Algebra I Professional Development

1. Algebra I Professional Development Quadratics

2. Module 6 Outcome • Participants will experience a rigorous Algebra I concept task

3. CCSS Domains on Quadratics • Algebra - Seeing Structure in Expressions • Algebra – Reasoning with Equations and Inequalities • Functions – Interpreting Functions • Functions – Linear, Quadratic, and Exponential Models

4. CCSS on Quadratics • A-REI.4. Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. • A-SSE.1. Interpret expressions that represent a quantity in terms of its context.★ a. Interpret parts of an expression, such as terms, factors, and coefficients. • A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

5. CCSS on Quadratics • F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. c. Graph polynomial functions, identifying zeros when suitable • F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. 9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. • F–LE.3. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

6. “Bend it Like Beckham”

7. “Bend it Like Beckham” Share, Discuss, and Analyze: • Whose kick went the highest? • Whose kick went the longest? • Be prepared to share your solution with the group

8. “Bend it Like Beckham” Group discussion: How do we make the mathematics accessible to all students? How can the four access strategies: • graphic organizers • cooperative groups • academic language development • instructional conversations be more explicitly embedded in the lesson?

9. Module 7 Outcome • Participants will work with the Thinking Through a Lesson Protocol (TTLP) to plan the implementation of the task in the classroom

10. Thinking Through a Lesson Protocol

11. Thinking Through a Lesson Protocol • How will we set upthe lesson? • How will the students explorethe concept? • How will the students share, discuss, and analyzetheir solutions?

12. Planning for Implementation: Thinking Through a Lesson Protocol Read through the lesson and discuss how the TTLP was used to design it. • What instructional strategies could be added to the lesson that would contribute to increased access for all learners? • EL • SEL • Gifted • SWD

13. Module 8 Outcome • Participants will learn about explicit strategies that foster the development of academic language

14. Compare and Contrast

15. Compare and Contrast How will this activity support the academic language development for your students? What questions can you ask to engage students with this activity?

16. Using the Language of Compare and Contrast

17. Using the Language of Compare and Contrast

18. Using the Language of Compare and Contrast

19. Using the Language of Compare and Contrast How will you use this with your students? What do you need to modify or add? Why is this activity important? When else can you use this activity with future lessons?

20. Module 9 Outcome • Participants will gain an increased understanding of strategies that increase students’ access to core mathematics content

21. Analyzing Quadratic Graphs y is always x squared

22. Analyzing Quadratic Graphs Take the cards out of your envelope and spread them out on your table. Match together the verbal descriptions, tabular representations, graphs, and symbolic representation.

23. Analyzing Quadratic Graphs In a small group, discuss what helped you to identify the members of each set? Each group will then share one set of four representations and explain how they identified the members of that set.

24. Analyzing Quadratic Graphs How does this activity enrich the students’ understanding of different quadratic representations? How might you use a similar type activity in a different unit of study?

25. Analyzing Quadratic Graphs

26. Analyzing Quadratic Graphs Each group will receive one of the comparing graphs sheet. Each member of the group will be receiving a blank transparency, a different colored marker, and a piece of graph paper. Each person in the group will graph one of the equations on a transparency—your group will have a total of five different graphs.

27. Analyzing Quadratic Graphs Now that your group has graphed each equation, layer your transparencies. What do you notice? What is causing this to happen? Generate two more equations which illustrate that you know what is causing the changes to occur.

28. Module 10 Outcome • Participants will learn explicit instructional conversations strategy that foster the development of academic language that increase students’ access to core mathematics content

29. The Quadratic Formula

30. Academic Language Development Strategy: • Instructional Conversation (Listening/Speaking)

31. “Mathematically Speaking…” • Instructional Conversation • The instructional conversation activity is used for review or guided practice. Student pairs are formed. Target vocabulary words are written on the IC chart in the left column. The 2 students write their names across the top. One student explains half of the completed task or a given problem to the other student as he or she tallies on the chart each time a target word is used in the explanation. Students keep talking until all target words have been used. The other student then takes a turn doing the same.

32. Academic Language Development • How can this strategy modeled be used with other concepts in this unit? • What changes do you foresee in your students’ understanding after utilizing these strategies? • How can this strategy specifically address EL needs? • How will you make time in your day-to-day lessons to incorporate these strategies?