Common Core High School Mathematics: Transforming Instructional Practice for a New Era 7.1

Learning Intentions & Success Criteria Learning Intentions: We are learning to deepen our understanding of the Common Core State Standards and the implications for teaching and learning mathematics. Success Criteria: We will be successful when we can describe how the content standards and math practice standards are evident in the implementation of a mathematical task. 7.2

Agenda Homework review and discussion Experimenting with patty paper Reading G-CO.1-8 Being precise with definitions Break Experimenting with GeoGebra Homework and closing remarks 7.3

7.4 Homework Review and Discussion Activity 1: Table Discussion: Discuss your write up for the day 6 math task Equations of Lines: Compare your strategies with others at your table. Reflect on how you might revise your own solution and/or presentation.

7.5 Experimenting with Patty Paper Find at least one way of performing each of the following constructions with patty paper: The perpendicular bisector of a segment The bisector of an angle An isosceles triangle An equilateral triangle Activity 2:

7.6 Experimenting with Patty Paper Draw a generic triangle on a piece of patty paper Find one median of your triangle Find the other two medians Compare with your table partners. Are you prepared to make a conjecture? Activity 2:

7.7 Reading G-CO.1-8 Read these standards from the high school Geometry conceptual category Turn and Talk: How do you see these standards in the activity you have just completed? How are these standards different from (or similar to) the geometry material that appears in your curriculum or textbook? Activity 3:

7.8 Being Precise with Definitions With a partner, develop precise definitions for each of the following geometric objects: angle circle perpendicular line parallel line line segment (Undefined notions: point, line, distance along a line, distance around a circular arc) Activity 4:

7.9 Being Precise with Definitions With a partner, develop precise definitions for each of the following geometric transformations: Rotation reflection Translation (Previously-defined notions: angle, circle, perpendicular line, parallel line, line segment) Activity 4:

Break 7.10

7.11 Experimenting with GeoGebra Find at least one way of performing each of the following constructions with Geogebra: The perpendicular bisector of a segment The bisector of an angle An isosceles triangle An equilateral triangle In each case, explain how you can tell that your construction is correct Activity 5:

7.12 Experimenting with GeoGebra Draw a generic triangle. (How do you know your triangle really is generic?) Construct the three medians of your triangle. Does the result confirm your earlier conjecture? Discuss the advantages and disadvantages of dynamic geometry software as compared to patty paper. Activity 5:

7.13 Experimenting with GeoGebra Play with the transformation tool in GeoGebra, until you feel comfortable carrying out each of the following: Reflecting a figure across a given line Rotating a figure around a given point Translating a figure by a given vector Activity 5:

7.14 Experimenting with GeoGebra Construct two intersecting lines, with a fixed (but arbitrary) angle between them. Reflect a simple figure across one of your lines, then reflect the reflection across your second line. What appears to be the result of performing these two reflections? Repeat with other figures, and other pairs of lines, until you are prepared to make a conjecture. Make your conjecture as precise as you can. Activity 5:

7.15 Experimenting with GeoGebra Repeat the previous activity, but starting with two parallel lines. What appears to be the result of performing two reflections in these parallel lines? Make as precise a conjecture as you can. Activity 5:

Learning Intentions & Success Criteria Learning Intentions: We are learning to deepen our understanding of the Common Core State Standards and the implications for teaching and learning mathematics. Success Criteria: We will be successful when we can describe how the content standards and math practice standards are evident in the implementation of a mathematical task. 7.16

7.17 Homework and Closing Remarks Homework (to be included in journal): Day 7 Math Task: Patty Paper Geometry Open Investigations 9.5 and 9.6 (pp ) Day 7 Class Reflection Reading Notes and Introduction in Michael Serra’s Patty Paper Geometry (pp. vii-x and 1-4) Activity 6: