Download Geometry_Units_of_Study - Asbury Park School District

Asbury Park High School
Unit Plan
Department: Mathematics
Course: Geometry
Unit designation: #1 Geometric Tools
Anticipated timeframe: Day 1-9
Standards addressed:
 G.CO.1
Experiment with transformations in the plane. Know precise definitions of angle, circle, perpendicular line,
parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance
around a circular arc.
 G.CO.12
Make geometric constructions. Make formal geometric constructions with a variety of tools and methods
(compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a
segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including
the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on
the line.G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a
tree trunk or a human torso as a cylinder)
 G. MG.2
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs
per cubic foot)
 N.Q.1
Reason quantitatively and use units to solve problems.
Transfer Goals:
 Visualizations help connect properties to real objects.
 Definitions establish meaning.
 There are many items that must be measured and there are various tools to do so.
 Conclusions come from basic facts and clear information.
Enduring Understandings:
Essential Questions:
 3 dimensional objects can be represented with 2
 How can one represent a 3-dimensional figure in 2
dimensional figures.
dimensions?
 Geometry is a math system built on accepted facts, terms,
 What are the foundations of geometry?
and definitions.
 How does one describe the parts of an angle?
 Number operations can be used to find and compare
measures of segments and angles
 Special angle pairs can identify relationships and find
angle measures
 Midpoints and lengths of any segment can be found
 Perimeter and area are two measures of figures.
Learners will know:
Learners will be able to:
 Figures have attributes
 Make nets for solid figures
 Terms appropriate to the content
 Define basic geometric figures
 Postulates are the foundations of proofs
 Measure line segments
 Key terms: pg. 70 chapter vocabulary (text); pg. 2, ELL
 Use distance and midpoint formulas
 Use a protractor to measure angles
Performance Tasks:
 Mid-unit quiz
 Unit test
 Group station products
Other Evidence:
 Daily class work
 Class participation
 Group collaborations
 Do Now quizzes
Authentic Assessment: “pull it all together”, pg. 69, choose 1 of 2
Anticipated daily sequence of activities:
 Nets and drawings (textbook 1-1)
 Points, lines, planes (1-2)
 Measuring segments (1-3)
 Measuring angles (1-4)
 Angle pairs (1-5)
 Basic constructions (1-6)
 Midpoint and distance in coordinate plane (1-7)
 Perimeter circumference, area (1-8)
Anticipated resources:
 Pearson/Prentice Hall Geometry text
 Student Skills Handbook
 Student Visual Glossary
 Spanish version of materials
 Pearson MathXL system and resources
 Pearson test bank generating software
 ALEKS
Asbury Park High School
Unit Plan
Department: Mathematics
Course: Geometry
Unit designation: #2 Logic and Reasoning
Anticipated timeframe: Day 9-14
Standards addressed:
 G.CO.9
Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are
congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding
angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the
segment’s endpoints.
 G.CO.10
Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a
triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of
two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
 G.CO.11
Prove geometric theorems. Prove theorems about parallelograms. Theorems include: opposite sides are
congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely,
rectangles are parallelograms with congruent diagonals.
Transfer Goals:
 It is often possible to verify complex truths by reasoning from simpler ones using deductive reasoning.
Enduring Understandings:
Essential Questions:
 Patterns can be used to discover relationships.
 How can you make a conjecture and prove it is true?
 Some relationships can be described using If-Then
statements.
 A definition is good if it can be written as a biconditional
 Algebraic properties of equality are used in geometry to
solve problems and support reasoning.
 True information and information that can be demonstrated
as true can be used to prove bigger ideas.
Learners will know:
Learners will be able to:
 Deductive and inductive reasoning
 Determine the truth of statements
 Inverse, converse, and contrapositive of statements
 Use true statements to prove other statements or
counterexamples to disprove them
 Terms appropriate to the content
 Create if-then statements
 What makes a good definition
 The Law of Detachment
 The Law of Syllogism
 Key terms: pg. 129 chapter vocabulary (text); pg. 80, ELL
Performance Tasks:
 Mid-unit quiz
 Unit test
 Group station products
Other Evidence:
 Daily class work
 Class participation
 Group collaborations
 Do Now quizzes
Authentic Assessment: “pull it all together”, pg. 128, choose 1 of 2
Anticipated daily sequence of activities:
 Patterns and inductive reasoning (text 2-1)
 Conditional statements (2-2)
 Biconditionals and definitions (2-3)
 Deductive reasoning (2-4)
 Reasoning in algebra and geometry (2-5)
 Proving angles equal (2-6)
Anticipated resources:

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
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Pearson/Prentice Hall Geometry text
Student Skills Handbook
Student Visual Glossary
Spanish version of materials
Pearson MathXL system and resources
Pearson test bank generating software
ALEKS
Asbury Park High School
Unit Plan
Department: Mathematics
Course: Geometry
Unit designation: #3 Lines
Anticipated timeframe: Day 15-24
Standards addressed:
 G.CO.1
Experiment with transformations in the plane. Know precise definitions of angle, circle, perpendicular line,
parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance
around a circular arc.
 G.CO.9
Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are
congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding
angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the
segment’s endpoints.
 G.CO.10
Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a
triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of
two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
 G.CO.12
Make geometric constructions. Make formal geometric constructions with a variety of tools and methods
(compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a
segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including
the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on
the line.
 G.CO.13
Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a
circle.
 G.GPE.5
Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a given point).
 G.MG.3
Apply geometric concepts in modeling situations. Apply geometric methods to solve design problems (e.g.,
designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid
systems based on ratios).
Transfer Goals:
 Everything can be located on a grid of some nature.
 Items in nature are related in many ways, can be used together to make new information
Enduring Understandings:
Essential Questions:
 Not all lines and not all planes intersect.
 How do you prove two lines are parallel?
 Intersections create special angle pairs
 How do you prove two lines are perpendicular?
 The sum of the angle measures of a triangle are always the
 What is the sum of the measures of a triangle?
same.
 How do you write an equation of a line in a coordinate
 A line can be graphed and its equation written when specific
plane?
facts are known.
 Comparing slopes of lines can determine whether they are
parallel or perpendicular, or not.
Learners will know:
Learners will be able to:
 Properties of the coordinate plane
 Find the measure of an angle indirectly
 Terms appropriate to the content
 Determine whether lines are parallel, perpendicular, or
neither.
 Characteristics of parallel and perpendicular lines
 Graph lines on a coordinate plane given the equation or the
 Terms involved with lines, intersections, and angles
slope and y-intercept.
 Key terms: pg. 206 chapter vocabulary (text); pg. 138, ELL
Performance Tasks:
 Mid-unit quiz
 Unit test
 Group station products
Other Evidence:
 Daily class work
 Class participation
 Group collaborations
 Do Now quizzes
Authentic Assessment: “pull it all together”, pg. 205, choose #1
Anticipated daily sequence of activities:
 Lines and angles (text 3-1)
 Parallel lines (3-2)
 Proving lines parallel (3-3)
 Perpendicular lines (3-4)
 Parallel lines and triangles (3-5)
 Constructing lines (3-6)
 Linear equations (3-7)
 Slopes vs. parallel/perpendicular (3-8)
Anticipated resources:
 Pearson/Prentice Hall Geometry text
 Student Skills Handbook
 Student Visual Glossary
 Spanish version of materials
 Pearson MathXL system and resources
 Pearson test bank generating software
 ALEKS
Asbury Park High School
Unit Plan
Department: Mathematics
Course: Geometry
Unit designation: #4 Triangles
Anticipated timeframe: Day 25-32
Standards addressed:
 G.CO.10
Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a
triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of
two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
 G.CO.12
Make geometric constructions. Make formal geometric constructions with a variety of tools and methods
(compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a
segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including
the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on
the line.
 G.CO.13
Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a
circle.
 G.SRT.5
Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve problems and to
prove relationships in geometric figures.
Transfer Goals:
 Identification of relationships between items can lead to an understanding of additional relationships.
 Larger ideas can be proven true by building upon known truths.
Enduring Understandings:
Essential Questions:
 Comparing the corresponding parts of two figures can show
 How do you identify corresponding parts of congruent
whether the figures are congruent
triangles?
 If two figures are congruent, then every corresponding part
 How do you show two triangles are congruent?
of them is identical
 How can you tell when a triangle is isosceles or equilateral?
 Isosceles and equilateral triangles have special relationships
Learners will know:
Learners will be able to:
 Triangle congruence theorems and postulates
 Write congruence statements for triangle pairs
 Terms appropriate to the content
 Demonstrate triangles are congruent through proofs
 Methods for identifying corresponding parts of figures
 Identify overlapping congruent triangles
 Steps in writing a proof
 Key terms: pg. 273 chapter vocabulary (text); pg. 216, ELL
Performance Tasks:
 Mid-unit quiz
 Unit test
 Group station products
Authentic Assessment: “pull it all together”, pg. 272, choose #2
Anticipated daily sequence of activities:
 Congruent figures (text 4-1)
 Triangle congruence (4-2; 4-3)
 Using corresponding parts of triangles (4-4)
 Special triangles (4-5)
 Right triangles (4-6)
 Overlapping triangles (4-7)
Anticipated resources:
 Pearson/Prentice Hall Geometry text
Other Evidence:
 Daily class work
 Class participation
 Group collaborations
 Do Now quizzes






Student Skills Handbook
Student Visual Glossary
Spanish version of materials
Pearson MathXL system and resources
Pearson test bank generating software
ALEKS
Asbury Park High School
Unit Plan
Department: Mathematics
Course: Geometry
Unit designation: #5 Parts of Triangles
Anticipated timeframe: Day 33-39
Standards addressed:
 A.CED.1
Create equations that describe numbers or relationship. Create equations and inequalities in one variable and use
them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and
exponential functions.*
 G.C.3
Understand and apply theorems about circles. Construct the inscribed and circumscribed circles of a triangle, and
prove properties of angles for a quadrilateral inscribed in a circle.
 G.CO.9
Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are
congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding
angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the
segment’s endpoints.
 G.CO.10
Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a
triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of
two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
 G.CO.12
Make geometric constructions. Make formal geometric constructions with a variety of tools and methods
(compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a
segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including
the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on
the line.
 G.SRT.5
Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve problems and to
prove relationships in geometric figures.
Transfer Goals:
 Breaking items into its parts can sometimes make it easier to learn more about it.
 There are many ways to arrive at a solution.
Enduring Understandings:
Essential Questions:
 The midsegment of a triangle can be used to find
 How is coordinate geometry used to find relationships
relationships
within triangles?
 Triangles are key to understanding bisectors
 How do you solve problems involving the measurements of
triangles?
 Bisectors can be used to help with triangle measures
 The measures of angles of a triangle are related to the length  How do you write indirect proofs
of the opposite side
 The length of medians and altitudes can be found from other
segments
 Indirect proofs provide a different way to a determined
result
 In indirect reasoning, when all possibilities are considered
and then all but one are proved false, the remaining
possibility must be true.
Learners will know:
Learners will be able to:
 How indirect proofs are formed
 Find the circumcenter of a triangle
 The relationships between parts of a triangle
 Find the orthocenter of a triangle
 Terms appropriate to the content
 Determine comparative measures of parts of triangles
 Key terms: pg. 341chapter vocabulary (text); pg. 282, ELL
 Find the exact measures of part of triangles
 Create indirect proofs
Performance Tasks:
 Mid-unit quiz
 Unit test
 Group station products
Other Evidence:
 Daily class work
 Class participation
 Group collaborations
 Do Now quizzes
Authentic Assessment: “pull it all together”, pg. 340, choose #1
Anticipated daily sequence of activities:
 Midsegments of triangles (text 5-1)
 Bisectors (5-2; 5-3)
 Medians and altitudes (5-4)
 Indirect proof (5-5)
 Inequalities in triangles (5-6; 5-7)
Anticipated resources:
 Pearson/Prentice Hall Geometry text
 Student Skills Handbook
 Student Visual Glossary
 Spanish version of materials
 Pearson MathXL system and resources
 Pearson test bank generating software
 ALEKS
Asbury Park High School
Unit Plan
Department: Mathematics
Course: Geometry
Unit designation: #6 Multi-sided shapes
Anticipated timeframe: Day 40-49
Standards addressed:
 G.CO.11
Prove geometric theorems. Prove theorems about parallelograms. Theorems include: opposite sides are
congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely,
rectangles are parallelograms with congruent diagonals.
 G.CO.12
Make geometric constructions. Make formal geometric constructions with a variety of tools and methods
(compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a
segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including
the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on
the line.
 G.GPE.4
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure
defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on
the circle centered at the origin and containing the point (0, 2).
 G.GPE.7
Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of
polygons and areas of triangles and rectangles, e.g., using the distance formula.
 G.SRT.5
Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve problems and to
prove relationships in geometric figures.
Transfer Goals:
 Items with specific properties often have special names
 Relationships between and within figures can be identified, isolated, and proven
Enduring Understandings:
Essential Questions:
 The sum of the measures of a polygon is related to the
 How can the sum of the measures of the angles in a polygon
number of sides
be determined?
 Certain quadrilaterals have specific properties and names
 How are quadrilaterals classified?
 Variables can be used to name coordinates in a figure to help  How can coordinate geometry be used to prove general
identify relationships between parts of the figure
relationships?
Learners will know:
Learners will be able to:
 The formula for deriving angle measures of a polygon
 Compute the sum of the angle measures for any polygon
 Properties of parallel and perpendicular lines to classify
 Graph a quadrilateral given coordinate
quadrilaterals
 Name all special quadrilaterals
 Ordered pairs in a coordinate plane
 Find midpoints and slopes of segments in a figure
 Terms appropriate to the content
 Demonstrate congruence of figures
 The names for special quadrilaterals
 The distance formula
 Key terms: pg. 420 chapter vocabulary (text); pg. 350, ELL
Performance Tasks:
 Mid-unit quiz
 Unit test
 Group station products
Authentic Assessment: “pull it all together”, pg. 419, choose #3
Anticipated daily sequence of activities:
 Polygon-angle sum theorems (text 6-1)
 Properties of parallelograms (6-2)
 Proving parallelograms (6-3)
Other Evidence:
 Daily class work
 Class participation
 Group collaborations
 Do Now quizzes






Properties of special quadrilaterals (6-4)
Conditions of special quadrilaterals (6-5)
Trapezoids and kites (6-6)
Polygons in coordinate plane (6-7)
Applying coordinate geometry (6-8)
Proofs using coordinate geometry (6-9)
Anticipated resources:
 Pearson/Prentice Hall Geometry text
 Student Skills Handbook
 Student Visual Glossary
 Spanish version of materials
 Pearson MathXL system and resources
 Pearson test bank generating software
 ALEKS
Asbury Park High School
Unit Plan
Department: Mathematics
Course: Geometry
Unit designation: #7 Similar Figures
Anticipated timeframe: Day 50-55
Standards addressed:
 A.CED.1
Create equations that describe numbers or relationship. Create equations and inequalities in one variable and use
them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and
exponential functions.
 G.GPE.5
Use coordinates to prove simple geometric theorems algebraically. Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or
perpendicular to a given line that passes through a given point).
 G.SRT.4
Prove theorems involving similarity. Prove theorems about triangles. Theorems include: a line parallel to one side
of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle
similarity.
 G.SRT.5
Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve problems and to
prove relationships in geometric figures.
Transfer Goals:
 Many things can be similar if enough of their components are the same
 Similar items can be compared for relative size
Enduring Understandings:
Essential Questions:
 Equations can be written with equal ratios and, with a
 How are proportions used to find the side lengths of
variable, can be solved to find the value of the variable.
polygons?
 Similarity can be determined from using ratios and
 How can two triangles be shown to be similar?
proportions
 How are corresponding parts of similar triangles identified?
 Lines intersecting parallel lines form proportional segments
 Triangles can be shown to be similar based on the
relationships of their parts
Learners will know:
Learners will be able to:
 Ratios
 Solve algebraic proportions
 Proportions
 Find the length of a side in a figure given sufficient
information
 Terms appropriate to the content
 Determine if two triangles are similar
 Similarity
 Key terms: pg. 480 chapter vocabulary (text); pg. 430, ELL
Performance Tasks:
 Mid-unit quiz
 Unit test
 Group station products
Authentic Assessment: “pull it all together”, pg. 479, choose #2
Anticipated daily sequence of activities:
 Ratios and proportions (text 7-1)
 Similar polygons (7-2)
 Proving triangles similar (7-3)
 Similarity with right triangles (7-4)
 Proportions in triangles (7-5)
Anticipated resources:
 Pearson/Prentice Hall Geometry text
Other Evidence:
 Daily class work
 Class participation
 Group collaborations
 Do Now quizzes






Student Skills Handbook
Student Visual Glossary
Spanish version of materials
Pearson MathXL system and resources
Pearson test bank generating software
ALEKS
Asbury Park High School
Unit Plan
Department: Mathematics
Course: Geometry
Unit designation: #8 Intro to Trigonometry
Anticipated timeframe: Day 56-62
Standards addressed:
 G.MG.1
Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to
describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
 G.SRT.4
Prove theorems involving similarity. Prove theorems about triangles. Theorems include: a line parallel to one side
of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle
similarity.
 G.SRT.7
Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship
between the sine and cosine of complementary angles.
 G.SRT.8
Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the
Pythagorean Theorem to solve right triangles in applied problems.
 G.SRT.10 Apply trigonometry to general triangles. Prove the Laws of Sines and Cosines and use them to solve problems.
 G.SRT.11 Apply trigonometry to general triangles. Understand and apply the Law of Sines and the Law of Cosines to find
unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
Transfer Goals:
 Values usually measured by hand can be determined through mathematical functions.
 What is done, can usually be undone by an inverse operation.
Enduring Understandings:
Essential Questions:
 If the lengths of two sides of a triangle are known, the third  How are side lengths found in a right triangle?
side can be determined
 How do trigonometric ratios relate to similar right triangles?
 Some right triangles have specific properties
 What is a vector?
 Ratios can be used to find measures of parts of a triangle if
certain other measures of the triangle are known
 Vectors can be used to model motion and direction
Learners will know:
Learners will be able to:
 The Pythagorean Theorem
 Find the length of a side or measure of an angle of a right
triangle given sufficient other measures
 Concepts of 30-60-90 and 45-45-90 triangles
 Determine triangles that are acute, obtuse, or right triangles
 Terms appropriate to the content
 Apply the definition of sine, cosine, and tangent.
 Trigonometric functions and their definitions
 Find inverse trigonometric function values
 Inverse trigonometric functions
 Determine the magnitude and direction of vectors
 Angle of depression or elevation
 Magnitude and direction for vectors
 Vector addition
 Key terms: pg. 534 chapter vocabulary (text); pg. 488, ELL
Performance Tasks:
 Mid-unit quiz
 Unit test
 Group station products
Authentic Assessment: “pull it all together”, pg. 533, choose #2
Anticipated daily sequence of activities:
 Pythagorean Theorem (text 8-1)
 Converse of Pythagorean Theorem (8-1)
 Special right triangles (8-2)
 Trigonometric functions (8-3)
Other Evidence:
 Daily class work
 Class participation
 Group collaborations
 Do Now quizzes
 Angles of elevation and depression (8-4)
 Vectors (internet or other resources)
Anticipated resources:
 Pearson/Prentice Hall Geometry text
 Student Skills Handbook
 Student Visual Glossary
 Spanish version of materials
 Pearson MathXL system and resources
 Pearson test bank generating software
 ALEKS
Asbury Park High School
Unit Plan
Department: Mathematics
Course: Geometry
Unit designation: #9 Transformations
Anticipated timeframe: Day 63-69
Standards addressed:
 G.CO.2
Experiment with transformations in the plane. Represent transformations in the plane using, e.g., transparencies
and geometry software; describe transformations as functions that take points in the plane as inputs and give
other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g.,
translation versus horizontal stretch).
 G.CO.3
Experiment with transformations in the plane. Given a rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself.
 G.CO.4
Experiment with transformations in the plane. Develop definitions of rotations, reflections, and translations in
terms of angles, circles, perpendicular lines, parallel lines, and line segments.
 G.CO.5
Experiment with transformations in the plane. Given a geometric figure and a rotation, reflection, or translation,
draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of
transformations that will carry a given figure onto another.
 G.CO.6
Understand congruence in terms of rigid motions. Use geometric descriptions of rigid motions to transform
figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of
congruence in terms of rigid motions to decide if they are congruent.
 G.CO.7
Understand congruence in terms of rigid motions. Use the definition of congruence in terms of rigid motions to
show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of
angles are congruent.
 G.CO.8
Understand congruence in terms of rigid motions. Explain how the criteria for triangle congruence (ASA, SAS,
and SSS) follow from the definition of congruence in terms of rigid motions.
 G.SRT.1a Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations
given by a center and a scale factor: A dilation takes a line not passing through the center of the dilation to a
parallel line, and leaves a line passing through the center unchanged.
 G.SRT.1b Understand similarity in terms of similarity transformations. Verify experimentally the properties of dilations
given by a center and a scale factor: The dilation of a line segment is longer or shorter in the ratio given by the
scale factor.
 G.SRT.2
Understand similarity in terms of similarity transformations. Given two figures, use the definition of similarity in
terms of similarity transformations to decide if they are similar; explain using similarity transformations the
meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of
all corresponding pairs of sides.
 G.SRT.3
Understand similarity in terms of similarity transformations. Use the properties of similarity transformations to
establish the AA criterion for two triangles to be similar.
Transfer Goals:
 Scale factors are used in many situations and more many purposes
 Many events are much alike although larger or smaller in scale or different in environment or relationship
Enduring Understandings:
Essential Questions:
 Figures can be moved without changing their size or shape
 How can a figure’s position change without changing its size
and shape?
 A scale factor is used to change the size of a figure to a
similar figure
 How can a figure’s size change without changing its shape?
 Identical figures can be mapped onto each other using
 How is a transformation represented in a coordinate plane?
reflections, translations and/or rotations
 How can symmetry in a figure be recognized
 Some shapes fit together to make a repeating pattern
 Some shapes appear unchanged after a reflection or rotation
Learners will know:
Learners will be able to:
 Translations
 Find coordinates of a figure following a translation,
reflection, rotation, or dilation.
 Reflections
 Identify the transformation type from given information
 Rotations
 Identify the type of symmetry between two figures
 Dilations
 Determine the ability of a figure to tessellate
 Isometry





Scale factor
Line of symmetry
Rotational symmetry
Tessellation
Key terms: pg. 602 chapter vocabulary (text); pg. 542, ELL
Performance Tasks:
 Mid-unit quiz
 Unit test
 Group station products
 Authentic Assessment: “pull it all together”, pg. 601, #2
Anticipated daily sequence of activities:
 Translations (text 9-1)
 Reflections (9-2)
 Rotations (9-3)
 Symmetry (9-3)
 Dilations (9-6)
 Composition of reflections (9-4)
 Tessellations (internet or other resources)
Anticipated resources:
 Pearson/Prentice Hall Geometry text
 Student Skills Handbook
 Student Visual Glossary
 Spanish version of materials
 Pearson MathXL system and resources
 Pearson test bank generating software
 ALEKS
 Identify the isometry between two congruent figures
Other Evidence:
 Daily class work
 Class participation
 Group collaborations
 Do Now quizzes
Asbury Park High School
Unit Plan
Department: Mathematics
Course: Geometry
Unit designation: #10 Inside the box
Anticipated timeframe: Day 70-76
Standards addressed:
 G.C.1
Understand and apply theorems about circles. Prove that all circles are similar.
 G.C.5
Find arc lengths and areas of sectors of circles. Derive using similarity the fact that the length of the arc
intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector.
 G.CO.1
Experiment with transformations in the plane. Know precise definitions of angle, circle, perpendicular line,
parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance
around a circular arc.
 G.CO.13
Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a
circle.
 G.GMD.1 Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the
circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments,
Cavalieri’s principle, and informal limit arguments.
 G.GMD.3 Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones,
and spheres to solve problems.
 G.GPE.7
Use coordinates to prove simple geometric theorems algebraically. Use coordinates to compute perimeters of
polygons and areas of triangles and rectangles, e.g., using the distance formula.
 G.MG.1
Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to
describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
 G.SRT.9
Apply trigonometry to general triangles. Derive the formula A = (1/2)ab sin(C) for the area of a triangle by
drawing an auxiliary line from a vertex perpendicular to the opposite side.
 S.CP.1
Describe events and subsets of a sample space (the set of outcomes) using characteristics (or categories) of the
outcomes, or as unions, intersections, or compliments of other events (“or”, “and”,”not”).
Transfer Goals:
 The value of new items can be found by using the familiar information
 Many things can be classified to help enable us to deal with them in the same way
Enduring Understandings:
Essential Questions:
 The area of a quadrilateral with two parallel sides can be
 How are the area and perimeter of a polygon found?
found by multiplying its height by the average of its bases.
 How are the area and circumference of a circle found?
 The area of a regular polygon is a function of the distance
 How do perimeters and areas of similar figures compare?
from its center to a side and its perimeter
 The length of an arc in a circle is related to the angle that
forms it.
 The area of portions of a circle formed by arcs and radii can
be found when its radius is known
Learners will know:
Learners will be able to:
 Formulas for finding areas and perimeters of various
 Find the area and perimeter of various polygons
polygons
 Find the area and circumference for circles
 Formulas for finding circumference and area of circles
 Find the ratio of the area between two figures
 Use of trigonometry to find area
 Find the measure of arc angles
 Terms appropriate to the content
 Find the length of arcs
 Key terms: pg. 676 chapter vocabulary (text); pg. 612, ELL  Find the area of portions of a figure
Performance Tasks:
 Mid-unit quiz
 Unit test
 Group station products
Other Evidence:
 Daily class work
 Class participation
 Group collaborations
 Do Now quizzes
Authentic Assessment: “pull it all together”, pg. 675, choose #1
Anticipated daily sequence of activities:
 Trigonometric functions and area (text 10-5)
 Circles and arcs (10-6)
 Areas of circles and sectors (10-7)
 Geometric probability (10-8)
Anticipated resources:
 Pearson/Prentice Hall Geometry text
 Student Skills Handbook
 Student Visual Glossary
 Spanish version of materials
 Pearson MathXL system and resources
 Pearson test bank generating software
 ALEKS
Asbury Park High School
Unit Plan
Department: Mathematics
Course: Geometry
Unit designation: #11 Outside & Inside the Figure
Anticipated timeframe: Day 77-84
Standards addressed:
 A.CED.4
Create equations that describe numbers or relationship. Rearrange formulas to highlight a quantity of interest,
using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight
resistance R.
 G.GMD.1 Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the
circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments,
Cavalieri’s principle, and informal limit arguments.
 G.GMD.2 Explain volume formulas and use them to solve problems. Give an informal argument using Cavalieri’s principle
for the formulas for the volume of a sphere and other solid figures.
 G.GMD.3 Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones,
and spheres to solve problems.
 G.GMD.4 Visualize relationships between two-dimensional and three-dimensional objects. Identify the shapes of twodimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by
rotations of two-dimensional objects.
 G.MG.1
Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to
describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
 G.MG.2
Apply geometric concepts in modeling situations. Apply concepts of density based on area and volume in
modeling situations (e.g., persons per square mile, BTUs per cubic foot).
Transfer Goals:
 Events and objects are the sum of their parts
 Events and objects can often be better understood by examining their details in a way that is not easily seen
Enduring Understandings:
Essential Questions:
 3 dimensional figures can be analyzed through the
 How are the intersection of a plane and a solid found?
relationships among their vertices, edges, and faces
 How is the surface area of a solid found?
 Surfaces areas of portions of a figure can be added to make
 How is the volume of a solid found?
the whole
 How do the volume and surface area of similar solids
 The volume and surface area of a figure can be found from
compare?
its key dimensions
 Ratios can be used to compare the areas and volumes of
similar solids
Learners will know:
Learners will be able to:
 How cross sections are formed
 Compute the volume and surface area of cylinders, prisms,
spheres, pyramids, and cones.
 Formulas for surface area and volume for cylinders, prisms,
spheres, pyramids, and cones
 Describe the figure formed by cross sections
 Terms appropriate to the content
 Count the number of edges and faces of various figures
 The role of ratio to similar solids
 Euler’s Formula
 Key terms: pg. 751 chapter vocabulary (text); pg. 686, ELL
Performance Tasks:
 Mid-unit quiz
 Unit test
 Group station products
Authentic Assessment: “pull it all together”, pg. 750, choose #2
Other Evidence:
 Daily class work
 Class participation
 Group collaborations
 Do Now quizzes
Anticipated daily sequence of activities:
 3 dimensional figures and cross sections (text 11-1)
 Prisms and cylinders (11-2)
 Pyramids and cones (11-3)
 Spheres (11-6)
 Areas and volumes of similar solids (11-7)
Anticipated resources:
 Pearson/Prentice Hall Geometry text
 Student Skills Handbook
 Student Visual Glossary
 Spanish version of materials
 Pearson MathXL system and resources
 Pearson test bank generating software
 ALEKS
Asbury Park High School
Unit Plan
Department: Mathematics
Course: Geometry
Unit designation: #12 Around and Through
Anticipated timeframe: Day 85-90
Standards addressed:
 G.C.2
Understand and apply theorems about circles. Identify and describe relationships among inscribed angles, radii,
and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a
diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the
circle.
 G.C.3
Understand and apply theorems about circles. Construct the inscribed and circumscribed circles of a triangle, and
prove properties of angles for a quadrilateral inscribed in a circle.
 G.C.4
Understand and apply theorems about circles. Construct a tangent line from a point outside a given circle to the
circle.
 G.GMD.4 Visualize relationships between two-dimensional and three-dimensional objects. Identify the shapes of twodimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by
rotations of two-dimensional objects.
 G.GPE.1
Translate between the geometric description and the equation for a conic section. Derive the equation of a circle
of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a
circle given by an equation.
Transfer Goals:

A locus can often help us see a pattern in a figure or events
 A circle is defined in a small number of ways, but its parts can be defined in many ways
Enduring Understandings:
Essential Questions:
 A radius of a circle and the tangent that intersects the
 How can relationships between arcs and angles of a circle be
endpoint of the radius have a special relationship
proven?
 Information about parts of a circle can be used to learn more  How do you find the measures of resulting angles, arcs, and
about other parts of the circle
segments when lines intersect in a circle or within a circle?
 The description of a locus can be used to sketch a geometric  How do you find the equation of a line in a coordinate
relationship
plane?
 Angles formed by intersecting lines have a special
relationship to the arcs those lines intercept.
 The information contained in the equation of a circle enables
the circle to be graphed on a coordinate plane
 The equation of a circle can be written if its radius and
center point are known
Learners will know:
Learners will be able to:
 Relationships between arcs and angles
 Find the lengths of various segments given information
about secants, chords, and radii of circles
 Properties of lines tangent to a circle

Find the arc of a circle given information about a secant and
 Secants and tangents infer angles
radius
 A center and radius of a circle is defined by its equation and

Graph a circle given its equation.
visa-versa.

Derive a circle’s center and radius from an equation
 Key terms: pg. 813 chapter vocabulary (text); pg. 760, ELL
 Graph a locus of points from its definition.

Performance Tasks:
 Mid-unit quiz
 Unit test
 Group station products
Authentic Assessment: “pull it all together”, pg. 812, choose #2
Other Evidence:
 Daily class work
 Class participation
 Group collaborations
 Do Now quizzes
Anticipated daily sequence of activities:
 Tangent lines (text 12-1)
 Chords and arcs (12-2)
 Inscribed angles (12-3)
 Angle measures and segment lengths (12-4)
 Circles in the coordinate plane (12-5)
 Locus (12-6)
Anticipated resources:
 Pearson/Prentice Hall Geometry text
 Student Skills Handbook
 Student Visual Glossary
 Spanish version of materials
 Pearson MathXL system and resources
 Pearson test bank generating software
 ALEKS