Honors Geometry Math Instructional Focus Units / 2016/2017 /

Last updated 7/27/2016

Year-At-A-Glance – Honors Geometry

1 / **This document is a living document. Changes/Updates will be made throughout the year.
PLEASE NOTE: Teachers may not have to do EVERY lesson in every chapter based on their assessment of their students up front.
Honors Geometry Math Instructional Focus Units / 2016/2017 /

Last updated 7/27/2016

1 / **This document is a living document. Changes/Updates will be made throughout the year.
PLEASE NOTE: Teachers may not have to do EVERY lesson in every chapter based on their assessment of their students up front.
Honors Geometry Math Instructional Focus Units / 2016/2017 /

Last updated 7/27/2016

Quarter (approximately) / Unit / Chapter(s) / Main Idea / Estimated Time (days)
Q1 / 1 / 1 / Tools for Geometry / 16
2 / 2 / Introduction to Proofs / 12
Q1/Q2 / 3 / 3 / Perimeter and Area / 13
Q2 / 4 / 4 / Three Dimensional Figures / 18
5 / 5 / Properties of Triangles / 7
Q3 / 6 / 6 / Similarity / 7
7 / 7 and 8 / Congruence / 16
8 / 9 / Trigonometry / 11
Q4 / 9 / 10 / Quadrilaterals / 13
10 / 11, 12 and 13 / Circles / 29
Throughout / Cognitive Tutor- Geometry modules / 29

Your feedback on the maps, timeline, and resource is greatly appreciated so changes and supplemental resources (if necessary) can be identified and added to future maps.

Common Core RP Progressions – Use for explanations of standards sequencing, pointing out cognitive difficulties and pedagogical solutions, and providing further detail of mathematical content.

HS Standards Geometry Course Major and Supporting Content Carnegie - Geometry Course Content Map

Focus 1: Tools for Geometry - This focus begins by addressing the building blocks of geometry which are the point, the line, and the plane. Students will construct line segments, midpoints, bisectors, angles, angle bisectors, perpendicular line, parallel lines, polygons, and points of currency. Students review translations as a rigid motion that preservesthe size and shape of segments, angles, and polygons. Students use the coordinate plane and algebra to determine characteristics, lines, segments and points of concurrency.
Big Ideas:
  • G.CO.A Experiment with transformations in the plane
  • G.CO.B Understand congruence in terms of rigid motions
  • G.CO.D Make geometric constructions
  • G.GPE.B Use coordinates to prove simple geometric theorems algebraically

Learning Goal and Scale:
Pre-requisite skills/standards:
  • Understand congruence and similarity using physical models, transparencies, or geometry software (8.G.A)
  • Understand and apply the Pythagorean Theorem (8.G.B)
  • Draw, construct and describe geometrical figures and describe the relationships between them (7.G.A)
  • Understand the connections between proportional relationships, lines, and linear equations. (8.EE.B)
  • Analyze and solve linear equations and pairs of simultaneous linear equations (8.EE.C)

Principal Resource
Carnegie Chapter 1 Tools for Geometry
Standards
G.CO.A.1
G.CO.A.2
G.CO.A.4
G.CO.A.5
G.CO.B.6
G.CO.D.12
G.CO.D.13
/ G.GPE.B.4
G.GPE.B.5
G.GPE.B.6
G.MG.A.1
G.MG.A.3 / Estimated Time
16 days
Focus 2:Introduction to Proofs - This topic focuses on the foundations of proof. Paragraph, two-column, construction, and flow chart proofs are presented. Proofs involving angles and parallel lines are completed.
Big Ideas:
  • G.CO.C Prove geometric theorems
  • G.CO.D Make geometric constructions

Learning Goal and Scale:
Pre-requisite skills/standards:
  • Understand congruence and similarity using physical models, transparencies, or geometry software (8.G.A)
  • Draw, construct and describe geometrical figures and describe the relationships between them (7.G.A)

Principal Resource
Carnegie Chapter 2: Introduction to Proofs
Standards
G.CO.C.9
G.CO.D.12 / Estimated Time
12 days
Focus 3 Perimeter and Area: Students will focus on calculating perimeter and area of figures represented on the coordinate plane, through the use of distance, midpoint, and slope.
Big Ideas:
  • G.GPE.B Use coordinates to prove simple geometric theorems algebraically
  • G.CO.B Understand congruence in terms of rigid motions
  • G.MG.A Apply geometric concepts in modeling situations

Learning Goal and Scale:
Pre-requisite skills/standards:
  • Understand the connections between proportional relationships, lines, and linear equations. (8.EE.B)
  • Understand congruence and similarity using physical models, transparencies, or geometry software (8.G.A)
  • Point-slope form

Principal Resource
Carnegie Chapter 3 Perimeter and Area of Geometric Figures on the Coordinate Grid
1 / **This document is a living document. Changes/Updates will be made throughout the year.
PLEASE NOTE: Teachers may not have to do EVERY lesson in every chapter based on their assessment of their students up front.
Honors Geometry Math Instructional Focus Units / 2016/2017 /

Last updated 7/27/2016

Standards
G.CO.B.6
G.GPE.B.4
G.GPE.B.5
G.GPE.B.7
G.MG.A.1
G.MG.A.2
G.MG.A.3 / Estimated Time
13 days
Focus 4: Three Dimensional Figures- This topic focuses on three-dimensional figures, beginning with rotating and stacking two-dimensional figures to create three-dimensional solids. Cavalieri’s principle is presented and is used to derive the formulas for a volume of a cone, pyramid, and sphere. The focus culminates with the topicsof cross sections and diagonals in three dimensions.
Big Ideas:
  • G.GMD.A Explain volume formulas and use them to solve problems
  • G.GMD.B Visualize relationships between two-dimensional and three-dimensional objects
  • G.MG.A Apply geometric concepts in modeling situations

Learning Goal and Scale:
Pre-requisite skills/standards:
  • Draw, construct and describe geometrical figures and describe the relationships between them (7.G.A)
  • Solve real‐life and mathematical problems involving angle measure, area, surface area, and volume (7.G.B)
  • Solve real‐world and mathematical problems involving volume of cylinders, cones and spheres (8.G.C)

Principal Resource
Carnegie Chapter 4 Three-Dimensional Figures
Standards
G.GMD.A.1
G.GMD.A.2 (+)
G.GMD.A.3
G.GMD.B.4
G.MG.A.1
G.MG.A.3 / Estimated Time
18 days
Focus 5 Properties of Triangles: Students focus on properties of triangles, beginning with classifying triangles on the coordinate plane. Theorems involving angles and side lengths of triangles are presented. Properties and theorems of 45º-45º-90º triangles and 30º-60º-90º triangles are introduced.
Big Ideas:
  • G.GPE.B Use coordinates to prove simple geometric theorems algebraically
  • G.CO.C Prove geometric theorems
  • G.CO.D Make geometric constructions
  • G.SRT.A Understand similarity in terms of similarity transformations
  • G.SRT.B Prove theorems using similarity

Learning Goal and Scale:
Pre-requisite skills/standards:
  • Understand the connections between proportional relationships, lines, and linear equations. (8.EE.B)
  • Understand congruence and similarity using physical models, transparencies, or geometry software (8.G.A)
  • Draw, construct and describe geometrical figures and describe the relationships between them (7.G.A)
  • Understand and apply the Pythagorean Theorem (8.G.B)
  • Point-slope form

Principal Resource
Carnegie Chapter 5 Properties of Triangles
Standards
G.GPE.B.5
G.CO.C.10
G.CO.D.12
G.MG.A.1 / Estimated Time
7 days
Focus 6 Similarity: Similar triangles are addressed and students will establish similar triangle theorems as well as theorems about proportionality. The topic leads student exploration of the conditions for triangle similarity and opportunities for applications of similar triangles.
Big Ideas:
  • G.GPE.B Use coordinates to prove simple geometric theorems algebraically
  • G.CO.C Prove geometric theorems
  • G.CO.D Make geometric constructions
  • G.SRT.A Understand similarity in terms of similarity transformations
  • G.SRT.B Prove theorems using similarity

Learning Goal and Scale:
Pre-requisite skills/standards:
  • Understand the connections between proportional relationships, lines, and linear equations. (8.EE.B)
  • Understand congruence and similarity using physical models, transparencies, or geometry software (8.G.A)
  • Draw, construct and describe geometrical figures and describe the relationships between them (7.G.A)
  • Understand and apply the Pythagorean Theorem (8.G.B)
  • Point-slope form

Principal Resource
Carnegie Chapter 6 Similarity through Transformations
**Skip 6.5 lesson, but can be used to teach converse.
Standards
G.SRT.A.1.a
G.SRT.A.1.b
G.SRT.A.2
G.SRT.A.3
G.SRT.B.4
G.SRT.B.5
G.GPE.B.7
G.MG.A.1 / Estimated Time
7 days
**Use Carnegie Learning Course 3- Chapter 7 lessons as needed for review of dilations- 1 day maximum
Focus 7: Congruence-This topic focuses on proving triangle congruence theorems and using the theorems to determine whether triangles are congruent.Triangle congruence is covered, including right triangle and isosceles triangle congruence theorems. Students are given opportunities to explore the congruence of corresponding parts of congruent triangles as well as continuing work with proof, introducing indirect proof, or proof bycontradiction. Throughout, students apply congruence theorems to solve problems.
Big Ideas:
  • G.CO.A Experiment with transformations in the plane
  • G.CO.B Understand congruence in terms of rigid motions
  • G.CO.C Prove geometric theorems
  • G.CO.D Make geometric constructions

Learning Goal and Scale:
Pre-requisite skills/standards:
  • Draw, construct and describe geometrical figures and describe the relationships between them (7.G.A)
  • Understand congruence and similarity using physical models, transparencies, or geometry software (8.G.A)

Principal Resource
Carnegie Chapter 7 Congruence through Transformations
Geometry for Enjoyment and Challenge- Chapter 3.2-3.7- Use in conjunction with Carnegie Chapter 7, and Carnegie 8.1, 8.2 for homework and supplemental lessons, as needed / Principal Resource
Carnegie Chapter 8 Using Congruence Theorems
Geometry for Enjoyment and Challenge- Chapter 3.2-3.7- Use in conjunction with Carnegie Chapter 7, and Carnegie 8.1, 8.2 for homework and supplemental lessons, as needed
Chapter 3.3-3.4 Problem supplements for CPCTC
Chapter 3.6-3.7 Problem supplements for Angle-Side Theorems
Chapter 4.4 Problem supplements for Equidistance Theorems
Standards
G.CO.A.2
G.CO.A.3
G.CO.A.5
G.CO.B.6
G.CO.B.7
G.CO.B.8
G.CO.C.9
G.CO.C.10
G.CO.D.12 / Estimated Time
11 days / Standards
G.CO.B.6
G.CO.B.7
G.CO.B.8
G.CO.C.10
G.CO.D.12
G.MG.A.1 / Estimated Time
8 days
Focus 8: Trigonometry- This topic introduces students to trigonometric ratios using right triangles. Students discover and analyze these ratios and solve application problems using them. Students also explore the reciprocals of the basic trigonometric ratios sine, cosine, and tangent, along with theirinverses to determine unknown angle measures. Deriving the Law of Sines and the Law of Cosines extends students’ understanding of trigonometry to apply to all triangles.
Big Ideas:
  • G.SRT.A Understand similarity in terms of similarity transformations
  • G.SRT.B Prove theorems using similarity
  • G.SRT.C Define trigonometric ratios and solve problems involving right triangles

Learning Goal and Scale:
Pre-requisite skills/standards:
  • Understand congruence and similarity using physical models, transparencies, or geometry software (8.G.A)
  • Understand and apply the Pythagorean Theorem (8.G.B)
  • Slope and distance formula

Principal Resource
Carnegie Chapter 9 Trigonometry
Carnegie Chapter 9.6 Student Assignments for additional word problems
Carnegie Chapter 9.6 Student Skills Practice for additional practice
Standards
G.SRT.A.3
G.SRT.B.5
G.SRT.C.6
G.SRT.C.7
G.SRT.C.8
G.MG.A.1
G.SRT.D.9 (+)
G.SRT.D.10 (+)
G.SRT.D.11 (+) / Estimated Time
11 days
Focus 9: Quadrilaterals- Focus is on properties of squares, rectangles, parallelograms, rhombi, kites, and trapezoids. The sum of interior and exterior angles of polygons is also included.
Big Ideas:
  • G.CO.C Prove geometric theorems
  • G.CO.D Make geometric constructions
  • G.SRT.C Define trigonometric ratios and solve problems involving right triangles
  • G.GPE.B Use coordinates to prove simple geometric theorems algebraically

Learning Goal and Scale:
Pre-requisite skills/standards:
  • Draw, construct and describe geometrical figures and describe the relationships between them (7.G.A)
  • Understand congruence and similarity using physical models, transparencies, or geometry software (8.G.A)
  • Understand and apply the Pythagorean Theorem (8.G.B)

Principal Resource
Carnegie Chapter 10 Quadrilaterals
Carnegie Chapter 10.7 Student Assignments for additional practice
Standards
G.CO.C.9
G.CO.C.11
G.CO.D.12
G.CO.D.13 / G.SRT.C.8
G.GPE.B.4
G.GPE.B.5
G.MG.A.1 / Estimated Time
13 days
Focus 10: Circles- This unit reviews information about circles, and then focuses on angles and arcs related to a circle, chords, and tangents. Several theorems related to circles are proven throughout the topic. Students will explore inscribed and circumscribed polygons as well as circles. Students determine relationships between central angles, arcs, arc lengths, areas of parts of circles, as well as linear velocity and angular velocity. Students will also explores circles, polygons, and parabolas on the coordinate plane. Key characteristics are used to write equations for these geometric figures.
Big Ideas:
  • G.CO.A Experiment with transformations in the plane
  • G.C.A Understand apply theorems about circles
  • G.GPE.B Use coordinates to prove simple geometric theorems algebraically
  • G.GPE.A Translate between the geometric descriptions and the equation of a conic section
  • G.SRT.C Define trigonometric rations and solve problems involving right triangles

Learning Goal and Scale:
Pre-requisite skills/standards:
  • Understand congruence and similarity using physical models, transparencies, or geometry software (8.G.A)
  • Solve real‐life and mathematical problems involving angle measure, area, surface area, and volume (7.G.B)
  • Understand and apply the Pythagorean Theorem (8.G.B)
  • Understand the connections between proportional relationships, lines, and linear equations. (8.EE.B)
  • Solve quadratic equations and inequalities in one variable (A-REI.B.4)

Principal Resource
Carnegie Chapter 11 Circles / Principal Resource
Carnegie Chapter 12 Arcs and Sectors of Circles / Principal Resource
Carnegie Chapter 13 Circles and Parabolas
***Recommended extension- add teacher created materials for graphing non-linear systems of inequalities
Standards
G.CO.A.1
G.C.A.1
G.C.A.2
G.C.A.4 (+)
G.MG.A.1 / Estimated Time
10 days / Standards
G.C.A.2
G.C.A.3
G.C.A.5
G.MG.A.1
G.MG.A.3 / Estimated Time
8 days / Standards
G.GPE.A.1
G.GPE.B.4
G.GPE.B.5
G.SRT.C.8
G.MG.A.1 / Estimated Time
11 days
1 / **This document is a living document. Changes/Updates will be made throughout the year.
PLEASE NOTE: Teachers may not have to do EVERY lesson in every chapter based on their assessment of their students up front.