Download Algebra I Detailed Objectives

Geometry Detailed Objectives
Throughout the course as appropriate
LG.1.G.6
Give justification for conclusions reached by deductive reasoning State and prove key basic theorems in geometry
(i.e., the Pythagorean theorem, the sum of the measures of the angles of a triangle is 180°, and the line joining the
midpoints of two sides of a triangle is parallel to the third side and half it’s length)
DMEC
Category
Logic and
Reasoning
Points, Lines,
Planes, etc.
Objectives
1. Compare and contrast inductive and deductive
reasoning.
2. Use Venn Diagrams to solve problems.
3. Use Matrix Logic to solve problems.
4. Identify the inverse, converse and contrapositive of a
statement.
5. Recognize and describe relationships derived from
figural patterns.
1. Represent points pictorially with proper identification.
2. Represent lines pictorially with proper identification.
3. Represent rays pictorially with proper identification.
4. Represent line segments pictorially with proper
identification.
5. Represent angles pictorially with proper identification.
6. Represent planes pictorially with proper identification.
2009-2010
SLEs
LG.1.G.1 Define, compare and
contrast inductive reasoning and
deductive reasoning for making
predictions based on real world
situations
• Venn diagrams
• matrix logic
• conditional statements
(statement, inverse,
converse, and
contrapositive)
• figural patterns
LG.1.G.3 Describe relationships
derived from geometric figures or
figural patterns.
LG.1.G.2 Represent points, lines, and
planes pictorially with proper
identification, as well as basic
concepts derived from these
undefined terms, such as segments,
rays, and angles
Category
Angle
relationships
Non-Euclidean
Geometries
Objectives
1. Solve problems involving complementary angles.
2. Solve problems involving supplementary angles.
3. Solve problems involving vertical angles.
4. Solve problems involving linear pairs of angles.
5. Solve problems involving angles formed by
perpendicular lines.
6. Solve problems involving parallel lines cut by a
transversal.
SLEs
LG.1.G.4 Apply, with and without
appropriate technology, definitions,
theorems, properties, and postulates
related to such topics as
complementary, supplementary,
vertical angles, linear pairs, and
angles formed by perpendicular lines
LG.1.G.5 Explore, with and without
appropriate technology, the
relationship between angles formed
by two lines cut by a transversal to
justify when lines are parallel
7. Perform basic Euclidean constructions.
M.3.G.5 Identify and apply properties
of and theorems about parallel and
perpendicular lines to prove other
theorems and perform basic
Euclidean constructions
R.4.G.9 Explore non-Euclidean
geometries, such as spherical
geometry and identify its unique
properties which result from a change
in the parallel postulate
1. Identify unique properties which result when the
parallel postulate is not included as one of the
postulates for a geometry.
Category
Slope and
Equations of
Lines
Objective
1. Identify horizontal and vertical lines by calculating the
slope.
2. Determine if sets of lines are parallel or perpendicular
by calculating their slope.
3. Write the equation of a line parallel to a line through a
point not on the line.
4. Write the equation of a line perpendicular to a line
through a given point.
5. Write the equation of the perpendicular bisector of a
line segment.
1. Prove the Pythagorean Theorem.
2. Use the Pythagorean Theorem and its converse to
solve problems.
Pythagorean
Theorem and
Related Topics
3. Find the distance between two points in a rectangular
coordinate system.
4. Find the coordinates of the midpoint of a line segment
in the coordinate plane.
SLEs
CGT.5.G.1 Use coordinate geometry
to find the slopes of parallel,
perpendicular, horizontal, and vertical
lines
CGT.5.G.2 Write the equation of a
line parallel to a line through a given
point not on the line
CGT.5.G.3 Write the equation of a
line perpendicular to a line through a
given point
CGT.5.G.4 Write the equation of the
perpendicular bisector of a line
segment
T.2.G.4 Apply the Pythagorean
Theorem and its converse in solving
practical problems
LG.1.G.6 State and prove key basic
theorems in geometry
CGT.5.G.1 Use coordinate geometry
to find the distance between two
points, the midpoint of segments.
5. Apply the triangle inequality to solve problems.
.
T.2.G.2 Investigate the measures of
segments to determine the existence
of triangles (triangle inequality
theorem)
Category
Special
Segments of
Triangles
Properties of
Polygons
Objective
1. Identify altitudes of triangles and use them to solve
problems.
2. Identify medians of triangles and use them to solve
problems.
3. Identify angle bisectors of triangles and use them to
solve problems.
4. Identify perpendicular bisectors of triangles and use
them to solve problems.
5. Identify midsegments of triangles and use them to
solve problems
1. Use properties of quadrilaterals to solve problems.
2. Solve problems involving the sum of the measures of
the interior angles of a polygon.
3. Solve problems involving the interior and exterior angle
measures of regular and irregular polygons.
4. Solve problems involving the number of sides and
angles of polygons.
5. Classify figures given the set of points that form the
vertices of the figure.
6. Prove theorems about polygons.
SLEs
T.2.G.3 Identify and use the special
segments of triangles (altitude,
median, angle bisector, perpendicular
bisector, and midsegment) to solve
problems
R.4.G.1 Explore and verify the
properties of quadrilaterals
R.4.G.2 Solve problems using
properties of polygons:
• sum of the measures of the
interior angles of a polygon
• interior and exterior angle
measure of a regular polygon
or irregular polygon
• number of sides or angles of a
polygon
CGT.5.G.5 Determine, given a set of
points, the type of figure based on its
properties (parallelogram, isosceles
triangle, trapezoid)
LG.1.G.6 State and prove key basic
theorems in geometry
Category
Proportional
Reasoning
Objective
SLEs
1. Find missing measures of figures based on congruence T.2.G.1 Apply congruence (SSS …)
and similarity (AA ...)
relationships.
correspondences and properties of
figures to find missing parts of
geometric figures and provide logical
justification
2. Find missing measures of figures based on similarity
relationships.
Trigonometry
3. Use properties of parallel lines and proportional
reasoning to find lengths of segments.
1. Use trigonometric ratios to find the measures of sides
of right triangles to solve problems.
2. Use trigonometric ratios to find the measures of angles
in right triangles to solve problems.
3. Use trigonometric ratios to solve problems involving
angles of elevation.
M.3.G.4 Use (given similar geometric
objects) proportional reasoning to
solve practical problems (including
scale drawings)
M.3.G.5 Use properties of parallel
lines and proportional reasoning to
find the lengths of segments
T.2.G.6 Use trigonometric ratios
(sine, cosine, tangent) to determine
lengths of sides and measures of
angles in right triangles, including
angles of elevation and angles of
depression
4. Use trigonometric ratios of solve problems involving
angles of depression.
T.2.G.7 Use similarity of right
triangles to express the sine, cosine,
and tangent of an angle in a right
triangle as a ratio of given including
angles of elevation and angles of
depression
5. Use the special right triangle relationships to solve
problems.
T.2.G.5 Use the special right triangle
relationships (30˚-60˚-90˚ and 45˚45˚-90˚) to solve problems
Category
Transformations
2-D
Representations
of 3-D Objects
Objectives
1. Draw and interpret the results of transformations and
successive transformations on figures in the coordinate
plane.
SLEs
CGT.5.G.7 Draw and interpret the
results of transformations and
successive transformations on figures
in the coordinate plane
• translations
• reflections
• rotations (90˚, 180˚, clockwise
and counterclockwise about
the origin)
• dilations (scale factor)
2. Identify and explain why figures tessellate.
R.4.G.3 Identify and explain why
figures tessellate
3. Identify the attributes of the five Platonic Solids.
1. Use orthographic drawings to represent threedimensional objects.
2. Use isometric drawings to represent three-dimensional
objects.
R.4.G.4 Identify the attributes of the
five Platonic Solids
R.4.G.7 Use orthographic drawings
(top, front, side) and isometric
drawings (corner) to represent threedimensional objects
3. Draw, examine and classify cross-sections of threedimensional objects.
R.4.G.8 Draw, examine, and classify
cross-sections of three-dimensional
objects
Category
Perimeter, Area ,
Volume
Objectives
1. Solve problems involving perimeter of polygons.
2. Solve problems involving the circumference of circles.
3. Solve problems involving perimeter of composite
figures.
4. Solve problems involving area of polygons.
5. Solve problems involving area of circles.
6. Solve problems involving area of composite figures.
7. Solve problems involving surface area of prisms.
8. Solve problems involving surface area of pyramids.
9. Solve problems involving surface area of cones.
10. Solve problems involving surface area of cylinders.
11. Solve problems involving surface area of spheres.
12. Solve problems involving the surface area of composite
objects.
13. Solve problems involving volume of prisms.
14. Solve problems involving volume of pyramids.
15. Solve problems involving volume of cones.
16. Solve problems involving volume of cylinders.
17. Solve problems involving volume of spheres.
18. Solve problems involving volume of composite objects.
SLEs
M.3.G.2 Apply, using appropriate
units, appropriate formulas (area,
perimeter, surface area, volume) to
solve application problems involving
polygons, prisms, pyramids, cones,
cylinders, spheres as well as
composite figures, expressing
solutions in both exact and
approximate forms
19. Relate changes in the measurement of one attribute of
an object to changes in the measurement of other
attributes.
M.3.G.3 Relate changes in the
measurement of one attribute of an
object to changes in other attributes
(Ex. How does changing the radius or
height of a cylinder affect its surface
area or volume?)
20. Use area models to calculate probabilities.
M.3.G.1 Calculate probabilities
arising in geometric contexts (Ex.
Find the probability of hitting a
particular ring on a dartboard.)
Category
Circles
Objectives
1. Write the equation of a circle in standard form given a
coordinate graph of the circle.
2. Write the equation of a circle in standard form given the
coordinates of the center of the circle and the radius of
the circle.
SLEs
CGT.5.G.6 Write, in standard form,
the equation of a circle given a graph
on a coordinate plane or the center
and radius of a circle
3. Use properties of central angles o a circle to solve
problems.
4. Use properties of central angles of circles to solve
problems.
5. Use properties of angles inscribed in circles to solve
problems.
6. Use properties of arc of circles to solve problems.
7. Use properties of chords of circles to solve problems.
8. Use properties of lines tangent to circles to solve
problems.
9. Use properties of lines secant to circles to solve
problems.
R.4.G.5 Investigate and use the
properties of angles (central and
inscribed) arcs, chords, tangents,
and secants to solve problems
involving circles
10. Solve problems using inscribed figures.
R.4.G.6 Solve problems using
inscribed and circumscribed figures
11. Solve problems using circumscribed figures.
Notes: Highlighting indicates areas not included in SLE’s from previous grade levels.