Regional Integrated Geometry Curriculum

Regional Integrated Geometry Curriculum

UNIT: Constructions Time frame for unit: 3 days

TOPIC: Angle Bisector Time frame for topic:.5 days

Prior Knowledge
8.G.0Construct the following, using a straight edge and compass: Segment congruent to a segment
Angle congruent to an angle
Perpendicular bisector
Angle bisector
Content Strands
G.G.17 Construct a bisector of a given angle, using a straightedge and compass, and justify the construction.
Concepts

Angle Bisector
Congruence
Radii
Angle
Triangle (CPCTC)
Measurement
Tools of construction and their use
Protractor (validating conjectures)

Essential Questions
What is an angle bisector?
How do you know that an angle has been bisected?
How do you use a compass and straightedge to construct an angle bisector?
Process/skills
G.PS.8 Determine information required to solve a problem, choose methods for obtaining the information, and define parameters for acceptable solutions.
G.RP.1 Recognize that mathematical ideas can be supported by a variety of strategies.
G.CM.2Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, and diagrams.
G.CN.4Understand how concepts, procedures, and mathematical results in one area of mathematics can be used to solve problems in other areas of mathematics.
G.R.3 Use representation as a tool for exploring and understanding mathematical ideas.
Vocabulary
Acute
Angle
Arc / Bisect
Compass
Congruent Angles
Construct / Obtuse
Radii
Rays
Vertex
Suggested assessments

Pre-assessment
Regents/State exams
Projects
Participation
Q-A Responses
Oral responses
Conversations

On-spot checks of class work
Homework
Observations of students’ work/behaviors
Students’ explanations

Draw a picture
Tests and Quizzes
T/F
Multiple Choice
Written Response
Ticket out the door

See Blackboard for specific Assessments*
Resources

Regional Integrated Geometry Curriculum

UNIT : ConstructionsTime frame for unit: 3 days

TOPIC: Perpendicular BisectorTime frame for topic: .5 days

Prior Knowledge
8.G.0Construct the following, using a straight edge and compass: Segment congruent to a segment
Angle congruent to an angle
Perpendicular bisector
Angle bisector
Content Strands
G.G.18 Construct the perpendicular bisector of a given segment, using a straightedge and compass, and justify the construction.
Concepts

Perpendicular Lines
Bisect
Right Angles
Properties of Isosceles Triangles (Median, Altitude, Angle Bisector to Base)

Measurement
Tools of construction and their use
Protractor (validating conjectures)

Essential Questions
How do you use a compass and straightedge to construct a perpendicular bisector of a segment?
How do you know that you have successfully completed a perpendicular bisector?
Process/skills
G.PS.8 Determine information required to solve a problem, choose methods for obtaining the information, and define parameters for acceptable solutions.
G.RP.1 Recognize that mathematical ideas can be supported by a variety of strategies.
G.CM.2Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, and diagrams.
G.CN.4Understand how concepts, procedures, and mathematical results in one area of mathematics can be used to solve problems in other. areas of mathematics.
G.R.3 Use representation as a tool for exploring and understanding mathematical ideas.
Vocabulary
Adjacent
Altitude
Bisector / Congruent segments
Isosceles
Linear pair
Median
Midpoint / Perpendicular
Right angles
Supplementary angles
Suggested assessments

Pre-assessment
Regents/State exams
Projects
Participation
Q-A Responses
Oral responses
Conversations

On-spot checks of class work
Homework
Observations of students’ work/behaviors
Students’ explanations

Draw a picture
Tests and Quizzes
T/F
Multiple Choice
Written Response
Ticket out the door

See Blackboard for specific Assessments*
Resources

Regional Integrated Geometry Curriculum

UNIT:ConstructionsTime frame for unit: 3 days

TOPIC: Parallel or perpendicular linesTime frame for topic: .5 days

through a given point

Prior Knowledge
8.G.0Construct the following, using a straight edge and compass: Segment congruent to a segment
Angle congruent to an angle
Perpendicular bisector
Angle bisector
Content Strands
G.G.19 Construct lines parallel (or perpendicular) to a given line through a given point, using a straightedge and compass, and justify the construction.
Concepts

2 points determine a unique line
Method of proving lines parallel
Copy an angle (construct congruent angles)
If alternate interior angles are congruent, then the lines are parallel.
Construct lines perpendicular using:
Point on the line
Point NOT on the line

Essential Questions
Why is it important to compare and contrast parallel and perpendicular lines?
How do you use the concept of congruent alternate interior angles to construct parallel lines?
Process/skills
G.PS.8 Determine information required to solve a problem, choose methods for obtaining the information, and define parameters for acceptable solutions.
G.RP.1 Recognize that mathematical ideas can be supported by a variety of strategies.
G.CM.2Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, and diagrams.
G.CN.4Understand how concepts, procedures, and mathematical results in one area of mathematics can be used to solve problems in other. areas of mathematics.
G.R.3 Use representation as a tool for exploring and understanding mathematical ideas.
Vocabulary
Alternate Exterior angles
Alternate Interior angles
Altitude
Corresponding angles / Isosceles
Linear Pair
Parallel
Perpendicular / Right angle
Supplementary
Transversal
Vertical Angles
Suggested assessments

Pre-assessment
Regents/State exams
Projects
Participation
Q-A Responses
Oral responses
Conversations

On-spot checks of class work
Homework
Observations of students’ work/behaviors
Students’ explanations

Draw a picture
Tests and Quizzes
T/F
Multiple Choice
Written Response
Ticket out the door

See Blackboard for specific Assessments*
Resources

Regional Integrated Geometry Curriculum

UNIT : ConstructionsTime frame for unit: 3 days

TOPIC: Equilateral TrianglesTime frame for topic:.5 days

Interior angle sum of a triangle
Types of triangles
Radii of the same circle are congruent
Equilateral vs. equiangular

Essential Questions
How do you use a compass and straightedge to construct an equilateral triangle?
Why is an equilateral triangle a regular polygon?
Process/skills
G.PS.8 Determine information required to solve a problem, choose methods for obtaining the information, and define parameters for acceptable solutions.
G.RP.1 Recognize that mathematical ideas can be supported by a variety of strategies.
G.CM.2Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, and diagrams.
G.CN.4Understand how concepts, procedures, and mathematical results in one area of mathematics can be used to solve problems in other. areas of mathematics.
G.R.3 Use representation as a tool for exploring and understanding mathematical ideas.
Vocabulary
Congruent
Equiangular
Equilateral / Interior angles
Isosceles
Regular Polygon / Right
Scalene
Vertex
Suggested assessments

Pre-assessment
Regents/State exams
Projects
Participation
Q-A Responses
Oral responses
Conversations

On-spot checks of class work
Homework
Observations of students’ work/behaviors
Students’ explanations

Draw a picture
Tests and Quizzes
T/F
Multiple Choice
Written Response
Ticket out the door

See Blackboard for specific Assessments*
Resources

Regional Integrated Geometry Curriculum

UNIT: LocusTime frame for unit: 7 days

TOPIC: Centers Related to a TriangleTime frame for topic:3 days

Prior Knowledge
8.G.0Construct the following, using a straight edge and compass: Segment congruent to a segment
Angle congruent to an angle Perpendicular bisector
Angle bisector
Content Strands
G.G.21 Investigate and apply the concurrence of medians, altitudes, angle bisectors, and perpendicular bisectors of triangles.
G.G.43 Investigate, justify, and apply theorems about the centroid of a triangle, dividing each median into segments whose lengths are in the ratio 2:1
Concepts

Complete appropriate constructions to locate the:
Incenter (angle bisectors)
Centroid (medians)
Orthocenter (altitudes)
Circumcenter (perpendicular bisectors)
Identify Euler’s line (optional)

Essential Questions
Which of the four centers always remain inside the triangle?
How does the type of triangle affect the location of each type of center?
Process/skills
G.PS.4 Construct various types of reasoning, arguments, justifications and methods of proof for problems.
G.RP.3 Investigate and evaluate conjectures in mathematical terms, using mathematical strategies to reach a conclusion.
G.CM.11 Understand and use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and geometric diagrams.
G.CN.2 Understand the corresponding procedures for similar problems or mathematical concepts.
G.R.1 Use physical objects, diagrams, charts, tables, graphs, symbols, equations, or objects created using technology as representations of mathematical concepts.
Vocabulary
Altitude
Angle bisector
Centroid
Circumcenter
Circumscribed
Collinear / Concurrent
Euler Line
Exterior
Incenter
Inscribed
Interior / Locus
Median
Midpoint
Orthocenter
Perpendicular bisector
Vertex
Suggested assessments

Pre-assessment
Regents/State exams
Projects
Participation
Q-A Responses
Oral responses
Conversations

On-spot checks of class work
Homework
Observations of students’ work/behaviors
Students’ explanations

Draw a picture
Tests and Quizzes
T/F
Multiple Choice
Written Response
Ticket out the door

See Blackboard for specific Assessments*
Resources

Regional Integrated Geometry Curriculum

UNIT : LocusTime frame for unit: 7 days

TOPIC: Compound LociTime frame for topic:3 days

5 Fundamental Loci
Given distance from a point
Equidistant from 2 points
Given distance from a line
Equidistant from 2 parallel lines
Equidistant from 2 intersecting lines
Solve problems involving 2 or more fundamental loci, including centers of triangles (G.G.21).

Essential Questions
How can each of the 5 fundamental loci be applied to a real world context?
Process/skills
G.PS.4 Construct various types of reasoning, arguments, justifications and methods of proof for problems.
G.RP.3 Investigate and evaluate conjectures in mathematical terms, using mathematical strategies to reach a conclusion.
G.CM.11 Understand and use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and geometric diagrams.
G.CN.2 Understand the corresponding procedures for similar problems or mathematical concepts.
G.R.1 Use physical objects, diagrams, charts, tables, graphs, symbols, equations, or objects created using technology as representations of mathematical concepts.
Vocabulary
Abscissa
Altitude
Angle bisector
Centroid
Circumcenter
Circumscribed / Inscribed
Interior
Intersections
Median
Midpoint
Ordinate / Orthocenter
Parallel
Perpendicular
Perpendicular bisector
Vertex
Suggested assessments

Pre-assessment
Regents/State exams
Projects
Participation
Q-A Responses
Oral responses
Conversations

On-spot checks of class work
Homework
Observations of students’ work/behaviors
Students’ explanations

Draw a picture
Tests and Quizzes
T/F
Multiple Choice
Written Response
Ticket out the door

See Blackboard for specific Assessments*
Resources