Unit 6: 2D & 3D 

Objects & Conics

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 6: 2D & 3D Objects & Conics (Up to 30 days)

Two big ideas of this unit are finding the volume of curved objects and using them to model problems and design solutions.  Both standards, G-GMD.3 & G-MG.3, “live” in Claim 4; therefore, context, using mathematics to model the real-world, and solving problems should be the continual focus.  Depth for finding the volume of curved objects includes examining informal arguments for formulas used, scale factors, cross-sections of 3D objects, and rotations of 2D objects.  The final big idea of this unit is deriving the equation of conic sections.  The design team chose deriving the equation of a circle as an essential standard; however, depth can be explored through the supporting standard of deriving the equation of a parabola.  Deriving equations of conic sections can be an interleaving or reengagement of work done in Unit 5, done here if skipped in Unit 5 or if only deriving the equation of a circle was done in Unit 5 it can be extended here to deriving the equation of a parabola.  Time permitting, work with parabolas could be an excuse to reengage with quadratics from Algebra 1 before students move to Algebra 2 after a “year away from Algebra 1,” especially considering potential gaps in learning due to COVID. 

Unit 6 & The Need to Examine Claim 4

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.  While students should still be able to communicate their reasoning, the emphasis of this instruction is Claim 4 Modeling & Data AnalysisStudents should be primarily engaged with SMP #4: Model with Mathematics.  Teachers should devote time to understand Claim 4 for themselves, especially the Assessment Targets, Task Models and Examples.

Vocabulary, Tools & Developmental Notes from SBAC

Claim 4, Modeling and Data Analysis: Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve

problems.

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