# Geometry CC PD 2013

### Reflections of Geometry CC Summer PD

## Standards of Mathematical Practices with Teacher Summary's

## Constructions

## Teachers performed constructions with patty paper, a mirra, compass, and Geometers Sketchpad

## Quadrilaterals

## Parallelogram opposite sides congruent & parallel non consecutive angles congruent | ## Rectangle opposite sides congruent & parallel angles congruent since they are all 90 degrees diagonals congruent | ## Square equiangular equlateral diagonals congruent |

## Trapezoid one pair of parallel sides | ## Equilateral Triangle all sides congruent (equilateral) all angles congruent (equiangular) | ## Right Triangle one angle whose measure is 90 degrees |

## Isosceles Triangle at least 2 sides are congruent | ## Right Isosceles Triangle at least 2 sides are congruent and one measure is 90 degrees | ## Kite 2 pairs of consecutive congruent sides 3 pairs of congruent triangles diagonals intersect at right angles non consecutive angles are equal |

## Geometers Sketchpad Investigations

## Triangle Center Investigations

## Word Wall

## Can you create a picture from vocabulary?

## Making Conjectures from Quadrilateral Investigations

## Euler Line Investgations

## Teachers explored the relationships with the various triangle centers

## Coordinate Geometry

## Transformation Geometry Investigating different transformations | ## Reflections Investigating conjectures of relflections | ## Rotations Investigating conjectures of rotations |

Using the Geometry Cognitive Tutor Software, teachers completed the transformations module to improve their skills. http://www.carnegielearning.com/ | ## Greenville Area Map Some great Geometry concepts can utilize maps. Students would be able to apply concepts such as the incenter, circumcenter, distance formula, midpoint formula, equations of lines, ... | ## Map Problems Some problems were discussed such as using maps for finding the perfect location of a trama center, a mall, cell tower, irrigation, ... |

## Greenville Area Map

## Broken Plate Problem Exploring possible solutions | ## Broken Plate Problem Exploring another different solution | ## Mall Problem Finding the best location of a mall using Geometry |

## Compositions of Transformations

## Lessons and Activities

## Lessons Learned

Deepen students thinking with higher order questions.

- What is it?
- How do I find it?
- Why do I care?
- Where is it located?
- Why is it important?
- Show me your evidence.
- How does this connect to what you already know?
- What new questions do you have?
- What is the relationship?
- Is there a ...?
- Is slope important...?
- How many different ways...?
- How did you know?

-Our standards are not a checklist or a to do, but ideas that are to be connected and show relationships.

-Students need to know how to use tools strategically and know there is more than one tool they can use to solve a problem. i.e. patty paper, mirra, compas, technology.

-Technology drives what students can do today. Students are able to explore more now.

-Students are more empowered with tech now more then ever (from beyond the classic setting with just compass and straightedge)

-With tech you can do so much more not just pressing buttons that allows room for discovery.

-You want your students to improve their critical thinking from whenever you get them.

-Teachers complain: "these kids don't think." If you have them a whole year, the following year teacher should see improved thinking and reasoning.

Encourage further thinking with

-I notice...

-I wonder...

-Rigor in Geometry goes way beyond just solving a quadratic equation, instead ask students, "What is the system of equations that defines the quadrilateral?"

-Write the equation of the perpendicular lines for this...

-All students need hands on learning from low math skill level to advanced.