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Division: Special Education
Course Number: MTH2N1/MTH2N2
Course Title: Instructional Geometry
Course Description: This course integrates the basic principles of geometry and
algebra. This sequence is for students who would like a complete year of
geometry while strengthening algebraic skills. Students study such topics as
triangle congruence, similarity, parallelism, quadrilaterals, circles and use of
dynamic geometry software. Logic is studied without the use of formal proof.
Completion of this course prepares a student for further work in Advanced
Algebra Collaborative. This course is set up to support each student and reflect
the flexibility necessary to adapt to the individualized needs of each student with
respect to modifications, pace, and accommodations.
Content Objectives
By the end of the course, student will be able to:
A. Use coordinate geometry to investigate basic geometric terms.
B. Understand and apply the components of a deductive structure.
C. State and apply properties and theorems relating to parallel lines.
D. Solve problems using triangles, including proving triangles congruent and
understand and apply basic transformations.
H. Investigate and apply special segments and inequality relationships in
triangles.
I. Understand and apply properties of Proportions and Similarity.
J. Solve right triangle problems using Pythagorean Theorem, 30-60-90.
K. Understand and apply properties of quadrilaterals.
L. Apply theorems relating to properties of circles, i.e., circumferences,
finding the measure of angles, arcs, chords, secants segments, and
tangent segments.
M. Find the area and perimeter of polygons
N. Find surface area and volume of right prisms, cylinders, cones, pyramids
and spheres.
College Readiness Standards
By the end of this course, students’ will be able to:
A. Apply basic Operations and applications.
B. Understand numbers: concepts & properties.
C. Understand graphical representations.
D. Exhibit knowledge of slope.
E. Understand properties of plane figures.
F. Apply measurement.
G. Apply funtions
H. Incorporate and utilize reading strategies to determine the meaning of a
word.
Social-Emotional Learning Objectives:
By the end of this course students will be able to:
A. Develop self-awareness skills.
B. Develop social awareness skills.
C. Develop self-management skills.
D. Relationship Skills.
E. Develop responsible decision making skills.
Content Learning Targets
Use coordinate geometry to investigate basic geometric terms.
1. Identify and name new geometry terms (points, lines, planes, rays,
segments, distance)
2. Apply segment relationships (addition, bisectors, congruence)
3. Find distance and midpoint on a number line and coordinate plane
4. Classify and measure angles
5. Name an angle and its parts
6. Identify and apply angle relationships (addition, congruence,
bisectors, vertical, linear pair,
supplementary, complementary,
perpendicular)
7. Identify polygons and solve equations using perimeter.
B.
Understand and apply the components of a deductive structure.
1. I can write conditional statements and their converses.
2. I can find counterexamples to disprove conjectures.
State and apply properties and theorems relating to parallel lines.
1. I can identify parallel, intersecting, and skew lines
2. I can identify angle pairs created by a pair of lines and a transversal
3. I can use angle pair relationships created by parallel lines and a
transversal to find
measures and show lines are
parallelare parallel
4. I can identify and use slopes of lines, including parallel and
perpendicular lines
5. I can write equations of lines, including parallel and perpendicular
lines
D.
Solve problems using triangles, including proving triangles
congruent and understand and apply basic
transformations.
1. I can identify transformations and complete reflections on the
coordinate plane.
2. I can classify triangles by their sides and angles.
3. I can apply the exterior angle theorem and use it to set up and solve
algebraic equations.
4. I can identify the sum of the angles in a triangle and use it to set up
and solve algebraic equations.
5. I can apply the properties of isosceles triangles and use them to set
up and solve algebraic equations.
6. I can identify congruent triangles and corresponding parts and use
them to set up and solve algebraic
equations.
7. I can prove triangles congruent using the SAS, SSS, ASA, HL, and
AAS postulates.
H. Investigate and apply special segments and inequality relationships in
triangles.
1. I can identify medians and use them to set up and solve algebraic
equations.
2. I can identify altitudes and use them to set up and solve algebraic
equations.
3. I can identify angle bisectors and use them to set up and solve
algebraic equations.
4. I can identify perpendicular bisectors and use them to set up and
solve algebraic equations.
5. I can determine if three segments can form a triangle.
6. I can recognize and apply properties of inequalities to the
relationships between angles and sides of a
triangle.
I. Understand and apply properties of Proportions and Similarity.
1. I can write ratios and solve proportions
2. I can identify similar figures and use scale factors to set up and
solve problems
3. I can identify similar triangles using AA~, SSS~, and SAS~
4. I can recognize and use proportional relationships of corresponding
perimeters, angle bisectors,
altitudes, and medians of
similar triangles.
Solve right triangle problems using Pythagorean Theorem, 30-60-90
and 45-45-90 right triangles and
trigonometry.
1. I can simplify radicals.
2. I can use and apply the Pythagorean theorem.
3. I can use and apply properties of similar triangles involving special
right triangles (30-60-90 and
45-90).
4. I can identify and use trigonometric ratios to find sides and angles
of right triangles.
J.
Understand and apply properties of quadrilaterals.
1. I can find the sum of the measures of the interior/exterior angles of
a polygon.
2. I can identify the properties of parallelograms and use them to set
up and solve algebraic equations.
3. I can identify the properties of rectangles and use them to set up
and solve algebraic equations.
4. I can identify the properties of rhombi and use them to set up and
solve algebraic equations.
5. I can identify the properties of squares and use them to set up and
solve algebraic equations.
6. I can identify the properties of trapezoids and use them to set up
and solve algebraic equations.
K. Apply theorems relating to properties of circles, i.e., circumferences, finding
the measure of angles, arcs, chords, secants segments, and tangent segments.
1. I can identify parts of a circle.
2. I can find the measures of central or inscribed.
3. I can find the measures of interior/exterior angles of a circle.
4. I can use the properties of tangents.
5. I can recognize and use relationships between chords and distance
from center of a circle.
L. Find the area and perimeter of polygons
1. I can find the area of rectangles and justify its formula.
2. I can find the area of parallelograms and justify its formula.
3. I can find the area of triangles and justify its formula.
4. I can find the area of trapezoids and justify its formula.
5. I can find the area of rhombi and justify its formula.
6. I can find the area of regular polygons and justify its formula.
7. I can find the area of circles and justify its formula.
8. I can find the area of shaded regions and irregular shapes.
M. Find surface area and volume of right prisms, cylinders, cones, pyramids
and spheres.
1. I can find the surface area and volume of right prisms.
2. I can find the surface area and volume of right cylinders.
3. I can find the surface area and volume of right pyramids.
4. I can find the surface area and volume of right cones.
5. I can find the surface area and volume of spheres.
College Readiness Learning Targets
A. Basic Operations and applications
1. Perform common conversions
B. Numbers: Concepts & Properties
Work with squares and square roots of numbers.
C. Graphical Representations
Comprehend the concept of length on the number line.
D. Exhibit knowledge of slope.
Determine the slope of a line from points or equations.
Find the midpoint of a line segment.
Interpret and use information from graphs in the coordinate plane.
Use the distance formula.
Use properties of parallel and perpendicular lines to determine an equation of a
line or coordinates of a point.
E. Properties of Plane Figures
Exhibit some knowledge of the angles associated with parallel lines.
Find the measure of an angle using properties of parallel lines.
Exhibit knowledge of basic angle properties and special sums of angle measures
( e.g., 90|°, 180°, 360°)
Use several angle properties to find an unknown angle measure.
Use properties of isosceles triangles.
Apply properties of 30°, -60°, -90°, 45° -45°-90°, similar and congruent triangles.
Use the Pythagorean theorem.
Draw conclusions based on a set of conditions.
Use relationships among angles, arcs, and distances in a circle.
F. Measurement
Estimate or calculate the length of a line based on other lengths given on a
geometric figure.
Compute the perimeter of polygons when all side lengths are given
Compute the area of rectangles when whole number dimensions are given.
Conpute the area and perimeter of triangles and rectangles in simple problems.
Use geometric formulas when all necessary information is given.
Compute the area of triangles and rectangles when one or more additional
simple steps are required.
Compute the area and circumference of circles after identifying necessary
information.
Compute the perimeter of simple composite geometric figures with unknown side
lengths.
Use scale factors to determine the magnitude of a size change.
Compute the area of composite geometric figures when planning or visualization
is required.
G. Funtions
Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of
give side lengths.
Apply basic trigonometric ratios to solve right-triangle problems.
H.
of a word.
Incorporate and utilize reading strategies to determine the meaning
1.
Understand the implication of a familiar word or phrase as
related to geometry.
2.
Use context to understand basic geometry language.
Social-Emotional Learning Targets
A. Self Awareness
1. I can predict my emotions given a potential event or series of
events.
2. I recognize when I am beginning to feel stressed.
B. Social Awareness
1. I can explain what it means to be empathetic.
2. I listen attentively to understand another person’s feelings
and/or perspectives.
3. I compare and contrast different types of relationships and their
different expectations for
behavior.
C. Self-Management
1. I apply healthy strategies to decrease my stress level.
2. I create individualized short-term and long-term goals for myself.
3. I monitor and evaluate my progress towards reaching my goals.
4. I identify various resources to help me reach my goals.
D. Relationship Skills
1. I identify effective ways to positively influence others.
2. I communicate my emotions to others in healthy ways.
3. I invite and welcome feedback from others.
D. Responsible Decision Making
1. I can articulate socially defined ethics and norms.
2. I choose to be encouraging, kind, and polite toward others.
3. I make decisions based on my personal values, ethics and my
knowledgeable of social norms.