solve applied problems about triangles using the law of cosines.
6. Graph the functions of the form Asin(Bt +C), Acos(Bt + C), and Atan(Bt + C) and
know the meaning of the terms frequency, amplitude, phase shift and period.
7. Simplify trigonometric expressions using identities and verify simple trigonometric
identities including sin2x + cos2x = 1, sum, difference, double angle and half-angle
formulas for sine and cosine.
8. Find all the solutions of a trigonometric equation on various intervals.
9. Know and be able to use the definitions of the inverse trigonometric functions and
related methods to solve problems such as find cos(x) and tan(x) given the value of
sin x and the quadrant containing the terminal side.
Product(s):
The students will explain how to layout a n-gon sided house.
Task Description:
The pair of student will receive from the instructor the number of sides and the length of walls to
be setup for the construction of a n-gon house.
1) Write an explanation of the layout of the house including geometric justifications for the steps.
2) Physical construction of lay out of footings.
Special Notes:
Page 4
PERFORMANCE PACKAGE TASK 1
Geometry congruence theorems
LESSON CHECK LIST TASK 1
The purpose of the checklist is to provide feedback to the student about his/her work relative to the
content standard. Have the standard available for reference.
Y=Yes
N=Needs Improvement
Student
Teacher
________
Constructions complete and accurate of ASA, SSA, etc.
________
________
Theorem puzzles copied on paper are complete and accurate
________
________
Sketch pad introduction activities complete and accurate
________
________
Sketch pad theorems print out are complete and accurate
________
________
Real world application of any of the 5 theorems applied correct.
________
Overall Comments (information about student progress, quality of the work, next steps for teacher and
student, needed adjustments in the teaching and learning processes, and problems to be addressed):
Feed Back Check List
________
Write up follow geometry theorems and in the right context.
_________
________
Description of layout is accurate
_________
________
All measurements and angles correct for n-gon write up.
_________
________
Construction of footing layout accurate and
complete according to write up .
_________
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