Welcome to TNCore Training!

1. Welcome to TNCore Training! Introduction of 2013 CCSS Training Tennessee Department of Education High School Mathematics Geometry

2. What this is / What it is not

3. Core Beliefs

4. Norms • Keep students at the center of focus and decision-making • Be present and engaged – limit distractions, if urgent matters come up, step outside • Monitor air time and share your voice - you’ll know which applies to you! • Challenge with respect – disagreement can be healthy, respect all intentions • Be solutions oriented – for the good of the group, look for the possible • Risk productive struggle - this is safe space to get out of your comfort zone • Balance urgency and patience - we need to see dramatic change and change will happen over time • Any other norms desired to facilitate your learning?

5. Emily Barton Video

6. Supporting Rigorous Mathematics Teaching and Learning Deepening Our Understanding of CCSS Via A Constructed Response Assessment Tennessee Department of Education High School Mathematics Geometry

7. Session Goals Participants will: • deepen understanding of the Common Core State Standards (CCSS) for Mathematical Practice and Mathematical Content; • understand how Constructed Response Assessments (CRAs) assess the CCSS for both Mathematical Content and Practice; and • understand the ways in which CRAs assess students’ conceptual understanding.

8. Overview of Activities Participants will: • analyze Constructed Response Assessments (CRAs) in order to determine the way the assessments are assessing the CCSSM; • analyze and discuss the CCSS for Mathematical Content and Mathematical Practice; • discuss the CCSS related to the tasks and the implications for instruction and learning.

9. The Common Core State Standards The standards consist of: • The CCSS for Mathematical Content • The CCSS for Mathematical Practice

10. Tennessee Focus Clusters Geometry • Understand congruence in terms of rigid motions. • Prove geometric theorems. • Define trigonometric ratios and solve problems involving right triangles. • Use coordinates to prove simple geometric theorems algebraically.

11. The CCSS for Mathematical ContentCCSS Conceptual Category – Geometry Common Core State Standards, 2010

12. The CCSS for Mathematical ContentCCSS Conceptual Category – Geometry Common Core State Standards, 2010

13. The CCSS for Mathematical ContentCCSS Conceptual Category – Geometry Common Core State Standards, 2010

14. The CCSS for Mathematical ContentCCSS Conceptual Category – Geometry Common Core State Standards, 2010

15. Analyzing aConstructed Response Assessment

16. Analyzing Assessment Items(Private Think Time) Four assessment items have been provided: • Park City Task • Getting in Shape Task • Lucio’s Ride Task • Congruent Triangles Task For each assessment item: • solve the assessment item; and • make connections between the standard(s) and the assessment item.

17. 1. Park City Task Park City is laid out on a grid like the one below, where each line represents a street in the city, and each unit on the grid represents one mile. Four other streets in the city are represented by , and . • Dionne claims that the figure formed by , , , and is a parallelogram. Do you agree or disagree with Dionne? Use mathematical reasoning to explain why or why not. • Triangle AFE encloses a park located in the city. Describe, in words, two methods that use information in the diagram to determine the area of the park. • Find the exact area of the park.

18. 2. Getting in Shape Task Points A (12, 10), J (16, 18), and Q (28, 12) are plotted on the coordinate plane below. • What are the coordinates of a point M such that the quadrilateral with vertices M, A, J, and Q is a parallelogram, but not a rectangle? • Prove that the quadrilateral with vertices M, A, J and Q is a parallelogram. • Prove that the quadrilateral with vertices M, A, J and Q is not a rectangle. • Determine the perimeter of your parallelogram. .

19. 3. Lucio’sRide • When placed on a grid where each unit represents one mile, State Highway 111 runs along the line x + 3, and State Highway 213 runs along the linex - . • The following locations are represented by points on the grid: • Lucio’s house is located at (3, –1). • His school is located at (–1, –4). • A grocery store is located at (–4, 0). • His friend’s house is located at (0, 3). • Is the quadrilateral formed by connecting the four locations a square? Explain why or why not. Use slopes as part of the explanation. • Lucio is planning to ride his bike ride tomorrow. In the morning, he plans to ride his bike from his house to school. After school, he will ride to the grocery store and then to his friend’s house. Next, he will ride his bike home. The four locations are connected by roads. How far is Lucio planning to ride his bike tomorrow if he plans to take the shortest route? Support your response by showing the calculations used to determine your answer.

20. 4. Congruent Triangles • Locate and label point M on such that it is of the distance from point S to point U. Locate and label point T on such that it is of the distance from point S to point N. Locate and label point Q on such that it is of the distance from point N to point U. • Prove triangles TNQ and QMT are congruent.

21. Discussing Content Standards (Small Group Time) For each assessment item: With your small group, find evidence in tasks 3 and 4 for the content standard(s) that will be assessed.

22. 3. Lucio’s Ride Common Core State Standards, 2010

23. 4. Congruent Triangles Common Core State Standards, 2010

24. David Williams Video

25. Determining the Standards for Mathematical Practice Associated with the Constructed Response Assessment

26. Getting Familiar with the CCSS for Mathematical Practice(Private Think Time) Count off by 8. Each person reads one of the CCSS for Mathematical Practice. Read your assigned Mathematical Practice. Be prepared to share the “gist” of the Mathematical Practice.

27. The CCSS for Mathematical Practice Common Core State Standards for Mathematics, 2010, NGA Center/CCSSO • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

28. Discussing Practice Standards(Small Group Time) Each person has a moment to share important information about his/her assigned Mathematical Practice.

29. Bridge to Practice: Practice Standards Choose the Practice Standards students will have the opportunity to use while solving these tasks we have focused on and find evidence to support them. Using the Assessment to Think About Instruction In order for students to perform well on the CRA, what are the implications for instruction? • What kinds of instructional tasks will need to be used in the classroom? • What will teaching and learning look like and sound like in the classroom? Complete the Instructional Task Work all of the instructional task “Building a New Playground” and be prepared to talk about the task and the CCSSM Content and Practice Standards associated with it.