Download Hope College Prep High School: Geometry Curriculum Map 2014

Hope College Prep High School: Geometry Curriculum Map 2014-2015
Teacher
First and Last Name
Maurice P. Schwartz
Course
Geometry
Subject Area
Mathematics
Grade Level
10
Units Calendar
Unit 1 Title
Foundations for Geometry
Dates (school calendar weeks)
Sep 2 - Sep 30
Unit 2 Title
Parallel and Perpendicular Lines
Dates (school calendar weeks)
Oct 1 - Oct 29
Unit 3 Title
Triangle Congruence
Dates (school calendar weeks)
Oct 30 - Dec 12, Q
Unit 4 Title
Properties of Triangles
Dates (school calendar weeks)
Dec 15 - Jan 26
Unit 5 Title
Polygons and Quadrilaterals
Dates (school calendar weeks)
Jan 27 - Feb 25, Q
Unit 6 Title
Similarity
Dates (school calendar weeks)
Feb 26 - Mar 25
Unit 7 Title
Right Triangles and Trigonometry
Dates (school calendar weeks)
Mar 26 - May 7, Q
Unit 8 Title
Circles
Dates (school calendar weeks)
May 8 - Jun 16, Q
Unit 1 Summary + Curriculum Alignment
Unit Title
Foundations for Geometry
Major Topics
Understanding points, lines, planes, angles, segments, midpoint, and distance in the coordinate plane.
Description of
Find the distance between two vertices of a rectangle in the coordinate plane.
Primary
Performance Task
NOTE: One task
per unit
Common Core
Standard(s)
Related to Task
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.
CRS Supporting
Skills
College
Bound
GR 20-23 401
GR 24-27 504
Accelerated
GR 20-23 401
GR 24-27 504
Honors
GR 20-23 401
GR 24-27 504
GR 28-32 603
Industry or
Subject Specific
Standards
Interdisciplinary
Integrations /
Thematic
Connections
Algebra: Unit Conversions
Connections to
Writing
Framework
Find an unfamiliar term and write the definition in their student journal.
Cornell Notes Summary
Assessment
Supplementary
Text
Diagnostic/
Pre-Assessment
Using a protractor, measure an acute angle in degrees.
Formative
Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes,
Homework, Discovery Activities
Summative
Tests, MARS Task
Description/ Title
Geometry
Foundations
V3.0 Units 1-5
Lexile
Flesch
Reading Ease
Nonfiction, Informational
Informational
Flesch-Kincaid Reading Level
Framing Questions
Essential
Question(s)
How does knowledge of geometry help in your everyday life?
Unit Content
Questions
Explain why we can only draw representations of points, lines and planes. What are the “essential components” of
angles? Explain midpoint and distance in the coordinate plane.
Unit 2 Summary + Curriculum Alignment
Unit Title
Parallel and Perpendicular Lines
Major Topics
Parallel and Perpendicular Lines, Angles Formed by Parallel Lines and Transversals, Slope.
Description of
Primary
Performance
Task
Find which angles, formed by two parallel lines cut by a transversal, are congruent and which angles are
supplementary.
NOTE: One
task per unit
Common Core CC.9-12.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
Standard(s)
Related to Task congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment
are exactly those equidistant from the segment’s endpoints.
CC.9-12.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.
CC.9-12.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).
CRS Supporting College
Skills
Bound
PPF 16-19 301
PPF 20-23 401
GR 20-23 403
Accelerated
PPF 16-19 301
PPF 20-23 401
GR 20-23 403
Honors
GR 28-32 604
PPF 16-19 301
PPF 20-23 401
GR 20-23 403
Industry or
Subject
Specific
Standards
Interdisciplinar
y Integrations /
Algebra: Equations of Lines in the Coordinate Plane
Thematic
Connections
Connections to Find an unfamiliar term and write the definition in their student journal.
Writing
Cornell Notes Summary
Framework
Assessment
Diagnostic/
Pre-Assessment
Using a protractor, draw a right angle.
Formative
Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes, Homework,
Discovery Activities
Summative
Tests, MARS Task
Supplementary Description/ Title
Geometry
Nonfiction, Informational
Informational
Text
Foundations V3.0
Units 1-5
Flesch
Reading Ease
Lexile
Flesch-Kincaid Reading Level
Framing Questions
Essential
Question(s)
What would “things” look like without parallel and perpendicular lines?
Unit Content
Questions
What angles are formed when parallel lines are cut by a transversal?
Unit 3 Summary + Curriculum Alignment
Unit Title
Triangle Congruence
Major Topics
Classifying Triangles, Angle Relationships in Triangles, Triangle Congruence Postulates
Description of
Primary
Performance
Task
What is the least amount of information needed to show that two triangles are congruent?
NOTE: One task
per unit
Common Core CC.9-12.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.
Standard(s)
Related to Task CC.9-12.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.
CRS Supporting College
Skills
Bound
PPF 24-27 501, 503
PPF 20-23 402
Accelerated
PPF 24-27 501, 503
PPF 20-23 402
Honors
PPF 24-27 501, 503
PPF 20-23 402
Industry or
Subject Specific
Standards
Interdisciplinar
y Integrations /
Algebra: Quadratic Equations
Thematic
Connections
Connections to Find an unfamiliar term and write the definition in their student journal.
Writing
Cornell Notes Summary
Framework
Assessment
Diagnostic/
Pre-Assessment
Using a straight edge and compass, draw two congruent triangles.
Formative
Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes, Homework,
Discovery Activities
Summative
Tests, MARS Task
Supplementary
Text
Description/ Title
Geometry
Foundations V3.0 Nonfiction, Informational
Units 1-5
Flesch
Reading Ease
Lexile
Informational
Flesch-Kincaid Reading Level
Framing Questions
Essential
Question(s)
Where are triangles so important?
Unit Content
Questions
What is the least amount of information needed to show that two triangles are identical? Why is this
important?
Unit 4 Summary + Curriculum Alignment
Unit Title
Properties of Triangles
Major Topics
Perpendicular and Angle Bisectors, Midsegments, Pythagorean Theorem.
Description of
Primary
Performance
Task
What are Pythagorean triples?
NOTE: One task
per unit
Common Core CC.9-12.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
Standard(s)
Related to Task congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment
are exactly those equidistant from the segment’s endpoints.
CC.9-12.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.
CRS Supporting College
Skills
Bound
M 13-15 201
PPF 20-23 402
PPF 24-27 501
Accelerated
M 13-15 201
PPF 20-23 402
PPF 24-27 501
Honors
PPF 28-32 602
M 13-15 201
PPF 20-23 402
PPF 24-27 501
Industry or
Subject Specific
Standards
Interdisciplinar
y Integrations /
Algebra: Solving Equations with Radicals.
Thematic
Connections
Connections to Find an unfamiliar term and write the definition in their student journal.
Writing
Cornell Notes Summary
Framework
Assessment
Supplementary
Text
Diagnostic/
Pre-Assessment
Using a compass and straight edge, bisect a line segment.
Formative
Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes, Homework,
Discovery Activities
Summative
Tests, MARS Task
Description/ Title
Geometry
Foundations V3.0 Nonfiction, Informational
Units 1-5
Flesch
Reading Ease
Lexile
Informational
Flesch-Kincaid Reading Level
Framing Questions
Essential
Question(s)
What would “things” look like without right angles?
Unit Content
Questions
What is the least amount of information needed to solve each type of triangle?
Unit 5 Summary + Curriculum Alignment
Unit Title
Polygons and Quadrilaterals
Major Topics
Properties of Polygons, Parallelograms, and Quadrilaterals.
Description of
Primary
Performance
Task
How do you find the perimeter of a parallelogram?
NOTE: One task
per unit
Common Core CC.9-12.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
Standard(s)
Related to Task each other, and conversely, rectangles are parallelograms with congruent diagonals.
CRS Supporting College
Skills
Bound
M 13-15 201
M 16-19 301,302
PPF 24-27 501
M 20-23 401
M 24-27 501,503
Accelerated
M 13-15 201
M 16-19 301,302
PPF 24-27 501
M 20-23 401
M 24-27 501,503
Honors
M 13-15 201
M 16-19 301,302
PPF 24-27 501
M 20-23 401
M 24-27 501,503
Industry or
Subject Specific
Standards
Interdisciplinar
y Integrations /
Algebra: Solving a Formula for a Variable
Thematic
Connections
Connections to Find an unfamiliar term and write the definition in their student journal.
Writing
Cornell Notes Summary
Framework
Assessment
Supplementary
Text
Diagnostic/
Pre-Assessment
Use the Pythagorean theorem to find the diagonal of a rectangle.
Formative
Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes,
Homework, Discovery Activities
Summative
Tests, MARS Task
Description/ Title
Geometry
Foundations
V3.0 Units 1-5
Flesch
Reading Ease
Lexile
Nonfiction, Informational
Informational
Flesch-Kincaid Reading Level
Framing Questions
Essential
Question(s)
What does the word “polygon” mean?
Unit Content
Questions
What information about triangles can be used to solve polygons?
Unit 6 Summary + Curriculum Alignment
Unit Title
Similarity
Major Topics
Ratio and Proportion, Triangle Similarity Postulates, Indirect Measurement
Description of How do you measure the height of a tree?
Primary
Performance
Task
NOTE: One
task per unit
Common
Core
Standard(s)
Related to
Task
CC.9-12.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.
CC.9-12.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.
CRS
Supporting
Skills
College Bound PPF 24-27 501
Accelerated
PPF 24-27 501
Honors
BOA 33-36 701
PPF 24-27 501
PPF 28-32 601
Industry or
Subject
Specific
Standards
Interdisciplina
ry
Integrations / Algebra: Direct Variation
Thematic
Connections
Connections
to Writing
Framework
Assessment
Find an unfamiliar term and write the definition in their student journal.
Cornell Notes Summary
Diagnostic/
Pre-Assessment
Use cross-products to solve a proportion.
Formative
Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes,
Homework, Discovery Activities
Summative
Tests, MARS Task
Description/ Title
Geometry
Foundations
V3.0 Units 1-5
Supplementar
y Text
Nonfiction, Informational
Flesch
Reading
Ease
Lexile
Informational
Flesch-Kincaid Reading Level
Framing Questions
Essential
Question(s)
How could you measure the height of an inaccessible object?
Unit Content
Questions
What is the least amount of information needed to show two triangles are similar? Why is this important?
Unit 7 Summary + Curriculum Alignment
Unit Title
Right Triangle Trigonometry
Major Topics
Trigonometric Ratios, Solving Right Triangles
Description of
Primary
Performance
Task
How do you measure the height of a skyscraper?
NOTE: One task
per unit
Common Core CC.9-12.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.
Standard(s)
Related to Task
CRS Supporting College
Skills
Bound
Accelerated
F 24-27 50
F 24-27 502
Honors
F 24-27 502
F 28-32 602
F 33-36 702
Industry or
Subject Specific
Standards
Interdisciplinar
y Integrations /
Algebra: Inverse Functions
Thematic
Connections
Connections to Find an unfamiliar term and write the definition in their student journal.
Writing
Cornell Notes Summary
Framework
Assessment
Supplementary
Text
Diagnostic/
Pre-Assessment
Using a calculator, find the ratio of two numbers.
Formative
Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes,
Homework, Discovery Activities
Summative
Tests, MARS Task
Description/ Title
Geometry
Foundations
V3.0 Units 1-5
Nonfiction, Informational
Flesch
Reading Ease
Lexile
Informational
Flesch-Kincaid Reading Level
Framing Questions
Essential
Question(s)
What does the word “trigonometry” mean?
Unit Content
Questions
Why is the Pythagorean Theorem so useful?
Unit 8 Summary + Curriculum Alignment
Unit Title
Circles
Major Topics
Lines and Arcs in Circles, Angles and Segments in Circles.
Description of
Primary
Performance
Task
How do you find the area of a sector?
NOTE: One task
per unit
Common Core CC.9-12.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
Standard(s)
Related to Task 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.
CC.9-12.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.
CRS Supporting College
Skills
Bound
M 24-27 502
M 13-15 201
Accelerated
M 24-27 502
M 13-15 201
Honors
M 24-27 502
PPF 33-36 703
M 13-15 201
Industry or
Subject Specific
Standards
Interdisciplinar
y Integrations /
Data Analysis: Circle Graphs
Thematic
Connections
Connections to Find an unfamiliar term and write the definition in their student journal.
Writing
Cornell Notes Summary
Framework
Assessment
Supplementary
Text
Diagnostic/
Pre-Assessment
How does the area of a circle change if you double the diameter?
Formative
Problem of the Day, Questions and Answers, Classwork, Group Work, Quizzes,
Homework, Discovery Activities
Summative
Tests, MARS Task
Description/ Title
Geometry
Foundations
V3.0 Units 1-5
Lexile
Nonfiction, Informational
Flesch
Reading Ease
Framing Questions
Essential
Question(s)
What special number is so essential with circles?
Unit Content
Questions
What are two important segments inside a circle?
Informational
Flesch-Kincaid Reading Level