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MIFFLIN COUNTY SCHOOL DISTRICT
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MCSD Mathematics Curriculum
Geometry
Planned Instruction
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Title of Planned Instruction:
Geometry |
| Subject Area: Mathematics Grade Level:
Grades 10-12 |
| Prerequisites: Algebra II Course Description:
This course builds concepts and skills that can be used to
describe, analyze, and understand the basic shapes that surround
us. Problem solving, reasoning, and logic are other skills that
are sharpened by taking this course.
Required Time: 180 days
Major Text(s) and Resources: |
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Merrill Geometry: Applications and
Connections,
Copyright 1995 by Glencoe Division, Macmillan/McGraw-Hill |
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Names of District Subject Area Curriculum Writing Committee: |
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- Clint N. Aurand - Indian Valley High School
- John M. Haubrick - Lewistown High School
- Yvonne L. Hoppel - Indian Valley High School
- Mary O. Mulkey - Lewistown High School
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Date of Board Approval: July 24, 2003 |
| Major Topics |
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- Geometry foundations
- Quadrilaterals
- Reasoning and proof
- Similarity
- Parallel and perpendicular
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- Right triangles and trigonometry
- Congruent triangles and applications
- Circles
- Transformations
- Area and volume
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| Course Objectives and Performance Indicators |
Strand: 2.2
Standard: Computation and Estimation
Course: Geometry |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.2.11A |
Develop and use computation
concepts, operations and procedures with real numbers in problem-solving
situations. |
Perform calculations that
might require multiple steps and operations involving real numbers.
Solve problems by using one or more of the following techniques: list the
possibilities, process of elimination, draw a diagram, identify sub goals,
work backwards, look for a pattern, solve a simpler problem, use graphs,
use guess and check, make a decision, make a model, write an equation, or
make a table. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.11B |
Use estimation to solve
problems for which an exact answer is not needed. |
Use the Pythagorean Theorem
to estimate answers to "right triangle" situation problems. Use formulas
to estimate answers to problems relating to area, perimeter, or volume.
Use the trigonometric functions (sine, cosine, and tangent) and special
triangle tools to estimate answers to "triangle" problems. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.11F |
Demonstrate skills for
using scientific and graphing calculators. |
Use a scientific or
graphing calculator to calculate operations involving real numbers. Use
a scientific or graphing calculator to find the values of trigonometric
functions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.3
Standard: Measurement and Estimation
Course: Geometry |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.3.11A |
Select and use appropriate
units and tools to the degree of accuracy required in particular
measurement situations. |
Use a protractor to measure
an angle to the nearest degree. Use a ruler (metric and standard) to
measure a segment.
Select appropriate units for a given problem situation.
Develop and use formulas to find perimeter and area of two dimensional
figures.
Develop and use formulas to find surface area and volume of three
dimensional figures.
Develop procedures, which could include formulas, for estimating
measurements of two dimensional and three dimensional figures (area,
volume, distance, perimeter, and angles). |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.3.11B |
Measure and compare angles
in degrees. |
Use a protractor to measure
an angle to the nearest degree. Distinguish between acute, right,
obtuse, and straight angles. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.3.11C |
Demonstrate the ability to
produce measures with specified levels of precision. |
Create a proportion
relating to scale measurements and use it to find missing pieces in the
problem. Make a scale drawing of a real object.
Estimate the distance between two cities. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.4
Standard: Mathematical Reasoning and Connections
Course: Geometry |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.4.11A |
Use direct proofs, indirect
proofs or proof by contradiction to validate conjectures. |
Use indirect reasoning and
indirect proof to reach a conclusion. Use direct proof to reach a
conclusion.
Make conjectures and perform tests in search of a counter example. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.11B |
Construct valid arguments
from stated facts. |
Write valid arguments from
stated facts. Use if…then statements to construct valid arguments.
Distinguish between inductive and deductive reasoning by using the
correct type in a given situation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.11C |
Determine the validity of
an argument. |
Determine if an answer is
reasonable by identifying reasons why (or why not) the answer makes sense. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.11E |
Demonstrate mathematical
solutions to problems. |
Solve problems that
integrate real world situations and geometry. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.5
Standard: Mathematical Problem Solving and Communication
Course: Geometry |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.5.11A |
Select and use appropriate
mathematical concepts and techniques from different areas of mathematics
and apply them to solving non-routine and multi-step problems. |
Select, use, and display
all of the mathematical procedures that are necessary to the solution of a
problem situation and achieve the correct answer. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.11B |
Use symbols, mathematical
terminology, standard notation, mathematical rules, graphing and other
types of mathematical representations to communicate observations,
predictions, concepts, procedures, generalizations, ideas and results. |
Communicate all of the
mathematical procedures, concepts, conclusions, etc. necessary to the
solution of a problem situation using correct and appropriate mathematical
representations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.11C |
Present mathematical
procedures and results clearly, systematically, succinctly and correctly. |
Present all of the
procedures important to the solution of a problem in ways that are
understandable. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.11D |
Conclude a solution process
with a summary of results and evaluate the degree to which the results
obtained represent an acceptable response to the initial problem and why
the reasoning is valid. |
Explain how a problem was
solved and why the chosen procedures were used. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.9
Standard: Geometry
Course: Geometry |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.9.11A |
Construct geometric figures
using (dynamic, if possible) geometry tools (e.g., Geometer’s Sketchpad,
Cabri Geometre). |
Construct geometric figures
using (dynamic, if possible) geometry tools (Geometer’s Sketchpad, Cabri
Geometre). Construct figures incorporating perpendicular and parallel
lines, the perpendicular bisector of a line segment and an angle bisector
using geometry tools or computer software.
If possible, construct the incenter, circumcenter, orthocenter, and
centroid of a triangle using computer software. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.9.11B |
Prove that two triangles
are congruent or similar using algebraic, coordinate and deductive proofs. |
Distinguish between similar
and congruent polygons. Identify corresponding parts, given congruent
triangles.
Identify the justification for congruency (SSS, SAS, ASA, AAS), given
triangles with appropriate corresponding parts marked as congruent.
Recognize and use tests (HA, LA, LL, HL) for congruence of right
triangles. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.9.11C |
Identify and prove the
properties of quadrilaterals involving opposite sides and angles,
consecutive sides and angles and diagonals using deductive proofs. |
Identify different types of
quadrilaterals (rectangles, squares, parallelograms, rhombi, and
trapezoids).
Recognize and define a parallelogram.
Recognize, use, and prove the properties of a parallelogram.
Recognize and apply the conditions that ensure that a quadrilateral is
a parallelogram.
Recognize the properties of rectangles, squares, rhombi, and
trapezoids. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.9.11D |
Identify corresponding
parts in congruent triangles to solve problems. |
Identify congruent
triangles. Name and label corresponding parts of congruent triangles. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.9.11E |
Solve problems involving
inscribed and circumscribed polygons. |
Recognize and find the
measure of inscribed angles. Use properties of inscribed figures to
answer questions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.9.11F |
Use the properties of
angles, arcs, chords, tangents and secants to solve problems involving
circles. |
Identify the parts of a
circle. Determine relationships between lines and circles.
Recognize major or minor arcs or semicircles.
Find the measures of arcs and central angles.
Recognize and use the relationship between arcs, chords, and diameters
of a circle.
Use properties of tangents to solve problems.
Find the measures of angles formed by intersecting secants and tangents
in relation to intercepted arcs.
Use properties of chords, secants, and tangents to solve problems. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.9.11G |
Solve problems using
analytic geometry. |
Graph ordered pairs on a
coordinate plane. Find the distance between two points on a coordinate
plane.
Find the midpoint of a line on a coordinate plane.
Solve problems using analytic geometry.
Find slope and use to determine if lines are parallel or perpendicular. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.9.11H |
Construct a geometric
figure and its image using various transformations. |
Use simple geometric
figures (e.g., triangles, squares) to create, through rotation,
transformational figures in three dimensions. Construct a geometric
figure using reflections, translations, rotations, glide reflections,
distortions, and dilations.
If possible, generate transformations using computer software.
Use properties of transformations to solve problems and model real life
situations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.9.11I |
Model situations
geometrically to formulate and solve problems. |
Construct parallel lines,
draw a transversal and measure and compare angles formed (e.g., alternate
interior and exterior angles). Analyze geometric patterns (e.g.,
tessellations, sequences of shapes) and develop descriptions of the
patterns from a transformational standpoint.
Use properties of parallel lines in proofs.
Identify, name, draw, and list properties of squares, cubes, pyramids,
parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi,
circles, spheres, triangles, prisms, cones, and cylinders to help solve
problems.
Recognize and use triangle inequality theorem for one triangle.
Solve problems involving triangle inequalities. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.9.11J |
Analyze figures in terms of
the kinds of symmetries and other patterns they have. |
Identify types of symmetry
in geometric figures. Analyze objects to determine whether they
illustrate tessellations, symmetry, congruence, similarity, and scale. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.10
Standard: Trigonometry
Course: Geometry |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.10.11B |
Identify, create and solve
practical problems involving right triangles using the trigonometric
functions and the Pythagorean Theorem. |
Solve problems using
relationships between parts of a right triangle and the altitude of its
hypotenuse. Use the Pythagorean Theorem and its converse to solve
problems.
Use the properties of 45º-45º-90º, 30º-60º-90º, and 3-4-5 right
triangles (special triangle tools) to solve problems.
Express trigonometric ratios as fractions or decimals.
Recognize trigonometric relationships from right triangles.
Use a calculator to find values of trigonometric ratios or measures of
angles.
Recognize angles of depression or elevation.
Use trigonometry to solve problems.
Use trigonometry and indirect measurement to calculate heights of
objects. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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District Recommended Instructional Approaches For
the Course
To Drive Teacher’s Instructional Activities |
- Whole group instruction
- Small group instruction
- Projects
- Class discussion
- Peer evaluation
- Teacher and peer conferencing
- Oral presentations
- Individual instruction
- Research
- Dramatization
- Role playing
- Independent reading
- Read aloud
- Directed reading-thinking activities
- Modeling process
- Games
- Self-reflection
- Self-evaluation
- Independent study
- Guest speaker
- Guest reading
- Writing activities
- Thematic units
- Notebooks
- Study guides
- Computer technology
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