Students use the properties of circles to construct and understand different geometric figures, and lay the groundwork for constructing mathematical arguments through proof.
Math
Unit 1
10th Grade
In Unit 1, Constructions, Proof and Rigid Motion, students are introduced to the concept that figures can be created by just using a compass and straightedge using the properties of circles, and by doing so, properties of these figures are revealed. Transformations that preserve angle measure and distance are verified through constructions and practiced on and off the coordinate plane. These rigid motion transformations are introduced through points and line segments in this unit, and provide the foundation for rigid motion and congruence of two-dimensional figures in Unit 2. This unit lays the groundwork for constructing mathematical arguments through proof and use of precise mathematical vocabulary to express relationships.
Unit 1 begins with students identifying important components to define- emphasizing precision of language and notation as well as appropriate use of tools to represent geometric figures. Students are introduced to the concept of a construction, and use the properties of circles to construct basic geometric figures. In Topic B, students formalize understanding developed in middle school geometry of angles around a point, vertical angles, complementary angles, and supplementary angles through organizing statements and reasons for why relationships to construct a viable argument. Topic C merges the concepts of specificity of definitions, constructions, and proof to formalize rigid motions studied in 8th grade. Students learn that rigid motions can be used as a tool to show congruence. Students focus on rigid motions with points, line segments and angles in this unit through transformation both on and off the coordinate plane.
In the next unit, students use the concepts of constructions, proof, and rigid motions to establish congruence with two dimensional figures. Through the establishment of a solid foundation of precise vocabulary and developing arguments in Unit 1, students are able to use these strategies and theorems to identify and describe geometric relationships throughout the rest of the year.
Pacing: 21 instructional days (19 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 1 and should be given on the suggested assessment day or after completing the unit.
Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
Unit-specific Intellectual Prep
"undefined" terms (point, line, plane) | ray | line segment | polygon | collinear |
coplanar | orthocenter | proof | transitive property | supplementary |
rigid motions | translation | reflection | congruent | vector |
corresponding angles | alternate interior angles | auxiliary lines | regular | construction |
equidistant | bisect | perpendicular bisector | altitude | circumcenter |
identity | adjacent angles | complementary | angle/distance preservation | rotation |
corresponding parts | transformation | converse theorems | same side interior angles | alternate exterior angles |
Topic A: Constructions of Basic Geometric Figures
Topic B: Justification and Proof of Angle Measure
Topic C: Translations of Points, Line Segments, and Angles, and Parallel Line Relationships
Topic D: Reflections and Rotations of Points, Line Segments, and Angles
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 2
Congruence in Two Dimensions