Geometry Curriculum Map

Week I, Quarter I
CommonCoreState Standards
The students will:
G.CO.12Make formal geometric constructions with a variety of tools and methods (compass andstraightedge, 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 theperpendicular bisector of a line segment; and constructing a line parallel to a through a point not on the line.
G.GPE.6Find the point on a directed line segment between two given points that partitions the segment in agiven ratio.
G.GPE.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., usingthe distance formula
Unit One: Geometric Constructions
Formulas from Coordinate Geometry (Slope, Midpoint and Distance) (G.GPE.7)
Copying a Segment/Angle (G.CO.12, G.GPE.6)
Bisecting a Segment/Angle (G.CO.12, G.GPE.6)
  • Constructing Perpendicular Lines (G.CO.12, G.GPE.6)

Objectives:
The student will be able to:
findthe slope of a line or segment, given two points on that line or segment.
find or calculatethe distance between to
finds, length of a segment, or the midpoint of a segment given the endpoints.
copya given segment or angle using basic
construction tools.
useconstruction tools and procedures to bisecta segment or angle.
constructperpendicular lines.
constructperpendicular bisectors of segment. / Essential Question:
What are the basic tools for a geometric construction and how does a construction differ from a measurement?
Teacher Resources: / Media and Technology Resources:
Assessments:
Homework/Classwork: To be given daily on each introducedtopic.
Class Discussion: Students will be expected to be prepared for class, participate in class activities andactively engage in class discussion.
Baseline Assessment: The Baseline Assessment focused on Geometric Concepts will be given the 1stweek of classes. / Suggested Instructional Practices:
  • Note Taking Skills (guided notes)
  • Exit Tickets
  • Pre and Post Tests

Week II, Quarter I
CommonCoreState Standards
The students will:
G.CO.12Make 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 theperpendicular bisector of a line segment; and constructing a line parallel to a given line through a point noton the line.
G.CO.13Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Unit One: Geometric Constructions
Constructing the Perpendicular Bisectors (G.CO.12)
Constructing a Line Parallel to a Given Line Through a Point (G.CO.12)
Constructing Equilateral Triangles and Squares (G.CO.12, (G.CO.13)
Objectives:
The student will be able to:
constructperpendicular bisectors of segment.
constructa line that is parallel to a given line through a given point.
construct equilateral triangles using basic
construction tools.
constructsquares using basic construction
tools / Essential Question:
How do you use the basic constructions to perform more elaborate constructions?
Teacher Resources: / Media and Technology Resources:
Assessments:
Homework/Classwork: To be given daily on each introducedtopic.
Class Discussion: Students will be expected to be prepared for class, participate in class activities andactively engage in class discussion.
Test: on concepts involving Geometric
Constructions. / Suggested Instructional Practices:
  • Note Taking Skills (guided notes)
  • Exit Tickets
  • Pre and Post Tests

Week III, Quarter I
CommonCoreState Standards
The students will:
G.CO.9Prove 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 arecongruent; points on a perpendicular bisector of a line segment are exactly those equidistant from thesegment’s endpoints.
G.CO.10Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of atriangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
G.CO.11Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles areparallelograms with congruent diagonals.
Unit Two: Geometric Reasoning
Inductive Reasoning (G.CO.9, G.CO.10, G.CO.11)
Conditional Statements (G.CO.9, G.CO.10, G.CO.11)
Deductive Reasoning (G.CO.9, G.CO.10, G.CO.11)
Biconditional Statements (G.CO.9, G.CO.10, G.CO.11)
Objectives:
The student will be able to:
useinductive reasoning to identify patterns
and make conjectures.
disproveconjectures using counterexamples.
identify, write, andanalyzethe truth value ofa conditional statement.
writethe inverse, converse, and contrapositive of a conditional statement.
usedeductive reasoning.
write andanalyzebiconditional statements. / Essential Question:
Why is it important to include every logical step in a proof?
Teacher Resources: / Media and Technology Resources:
Assessments:
Homework?Classwork: To be given daily on each introducedtopic.
Class Discussion: Students will be expected to beprepared for class, participate in class activities and actively engage in class discussion.
Quiz: on concepts involving Reasoning and
Conditional Statements. / Suggested Instructional Practices:
  • Note Taking Skills (guided notes)
  • Exit Tickets
  • Pre and Post Tests

Week IV, Quarter I
CommonCoreState Standards
The students will:
G.CO.9Prove 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 arecongruent; points on a perpendicular bisector of a line segment are exactly those equidistant from thesegment’s endpoints.
G.CO.10Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of atriangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
G.CO.11Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles areparallelograms with congruent diagonals.
Unit Two: Geometric Reasoning
Algebraic Proofs (G.CO.9, G.CO.10, G.CO.11)
Geometric Proofs (G.CO.9, G.CO.10, G.CO.11)
Flowcharts and Paragraph Proofs * (G.CO.9, G.CO.10, G.CO.11)
Objectives:
The student will be able to:
writealgebraic proofs using properties of
equality and congruence. *
writetwo-column proofs. *
provegeometric concepts using deductive
reasoning.
writeflowcharts and paragraph proofs. * / Essential Question:
Why might there be more than one correct way to write a proof?
Teacher Resources: / Media and Technology Resources:
Assessments:
Homework/Classwork: To be given daily on each introducedtopic.
Class Discussion: Students will be expected to be prepared for class, participate in class activities andactively engage in class discussion..
Test: On concepts involving Geometric Reasoning. / Suggested Instructional Practices:
  • Note Taking Skills (guided notes)
  • Exit Tickets
  • Pre and Post Tests

Week V, Quarter I
CommonCoreState Standards
The Students Will:
G.CO.1Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based onthe undefined notions of point, line, distance along a line, and distance around a circular arc.
Unit Three: Lines - Parallel/Perpendicular
Lines and Angles (G.CO.1)
Angles Formed by Parallel Lines and Transversals (G.CO.1)
Objectives:
The student will be able to:
identifyvarious types of lines relationships.
identifyandfind measures of angles formed by two lines cut by a transversal.
applytheorems involving angles formed by
two lines cut by a transversal. / Essential Question:
How do you determine the measures of all the angles created by two parallel lines cut by a transversal, given only one angle’s measure?
Teacher Resources: / Media and Technology Resources:
Assessments:
Homework/Classwork: To be given daily on each introducedtopic.
Class Discussion: Students will be expected to be prepared for class, participate in class activities andactively engage in class discussion..
Quiz: On concepts involving Parallel and Perpendicular Lines. / Suggested Instructional Practices:
  • Note Taking Skills (guided notes)
  • Exit Tickets
  • Pre and Post Tests

Week VI, Quarter I
CommonCoreState Standards
The Students Will:
G.CO.9Prove 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 arecongruent; points on a perpendicular bisector of a line segment are exactly those equidistant from thesegment’s endpoints.
Unit Three: Lines - Parallel/Perpendicular
Proving Lines Parallel (G.CO.9)
Perpendicular Lines (G.CO.9)
Objectives:
The student will be able to:
provethat two lines are parallel or
perpendicular.
identifywhether lines are parallel,
perpendicular, or neither. / Essential Question:
How do you prove that two lines are parallel?
Teacher Resources: / Media and Technology Resources:
Assessments:
Homework/Classwork: To be given daily on each introducedtopic.
Class Discussion: Students will be expected to be prepared for class, participate in class activities andactively engage in class discussion..
Quiz: On concepts involving Parallel and Perpendicular Lines. / Suggested Instructional Practices:
  • Note Taking Skills (guided notes)
  • Exit Tickets
  • Pre and Post Tests

Week VII, Quarter I
CommonCoreState Standards
The Students Will:
G.GPE.5 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 givenpoint).
G.CO.9 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 arecongruent; points on a perpendicular bisector of a line segment are exactly those equidistant from thesegment’s endpoints.
Unit Three: Lines - Parallel/Perpendicular
Slopes and Lines (G.GPE.5, G.CO.9)
Lines in the Coordinate Plane (G.GPE.5, G.CO.9)
Objectives:
The student will be able to:
findthe slope of a line.
identifywhether lines are parallel,
perpendicular, or neither.
write andgraphlines in various forms.
classifylines / Essential Question:
By looking at the equations of two lines, how do you determine whether the lines are parallel, perpendicular, or neither?
Teacher Resources: / Media and Technology Resources:
Assessments:
Homework/Classwork: To be given daily on each introducedtopic.
Class Discussion: Students will be expected to be prepared for class, participate in class activities andactively engage in class discussion..
Test: On concepts involving Parallel and Perpendicular Lines / Suggested Instructional Practices:
  • Note Taking Skills (guided notes)
  • Exit Tickets
  • Pre and Post Tests

Week VIII, Quarter I
CommonCoreState Standards
The Students Will:
Unit
Classifying Triangles
Angle Relationship in Triangles
Objectives:
The student will be able to:
classify triangles by angle and side measures.
use classification to find missing angles and sides.
find interior or exterior angle measures in triangles. / Essential Question:
How can triangles fall into more than one triangle classification?
Teacher Resources: / Media and Technology Resources:
Assessments:
Homework/Classwork: To be given daily on each introducedtopic.
Class Discussion: Students will be expected to be prepared for class, participate in class activities andactively engage in class discussion..
Test: On concepts involving Triangle Basics. / Suggested Instructional Practices:
  • Note Taking Skills (guided notes)
  • Exit Tickets
  • Pre and Post Tests

Week I, Quarter II
CommonCoreState Standards
The Students Will:
G.CO.6Use 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 motionsto decide if they are congruent.
G.CO.7Use 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.8Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition ofcongruence in terms of rigid motions.
Unit Five: Triangle Congruence
Congruent Triangles (G.CO.6, G.CO.7, G.CO.8)
Triangle Congruence (SSS, SAS, ASA, AAS, HL, and CPCTC) (G.CO.6, G.CO.7, G.CO.8)
Objectives:
The student will be able to:
useproperties of congruent triangles.
construct a proof showing two triangles are congruent. *
construct a proof showing triangles congruence and applythatinformation to solve problems. *
applycongruence rules to parts of congruent triangles / Essential Question:
What are the “shortcuts” to prove that two triangles are congruent?
Teacher Resources: / Media and Technology Resources:
Assessments:
Homework/Classwork: To be given daily on each introducedtopic.
Class Discussion: Students will be expected to be prepared for class, participate in class activities andactively engage in class discussion..
Quiz: On concepts involving Triangle Basics and Triangle Congruency. / Suggested Instructional Practices:
  • Note Taking Skills (guided notes)
  • Exit Tickets
  • Pre and Post Tests

Week II, Quarter II
CommonCoreState Standards
The Students Will:
G.CO.8Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
G.CO.10Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of atriangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Unit Five: Triangle Congruence
Triangle Congruence (SSS, SAS, ASA, AAS, HL, and CPCTC) (G.CO.8)
Isosceles and Equilateral Triangle Properties (G.CO.10)
Objectives:
The student will be able to:
provetriangles are congruent and applythatinformation to solve problems. *
applycongruence rules to parts of congruenttriangles.
applyproperties of isosceles and equilateral
triangles.
solveproblems involving isosceles and
equilateral triangles. / Essential Question:
What is the difference between the concepts of equilateral and equiangular triangles?
Teacher Resources: / Media and Technology Resources:
Assessments:
Homework/Classwork: To be given daily on each introducedtopic.
Class Discussion: Students will be expected to be prepared for class, participate in class activities andactively engage in class discussion..
Test: On concepts involving Triangle Basics and Triangle Congruency. / Suggested Instructional Practices:
  • Note Taking Skills (guided notes)
  • Exit Tickets
  • Pre and Post Tests

Week III, Quarter II
CommonCoreState Standards
The Students Will:
G.CO.10Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of atriangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Unit Six: Triangle Properties and Attributes
Perpendicular and Angle Bisectors (G.CO.10)
Bisectors of Triangles (G.CO.10)
Circumcenters and Incenters * (G.CO.10)
Medians and Altitudes of Triangles (G.CO.10)
Centriods and Orthocenters * (G.CO.10)
Objectives:
The student will be able to:
prove andapplytheorems involving
perpendicular bisectors of segments and angle bisectors.
prove andapplyproperties of perpendicular bisector and angle bisectors of triangles.
applyproperties of medians of triangles.
applyproperties of altitudes of triangles.
findand workthe various centers related to triangles. * / Essential Question:
How do you determine the circumcenter, centroid, and the orthocenter of a triangle?
Teacher Resources: / Media and Technology Resources:
Assessments:
Homework/Classwork: To be given daily on each introducedtopic.
Class Discussion: Students will be expected to be prepared for class, participate in class activities andactively engage in class discussion..
Quiz: On concepts involving Triangle Properties and Attributes. / Suggested Instructional Practices:
  • Note Taking Skills (guided notes)
  • Exit Tickets
  • Pre and Post Tests

Week IV, Quarter II
CommonCoreState Standards
The Students Will:
G.SRT.4 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.5Use congruence and similarity criteria for triangles to solve problems and to prove relationships ingeometric figures.
Unit Six: Triangle Properties and Attributes
The Triangle Midsegment Theorem (G.SRT.4)
Inequalities in One Triangle (G.SRT.5)
Inequalities in Two Triangles (G.SRT.5)
Objectives:
The student will be able to:
proveand useproperties of triangle
midsegments.
applyinequalities in one triangle.
applyinequalities in two triangles. / Essential Question:
How do you determine whether three segments can make up the sides of a triangle?
Teacher Resources: / Media and Technology Resources:
Assessments:
Homework/Classwork: To be given daily on each introducedtopic.
Class Discussion: Students will be expected to be prepared for class, participate in class activities andactively engage in class discussion..
Quiz: On concepts involving Triangle Properties and Attributes. / Suggested Instructional Practices:
  • Note Taking Skills (guided notes)
  • Exit Tickets
  • Pre and Post Tests

Week V, Quarter II
CommonCoreState Standards
The Students Will:
G.SRT.4Prove 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.5Use congruence and similarity criteria for triangles to solve problems and to prove relationships ingeometric figures.
Unit Six: Triangle Properties and Attributes
The Pythagorean Theorem (G.SRT.4, G.SRT.5)
Applying Special Right Triangles (G.SRT.4, G.SRT.5)
Objectives:
The student will be able to:
usethe Pythagorean Theorem and its converse to solve various problems.
usethe Pythagorean inequalities to classify
triangles.
applyproperties of 45 45 900 _ _ triangles.
applyproperties of 30 60 900 _ _ triangles. / Essential Question:
How do you determine the classification of triangle using the concept of Pythagorean inequalities?
Teacher Resources: / Media and Technology Resources:
Assessments:
Homework/Classwork: To be given daily on each introducedtopic.
Class Discussion: Students will be expected to be prepared for class, participate in class activities andactively engage in class discussion..
Test: On concepts involving Triangle Properties and Attributes. / Suggested Instructional Practices:
  • Note Taking Skills (guided notes)
  • Exit Tickets
  • Pre and Post Tests

Week VI, Quarter II
CommonCoreState Standards
The Students Will:
G.CO.3Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
G.C.MA.3a Derive the formula for the relationship between the number of sides and sums of the interior andsums of the exterior angles of polygons and apply to the solutions of mathematical and contextual problems.
Unit Seven: Properties of Polygons and Quadrilaterals