Download Not Aligned Geometry

Course Title: Geometry
Instructional/Pacing Guide
Not Aligned to the 2011-2012 Benchmarks
Unit 1 Basics of Geometry and Reasoning
Time Frame: Weeks 1-5
Benchmark Week: 5
Week #
Dates
Standard(s)
2-5
8/29 – 9/23
1.0 Students demonstrate understanding
by identifying & giving examples of
undefined terms, axioms, theorems, &
inductive & deductive reasoning.
3.0 Students construct & judge the
validity of a logical argument & give
counterexamples to disprove a
statement.
16.0 Students perform basic
constructions with a straightedge &
compass, such as angle bisectors,
perpendicular bisectors, & the line
parallel to a given line through a point
off the line.
22.0 Students know the effect of rigid
motions on figures in the coordinate
plane & space, including rotations,
translations, & reflections.
Total number of questions on Benchmark: 14
Topic
Know the difference between
inductive and deductive
reasoning, and can identify
each.
Textbook
Connections
Number of
Questions on
CST
2
4
Know the definition of and can
provide a counterexample to
an argument.
Construct perpendicular
bisectors, and angle bisectors
with a compass.
Translations, reflections, and
rotations
4
3
Page 1 of 8
Last Revised: January 20, 2012
Course Title: Geometry
Instructional/Pacing Guide
Not Aligned to the 2011-2012 Benchmarks
Unit 2 Angle properties of Polygons
Time Frame: Weeks 6-8
Benchmark Week: 8
Week #
6-8
Dates
9/26 – 10/14
Standard(s)
2.0 Students write geometric proofs,
including proofs by contradiction.
6.0 Students know and are able to use
the triangle inequality theorem.
12.0 Students find & use measures of
sides & of interior & exterior angles of
triangles & polygons to classify figures
& solve problems.
Topic
Geometric Proofs
Textbook
Connections
Number of
Questions on
CST
3
Proofs by Contradiction
Triangle Inequality Theorem
1
5
Measures of Sides and Interior
and Exterior Angles
Total Number of Questions on Benchmark: 14
Page 2 of 8
Last Revised: January 20, 2012
Course Title: Geometry
Instructional/Pacing Guide
Not Aligned to the 2011-2012 Benchmarks
Unit 3: Parallel, Perpendicular and Properties of Quadrilaterals
Time Frame: Weeks 9-12
Benchmark Week: 12
Week #
9-12
Dates
10/17 – 11/11
Standard(s)
7.0 Students prove & use theorems
involving the properties of parallel lines
cut by a transversal, the properties of
quadrilaterals, & the properties of
circles.
4.0 Students prove basic theorems
involving congruence & similarity.
13.0 Students prove relationships
between angles in polygons by using
properties of complementary,
supplementary, vertical, & exterior
angles.
Topic
Textbook
Connections
Number of
Questions on
CST
Prove Parallelism theorems.
5 2/3
Solve for angles involving
parallel lines cut by a
transversal.
5
Know various properties of
quadrilaterals such as sum of
interior angles and diagonals.
2
Students know linear pair,
vertical, supplementary, and
complementary angles, and
use this knowledge to solve
problems in various contexts.
Construct a line parallel to a
given line through a point off
the line with a compass.
Number of questions on the Benchmark: 20
Page 3 of 8
Last Revised: January 20, 2012
Course Title: Geometry
Instructional/Pacing Guide
Not Aligned to the 2011-2012 Benchmarks
Unit 4: Area and Volume
Time Frame: Weeks 13-17
Benchmark Week: 17
Week #
13-17
Dates
11/14 – 12/09
Standard(s)
8.0 Students know, derive, & solve
problems involving the perimeter,
circumference, area, volume, lateral
area, & surface area of common
geometric figures.
9.0 Students compute the volumes &
surface areas of prisms, pyramids,
cylinders, cones, & spheres; & students
commit to memory the formulas for
prisms, pyramids, & cylinders.
10.0 Students compute areas of
polygons, including rectangles, scalene
triangles, equilateral triangles, rhombi,
parallelograms, & trapezoids
Number of Questions on the Benchmark: 20
Topic
Solving for area and perimeter
of various polygons
Finding the surface area and
volume of three-dimensional
figures
Textbook
Connections
Number of
Questions on
CST
4
2
4
Page 4 of 8
Last Revised: January 20, 2012
Course Title: Geometry
Instructional/Pacing Guide
Not Aligned to the 2011-2012 Benchmarks
Unit 5: Similarity and Congruence
Time Frame: Weeks 18-21
Benchmark Week: 21
Week #
18- 21
Dates
12/12– 01/13
Standard(s)
Topic
4.0 Students prove basic theorems
involving congruence & similarity.
5.0 Students prove that triangles are
congruent or similar, & they are able to
use the concept of corresponding parts
of congruent triangles.
11.0 Students determine how changes in
dimensions affect the perimeter, area, &
volume of common geometric figures &
solids.
Know properties of congruent
triangles.
Textbook
Connections
Number of
Questions on
CST
5
Know properties of similar
polygons including perimeters
and volume.
2
Know how to prove triangles
are congruent.
1
Know the effect on perimeter,
area, and volume when
changing the dimensions of a
polygon.
Number of Questions on the Benchmark: 20
Page 5 of 8
Last Revised: January 20, 2012
Course Title: Geometry
Instructional/Pacing Guide
Not Aligned to the 2011-2012 Benchmarks
Unit 6 : Pythagorean Theorem
Time Frame: Weeks 21-22
Benchmark Week: 22
Week #
21-22
Dates
01/23-02/03
Standard(s)
14.0 Students prove the Pythagorean
theorem.
15.0 Students use the Pythagorean
theorem to determine distance & find
missing lengths of sides of right
triangles.
17.0 Students prove theorems by using
coordinate geometry, including the
midpoint of a line segment, the distance
formula, & various forms of equations
of lines & circles.
Number of Questions on the Benchmark: 20
Topic
Pythagorean Theorem
Proving the Pythagorean
Theorem
Distance and Midpoint
Formulas
Textbook
Connections
Number of
Questions on
CST
1/3
2
3
Page 6 of 8
Last Revised: January 20, 2012
Course Title: Geometry
Instructional/Pacing Guide
Not Aligned to the 2011-2012 Benchmarks
Unit 7 Trigonometry
Time Frame: Weeks 23-24
Benchmark Week: 24
Week #
23-24
Dates
02/06 – 02/17
Standard(s)
18.0 Students know the definitions of
the basic trigonometric functions
defined by the angles of a right triangle.
They also know & are able to use
elementary relationships between them.
For example, tan( x ) = sin( x )/cos( x ),
(sin( x )) 2 + (cos( x )) 2 = 1.
19.0 Students use trigonometric
functions to solve for an unknown
length of a side of a right triangle, given
an angle & a length of a side.
20.0 Students know & are able to use
angle & side relationships in problems
with special right triangles, such as 30°,
60°, & 90° triangles & 45°, 45°, & 90°
triangles.
Number of Questions on the Benchmark: 20
Topic
Vocabulary relating to trig
functions.
Write trigonometric ratios.
Use elementary relationships
between trigonometric ratios.
Use trigonometric trig
functions to solve for an
unknown side length of a side
of a right triangle, given an
angle and a length of a side.
Use special right triangle
relationships to find missing
side lengths of 30-60-90 and
45-45-90 triangles.
Textbook
Connections
Number of
Questions on
CST
3
3
1
Page 7 of 8
Last Revised: January 20, 2012
Course Title: Geometry
Instructional/Pacing Guide
Not Aligned to the 2011-2012 Benchmarks
Unit 8 Circles
Time Frame: Weeks 25-28
Benchmark Week: 28
Week #
Dates
25-28
02/20 – 03/09
03/12 – 03/16
(CAHSEE)
Resume Unit 8
03/19 – 03/23
Standard(s)
Topic
21.0 Students prove & solve problems
regarding relationships among chords,
secants, tangents, inscribed angles, &
inscribed & circumscribed polygons of
circles.
Learn vocabulary relating to
circles
Use properties and theorems
about tangents.
Use arc addition postulate
Use Theorems about chords of
circles.
Use theorems about the
inscribed angles of a circle.
Use theorems about inscribed
polygons.
Use theorem about tangents
and chords.
Use theorems about lines
intersecting inside or outside a
circle.
Use theorems about
intersecting chords.
Use theorems about segments
of tangents and secants.
Identify the equation of a
circle given the center and
radius of the circle.
Identify the graph of a circle
when its equation is given.
Textbook
Connections
Number of
Questions on
CST
5
Number of Questions on the Benchmark: 20
Page 8 of 8
Last Revised: January 20, 2012