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 Algebra II

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 Algebra 2 • Extend the properties of exponents to rational exponents. • Write expressions in equivalent forms to solve problems. • Understand the relationship between zeros and factors of polynomials. • Build a function that models a relationship between two quantities.

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

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

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

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

15. Analyzing aConstructed Response Assessment

16. Analyzing Assessment Items(Private Think Time) Four assessment items have been provided: • Car Depreciation • Writing a Polynomial • Patterns in Patterns • One Rocket, Three Equations For each assessment item: • solve the assessment item; and • make connections between the standard(s) and the assessment item.

17. 1. Car Depreciation After you purchase a new car, it begins to lose value. As the years pass, more and more value is lost. This process is known as depreciation. • Carmen buys a new car for $24,500. Carmen’s new car loses 14% of its value each year through depreciation. Write a function that can be used to model the value of the car at the end of each year that Carmen owns the car. Justify your equation mathematically. • After Carmen buys the car, he adds an audio and speaker system worth $500. The audio system loses 15% of its value the minute it is installed into the car, and 7% of the remaining value each year through depreciation. Write a function that can be used to model the value of the car with the audio system and speakers at the end of each year that Carmen owns the car.

18. 2. Writing a Polynomial • Lisa claims that, since the point (0, 6) is on the graph, (x – 6) is a factor of this polynomial. Explain why you agree or disagree with Lisa’s claim. Identify all the zeroes of the function and use that information in your explanation. • Suppose a = . Write a function in factored form to represent this graph. Justify your equation mathematically. Recall that polynomial functions with only real number zeros can be written in factored form as follows: where each zn represents some real root of the function, and each pnis a whole number exponent greater than or equal to 1. Consider the graph of the polynomial function below.

19. 3. Patterns in Patterns Laura creates a design of circles embedded in each other for a poster. The largest circle has a diameter of 28 inches, and each successive circle has a diameter of the previous circle. • Write a function that can be used to determine the diameter of any circle drawn in the poster in this way. Explain the meaning of each term in your expression in the context of the problem. • Laura eventually draws 10 circles. Write and use a formula for the sum of a series to find the sum of the circumferences of the 10 circles, accurate to two decimal places. Show your work. 28 inches

20. 4. One Rocket, Three Equations • For his science project, Grady designs and launches a model rocket from the rooftop of an empty building. He places a sensor on the rocket to provide him with data about the height of the rocket (from ground level in feet) over time (in seconds) during the flight. • From the data returned by the sensor, Grady was able to write and graph a function modeling the height of the rocket over time. • Rewrite the function in vertex form. Then describe what this form of the function reveals in the context of the situation. • Rewrite the function by factoring completely. Then describe what this form of the function reveals in the context of the situation.

21. Discussing Content Standards (Small Group Time) For each assessment item: With your small group, find evidence in tasks 2 and 4 for the content standard(s) that will be assessed.

22. 2. Writing a Polynomial Common Core State Standards, 2010

23. 4. One Rocket, Three Equations 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 “Missing Function Task” and be prepared to talk about the task and the CCSSM Content and Practice Standards associated with it.