### Grades 9-12: Geometry - Company Logo

Rating:

http://schools.nyc.gov/NR/rdonlyres/49162FEC-37E2-4A96-93C1-6671664FACD5/0/NYCDOEHSMathCompanyLogo_Final.pdf

#### Common Core Standards

Content Standards

HSG.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

HSG.CO.6* Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

HSG.CO.7* Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

HSG.CO.9* Prove theorems about lines and angles.

Standards for Mathematical Practice

MP.1     Make sense of problems and persevere in solving them.

MP.3    Construct viable arguments and critique the reasoning of others.

MP.6    Attend to precision.

#### Description of Unit

The unit titled "Geometry - Company Logo"  is designed to last 3-4 weeks and uses investigation of rigid motion and geometric theorems to teach students how to verify congruence of plane figures and use the implications of congruence to solve problems and create proofs about geometric relationships. The Company Logo task asks students to visualize geometric shapes, identify plane figures and their attributes, prove triangles are congruent, determine the area of quadrilaterals, make geometric conjectures and justify geometric arguments.

#### Cautions

Connecticut teachers should be cautioned that the duration of the unit makes it difficult to go in depth. The application of this performance task also lacks rigor. The additional examples to address the needs of ELL and SPED students should be integrated into each lesson and not a list of examples at the end of the unit.  Not all lessons are fully developed and it is not clear how instruction should be developed from assessment results.

#### Rationale for Selection

This task is useful primarily due to the fact that its alignment with letter and spirit of CCSSM is excellent. The content was focused on the key concepts of rigid motion and proofs, but seems to give students the opportunity to develop skills and make connections within and outside of mathematics. There is an effective use of links to the internet to explore key concepts and skills with the use of geometry software and electronic calculators.  Examples of instructional activities, including a formative assessment lesson, are included.  Common misconceptions are identified and suggested teacher responses are included. As the entire unit seems to be organized around assessment, the unit project “Company Logo” is relevant and open-ended that allows students to construct their understanding of the critical content.  It contains aligned rubrics and annotated student work samples.