Unit 3:
Similarity
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 3: Similarity (Up to 20 days)
In the last unit, students used transformations to explore congruence (e.g. translation versus stretch); in this unit, they will use transformations to explore similarity (e.g. stretch versus dilation). Understanding similarity of two figures is the big idea of this unit; understanding dilations can certainly be embedded in this work. Similarity of triangles is another application and chance to go deeper with the concept, which could lead into solving problems and to proving relationships - other big ideas of this unit. Additional depth besides the work with dilations and triangles already stated could include proving theorems about triangles, parallel lines & proportionality, and the Pythagorean Theorem. Visualizing, verifying and using angle and side relationships to solve problems is another chance to explore triangles more deeply. Throughout the unit, students are reminded of and continue to develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Unit 3 & 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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