02.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP SCHOOL YEAR SESSION 2 30 SEPTEMBER 2015 BUT WHAT IF MY YARD IS MORE OF A RECTANGLE?

02.2 TODAY’S AGENDA  The Scaling Property for Area (Eureka Math TM G10 M3 L3)  “Big Ideas” discussion  Pre-observation tool  Modeling mentoring conversations  Break  Modeling mentoring conversations  Exploring the PRIME document  Homework and closing remarks

02.3 ACTIVITY 1 THE SCALING PROPERTY FOR AREA EUREKA MATH TM GRADE 10 MODULE 3 LESSON 3

02.4 ACTIVITY 1 THE SCALING PROPERTY FOR AREA Warm-up:  How many square feet in a square yard?

02.5 ACTIVITY 1 THE SCALING PROPERTY FOR AREA Turn and talk:  What is “area”?

02.6 ACTIVITY 1 THE SCALING PROPERTY FOR AREA How did we find the areas of figures like these?

02.7 ACTIVITY 1 THE SCALING PROPERTY FOR AREA Properties of Area:  “Moving property”: the area of a shape is not changed under a rigid motion. (Congruent shapes have equal areas.)  “Combining property”: the total area of two (or more) non- overlapping shapes is equal to the sum of their areas.

02.8 ACTIVITY 1 THE SCALING PROPERTY FOR AREA How would you find the area of this figure?

02.9 ACTIVITY 1 THE SCALING PROPERTY FOR AREA Lesson goals  To understand how a similarity transformation with scale factor r affects the area of a planar region  To understand the effect how scaling by factors of a and b in perpendicular directions affects the area of a planar region

02.10 ACTIVITY 1 THE SCALING PROPERTY FOR AREA Turn and talk:  What is a similarity transformation?  What do we mean when we say that one figure or region is similar to another?

02.11 ACTIVITY 1 THE SCALING PROPERTY FOR AREA  Complete the Exploratory Challenge, then discuss your results at your table.  Each person should complete one part of this activity, but make sure all 4 parts are done at each table  Make a conjecture, based on your results, as to what happens to the area of a planar region under a similarity transformation with scale factor r (where r could be any positive number)

02.12 ACTIVITY 1 THE SCALING PROPERTY FOR AREA Conjecture:  When a planar region is transformed by a similarity transformation with scale factor r, the area is multiplied by r 2  How could we prove our conjecture?

02.13 ACTIVITY 1 THE SCALING PROPERTY FOR AREA The Scaling Principle for Area:  If similar figures A and B are related by a scale factor r, their respective areas are related by a factor of r 2

02.14 ACTIVITY 1 THE SCALING PROPERTY FOR AREA  How many square feet in a square yard?  Use the ideas you have learned so far in this lesson to explain your answer.

02.15 ACTIVITY 1 THE SCALING PROPERTY FOR AREA Lesson goals  To understand how a similarity transformation with scale factor r affects the area of a planar region  To understand the effect how scaling by factors of a and b in perpendicular directions affects the area of a planar region

02.16 ACTIVITY 1 THE SCALING PROPERTY FOR AREA What is happening in this sequence of images?

02.17 ACTIVITY 1 THE SCALING PROPERTY FOR AREA Generalization: When a figure is scaled by factors a and b in two perpendicular directions, then its area is multiplied by a factor of ab

02.18 ACTIVITY 1 THE SCALING PROPERTY FOR AREA Generalization: When a figure is scaled by factors a and b in two perpendicular directions, then its area is multiplied by a factor of ab

02.19 ACTIVITY 1 THE SCALING PROPERTY FOR AREA Lesson goals  To understand how a similarity transformation with scale factor r affects the area of a planar region  To understand the effect how scaling by factors of a and b in perpendicular directions affects the area of a planar region

02.20 ACTIVITY 2 “BIG IDEAS” DISCUSSION FROM NCTM ESSENTIAL UNDERSTANDINGS FOR GEOMETRY GRADES 9-12

02.21 ACTIVITY 2 “BIG IDEAS” DISCUSSION  Consider the four Big Ideas and the Essential Understandings for Geometry.  What aspects of the Big Ideas and Essential Understandings did you see in the lesson? Cite specific evidence to back up your claim.

02.22 ACTIVITY 3 PRE-OBSERVATION TOOL

02.23 ACTIVITY 3 PRE-OBSERVATION TOOL Content Standards and Mathematics GoalsBig Ideas Standards for Mathematical PracticeMathematics Teaching Practices Record briefly how the lesson will address each of these areas.

02.24 ACTIVITY 4 MODELING MENTORING CONVERSATIONS

02.25 ACTIVITY 4 MODELING MENTORING CONVERSATIONS  Five phases of an instructional conference:  Launching  Reflecting  Reinforcing  Refining  Reflecting

Break

02.27 ACTIVITY 4 MODELING MENTORING CONVERSATIONS  Five phases of an instructional conference:  Launching  Reflecting  Reinforcing  Refining  Reflecting

02.28 ACTIVITY 5 THE PRIME FRAMEWORK

02.29 ACTIVITY 5 THE PRIME FRAMEWORK  Analysis of Leadership  Directions: Select one of the following scenarios. Brainstorm how a leader would address the challenges connected to the scenario. After brainstorming, summarize how you think an instructional leader would address the challenges connected to the scenario.

02.30 ACTIVITY 5 THE PRIME FRAMEWORK Four aspects of the PRIME Framework  Teaching and Learning  Equity  Assessment  Curriculum

02.31 ACTIVITY 5 THE PRIME FRAMEWORK  Principles (4)  Indicators (3 per Principle)  Stages (3 per Indicator)  Stage 1: Leadership of Self  Stage 2: Leadership of Others  Stage 3: Leadership of Community See pages Questions to Discuss:  In what ways does the framework help you describe the leadership work that you currently do?  In what ways does the framework help you identify ways in which you could expand your leadership?  What challenges and questions does the framework raise for you?

02.32  Read the overview of each Principle in the PRIME Framework, pp , , 34-35,  Read the three indicators and stages of the Principle that most applies to your leadership project.  Complete the Leadership Project Proposal and send it to the team. ACTIVITY 6 HOMEWORK AND CLOSING REMARKS