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Geometry is a way to understand the real world around us by basing arguments on concrete referents, modeling relationships, and applying mathematical principles to understand geometric properties and concepts using objects, drawings, diagrams, and actions.
The Story of Geometry - Unit 5: Circles (Up to 15 days)
As the title suggests, this unit deals with circles; however, students will also revisit constructions (Unit 1) in this new context. Depth in this unit also provides the chance to reengage with similarity (Unit 3) as students prove all circles are similar, the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality. The big ideas of this unit are examining the properties of circles, inscribed constructions, and deriving the equation of a circle. Time permitting, depth can be achieved by extending each concept. The properties of circles can be extended to include tangent lines. Constructions can be extended to inscribed and circumscribed circles of a triangle. Deriving equations can be extended to parabolas and finding the area of a sector.
Unit 5 & The Need to Examine Claim 3
Most of the geometry course is tested in Claim 3, Communicating Reasoning: Students clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Communicating reasoning should have begun in Unit 1, and it should be evident in instruction and assessment throughout this unit also. Students should be primarily engaged with SMP #3: Construct viable arguments and critique the reasoning of others. Teachers should devote time at the beginning of the year to understand Claim 3 for themselves, especially the Assessment Targets, Task Models and Examples.
Vocabulary, Tools & Developmental Notes from SBAC
Claim 3, Communicating Reasoning: Students clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.
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