# Modern Geometry Honors Curriculum

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```Modern Geometry Honors
Williamsport Area School District
Mathematics
Course Title:
Modern Geometry Honors
Unit
Unit Title
Page
Geometric Definitions
Duration
(Days)
12
1
2
Angles and Parallel Lines
14
7
3
12
13
4
Equations of Parallel and
Perpendicular Lines
Triangles
14
17
5
Logic and Reasoning
16
22
6
19
26
7
Right Triangles and
Similarity
Circles
19
32
8
14
39
9
Measuring in Space
12
45
10
Geometric Probability
12
50
1
Page 1
Modern Geometry Honors
Williamsport Area School District
Unit 1: Geometric Definitions
Big Idea:
Days: 12
Plane Geometry can be derived from three undefined terms.
Unit Essential Question:
How are the three undefined terms used
to establish definitions in geometry?
Concept
Concept Title
1.1
Points, Lines, and Planes
Duration
(Days)
1
1.2
Segments, Rays, and Parallel Lines
3
1.3
Measuring Segments
2
1.4
2
1.5
Coordinate Plane (Distance and Midpoint)
4
Page 2
Modern Geometry Honors
Concept 1.1
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Points, Lines, and Planes
2.5.11.A, 2.5.11.B
What are the basic building blocks of geometry?
Geometry, point, space, line, collinear, plane, coplanar, theorem, postulate
Learning Goals:
Descriptor
1.1.A
Identify and model points, lines, and
planes.
1.1.B
Identify collinear and coplanar points and
intersecting lines and planes in space.
Resources:
Glencoe Geometry: 1-1
Assessment Sources:
Daily Assignments
Eligible
Content
NA
Days
NA
0.5
0.5
Notes:
Page 3
Modern Geometry Honors
Williamsport Area School District
Concept 1.2
Segments, Rays, and Parallel Lines
Lesson Essential
Question(s):
2.3.11.A, 2.5.11.B, 2.9.11.A, M11.B.2.11
What is the difference between a line, a ray and a line segment? What is the
difference between parallel, intersecting, and skew lines (and planes)?
Vocabulary:
Segment, ray, opposite rays, parallel lines, skew lines, parallel planes
Learning Goals:
Descriptor
Eligible
Content
NA
Days
1.2.A
Identify the relationships between two
lines and two planes.
1.2.B
Identify and name segments, rays, lines,
and planes.
NA
0.5
1.2.C
lines, and planes.
NA
0.5
Resources:
Glencoe Geometry: 3-1
Assessment Sources:
Daily Assignments
Notes:
1
Page 4
Modern Geometry Honors
Williamsport Area School District
Concept 1.3
Measuring Segments
Lesson Essential
Question(s):
2.3.11.A, 2.5.11.B, 2.5.11.C, 2.8.11.D, 2.8.11. J, 2.9.11.A, 2.9.11.G,
M11.C.3.1.1
How is the length of segments used to determine congruency? What is
segment addition and how is it used?
Vocabulary:
Line segment, ray, congruent, segment, addition postulate, midpoint,
segment bisector
Learning Goals:
Descriptor
1.3.A
Define segments using two points.
1.3.B
Use segment postulates and the midpoint
to solve problems.
Resources:
Glencoe Geometry: 1-3, 2-7
Assessment Sources:
Daily Assignments
Eligible
Content
NA
Days
NA
1
1
Notes:
Page 5
Modern Geometry Honors
Concept 1.4
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
2.1.11.A, 2.2.11.A, 2.5.11.B, M11.A.1.1.1, M11.A.1.1.3, M11.A.2.2.1,
2.1.A1.A
How can we simplify a radical expression?
Radical, perfect square, square root, factor
Learning Goals:
Descriptor
1.4.A
Identify perfect squares and perfect
square factors.
1.4.B
Eligible
Content
A1.1.1.1.2
Days
0.5
0.5
Resources:
Glencoe Geometry: pages 744-745
Assessment Sources:
Daily Assignments
A1.1.1.1.2
Notes:
Page 6
Modern Geometry Honors
Concept 1.5
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Coordinate Plane (Distance and Midpoint)
2.5.11.B, 2.5.11.C, 2.8.11.D, 2.8.11.J, 2.9.11.B, 2.9.11.G, M11.C.3.1.1,
2.9.G.C
What is coordinate geometry? How can the midpoint of a segment be
determined on the coordinate plane? How can the distance formula be used
to solve problems and prove conjectures?
Radical, perfect square, square root, factor
Learning Goals:
Descriptor
1.5.A
Find the distance between two points.
Eligible
Content
G.2.1.2.1
1.5.B
Find the midpoint of a segment.
G.2.1.2.1
Resources:
Glencoe Geometry: 1-3
Assessment Sources:
Daily Assignments
Notes:
Additional 2 Days for Unit Review and Test
Days
1
1
Page 7
Modern Geometry Honors
Williamsport Area School District
Unit 2: Angles and Parallel Lines
Days: 16
Big Idea: Find the measure of angles to determine congruency.
Unit Essential Question:
What are angles and how are they measured, paired and classified?
Concept
Concept Title
2.1
Measuring Angles
Duration
(Days)
2
2.2
Special Angle Pairs
3
2.3
Transversals and Angle Pairs
2
2.4
Special Angles and Parallel Lines
4
2.5
Justifying Parallel and Perpendicular Lines
5
Page 8
Modern Geometry Honors
Williamsport Area School District
Concept 2.1
Measuring Angles
Lesson Essential
Question(s):
2.3.11.A, 2.3.11.B, 2.5.11.A, 2.5.11.B, M11.B.2.11, 2.3.G.C
What are angles, how are they measured, and how are the measures used to
determine their congruency? What is angle addition and how is it used?
Vocabulary:
Angle, vertex, acute, right, obtuse, straight angle, congruent angles,
Learning Goals:
Descriptor
2.1.A
Measure and classify angles.
2.1.B
Identify and use congruent angles and
bisector of an angle.
Resources:
Glencoe Geometry: 1-4
Assessment Sources:
Daily Assignments
Eligible
Content
G.2.2.1.1
Days
G.2.2.1.1
1
1
Notes:
Page 9
Modern Geometry Honors
Concept 2.2
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Special Angle Pairs
2.3.11.A, 2.3.11.B, 2.5.11.B, 2.9.11.A, M11.B.2.1.1, 2.3.G.C
How are pairs of angles classified?
Adjacent angles, vertical angle theorem, complementary angle theorem,
supplementary angle theorem, linear pair, angle bisector
Learning Goals:
Descriptor
2.2.A
Identify and use special angle pairs.
Eligible
Content
G.2.2.1.1
2.2.B
Use the properties of an angle bisector.
G.2.2.1.1
Resources:
Glencoe Geometry: 1-5
Assessment Sources:
Daily Assignments, Quiz
Notes:
Days
1
1
Page 10
Modern Geometry Honors
Concept 2.3
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Transversals and Angle Pairs
2.5.11.B, 2.3.G.C
How do we classify pairs of angles formed by two lines and a transversal?
Corresponding angle, alternate-interior angles, alternate-exterior angles,
consecutive interior angles, transversal
Learning Goals:
Descriptor
2.3.A
Name angles formed by a pair of lines
and a transversal.
Resources:
Glencoe Geometry: 3-1
Assessment Sources:
Daily Assignments
Eligible
Content
G.2.2.1.2
Days
2
Notes:
Page 11
Modern Geometry Honors
Williamsport Area School District
Concept 2.4
Angles and Parallel Lines
Lesson Essential
Question(s):
2.3.11.A, 2.3.11.B, 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, M11.B.2.1.1,
2.3.G.C
When a transversal intersects parallel lines, how do the angles' measures
compare?
Vocabulary:
Corresponding angles postulate, alternate interior angles theorem,
consecutive interior angles theorem, alternate exterior angles theorem,
perpendicular transversal theorem
Learning Goals:
Descriptor
2.4.A
Use the properties of parallel lines to find
congruent sides.
2.4.B
Determine angle measures using angle
relationships.
Resources:
Glencoe Geometry: 3-2
Assessment Sources:
Daily Assignments, Activity, Quiz
Eligible
Content
G.2.2.1.2
Days
G.2.2.1.2
3
1
Notes:
Page 12
Modern Geometry Honors
Concept 2.5
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Proving Lines Parallel
2.3.11.A, 2.3.11.B, 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, M11.B.2.1.1,
2.4.G.A
How can lines be proven parallel?
Converse of corresponding angles postulate, converse of alternate exterior
angles theorem, converse of consecutive interior angles theorem, converse of
alternate interior angle theorem, converse of perpendicular transversal
theorem
Learning Goals:
Descriptor
2.5.A
Recognize angle conditions that occur
with parallel lines.
2.5.B
Prove that two lines are parallel based on
given angle relationships.
Resources:
Glencoe Geometry: 3-5
Assessment Sources:
Daily Assignments, Activity
Notes:
Add 1 day for unit test
Eligible
Content
G.1.3.2.1
Days
G.1.3.2.1
2
2
Page 13
Modern Geometry Honors
Williamsport Area School District
Unit 3: Parallel and Perpendicular Lines
Big Idea:
Days: 12
Special relationships apply to angles formed by parallel and intersecting lines and
planes.
Unit Essential Question:
How are angles formed by transversals related?
Concept
Concept Title
3.1
Slopes of Parallel and Perpendicular Lines
Duration
(Days)
2
3.2
Equations of Parallel and Perpendicular
4
3.3
Systems of Equations and Inequalities
6
Page 14
Modern Geometry Honors
Concept 3.1
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Slopes of Parallel and Perpendicular Lines
2.5.11.A, 2.8.11.D, 2.8.11.J, 2.8.11.K, M11.C.3.1.2, M11.D.3.2.1, 2.9.G.C
How can slope determine if lines are parallel, perpendicular or neither?
Perpendicular, parallel, slope formula, slope-intercept form
Learning Goals:
Descriptor
3.1.A
Find slopes of lines.
3.1.B
Use slope to identify parallel and
perpendicular lines.
Resources:
Glencoe Geometry: 3-3
Assessment Sources:
Daily Assignments
Eligible
Content
G.2.1.3.1
Days
G.2.1.2.2
1
1
Notes:
Page 15
Modern Geometry Honors
Concept 3.2
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Equations of Parallel and Perpendicular Lines
2.3.11.A, 2.3.11.B, 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, M11.B.2.1.1
2.5.11.A, 2.8.11.D, 2.8.11.J, 2.8.11.K, M11.C.3.1.2, M11.D.3.2.1, 2.9.G.C,
2.1.A1.F, 2.8.A1.E, 2.8.A1.F
What is the difference between equations of parallel and perpendicular lines?
Point-slope form
Learning Goals:
Descriptor
3.2.A
Write an equation of a line given
3.2.B
Find the equation of a line that is parallel
or perpendicular to a given line that
passes through a given point.
Resources:
Glencoe Geometry: 3-4
Assessment Sources:
Daily Assignments, Quiz
Eligible
Content
A1.1.2.1.1
Days
G.2.1.2.2
2
2
Notes:
Page 16
Modern Geometry Honors
Concept 3.3
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Systems of Equations and Inequalities
2.2.11.F, 2.4.11.E, 2.5.11.A, 2.5.11.B, 2.5.11.C, 2.5.11.D, 2.8.11.D,
2.8.11.F, 2.8.11.G, 2.8.11.H, 2.8.11.J, 2.8.11.K, 2.8.11.L, 2.8.11.N, 2.9.11.I,
M11.C.3.1.1, M11.C.3.1.2, M11.D.4.1.1, M11.D.2.1.1, M11.D.2.1.2,
M11.D.2.1.3, M11.D.2.1.4, 2.8.G.B, 2.8.A1.E, 2.8.A1.F
How can systems of linear equations and inequalities be solved? How do
systems of equations and inequalities model real life situations? How can
systems of equations and inequalities help solve geometry problems?
Point of intersection, consistent, inconsistent, dependent, independent,
parallel, perpendicular, coinciding lines, substitution, elimination, linear
combination, feasible region
Learning Goals:
Descriptor
Eligible
Content
A1.1.3.2.1
Days
3.3.A
Graph systems of equations and
inequalities.
3.3.B
Solve systems of equations.
A1.1.2.2.1
1
3.3.C
Use systems of equations and inequalities
to solve coordinate geometry problems.
G.2.1.4.1
2
Resources:
Glencoe Geometry: p. 742-743
Assessment Sources:
Daily Assignments, Activity
Notes:
Additional 2 Days for Unit Review and Test
1
Page 17
Modern Geometry Honors
Williamsport Area School District
Unit 4: Triangles
Days: 14
The classification and properties of triangles can be determined by their distinct
characteristics.
Big Idea:
Unit Essential Question:
What special properties exist for each type of triangle?
How can congruency be determined?
Concept
Concept Title
4.1
Classify Triangles
Duration
(Days)
2
4.2
Angles of Triangles
5
4.3
Isosceles and Equilateral Triangles
3
4.4
Congruent Triangles
4
Page 18
Modern Geometry Honors
Williamsport Area School District
Concept 4.1
Classify Triangles
Lesson Essential
Question(s):
2.5.11.B, M11.B.2.1.1, M11.C.1.2.3, 2.9.G.A
What are the different types of triangles based on side and angle measure?
How can the existence of a triangle be determined? What is the correlation
between the longest side and the largest angle?
Vocabulary:
Acute, right, obtuse, straight, scalene, isosceles, equilateral, equiangular,
regular, triangle inequality
Learning Goals:
Descriptor
4.1.A
Identify and classify triangles by angles.
Eligible
Content
G.1.2.1.1
4.1.B
Identify and classify triangles by sides.
G.1.2.1.1
Resources:
Glencoe Geometry: 4-1
Assessment Sources:
Daily Assignments
Days
1
1
Notes:
Page 19
Modern Geometry Honors
Williamsport Area School District
Concept 4.2
Angles of Triangles
Lesson Essential
Question(s):
2.4.11.A, 2.4.11.B, 2.5.11.B, M11.B.2.1.1, 2.9.G.A
What are the interior and exterior angle sums of a triangle? What is the
relationship between an exterior angle of a triangle and its remote interior
angles?
Vocabulary:
Interior angle sum, remote interior angles, exterior angle, exterior angle sum
Learning Goals:
Descriptor
4.2.A
Apply the angle sum theorem.
Eligible
Content
G.1.2.1.1
4.2.B
Apply the exterior angle theorem.
G.1.2.1.1
Resources:
Glencoe Geometry: 4-2
Assessment Sources:
Daily Assignments
Notes:
Days
2
2
Page 20
Modern Geometry Honors
Concept 4.3
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Isosceles and Equilateral Triangles
M11.C.1.2.3, 2.9.G.A
What properties are unique to isosceles and equilateral triangles?
Isosceles, isosceles triangle theorem, converse of isosceles triangle theorem,
equilangular
Learning Goals:
Descriptor
4.3.A
Use properties of isosceles triangles.
Eligible
Content
G.1.2.1.3
4.3.B
Use properties of equilateral triangles.
G.1.2.1.3
Resources:
Glencoe Geometry: 4-6
Assessment Sources:
Daily Assignments
Days
2
1
Notes:
Page 21
Modern Geometry Honors
Williamsport Area School District
Concept 4.4
Congruent Triangles
Lesson Essential
Question(s):
2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, 2.9.11.B, 2.9.11.D, M11.C.1.2.1,
M11.C.1.3.1, 2.9.G.A, 2.9.G.B
How can we identify corresponding parts of congruent triangles? What
relationships exist between corresponding parts of congruent triangles?
Vocabulary:
Congruent triangles, corresponding angles, corresponding sides,
corresponding parts of congruent triangles are congruent (CPCTC)
Learning Goals:
Descriptor
4.4.A
Name and label corresponding parts of
congruent triangles.
Resources:
Glencoe Geometry: 4-3
Assessment Sources:
Daily Assignments, Quiz
Notes:
Additional 2 days for Review and Test
Eligible
Content
G.1.3.1.1
Days
2
Page 22
Modern Geometry Honors
Williamsport Area School District
Unit 5: Logic and Reasoning
Big Idea:
Days: 16
Spatial reasoning and visualization are ways to orient thinking about the physical
world.
Unit Essential Question:
What strategies can we use to draw conclusions in geometry?
Concept
Concept Title
5.1
Reasoning
Duration
(Days)
3
5.2
Introduction to Proofs
5
5.3
Proving Triangles Congruent
8
Page 23
Modern Geometry Honors
Concept 5.1
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Reasoning
2.3.11.A, 2.3.11.B, 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.4.11.D, 2.5.11.B,
M11.B.2.1.1
How do conditional statements support geometric reasoning? What is the
difference between inductive and deductive reasoning? What strategies can
we use to draw conclusions in geometry?
Conjecture, inductive reasoning, counterexample, deductive reasoning,
conditional/if-then statement, hypothesis, conclusion, converse, inverse,
contra-positive, bi-conditional
Learning Goals:
Descriptor
Eligible
Content
NA
Days
5.1.A
Make conjectures based on inductive
reasoning.
5.1.B
Find counterexamples of conjectures.
2.4.G.A
1
5.1.C
Analyze if-then statements and write the
converse, inverse, and contra-positive.
2.4.G.B
1
Resources:
Glencoe Geometry: 2-1, 2-3, 2-4
Assessment Sources:
Daily Assignments
Notes:
Optional Activities Available
1
Page 24
Modern Geometry Honors
Concept 5.2
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Introduction to Proofs
2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, 2.5.11.C, 2.5.11.D, M11.B.2.1.1,
2.4.G.A
What are proofs? How do you construct a proof?
Conjecture, inductive reasoning, counterexample, deductive reasoning,
conditional/if-then statement, hypothesis, conclusion, converse, inverse,
contra-positive, bi-conditional
Learning Goals:
Descriptor
5.2.A
Write two-column algebraic and
geometric proofs.
5.2.B
Use properties of equality in geometry
proofs.
Resources:
Glencoe Geometry: 2-5, 2-6
Assessment Sources:
Daily Assignments
Notes:
Quiz
Eligible
Content
G.1.3.2.1
Days
G.1.3.2.1
2
2
Page 25
Modern Geometry Honors
Concept 5.3
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Proving Triangles Congruent
2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, 2.9.11.B, 2.9.11.D, M11.C.1.2.1,
M11.C.1.3.1, 2.9.G.B, 2.4.G.A
What are the ways to prove triangles congruent?
SSS, SAS, ASA AAS, & HL
Learning Goals:
Descriptor
Eligible
Content
G.1.3.1.1
Days
5.3.A
Use the SSS and SAS Postulates to test
for triangle congruence.
5.3.B
Use the ASA Postulate and AAS
Theorem to test for triangle congruence.
G.1.3.2.1
2
5.3.C
Use the HL Postulate to test for triangle
congruence.
G.1.3.2.1
2
Resources:
Glencoe Geometry: 4-4 and 4-5
Assessment Sources:
Daily Assignments, Quiz
Notes:
Additional 2 Days for Unit Review and Test
2
Page 26
Modern Geometry Honors
Williamsport Area School District
Unit 6: Right Triangles and Similarity
Big Idea:
Days: 19
Right triangles and similar figures have a broad range of relationships that lead to
many
applications and uses.
Unit Essential Questions:
What are the different methods that can be used to solve right triangles?
How can similar figures be used to find missing
lengths and angle measures?
Concept
Concept Title
6.1
Pythagorean Theorem
Duration
(Days)
3
6.2
Triangles 45, 45, 90
1
6.3
Triangles 30, 60, 90
3
6.4
Similar Figures
4
6.5
Right Triangle Trigonometry
6
6.6
Law of Sines
1
6.7
Law of Cosines
1
Page 27
Modern Geometry Honors
Williamsport Area School District
Concept 6.1
Pythagorean Theorem
Lesson Essential
Question(s):
2.2.11.A, 2.5.11.B, M11.A.1.1.3, M11.A.2.2.1, 2.1.11.A, 2.4.11.B, 2.4.11.C,
2.10.11.B, M11.A.1.1.1, M11.C.1.2.1, M11.C.1.4.1, 2.10.G.A
How would we simplify a radical expression? How and when can the
Pythagorean Theorem be used to find a missing side length? How can the
converse of the Pythagorean Theorem be used to determine the type of
triangle?
Vocabulary:
Radical, perfect square, square root, legs, hypotenuse, Pythagorean triple
Learning Goals:
Descriptor
Eligible
Content
G.2.1.1.1
Days
6.1.A
6.1.B
Find the missing side of a right triangle
using the Pythagorean Theorem.
G.2.1.1.1
0.5
6.1.C
Determine whether a triangle is a right
triangle.
G.2.1.1.1
1
Resources:
Glencoe Geometry: 7-2
Assessment Sources:
Daily Assignments, Quiz
Notes:
0.5
Page 28
Modern Geometry Honors
Williamsport Area School District
Concept 6.2
Triangles 45, 45, 90
Lesson Essential
Question(s):
2.1.11.A, 2.10.11.B, M11.A.1.1.3, M11.A.2.1.3, M11.A.2.2.1, M11.C.1.2.1,
M11.C.1.2.3, 2.10.G.A
How do we determine the ratios of the sides in a 45, 45, 90 special right
triangle?
Vocabulary:
45, 45, 90 triangle
Learning Goals:
Descriptor
6.2.A
Use properties of a 45, 45, 90 triangle
Resources:
Glencoe Geometry: 7-3
Assessment Sources:
Daily Assignments
Notes:
Interactive GSP File Available
Eligible
Content
G.2.1.1.1
Days
1
Page 29
Modern Geometry Honors
Williamsport Area School District
Concept 6.3
Triangles 30, 60, 90
Lesson Essential
Question(s):
2.1.11.A, 2.10.11.B, M11.A.1.1.3, M11.A.2.1.3, M11.A.2.2.1, M11.C.1.2.1,
M11.C.1.2.3, 2.10.G.A
How do we determine the ratios of the sides in a 30, 60, 90 special right
triangle?
Vocabulary:
30, 60, 90 triangle
Learning Goals:
Descriptor
6.3.A
Use the properties of 30, 60, 90 triangles.
Resources:
Glencoe Geometry: 7-3
Assessment Sources:
Daily Assignments, Quiz
Notes:
Interactive GSP File Available
Eligible
Content
G.2.1.1.1
Days
2
Page 30
Modern Geometry Honors
Concept 6.4
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Similar Figures
2.5.11.B, M11.A.2.1.3, M11.B.2.1.1, M11.C.1.3.1, 2.2.11.A, 2.5.11.A,
M11.A.2.1.2, M11.A.2.1.3, M11.B.2.3.1, M11.C.1.3.1, 2.2.11.A, 2.4.11.E,
2.5.11.A, 2.8.11.D, 2.9.11.I, M11.A.2.1.2, M11.A.2.1.3, M11.C.1.3.1,
2.9.G.B
How can figures be identified as similar? How can we find the relationship
between similar figures? How do we create and solve proportions to find
missing parts of similar figures?
Similar, ratio, proportion, scale factor, cross products
Learning Goals:
Descriptor
6.4.A
Identify similar triangles.
Eligible
Content
G.1.3.1.2
6.4.B
Solve problems using a scale factor.
G.1.3.1.2
1
6.4.C
Solve problems using proportions.
G.1.3.1.2
2
Resources:
Glencoe Geometry: 6-2
Assessment Sources:
Daily Assignments
Days
1
Notes:
Page 31
Modern Geometry Honors
Williamsport Area School District
Concept 6.5
Right Triangle Trigonometry
Lesson Essential
Question(s):
2.1.11.A, 2.4.11.E, 2.5.11.A, 2.5.11.B, 2.8.11.D, 2.9.11.I, 2.10.11.B,
M11.A.1.1.1, M11.A.1.1.3, M11.A.2.1.3, M11.C.1.2.1, 2.10.G.A
What are the trigonometric ratios? How do we use them to solve triangles?
How can trigonometric be used to solve real-world problems?
Vocabulary:
Sine, cosine, tangent, opposite, adjacent, hypotenuse, angle of elevation,
angle of depression
Learning Goals:
Descriptor
6.5.A
Find trigonometric ratios using right
triangles.
6.5.B
Solve problems using trigonometric
ratios.
Resources:
Glencoe Geometry: 7-4
Assessment Sources:
Daily Assignments
Eligible
Content
G.2.1.1.2
Days
G.2.1.1.2
2
2
Notes:
Page 32
Modern Geometry Honors
Concept 6.6
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Law of Sines
2.1.11.A, 2.4.11.E, 2.5.11.A, 2.5.11.B, 2.8.11.D, 2.9.11.I, 2.10.11.B,
M11.A.1.1.1, M11.A.1.1.3, M11.A.2.1.3, M11.C.1.2.1, 2.10.G.A
What is Law of Sines? When is it used? How do we use it to solve
triangles?
How can trigonometry be used to solve real-world problems?
Law of Sines
Learning Goals:
Descriptor
6.5.A
Solve triangles using Law of Sines.
Eligible
Content
G.2.1.1.2
6.5.B
Solve problems using Law of Sines.
G.2.1.1.2
Resources:
Glencoe Geometry: 7-6
Assessment Sources:
Daily Assignments
Days
1
1
Notes:
Page 33
Modern Geometry Honors
Williamsport Area School District
Concept 6.7
Law of Cosines
Lesson Essential
Question(s):
2.1.11.A, 2.4.11.E, 2.5.11.A, 2.5.11.B, 2.8.11.D, 2.9.11.I, 2.10.11.B,
M11.A.1.1.1, M11.A.1.1.3, M11.A.2.1.3, M11.C.1.2.1, 2.10.G.A
What is Law of Cosines? When is it used? How do we use it to solve
triangles? How can trigonometry be used to solve real-world problems?
Vocabulary:
Law of Cosines
Learning Goals:
Descriptor
6.5.A
Solve triangles using Law of Cosines.
Eligible
Content
G.2.1.1.2
6.5.B
Solve problems using Law of Cosines.
G.2.1.1.2
Resources:
Glencoe Geometry: 7-7
Assessment Sources:
Daily Assignments
Notes:
Additional 2 Days for Unit Review and Test
Days
1
1
Page 34
Modern Geometry Honors
Williamsport Area School District
Unit 7: Circles
Days: 19
Big Idea: The properties
of angles, arcs, chords, tangents and secants can be used to solve
problems involving circles.
Unit Essential Question:
What are the relationships between a circle and its arcs, lines,
segments and angles?
Concept
Concept Title
7.1
Introduction to Circles
Duration
(Days)
2
7.2
Arcs and Chords
4
7.3
Inscribed Angles
2
7.4
Areas of Circle and Sectors
3
7.5
Tangents of Circles
2
7.6
Secants, Tangents, and Angle Measures
6
Page 35
Modern Geometry Honors
Concept 7.1
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Introduction to Circles
2.5.11.B, M11.C.1.1.1, M11.C.1.1.2, 2.9.G.A, 2.11.G.C, 2.3.G.C
What are the basic components of a circle?
Radius, diameter, chord, circle, circumference, secant
Learning Goals:
Descriptor
7.1.A
Identify and use parts of circles.
7.1.B
Solve problems involving circumference
of a circle.
Resources:
Glencoe Geometry: 10-1
Assessment Sources:
Daily Assignments
Notes:
Investigation Available for Discovering Pi
Eligible
Content
G.1.1.1.1
Days
G.2.2.2.1
1
1
Page 36
Modern Geometry Honors
Williamsport Area School District
Concept 7.2
Arcs and Chords
Lesson Essential
Question(s):
2.9.11.F, M11.C.1.1.2, 2.9.G.A, 2.1.G.C, 2.6.A1.E
How do you determine the measure of an arc in a circle? How do you
determine the circumference of a circle and/or an arc length?
Vocabulary:
Arc measure, minor arc, major arc, semicircle, arc, central angle, sum of
central angles, arc length
Learning Goals:
Descriptor
Eligible
Content
G.1.1.1.2
Days
7.2.A
Recognize and use relationships between
arcs and central angles.
7.2.B
Recognize and use relationships between
arcs, chords, and diameters.
G.1.1.1.3
1
7.2.C
Create and analyze pie charts.
A1.2.3.2.1
1
Resources:
Glencoe Geometry: 10-2, 10-3
Assessment Sources:
Activity, Daily Assignments
Notes:
1
Page 37
Modern Geometry Honors
Williamsport Area School District
Concept 7.3
Inscribed Angles
Lesson Essential
Question(s):
2.9.11.E, 2.9.11.F, M11.B.2.1.1, M11.C.1.1.2, 2.3.G.C
How is the measure of a central angle or an inscribed angle related to the
measure of the intercepted arc?
Vocabulary:
Inscribed angle, inscribed angle theorem, intercepted arc
Learning Goals:
Descriptor
7.3.A
Find measures of inscribed angles.
7.3.B
Find measures of angles of inscribed
polygons.
Resources:
Glencoe Geometry: 10-4
Assessment Sources:
Daily Assignments
Eligible
Content
G.2.2.2.2
Days
G.2.2.2.2
1
1
Notes:
Page 38
Modern Geometry Honors
Concept 7.4
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Areas of Circles and Sectors
2.2.11.A, 2.9.11.F, M11.C.1.1.1, M11.B.2.3.1, M11.B.2.2.4, M11.C.1.1.2,
2.11.G.C, 2.3.G.C
How do you find the area of a circle or a sector?
Area, sector
Learning Goals:
Descriptor
7.4.A
Find the area of a circle.
Eligible
Content
G.2.2.2.1
7.4.B
Find the area of a sector in a circle.
G.2.2.2.5
Resources:
Glencoe Geometry: 11-5
Assessment Sources:
Daily Assignments, Quiz
Notes:
Days
1
1
Page 39
Modern Geometry Honors
Williamsport Area School District
Concept 7.5
Tangents of Circles
Lesson Essential
Question(s):
2.9.11.F, M11.C.1.1.1, 2.9.G.A
How is the tangent of a circle related to the circle's radius at the point of
tangency?
Vocabulary:
Tangent, point of tangency, circumscribed
Learning Goals:
Descriptor
7.5.A
Use properties of tangents.
7.5.B
Solve problems involving circumscribed
polygons.
Resources:
Glencoe Geometry: 10-5
Assessment Sources:
Daily Assignments
Eligible
Content
G.1.1.1.1
Days
NA
1
1
Notes:
Page 40
Modern Geometry Honors
Williamsport Area School District
Concept 7.6
Secants, Tangents, and Angle Measures
Lesson Essential
Question(s):
2.9.11.F, M11.C.1.1.1, 2.9.G.A
How do you find the measure of angles or segments formed by secants and
tangents?
Vocabulary:
Secant, secant-secant, secant-tangent, tangent-tangent
Learning Goals:
Descriptor
7.6.A
Find measures of angles formed by lines
intersecting on or inside the circle.
7.6.B
Find measures of angles formed by lines
intersecting outside the circle.
Resources:
Glencoe Geometry: 10-6
Assessment Sources:
Daily Assignments
Notes:
Additional 2 Days for Unit Review and Test
Eligible
Content
G.1.1.1.3
Days
G.1.1.1.3
2
2
Page 41
Modern Geometry Honors
Williamsport Area School District
Big Idea:
Days: 14
We classify polygons by examining their sides and angles.
Unit Essential Question:
How can we use the properties of polygons
to describe their sides and angles?
Concept
Concept Title
8.1
Duration
(Days)
2
8.2
Parallelograms
2
8.3
Rectangles
2
8.4
Rhombi and Squares
3
8.5
Trapezoids
5
Page 42
Modern Geometry Honors
Concept 8.1
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
2.5.11.B, 2.5.11.C, M11.C.1.2.2, 2.9.G.A, 2.9.G.C
What properties distinguish one quadrilateral from another?
Quadrilateral, parallelogram, rectangle, rhombus, square, trapezoid, isosceles
trapezoid, kite
Learning Goals:
Descriptor
8.1.A
Resources:
Glencoe Geometry: 8-1
Assessment Sources:
Daily Assignments
Eligible
Content
G.1.2.1.1
G.2.1.2.1
G.2.1.2.2
G.2.1.2.3
Days
2
Notes:
Page 43
Modern Geometry Honors
Concept 8.2
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Parallelograms
2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, 2.5.11.C, 2.9.11.C, M11.C.1.2.2,
M11.C.1.3.1, 2.9.G.A, 2.9.G.C
What are the properties of parallelograms?
Opposite sides, opposite angles, consecutive sides, consecutive angles,
diagonals
Learning Goals:
Descriptor
8.2.A
Recognize and apply properties of the
sides and angles of parallelograms.
8.2.B
Recognize and apply properties of the
diagonals of parallelograms.
Resources:
Glencoe Geometry: 8-2
Assessment Sources:
Daily Assignments
Eligible
Content
G.1.2.1.2
Days
G.2.1.2.3
1
1
Notes:
Page 44
Modern Geometry Honors
Concept 8.3
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Rectangles
2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, 2.5.11.C, 2.9.11.C, M11.C.1.2.2,
2.9.G.A, 2.9.G.C
What are the properties of a rectangle?
Rectangle
Learning Goals:
Descriptor
8.3.A
Recognize and apply properties of
rectangles.
8.3.B
Determine whether parallelograms are
rectangles.
Resources:
Glencoe Geometry: 8-4
Assessment Sources:
Daily Assignments
Eligible
Content
G.1.2.1.2
Days
G.2.1.2.2
1
1
Notes:
Page 45
Modern Geometry Honors
Concept 8.4
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Rhombi and Squares
2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, 2.5.11.C, 2.9.11.C, M11.C.1.2.2,
2.9.G.A, 2.9.G.C
What are the properties of rhombi and squares?
Rhombus, square
Learning Goals:
Descriptor
Eligible
Content
G.1.2.1.2
Days
8.4.A
Recognize and apply properties of a
rhombus.
8.4.B
Recognize and apply properties of a
square.
G.1.2.1.4
1
8.4.C
Determine if a parallelogram is a
rhombus or a square.
G.1.2.1.4
1
Resources:
Glencoe Geometry: 8-5
Assessment Sources:
Daily Assignments, Quiz
1
Notes:
Page 46
Modern Geometry Honors
Williamsport Area School District
Concept 8.5
Trapezoids
Lesson Essential
Question(s):
2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, 2.5.11.C, 2.9.11.C, M11.C.1.2.2
Why is a trapezoid not a parallelogram? What are the properties of the
median of a trapezoid?
Vocabulary:
Trapezoid, base, median, base angles, legs, isosceles trapezoid
Learning Goals:
Descriptor
8.5.A
Recognize and apply properties of
trapezoids.
8.5.B
Determine whether a parallelogram is a
trapezoid or isosceles trapezoid.
Resources:
Glencoe Geometry: 8-6
Assessment Sources:
Daily Assignments
Notes:
GSP Review Activity Available
Additional 2 Days for Unit Review and Test
Eligible
Content
G.1.2.1.2
Days
G.2.1.2.1
2
1
Page 47
Modern Geometry Honors
Williamsport Area School District
Unit 9: Measuring in Space
Big Idea:
Days: 12
Polygons and geometric shapes can be described by the space they occupy.
Unit Essential Question
How are polygons and geometric shapes measured?
What strategies and formulas can be used to find perimeter, area,
surface area, lateral area, and volume?
Concept
Concept Title
9.1
Irregular Shapes
Duration
(Days)
2
9.2
Rectangular Prisms and Cylinders
3
9.3
Pyramids, Cones, and Spheres
3
9.4
Changing Linear Dimensions
4
Page 48
Modern Geometry Honors
Concept 9.1
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Irregular Shapes
2.2.11.A, 2.2.11.B, 2.3.11.A, 2.4.11.E, 2.5.11.A, 2.5.11.B, 2.5.11.C,
2.8.11.D, 2.9.11.I, M11.B.2.2.3, 2.3.G.C, 2.11.G.C
How do we find the perimeter and area of an irregular shape?
Irregular shape
Descriptor
9.1.A
Find areas and perimeters of irregular
shapes.
Resources:
Glencoe Geometry: 11-4
Assessment Sources:
Daily Assignments
Eligible
Content
G.2.2.2.1
G.2.2.2.2
G.2.2.2.4
Days
2
Notes:
Page 49
Modern Geometry Honors
Williamsport Area School District
Concept 9.2
Rectangular Prisms and Cylinders
Lesson Essential
Question(s):
2.2.11.E, 2.4.11.E, 2.5.11.A, 2.5.11.B, 2.5.11.C, 2.8.11.D, 2.9.11.I,
M11.B.2.2.1, M11.B.2.2.2, 2.3.G.C, 2.9.G.A
How is the base of a prism or cylinder used to determine its surface area and
volume?
Vocabulary:
Prism, rectangular prism, cylinder, lateral area, surface area, volume
Learning Goals:
Descriptor
9.2.A
Find the surface area of rectangular
prisms and cylinders.
9.2.B
Find the volume of rectangular prisms
and cylinders.
Resources:
Glencoe Geometry: 12-3, 13-1
Assessment Sources:
Daily Assignments, Activity
Eligible
Content
G.1.1.1.4
G.1.2.1.5
G.2.3.1.1
G.2.3.1.2
G.2.3.1.3
Days
1
2
Notes:
Page 50
Modern Geometry Honors
Concept 9.3
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Pyramids, Cones, and Spheres
2.2.11.E, 2.4.11.E, 2.5.11.A, 2.5.11.B, 2.5.11.C, 2.5.11.D, 2.8.11.D, 2.9.11.I,
M11.B.2.2.1, M11.B.2.2.2, 2.3.G.C, 2.9.G.A
How can we find the surface area and volume of pyramids and cones?
How do we solve problems involving the surface area and volume of a
sphere?
Pyramids, slant height, cone, sphere
Learning Goals:
Descriptor
9.3.A
Find the surface area of a pyramid, cone,
and sphere.
Eligible
Content
G.1.2.1.5
G.2.3.1.1
9.3.B
Find the volume of a pyramid, cone, and
sphere.
G.2.3.1.2
G.2.3.1.3
Resources:
Glencoe Geometry: 12-5, 12-6, 12-7, 13-2, 13-3
Assessment Sources:
Daily Assignments
Notes:
Days
1
1
Page 51
Modern Geometry Honors
Concept 9.4
Lesson Essential
Question(s):
Vocabulary:
Williamsport Area School District
Changing Linear Dimensions
2.5.11.A, 2.5.11.C, 2.5.11.D, 2.8.11.D, 2.9.11.I, M11.A.2.1.3, M11.B.2.2.1,
M11.B.2.2.2, M11.B.2.2.4, M11.D.3.1.2, 2.3.G.E, 2.1.G.C, 2.9.G.B
How does a change in a linear dimension of a figure affect its volume?
Linear dimensions, factor
Learning Goals:
Descriptor
9.4.A
Describe how a change in the linear
dimension of a figure affects its
perimeter, circumference, area, or
volume.
Resources:
PSSA Coach Book: Chapter 2
Assessment Sources:
Daily Assignments
Notes:
Additional 2 Days for Unit Review and Test
Eligible
Content
G.1.3.1.1
G.1.3.1.2
G.2.2.3.1
G.2.3.2.1
Days
2
Page 52
Modern Geometry Honors
Williamsport Area School District
Unit 10: Geometric Probability
Days: 12
We can use of dimensions of geometric figures, combinations, and permutations to find
probability and odds.
Big Idea:
Unit Essential Question:
What is the difference between combinations and permutations
and how to they relate to probability and odds?
Concept
Concept Title
10.1
Simple Probability and Odds
Duration
(Days)
2
10.2
Combinations
4
10.3
Permutations
6
Page 53
Modern Geometry Honors
Williamsport Area School District
Concept 10.1
Simple Probability and Odds
Lesson Essential
Question(s):
2.2.11.A, 2.2.11.F, 2.7.11.A, 2.7.11.B, 2.7.11.C, 2.7.11.D, 2.7.11.E,
M11.E.3.1.1, M11.E.3.1.2, M11.E.3.2.1, M11.E.4.1.2, 2.7.G.A
How do you use probability to predict outcomes? What is the difference
between odds and probability?
Vocabulary:
Probability, odds, sample space, simple event
Learning Goals:
Descriptor
10.1.A Find the probability that a simple event
will occur.
10.1.B Express probability as odds.
Eligible
Content
G.2.2.4.1
Days
G.2.2.4.1
1
Resources:
Glencoe Geometry: 11-5, PSSA Coach Book: Chapter 5
Assessment Sources:
Daily Assignments, Activity
1
Notes:
Page 54
Modern Geometry Honors
Concept 10.2
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Combinations
2.2.11.A, 2.2.11.F, 2.7.11.A, 2.7.11.B, 2.7.11.C, 2.7.11.D, 2.7.11.E,
M11.E.3.1.1, M11.E.3.1.2, M11.E.3.2.1, M11.E.4.1.2, 2.7.G.A
When is it relevant to use a combination?
Combination, factorial
Descriptor
10.2.A Solve counting problems using
combinations.
10.2.B Solve probability problems using
combinations.
Resources:
PSSA Coach Book: Chapter 5
Assessment Sources:
Daily Assignments, Activity
Eligible
Content
G.2.2.4.1
Days
G.2.2.4.1
2
2
Notes:
Page 55
Modern Geometry Honors
Concept 10.3
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
Williamsport Area School District
Permutations
2.2.11.A, 2.2.11.F, 2.7.11.A, 2.7.11.B, 2.7.11.C, 2.7.11.D, 2.7.11.E,
M11.E.3.1.1, M11.E.3.1.2, M11.E.3.2.1, M11.E.4.1.2, 2.7.G.A
How do you decide when to use a permutation verses a combination?
Permutation
Descriptor
Eligible
Content
G.2.2.4.1
Days
10.3.B Solve probability problems using
permutations.
G.2.2.4.1
1
10.3.C Determine whether to use a combination
or a permutation.
G.2.2.4.1
1
10.3.A Solve counting problems using
permutations.
Resources:
PSSA Coach Book: Chapter 5
Assessment Sources:
Daily Assignments, Quiz
Notes:
Additional 3 Days for Quiz, Unit Review, and Test
1
Page 56
Modern Geometry Honors
Williamsport Area School District