Big Ideas Geometry Chapters 1-3
August – October (8 weeks); 1st Semester
Embedded Files
Chapter Title(s):
Basics of Geometry (Chapter 1)
Reasoning and Proofs (Chapter 2)
Parallel and Perpendicular Lines (Chapter 3)
Prepared Graduates:
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning.
Standard(s):
4. Geometry
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
HS.G-CO.A. Congruence: Experiment with transformations in the plane.
State precise definitions of angle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line. (CCSS: HS.G-CO.A.1)
HS.G-CO.C. Congruence: 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. (CCSS∘: HS.G-CO.C.9)
HS.G-CO.D. Congruence: 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. (CCSS: HS.G-CO.D.12)
HS.G-GPE.B. Expressing Geometric Properties with Equations: 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). (CCSS: HS.G-GPE.B.5)
Find the point on a directed line segment between two given points that partitions the segment in a given ratio. (CCSS: HS.G-GPE.B.6)
Use coordinates and the distance formula to compute perimeters of polygons and areas of triangles and rectangles.⭑ (CCSS: HS.G-GPE.B.7)
A star symbol (⭑) represents grade level expectations and evidence outcomes that make up a mathematical modeling standards category.
Additional Colorado Academic Standards Resources:
Please visit the complete 2020 Colorado Academic Standards for High School Mathematics to view the following:
Colorado Essential Skills and Mathematical Practices connections
Inquiry Questions
Coherence Connections
Prior Knowledge Connections:
Establish facts about the angle sum of triangles and angles created when parallel lines are cut by a transversal (Grade 8)
Supplementary, complementary, vertical, and adjacent angles (Grade 7)
Academic Vocabulary & Language Expectations:
Undefined terms, point, line, plane, collinear points, coplanar points, defined terms, line segment, segment, endpoints, ray, opposite rays, intersection, postulate, axiom, coordinate, distance, construction, congruent segments, between, midpoint, segment bisector, angle, vertex, sides, interior of the angle, exterior of the angle, measure, acute angle, right angle, obtuse angle, straight angle, congruent angles, angle bisector, adjacent angles, complementary angles, supplementary angles, linear pair, vertical angles, conditional statement, if-then form, hypothesis, conclusion, negation, converse, inverse, contrapositive, equivalent statements, perpendicular lines, biconditional statement, truth value, truth table, conjecture, inductive reasoning, counterexample, deductive reasoning, line perpendicular to a plane, proof, two-column proof, theorem, flowchart proof, flow proof, paragraph proof, parallel lines, skew lines, parallel planes, transversal, corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles, distance from a point to a line, perpendicular bisector, directed line segment, perpendicular lines
Assessments:
SAT Suite Educator Question Bank (Content Domains: Algebra, Geometry and Trigonometry)
Instructional Resources & Notes:
Big Ideas Geometry Chapters 1-3
Supplemental Lesson Resources: Chapter 1, Chapter 2, Chapter 3
Additional Modeling Tasks
How Much Water? (References: Completing the Modeling Cycle, Advice on Modeling)
Notes:
Combine lessons within Chapters 1-2 to ensure adequate time is provided for Chapter 3. Chapters 1-2 should be assessed together.
Algebra 1 Review:
In addition to the Review & Refresh exercises included with each Big Ideas Geometry lesson, the following resources can be used for curating frequent, ongoing mixed review exercise sets of key Algebra 1 concepts and skills. These resources focus on linear equations, linear functions, systems of equations & inequalities, exponential functions, quadratic functions, and quadratic equations:
Algebra Warm-Ups for Geometry Teachers (Geoff Krall)
SAT Suite Educator Question Bank (Content Domains: Algebra, Advanced Math)
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