Download Honors Geometry Curriculum Maps

Grade Level: Honors Geometry
Chapter #1: The Tools of Geometry
Key Learning(s): Students will learn the
basic geometry terms and there use for
continuing geometry.
Optional Instructional Tools
Ruler, protractor, graph/number
line paper
Unit Essential Question(s): Why is it
important to learn the basic geometry terms
and concepts before continuing the course?
Concept:
Concept:
Points, Lines & Planes
(1.1 – 1 day)
Segment Measure
(1.2, 1.3 – 3 days)
Lesson EQ’s:
What are the basic terms and their
importance to Geometry?
Lesson EQ’s:
How are the lengths of segments
used in everyday life?
Vocabulary:
Point, line, plane, collinear,
coplanar, space
Vocabulary:
Line segment, segment addition
postulate, between, congruent,
precision, constructions, midpoint,
segment bisector, distance
Standards:
Standards:
M11.C.3.1.1 Calculate the distance and/or
midpoint between 2 points on a number line
or on a coordinate plane
G.2.1.2.1 Calculate the distance and/or
midpoint between two points on a number
line or on a coordinate plane
CC2.3HS.A.11 Apply coordinate geometry to
prove simple geometric theorems
algebraically.
Concept:
Angle Pairs
(1.5 – 1 day)
Lesson EQ’s:
How are the pairs of angles
classified?
Vocabulary:
Vertical angles, linear angles,
adjacent angles, complementary
angles, supplementary angles
Standards:
M11.B.2.1.1 Measure and/or compare
angles in degrees (up to 360) (protractor
must be provided or drawn).
Grade Level: Honors Geometry
Honors Geometry Learning Map (updated 3/13)
Concept:
Angle Measure
(1.4 – 2 days)
Lesson EQ’s:
Why do we need to
understand and use angles in
Geometry?
Vocabulary:
Degree, vertex, ray, opposite
ray, angles, sides, interior,
exterior, acute angle, obtuse
angle, right angle
Standards:
M11.B.2.1.1 Measure and/or
compare angles in degrees (up to
360) (protractor must be provided or
drawn).
Chapter #2: Reasoning and Proofs
Key Learning(s): inductive reasoning,
paragraph proofs, two-column algebraic and
geometric proofs
Unit Essential Question(s): What
strategies can we use to base conclusions in
geometry and how are they used?
Concept:
Types of Reasoning
(2.1, 2.3 – 2 days)
Lesson EQ’s:
Why are conjectures and
counterexamples essential
to inductive reasoning?
Concept:
Paragraph proofs
(supplemental 2.5 – 2
days)
Lesson EQ’s:
How can we use paragraphs
to explain problems?
Concept:
Constructing Proofs
(2.6 – 2 days)
Vocabulary:
conjecture, counterexample,
hypothesis, conclusion
Vocabulary:
Paragraph proof, open
ended, explain, support
Standards:
Standards:
Lesson EQ’s:
How are postulates,
axioms, and theorems
used to show that a
statement is valid?
Vocabulary:
Postulate, axiom, theorem,
proof, two-column proof,
algebra proofs
Standards:
G.1.3.2.1 Write, analyze, complete, or
identify formal proofs (e.g., direct and/or
indirect proofs/proofs by contradiction)
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to geometric
figures.
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to geometric
figures.
CC2.3.HS.A.6 Verify and apply theorems
involving similarity as they relate to plane
figures.
CC2.3.HS.A.8Apply geometric theorems to
verify properties of circles.
CC2.2.HS.C.9 Prove the Pythagorean
identity and use it to calculate
trigonometric ratios.
G.1.3.2.1 Write, analyze, complete, or
identify formal proofs (e.g., direct and/or
indirect proofs/proofs by contradiction)
CC2.3.HS.A.3 Verify and apply
geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.3 Verify and apply
geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.6 Verify and apply
theorems involving similarity as they
relate to plane figures.
CC2.3.HS.A.8Apply geometric theorems
to verify properties of circles.
CC2.2.HS.C.9 Prove the Pythagorean
identity and use it to calculate
trigonometric ratios.
Honors Geometry Learning Map (updated 3/13)
Concept:
Concept:
Proving Segment
Relationships (2.7- 1 days)
Vocabulary:
Proving Angle
Relationships
(2.8 - 1 days)
Lesson EQ’s:
If two congruent angles form
a linear pair, then what type
of angles are they?
Vocabulary:
Standards:
Standards:
G.1.3.2.1 Write, analyze, complete, or
identify formal proofs (e.g., direct and/or
indirect proofs/proofs by contradiction)
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to geometric
figures.
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to geometric
figures.
CC2.3.HS.A.6 Verify and apply theorems
involving similarity as they relate to plane
figures.
CC2.3.HS.A.8Apply geometric theorems to
verify properties of circles.
CC2.2.HS.C.9 Prove the Pythagorean
identity and use it to calculate
trigonometric ratios.
G.1.3.2.1 Write, analyze, complete, or
identify formal proofs (e.g., direct and/or
indirect proofs/proofs by contradiction)
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to geometric
figures.
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to geometric
figures.
CC2.3.HS.A.6 Verify and apply theorems
involving similarity as they relate to plane
figures.
CC2.3.HS.A.8Apply geometric theorems to
verify properties of circles.
CC2.2.HS.C.9 Prove the Pythagorean
identity and use it to calculate
trigonometric ratios.
Concept:
Concept:
Logic
(2.2 – 1 day)
Lesson EQ’s:
How do you set up a truth
table?
Deductive Reasoning
(2.4 – 1 day)
Lesson EQ’s:
What is the difference
between the Law of
Detachment and the Law of
Syllogism?
Vocabulary: Deductive
Reasoning, Law of
Detachment, Law of
Syllogism
Lesson EQ’s:
What is the proof of the
segment addition postulate?
Vocabulary: disjunction,
conjunction, truth table,
compound statement,
negation, truth value,
statement
Standards:
G.1.3.2.1 Write, analyze, complete, or
identify formal proofs (e.g., direct and/or
indirect proofs/proofs by contradiction)
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to geometric
figures.
CC2.3.HS.A.6 Verify and apply theorems
involving similarity as they relate to plane
figures.
CC2.3.HS.A.8Apply geometric theorems to
verify properties of circles.
CC2.2.HS.C.9 Prove the Pythagorean
identity and use it to calculate
trigonometric ratios.
Standards:
G.1.3.2.1 Write, analyze, complete, or
identify formal proofs (e.g., direct and/or
indirect proofs/proofs by contradiction)
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to geometric
figures.
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to geometric
figures.
CC2.3.HS.A.6 Verify and apply theorems
involving similarity as they relate to plane
figures.
CC2.3.HS.A.8Apply geometric theorems to
verify properties of circles.
CC2.2.HS.C.9 Prove the Pythagorean
identity and use it to calculate
trigonometric ratios.
Honors Geometry Learning Map (updated 3/13)
Grade Level: Honors Geometry
Chapter #3: Perpendicular and Parallel Lines
Key Learning(s): Students will learn about
perpendicular and parallel lines. They will be
able to write the equation of a line given
certain characteristics.
Unit Essential Question(s): How are
points, lines, and planes related?
Concept:
Parallel lines,
transversals, and angles
(3.1, 3.2, 3.5 – 4 days)
Lesson EQ’s:
What relationships are created
with lines and planes?
Concept:
Lines in the coordinate
plane
(3.3, 3.4 – 3 days)
Concept:
Perpendicular lines and
distance
(3.6 – 2 days)
Lesson EQ’s:
How do slope and linear
equations relate to parallel and
perpendicular lines?
Vocabulary:
Slope, rate of change, slopeintercept form, point-slope form
Lesson EQ’s:
Why are perpendicular lines
important to distance in
geometry?
Vocabulary:
Equidistant
Standards:
Standards:
Standards:
M11.B.2.1.1 Measure and/or compare
angles in degrees (up to 360) (protractor
must be provided or drawn).
G.2.2.1.2 Use properties of angles
formed when two parallel lines are cut by
a transversal to find the measures of
missing angles
G.2.2.1.1 Use properties of angles
formed by intersecting lines to find the
measures of missing angles
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to
geometric figures.
M11.C.3.1.2 Relate slope to
perpendicularity and/or parallelism (limit
to linear algebraic expressions; slope
formula provided on the reference sheet)
M11.D.3.2.1 Apply the formula for the
slope of a line to solve problems (formula
given on reference sheet)
M11.D.3.2.2 Given the graph of the line,
2 points on the line, or the slope and a
point on a line, write or identify the linear
equation in point-slope, standard and/or
slope-intercept form
M11.D.3.2.3 Compute the slope and/or yintercept represented by a linear equation
or graph
G 2.1.2.2 Relate slope to
perpendicularity and/or parallelism (limit
to linear algebraic equations)
CC2.3.HS.A.11 Apply coordinate
geometry to prove simple geometric
theorems algebraically.
M11.C.3.1.2 Relate slope to
perpendicularity and/or parallelism (limit
to linear algebraic expressions; slope
formula provided on the reference sheet)
G 2.1.2.2 Relate slope to
perpendicularity and/or parallelism (limit
to linear algebraic equations)
CC2.3.HS.A.11 Apply coordinate
geometry to prove simple geometric
theorems algebraically.
G.2.1.4.1 Solve or graph systems of
equations or systems of inequalities
within a problem situation using
coordinate geometry.
CC2.2.HS.D.9 Use reasoning to solve
equations and justify the solution
method.
CC2.2.HS.D.10 Represent, solve and
interpret equations/inequalities
and systems of equations/inequalities
algebraically and graphically.
Vocabulary:
Parallel lines and planes,
perpendicular lines, skew lines,
transversal, consecutive,
alternate, corresponding,
interior/exterior
Honors Geometry Learning Map (updated 3/13)
Grade Level: Honors Geometry
Chapter #4: Congruent Triangles
Key Learning(s): We will discuss how
triangles sides and angles can relate to
geometry.
Unit Essential Question(s):
How are the sides and angles of triangles used in geometry?
Concept:
Classifying triangles and
angle measures of
triangles
(4.1, 4.2 – 2 days)
Concept:
Triangle Congruence
(4.3, 4.4, 4.5, HL – 4 days)
**two column proofs
Concept:
Isosceles Triangle
Theorem
(4.6 – 2 days) **two
column proofs
Lesson EQ’s:
How can we use sides and angles
of triangles to classify them?
Lesson EQ’s:
How can we use the triangle
theorems to prove triangles are
congruent?
Lesson EQ’s:
What properties of isosceles
triangles help us to find
unknown measurements?
Vocabulary:
acute, obtuse, right, equilangular,
scalene, isosceles, equilateral
Vocabulary:
Congruent triangles, included
angle, included side
Vocabulary:
Vertex angle, base angle
Standards:
Standards:
Standards:
M11.C.1.2.3 Identify and/or use
properties of isosceles and equilateral
triangles
G1.2.1.3 Identify and/or use properties
of isosceles and equilateral triangles
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
M11.C.1.3.1 Identify and/or use properties
of congruent and similar polygons or solids
G1.2.1.3 Identify and/or use properties
of isosceles and equilateral triangles
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
M11.C.1.2.3 Identify and/or use
properties of isosceles and equilateral
triangles
Honors Geometry Learning Map (updated 3/13)
G.1.2.1.1 Identify and/or use
properties of triangles
G1.2.1.3 Identify and/or use
properties of isosceles and equilateral
triangles
CC2.3.HS.A.3 Verify and apply
geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
Grade Level: Honors Geometry
Chapter #5: Relationships in Triangles
Key Learning(s): We will discuss how
triangles sides and angles can relate to
geometry.
Unit Essential Question(s):
How are the sides and angles of triangles used in geometry?
Concept:
Concept:
Bisectors, medians and
altitudes (5.1 – 1 days)
Triangle Inequalities
(5.2,5.4 – 2 days)
Lesson EQ’s:
How do we use medians, altitudes
and bisectors in triangles?
Vocabulary:
Perpendicular bisector
Median, altitude
Standards:
Lesson EQ’s:
How can inequalities be used in
triangles?
Vocabulary:
Triangle Inequality Theorem
M11.C.1.2.1 Identify and/or use
properties of triangles (e.g., medians,
altitudes, angle bisectors, side/angle
relationships, Triangle Inequality Theorem)
M11.C.1.2.1 Identify and/or use
properties of triangles (e.g., medians,
altitudes, angle bisectors, side/angle
relationships, Triangle Inequality
Theorem)
G.1.2.1.1 Identify and/or use
properties of triangles
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
Standards:
G.1.2.1.1 Identify and/or use
properties of triangles
CC2.3.HS.A.3 Verify and apply
geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
Honors Geometry Learning Map (updated 3/13)
Concept:
Indirect Proofs
(5.3 – 2 days)
Lesson EQ’s:
How does indirect reasoning
work?
Vocabulary:
Proof by contradiction, indirect
reasoning, indirect proof
Grade Level: Honors Geometry
Chapter #6 and Lesson 1-6: Polygons
Key Learning(s): polygons, parallelograms,
rectangle, rhombus, square, trapezoid
Unit Essential Question(s):
How can we apply the properties of polygons to determine certain figures?
Concept:
Basics of Polygons
(1.6, 6.1 – 1 days)
Lesson EQ’s:
How dose the name of a polygon
relate to finding their angle
measures?
Vocabulary:
Polygon, diagonal, concave,
convex, n-gon, regular polygon,
interior angle sum, exterior angle
sum
Standards:
M11.C.1.2.2 Identify and/or use
properties of quadrilaterals (e.g.,parallel
sides, diagonals, bisectors, congruent
sides/angles and
G.1.2.1.4 Identify and/or use properties of
regular polygons
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
Concept:
Concept:
Basic Parallelograms
(6.2, 6.3 – 3 days)
Rectangles
(6.4 – 1 day)
Lesson EQ’s:
How can the properties of sides
and angles of polygons be used to
ensure a quadrilateral is a
parallelogram?
Vocabulary:
parallelogram
Lesson EQ’s:
How do the properties of special
parallelograms differ?
Standards:
Standards:
M11.C.1.2.2 Identify and/or use
properties of quadrilaterals (e.g.,parallel
sides, diagonals, bisectors, congruent
sides/angles and
M11.C.1.2.2 Identify and/or use
properties of quadrilaterals (e.g.,parallel
sides, diagonals, bisectors, congruent
sides/angles and
G.1.2.1.2 Identify and/or use
G.1.2.1.2 Identify and/or use
properties of quadrilaterals
properties of quadrilaterals
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
CC2.3.HS.A.3 Verify and apply
geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
Honors Geometry Learning Map (updated 3/13)
Vocabulary:
Rectangle, rhombus, square
Concept:
Rhombi, Squares, Kites
(6.5 and Kites ext– 2 days)
Lesson EQ’s:
How can we identify a shape on
the coordinate plane using the
slope and distance formula?
Vocabulary:
none
Standards:
M11.C.1.2.2 Identify and/or use
properties of quadrilaterals (e.g.,parallel
sides, diagonals, bisectors, congruent
sides/angles and
M11.C.3.1.1 Calculate the distance and/or
midpoint between 2 points on a number
line or on a coordinate plane (formula
provided on the reference sheet).
M11.C.3.1.2 Relate slope to
perpendicularity and/or parallelism (limit to
linear algebraic expressions; slope formula
provided on the reference sheet)
G.1.2.1.2 Identify and/or use
properties of quadrilaterals
G 2.1.2.3: Use slope, distance, and/or
midpoint between two points on a
coordinate plane to establish properties of
a 2-dimensional shape
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
CC2.3.HS.A.11 Apply coordinate geometry
to prove simple geometric theorems
algebraically.
Concept:
Trapezoids
(6.6 – 2 days)
Lesson EQ’s:
How can we use the properties of
trapezoids to find missing values?
Vocabulary:
Trapezoid, Isosceles trapezoid,
median
Standards:
M11.C.1.2.2 Identify and/or use
properties of quadrilaterals (e.g.,parallel
sides, diagonals, bisectors, congruent
sides/angles and
G.1.2.1.2 Identify and/or use
properties of quadrilaterals
G 2.1.2.3: Use slope, distance, and/or
midpoint between two points on a
coordinate plane to establish properties of
a 2-dimensional shape
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to
geometric figures.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
CC2.3.HS.A.11 Apply coordinate geometry
to prove simple geometric theorems
algebraically.
**High School Midterms after this unit**
Honors Geometry Learning Map (updated 3/13)
Grade Level: Honors Geometry
Chapter #7: Proportions and Similarity
Key Learning(s):
Ratios, similar figures, proportions
Unit Essential Question(s):
How can ratios and proportions be
used to find similarity in figures?
Concept:
Proportions
(7.1 – 1 days)
* word problems
Lesson EQ’s:
How can we use proportions
to determine missing
information?
Concept:
Similar Figures
(7.2,7.3 – 3 days)
Concept:
Proportional Parts
(7.4, 7.5 – 3 days)
Lesson EQ’s:
How do we use proportions
to determine missing sides
or lengths of figures?
Lesson EQ’s:
How can we use
proportional relationships
of similar figures in order
to find other
measurements?
Vocabulary:
Proportion, ratio, cross
product
Standards:
Vocabulary:
Similar polygons, scale
factor
Standards:
Vocabulary:
midsegment
M11.A.2.1.3 Identify and/or use
proportional relationships in problem
solving settings
M11.C.1.3.1 Identify and/or use properties
of congruent and similar polygons or solids
M11.A.2.1.3 Identify and/or use
proportional relationships in problem
solving settings
M11.C.1.3.1 Identify and/or use
properties of congruent and similar
polygons or solids
G.1.3.1.1 Identify and/or use
properties of congruent and similar
polygons or solids
G.1.3.1.2 Identify and/or use proportional
relationships in similar figures
CC2.3.HS.A.2 Apply rigid transformations
to determine and explain congruence.
CC2.3.HS.A.5 Create justifications based
on transformations to establish similarity of
plane figures.
CC2.3.HS.A.6 Verify and apply theorems
involving similarity as they relate to plane
figures.
G.1.3.1.1 Identify and/or use
properties of congruent and similar
polygons or solids
G.1.3.1.2 Identify and/or use proportional
relationships in similar figures
CC2.3.HS.A.2 Apply rigid transformations
to determine and explain congruence.
CC2.3.HS.A.5 Create justifications based
on transformations to establish similarity of
plane figures.
CC2.3.HS.A.6 Verify and apply theorems
involving similarity as they relate to plane
figures.
Grade Level: Honors Geometry
Honors Geometry Learning Map (updated 3/13)
Standards:
G.1.3.1.1 Identify and/or use
properties of congruent and similar
polygons or solids
G.1.3.1.2 Identify and/or use
proportional relationships in similar
figures
CC2.3.HS.A.2 Apply rigid
transformations to determine and
explain congruence.
CC2.3.HS.A.5 Create justifications
based on transformations to establish
similarity of plane figures.
CC2.3.HS.A.6 Verify and apply
theorems involving similarity as they
relate to plane figures.
Chapter #8: Right Triangles and Trigonometry
Key Learning(s): radicals, geometric mean,
right triangles, trigonometry
Unit Essential Question(s): What
relationships exist with sides and angles of
right triangles?
Concept:
Concept:
Radicals
(supplemental – 1 days)
Lesson EQ’s:
How can we use square roots in
geometry?
Vocabulary: radical, rationalized
denominator
Standards:
M11.A.1.1.3 Simplify square roots.
A1.1.1.1.2 Simplify square roots
CC(ALg1)2.1.8.E.1 Distinguish between
rational and irrational numbers using their
properties.
CC(Alg1)2.1.8.E.4 Estimate irrational
numbers by comparing them to rational
numbers.
CC(Alg1)2.1.HS.F.1 Apply and extend the
properties of exponents to solve
problems with rational exponents.
CC(Alg1)2.1.HS.F.2 Apply properties of
rational and irrational numbers to solve
real world or mathematical problems.
Geometric Mean
(8.1 – 2 days)
Lesson EQ’s:
How do you use the geometric
mean to find unknown sides in
right triangles?
Vocabulary: geometric mean
Standards:
M11.C.1.2.1 Identify and/or use
properties of triangles (e.g., medians,
altitudes, angle bisectors, side/angle
relationships, Triangle Inequality Theorem)
Concept:
Trigonometry
(8.4, 8.5 – 3 days)
Lesson EQ’s:
How do fractions contribute to solving
problems in right triangles?
Vocabulary: trigonometry, trig ratio,
sine, cosine, tangent, angle of
elevation, angle of depression
Standards:
G.2.1.1.2 Use trigonometric ratios to write
and/or solve problems involving right triangles
CC2.3.HS.A.7 Apply trigonometric ratios to
solve problems involving right triangles.
CC2.2.HS.C.9 Prove the Pythagorean identity
and use it to calculate
trigonometric ratios.
Concept:
Right Triangles
(8.2, 8.3 – 2 days)
Lesson EQ’s:
How can we apply the
Pythagorean Theorem to solve
real world problems?
Vocabulary: Pythagorean
theorem, special right triangles
Standards:
M11.C.1.4.1 Find the measure of a side
of a right triangle using the Pythagorean
Theorem (Pythagorean Theorem
included on the reference sheet)
G.2.1.1.1 Use the Pythagorean
theorem to write and/or solve problems
involving right triangles
CC2.3.HS.A.7 Apply trigonometric ratios
to solve problems involving right
triangles.
CC2.2.HS.C.9 Prove the Pythagorean
identity and use it to calculate
trigonometric ratios.
Concept:
Law of Sines and Cosines
(8.6, 8.7 – 3 Days)
Lesson EQ’s:
How can we use the laws to solve for
missing measures in non right
triangles?
Vocabulary: Law of Sines, Law of
Cosines, Solving a Triangle
Standards:
G.2.1.1.2 Use trigonometric ratios to write
and/or solve problems involving right triangles
CC2.3.HS.A.7 Apply trigonometric ratios to
solve problems involving right triangles.
CC2.2.HS.C.9 Prove the Pythagorean identity
and use it to calculate
trigonometric ratios.
Grade Level: Honors Geometry
Honors Geometry Learning Map (updated 3/13)
Chapter #10: Circles
Key Learning(s): parts of circles, relationships with
arcs, chords and diameters, inscribed angles and
tangents of circles
Unit Essential Question(s): How do you apply the
relationships among circles, lines, segments, and the
angles they form? How does change in the linear
dimension of a figure affect its perimeter, circumference
and area?
Concept:
Basics of Circles
(10.1,10.2 – 2 days)
Concept:
Arcs and Chords
(10.3 – 2 days)
Concept:
Inscribed Angles
(10.4 – 1 days)
Lesson EQ’s:
How can we use the parts of
circles to solve problems about
their dimension, length and
measurement?
Vocabulary:
Circle, center, chord, radius,
diameter, circumference,
semicircle, central angles, minor
arc, major arc
Standards:
Lesson EQ’s:
What relationships of arcs, chords
and diameters are used in circles?
Lesson EQ’s:
How can we find the measures
of inscribed angles and
polygons?
Vocabulary:
Inscribed, circumscribed
Vocabulary:
intercepted
Standards:
Standards:
M11.C.1.1.1 Identify and/or use the
properties of a radius, diameter and/or
tangent of a circle (given numbers should
be whole)
M11.C.1.1.2 Identify and/or use the
properties of arcs, semicircles, inscribed
angles and/or central angles
G.1.1.1.1 Identify, determine, and/or use
the radius, diameter, segment, and/or
tangent of a circle
CC2.3.HS.A.8 Apply geometric theorems
to verify properties of circles.
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
G.2.2.3.1 Describe how a change in the
linear dimension of a figure affects its
perimeter, circumference, and area (e.g.,
How does changing the length of the
radius of a circle affect the circumference
of the circle?).
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.3.HS.A.8 Apply geometric theorems
to verify properties of circles.
M11.C.1.1.1 Identify and/or use the
properties of a radius, diameter and/or
tangent of a circle (given numbers should
be whole)
M11.C.1.1.2 Identify and/or use the
properties of arcs, semicircles, inscribed
angles and/or central angles
G.1.1.1.1 Identify, determine, and/or use
the radius, diameter, segment, and/or
tangent of a circle
G.1.1.1.2 Identify, determine, and/or use
the arcs, semicircles, sectors, and/or
angles of a circle
CC2.3.HS.A.8 Apply geometric theorems
to verify properties of circles.
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
G.2.2.3.1 Describe how a change in the
linear dimension of a figure affects its
perimeter, circumference, and area (e.g.,
How does changing the length of the
radius of a circle affect the circumference
of the circle?).
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.3.HS.A.8 Apply geometric theorems
to verify properties of circles.
M11.C.1.1.1 Identify and/or use the
properties of a radius, diameter and/or
tangent of a circle (given numbers
should be whole)
M11.C.1.1.2 Identify and/or use the
properties of arcs, semicircles, inscribed
angles and/or central angles
G.1.1.1.1 Identify, determine, and/or
use the radius, diameter, segment,
and/or tangent of a circle
G.1.1.1.2 Identify, determine, and/or
use the arcs, semicircles, sectors,
and/or angles of a circle
CC2.3.HS.A.8 Apply geometric
theorems to verify properties of circles.
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
Honors Geometry Learning Map (updated 3/13)
Concept:
Tangents
(10.5 – 1 days)
Lesson EQ’s:
How can you use the properties
of a tangent to a circle?
Concept:
Secants, tangents, and
angle measures
(10.6 – 2 days)
Concept:
Special Segments in
Circles
(10.7 – 2 days)
Lesson EQ’s:
What is the relationship of
segments that intersect inside or
outside a circle?
Vocabulary:
Tangent, point of tangency
Standards:
Lesson EQ’s:
How do you find measures of
angles formed by lines
intersecting on, inside or outside
a circle?
Vocabulary:
Secant
Standards:
M11.C.1.1.1 Identify and/or use the
properties of a radius, diameter and/or
tangent of a circle (given numbers should
be whole)
M11.C.1.1.2 Identify and/or use the
properties of arcs, semicircles, inscribed
angles and/or central angles
G.1.1.1.3 Use chords, tangents, and
secants to find missing arc measures or
missing segment measures
CC2.3.HS.A.8 Apply geometric theorems
to verify properties of circles.
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
M11.C.1.1.1 Identify and/or use the
properties of a radius, diameter and/or
tangent of a circle (given numbers should
be whole)
M11.C.1.1.2 Identify and/or use the
properties of arcs, semicircles, inscribed
angles and/or central angles
G.1.1.1.3 Use chords, tangents, and
secants to find missing arc measures or
missing segment measures
CC2.3.HS.A.8 Apply geometric theorems
to verify properties of circles.
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
M11.C.1.1.1 Identify and/or use the
properties of a radius, diameter and/or
tangent of a circle (given numbers should
be whole)
M11.C.1.1.2 Identify and/or use the
properties of arcs, semicircles, inscribed
angles and/or central angles
G.2.2.2.5 Find the area of a sector of a
circle.
CC2.3.HS.A.3 Verify and apply
geometric theorems as they relate to
geometric figures.
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.2.HS.C.1 Use the concept and
notation of functions to interpret
and apply them in terms of their context.
Concept:
Equations of Circles
(10.8 – 1 days)
Lesson EQ’s:
How do write the equation of a
circle given the center and radius?
Vocabulary:
Standards:
M11.C.1.1.1 Identify and/or use the
properties of a radius, diameter and/or
tangent of a circle (given numbers should
be whole)
M11.C.1.1.2 Identify and/or use the
properties of arcs, semicircles, inscribed
angles and/or central angles
Grade Level: Honors Geometry
Honors Geometry Learning Map (updated 3/13)
Vocabulary:
Standards:
Chapter #11: Area and Perimeter
Key Learning(s): Area and perimeter of
different shapes
Unit Essential Question(s):
How are the dimensions of twodimensional figures used in the real
world? How does change in the linear
dimension of a figure affect its
perimeter, circumference and area?
Concept:
Parallelograms
(11.1 – 1 day)
Concept:
Concept:
Triangles, Trapezoids and
Rhombi
(11.2 – 2 days)
Area of Regular
Polygons and Circles
(11.3 – 2 Days)
Lesson EQ’s:
How do you find the area and
perimeter of basic figures?
Lesson EQ’s:
What is the formula for the area of
a trapezoid?
Vocabulary:
Height of a parallelogram
Standards:
Vocabulary:
Lesson EQ’s:
What does an apothem have to
do with the formula for area of a
regular polygon?
Vocabulary:
Apothem
Standards:
M11.B.2.2.4 Find the measurement of a
missing length given the perimeter,
circumference, area or volume.
M11.B.2.3.1 Describe how a change in
the linear dimension of a figure affects its
perimeter, circumference, area or volume.
G.2.2.2.2 Find the measurement of a
missing length, given the perimeter,
circumference, or area
G.2.2.2.3 Find the side lengths of a
polygon with a given perimeter to
maximize the area of the polygon
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to geometric
figures.
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.2.HS.C.1 Use the concept and
notation of functions to interpret
and apply them in terms of their context.
M11.B.2.2.4 Find the measurement of a
missing length given the perimeter,
circumference, area or volume.
M11.B.2.3.1 Describe how a change in
the linear dimension of a figure affects its
perimeter, circumference, area or volume.
G.2.2.2.2 Find the measurement of a
missing length, given the perimeter,
circumference, or area
G.2.2.2.3 Find the side lengths of a
polygon with a given perimeter to
maximize the area of the polygon
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to geometric
figures.
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.2.HS.C.1 Use the concept and
notation of functions to interpret
and apply them in terms of their context.
Standards:
Honors Geometry Learning Map (updated 3/13)
M11.B.2.2.4 Find the measurement of a
missing length given the perimeter,
circumference, area or volume.
M11.B.2.3.1 Describe how a change in
the linear dimension of a figure affects
its perimeter, circumference, area or
volume.
G.2.2.4.1 Use area models to find
properties
CC2.3.HS.A.14 Apply geometric
concepts to model and solve real world
problems.
Concept:
Irregular or Composite
Figures and Shaded
Figures
(11.4 – 1 day)
Lesson EQ’s:
How do you find the area of a
composite figure?
Vocabulary:
Composite figure
Standards:
M11.B.2.2.4 Find the measurement of a
missing length given the perimeter,
circumference, area or volume.
M11.B.2.3.1 Describe how a change in
the linear dimension of a figure affects its
perimeter, circumference, area or volume.
G.2.2.2.2 Find the measurement of a
missing length, given the perimeter,
circumference, or area
G.2.2.2.3 Find the side lengths of a
polygon with a given perimeter to
maximize the area of the polygon
CC2.3.HS.A.3 Verify and apply geometric
theorems as they relate to geometric
figures.
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.2.HS.C.1 Use the concept and
notation of functions to interpret
and apply them in terms of their context.
Concept:
Geometric Probability and
Area of Sectors
(11.5 – 2 days)
Lesson EQ’s:
When calculating Geometric
Probability what two conditions do
we assume?
Vocabulary:
Geometric probability, sector,
segment
Standards:
M11.B.2.2.4 Find the measurement of a
missing length given the perimeter,
circumference, area or volume.
M11.B.2.3.1 Describe how a change in
the linear dimension of a figure affects its
perimeter, circumference, area or volume.
G.2.2.4.1 Use area models to find
properties
CC2.3.HS.A.14 Apply geometric concepts
to model and solve real world problems.
Grade Level: Honors Geometry
Honors Geometry Learning Map (updated 3/13)
Chapters #12 & 13 and Lesson 1-7: Surface Area and Volume
Key Learning(s): Surface area and volume of different
shapes
Unit Essential Question(s): How are the dimensions
of three-dimensional figures used in the real world?
How does change in the linear dimension of a figure
affect its surface area and volume? How do you find
the measurement of the missing length given the
surface area or volume?
Concept:
Concept:
Concept:
Three dimensional figures
(1.7, 12.1 – 2 days)
Prisms
(12.2, 13.1 – 2 days)
Pyramids
(12.4, 13.2 – 2 days)
Lesson EQ’s:
How does the two-dimensional
make up of three-dimensional
figures relate to their formulas?
Vocabulary:
Face, edges, prism, regular prism,
pyramid, platonic solids, cylinder,
cone, sphere
Standards:
Lesson EQ’s:
Why are there several ways to
solve for the dimensions of
prisms?
Vocabulary:
Surface area, volume, Dimension
change
Lesson EQ’s:
How do you find the volume and
surface area of a pyramid?
Standards:
Standards:
M11.B.2.3.1 Describe how a change in
the linear dimension of a figure affects its
perimeter, circumference, area or volume.
M11.B.2.2.1 Calculate the surface area of
prisms, cylinders, cones, pyramids and/or
spheres. Formulas are provided on the
reference sheet
M11.B.2.2.2 Calculate the volume of
prisms, cylinders, cones, pyramids and/or
spheres. Formulas are provided on the
reference sheet
G.1.1.1.4: Identify and/or use the
properties of pyramids and prisms
G.2.3.1.1 Calculate the surface area of
prisms, cylinders, cones, pyramids, and/or
spheres. Formulas are provided on a
reference sheet
G.2.3.1.2 Calculate the volume of prisms,
cylinders, cones, pyramids, and/or
spheres. Formulas are provided on a
reference sheet
CC2.3.HS.A.8 Apply geometric theorems
to verify properties of circles.
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects
CC2.3.HS.A.14 Apply geometric concepts
to model and solve real world problems.
CC2.3.HS.A.12 Explain volume formulas
and use them to solve problems..
M11.B.2.3.1 Describe how a change in
the linear dimension of a figure affects
its perimeter, circumference, area or
volume.
M11.B.2.2.1 Calculate the surface area
of prisms, cylinders, cones, pyramids
and/or spheres. Formulas are provided
on the
reference sheet
M11.B.2.2.2 Calculate the volume of
prisms, cylinders, cones, pyramids
and/or spheres. Formulas are provided
on the reference sheet
G.1.1.1.4: Identify and/or use the
properties of pyramids and prisms
G.2.3.1.1 Calculate the surface area of
prisms, cylinders, cones, pyramids,
and/or spheres. Formulas are provided
on a reference sheet
G.2.3.1.2 Calculate the volume of
prisms, cylinders, cones, pyramids,
and/or spheres. Formulas are provided
on a reference sheet
CC2.3.HS.A.8 Apply geometric
theorems to verify properties of circles.
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects.
CC2.3.HS.A.14 Apply geometric
concepts to model and solve real world
problems.
CC2.3.HS.A.12 Explain volume
formulas and use them to solve
problems..
Honors Geometry Learning Map (updated 3/13)
Vocabulary:
Concept:
Concept:
Concept:
Cylinders & Cones
(12.3, 13.1, 12.5, 13.2 –3
days)
Sphere
(12.6, 13.3 – 2 days)
Lesson EQ’s:
How do you find the surface area
and volume of a cylinder?
What are the parts of the cone
necessary to find surface area nd
volume?
Vocabulary:
Axis, right cylinder Circular cone,
right cone, oblique cone
Standards:
Lesson EQ’s:
What uses do volume and surface
area have for a sphere?
Lesson EQ’s:
How do you determine if two
solids are congruent or similar?
Vocabulary:
Vocabulary:
Similar Solids, Congruent Solids
Standards:
Standards:
M11.B.2.3.1 Describe how a change in
the linear dimension of a figure affects its
perimeter, circumference, area or volume.
M11.B.2.2.1 Calculate the surface area of
prisms, cylinders, cones, pyramids and/or
spheres. Formulas are provided on the
reference sheet
M11.B.2.2.2 Calculate the volume of
prisms, cylinders, cones, pyramids and/or
spheres. Formulas are provided on the
reference sheet
G.1.1.1.4 Identify and/or use the
properties of a cylinder or sphere
G.2.3.1.1 Calculate the surface area of
prisms, cylinders, cones, pyramids, and/or
spheres. Formulas are provided on a
reference sheet
G.2.3.1.2 Calculate the volume of prisms,
cylinders, cones, pyramids, and/or
spheres. Formulas are provided on a
reference sheet
CC2.3.HS.A.8 Apply geometric theorems
to verify properties of circles.
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects
CC2.3.HS.A.14 Apply geometric concepts
to model and solve real world problems.
CC2.3.HS.A.12 Explain volume formulas
and use them to solve problems.
G.2.3.2.1 Describe how a change in the linear
dimension of a figure affects its surface area or
volume (e.g., How does changing the length of
the edge of a cube affect the volume of the
cube?).
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and threedimensional objects.
M11.B.2.3.1 Describe how a change in
the linear dimension of a figure affects its
perimeter, circumference, area or volume.
M11.B.2.2.1 Calculate the surface area of
prisms, cylinders, cones, pyramids and/or
spheres. Formulas are provided on the
reference sheet
M11.B.2.2.2 Calculate the volume of
prisms, cylinders, cones, pyramids and/or
spheres. Formulas are provided on the
reference sheet
G.2.3.1.1 Calculate the surface area of
prisms, cylinders, cones, pyramids, and/or
spheres. Formulas are provided on a
reference sheet
G.2.3.1.2 Calculate the volume of prisms,
cylinders, cones, pyramids, and/or
spheres. Formulas are provided on a
reference sheet
CC2.3.HS.A.8 Apply geometric theorems
to verify properties of circles.
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects
CC2.3.HS.A.14 Apply geometric concepts
to model and solve real world problems.
CC2.3.HS.A.12 Explain volume formulas
and use them to solve problems..
G.2.3.2.1 Describe how a change in the linear
dimension of a figure affects its surface area or
volume (e.g., How does changing the length of
the edge of a cube affect the volume of the
cube?).
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and threedimensional objects.
M11.B.2.3.1 Describe how a change in
the linear dimension of a figure affects its
perimeter, circumference, area or volume.
M11.B.2.2.1 Calculate the surface area of
prisms, cylinders, cones, pyramids and/or
spheres. Formulas are provided on the
reference sheet
M11.B.2.2.2 Calculate the volume of
prisms, cylinders, cones, pyramids and/or
spheres. Formulas are provided on the
reference sheet
G.1.1.1.4 Identify and/or use the
properties of a cylinder or sphere
G.2.3.1.1 Calculate the surface area of
prisms, cylinders, cones, pyramids, and/or
spheres. Formulas are provided on a
reference sheet
G.2.3.1.2 Calculate the volume of prisms,
cylinders, cones, pyramids, and/or
spheres. Formulas are provided on a
reference sheet
CC2.3.HS.A.8 Apply geometric theorems
to verify properties of circles.
CC2.3.HS.A.9 Extend the concept of
similarity to determine arc lengths
and areas of sectors of circles.
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and
three-dimensional objects
CC2.3.HS.A.14 Apply geometric concepts
to model and solve real world problems.
CC2.3.HS.A.12 Explain volume formulas
and use them to solve problems..
G.2.3.2.1 Describe how a change in the linear
dimension of a figure affects its surface area or
volume (e.g., How does changing the length of
the edge of a cube affect the volume of the
cube?).
CC2.3.HS.A.13 Analyze relationships
between two-dimensional and threedimensional objects.
Honors Geometry Learning Map (updated 3/13)
Congruent and Similar
Solids
(13.4 – 1 days)