Reflecting on Practice 1 Reflecting on Practice Making

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Reflecting on Practice … 1

Reflecting on Practice … 1

Reflecting on Practice: Making Connections that Support Learning Unit 1, Session 1 2016 Reflecting

Reflecting on Practice: Making Connections that Support Learning Unit 1, Session 1 2016 Reflecting on Practice Park City Mathematics Institute 2

At your table: • What are five connections that link your table group members

At your table: • What are five connections that link your table group members together? Reflecting on Practice Park City Mathematics Institute 3

Grade 6. Geometry: Solve real-world and mathematical problems involving area, surface area and volume

Grade 6. Geometry: Solve real-world and mathematical problems involving area, surface area and volume 1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real world and mathematical problems. Reflecting on Practice Park City Mathematics Institute CCSS 2011 4

Find another triangle that has the same area but is not congruent Reflecting on

Find another triangle that has the same area but is not congruent Reflecting on Practice Park City Mathematics Institute 5

Area of a triangle • What prior knowledge would students need to do this

Area of a triangle • What prior knowledge would students need to do this problem in sixth grade? • What extended learning happens in the rest of middle school and into high school? Reflecting on Practice Park City Mathematics Institute 6

Norms • Make sure everyone has been heard from • Make sure everyone has

Norms • Make sure everyone has been heard from • Make sure everyone has a voice • Not just listening, but valuing each other's opinions Reflecting on Practice Park City Mathematics Institute 10

Decide in which of the grade levels K 2, 3 -5, 6, 7, 8,

Decide in which of the grade levels K 2, 3 -5, 6, 7, 8, 9 -12 the item belongs based on the CCSSM (or typical state standards). When you agree as a table, place it on the appropriate "grade sheet". Reflecting on Practice Park City Mathematics Institute 11

Observing… Having seen other tables, is there anything you would change? Did any of

Observing… Having seen other tables, is there anything you would change? Did any of the pairings surprise you? Reflecting on Practice Park City Mathematics Institute 12

Why is it important to think about where concepts are taught? Reflecting on Practice

Why is it important to think about where concepts are taught? Reflecting on Practice Park City Mathematics Institute 13

Graham Fletcher Identify the point that you think Graham is trying to make. Reflecting

Graham Fletcher Identify the point that you think Graham is trying to make. Reflecting on Practice Park City Mathematics Institute 14

Exit Ticket We're going to ask you to select your top three choices from

Exit Ticket We're going to ask you to select your top three choices from the 6 content areas: – Expressions & Equations – Probability & Statistics – Ratios & Proportional Relationships – Geometry – Number Systems – Functions Reflecting on Practice Park City Mathematics Institute 15

Each group will create a "presentation" related to their content area that includes: •

Each group will create a "presentation" related to their content area that includes: • What is different from current or former practice • How the ideas grow from grade-t 0 -grade beginning in elementary and extending through high school • Any subtle shifts in the ways of thinking about or approaching the content or procedures related to the content • A display or map of your progression. • Anything that surprised you. Reflecting on Practice Park City Mathematics Institute 16

Soooo… 1) Fill out your exit slip. 2) Check your email this afternoon to

Soooo… 1) Fill out your exit slip. 2) Check your email this afternoon to see to which group you’re assigned. 3) Spend some time skimming through your progressions. bit. ly/pcmi 16 progressions 4) Be sure you’ve completed the survey at tinyurl. com/welcometorop (on laptop or phone) Based on the NCTM Principles to Action for Effective Teaching Bring your laptop tomorrow! Reflecting on Practice Park City Mathematics Institute 17

“Independent” Working Groups Grindelwald (check Workbook for table assignment) Research Data course Interlaken Geometry

“Independent” Working Groups Grindelwald (check Workbook for table assignment) Research Data course Interlaken Geometry St. Moritz Statistics Davos Lesson Study Emmental TLP Live Gruyères You. Tube Neuchâtel Reflecting on Practice Park City Mathematics Institute 18

References • Common Core Standards. College and Career Standards for Mathematics 2010). Council of

References • Common Core Standards. College and Career Standards for Mathematics 2010). Council of Chief State School Officers (CCSSO) and (National Governor’s Association (NGA). • Common Core Standards Progressions: (2011). http: //math. arizona. edu/~ime/progressions/ Reflecting on Practice Park City Mathematics Institute 19