1. WELCOME HIGH SCHOOL EDUCATORS Help yourself to breakfast. Please have a seat in a desk with your subject-specific materials. Introduce yourself to the people sitting in your area. - Name - School - What are you most concerned about for this upcoming school year? - What are you most excited about for this upcoming school year?

2. HIGH SCHOOL UNPACKING THE STANDARDS iZone Retreat University of Memphis Thursday, June 18, 2015

3. AGENDA Overview of High School Standards Mathematics Practices Teaching Mathematics Practices Unpack the 1 st Quarter Standards Lunch Examples of the 1 st Quarter Standards Breakout for Blueprint and Resources

4. TN ACADEMIC STANDARDS

5. HIGH SCHOOL CONCEPTUAL CATEGORIES Number and Quantity Algebra Functions Modeling Geometry Statistics & Probability

6. NUMBER AND QUANTITY OVERVIEW The Real Number System Extend the properties of exponents to rational exponents Use properties of rational and irrational numbers. Quantities Reason quantitatively and use units to solve problems The Complex Number System Perform arithmetic operations with complex numbers Represent complex numbers and their operations on the complex plane Use complex numbers in polynomial identities and equations Vector and Matrix Quantities Represent and model with vector quantities. Perform operations on vectors. Perform operations on matrices and use matrices in applications.

7. ALGEBRA OVERVIEW Seeing Structure in Expressions Interpret the structure of expressions Write expressions in equivalent forms to solve problems Arithmetic with Polynomials and Rational Functions Perform arithmetic operations on polynomials Understand the relationship between zeros and factors of polynomials Use polynomial identities to solve problems Rewrite rational functions Creating Equations Create equations that describe numbers or relationships Reasoning with Equations and Inequalities Understand solving equations as a process of reasoning and explain the reasoning Solve equations and inequalities in one variable Solve systems of equations Represent and solve equations and inequalities graphically

8. FUNCTIONS OVERVIEW Interpreting Functions Understand the concept of a function and use function notation Interpret functions that arise in applications in terms of the context Analyze functions using different representations Building Functions Build a function that models a relationship between two quantities Build new functions from existing functions Linear, Quadratic, and Exponential Models Construct and compare linear and exponential models and solve problems Interpret expressions for functions in terms of the situation they model Trigonometric Functions Extend the domain of trigonometric functions using the unit circle Model periodic phenomena with trigonometric functions Prove and apply trigonometric identities

9. MODELING * Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (*).

10. GEOMETRY OVERVIEW Congruence Experiment with transformations in the plane Understand congruence in terms of rigid motions Prove geometric theorems Make geometric constructions Similarity, Right Triangles, and Trigonometry Understand similarity in terms of similarity transformations Prove theorems involving similarity Define trigonometric ratios and solve problems involving right triangles Apply trigonometry to general triangles Circles Understand and apply theorems about circles Find arc lengths and areas of sectors of circles

11. GEOMETRY OVERVIEW CONTINUED Expressing Geometric Properties with Equations Translate between the geometric description and the equation for a conic section Use coordinates to prove simple geometric theorems algebraically Geometric Measurement and Dimension Explain volume formulas and use them to solve problems Visualize relationships between two-dimensional and three-dimensional objects Modeling with Geometry Apply geometric concepts in modeling situations

12. STATISTICS & PROBABILITY OVERVIEW Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a single count or measurement variable Summarize, represent, and interpret data on two categorical and quantitative variables Interpret linear models Making Inferences and Justifying Conclusions Understand and evaluate random processes underlying statistical experiments Make inferences and justify conclusions from sample surveys, experiments and observational studies Conditional Probability and the Rules of Probability Understand independence and conditional probability and use them to interpret data Use the rules of probability to compute probabilities of compound events in a uniform probability model Using Probability to Make Decisions Calculate expected values and use them to solve problems Use probability to evaluate outcomes of decisions

13. DOMAINS BY GRADE BANDS K12345678 Geometry Measurement & Data Statistics & Probability No. and Operations Base 10 The Number System Operations and Algebraic Thinking Operations and Algebraic Thinking Expressions and Equations Counting Cardinality Number and Operations Fractions Ratios and Proportions Relationships Functions

14. FLUENCY “Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently.

15. MATHEMATICAL PRACTICES 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning.

16. MP 1 MAKE SENSE OF PROBLEMS AND PERSEVERE IN SOLVING THEM Mathematically proficient students interpret and make meaning of the problem looking for starting points. They analyze what is given to find the meaning of the problem. They plan a solution pathway instead of jumping to a solution. These students can monitor their progress and change the approach if necessary. They see relationships between various representations. They relate current situations to concepts or skills previously learned and connect mathematical ideas to one another. They may check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?”

17. MP 2 REASON ABSTRACTLY AND QUANTITATIVELY Mathematically proficient students make sense of quantities and their relationships. They are able to decontextualize (represent a situation symbolically and manipulate the symbols) and contextualize (make meaning of the symbols in a problem) quantitative relationships.

18. MP 3 CONSTRUCT VIABLE ARGUMENTS AND CRITIQUE THE REASONING OF OTHERS Mathematically proficient students analyze problems and use stated mathematical assumptions, definitions, and established results in constructing arguments. They further refine their mathematical communication skills through mathematical discussions in which they critically evaluate their own thinking and the thinking of other students. They pose questions like “How did you get that?”, “Why is that true?” “Does that always work?” They explain their thinking to others and respond to others’ thinking.

19. MP 4 MODEL WITH MATHEMATICS Mathematically proficient students understand that models are a way to reason quantitatively and abstractly (able to decontextualize and contextualize). Students model problem situations symbolically, graphically, tabularly, and contextually. Students form expressions, equations, or inequalities from real world contexts and connect symbolic and graphical representations. Students need many opportunities to connect and explain the connections between the different representations. They should be able to use all of these representations as appropriate to a problem context.

20. MP 5 USE APPROPRIATE TOOLS STRATEGICALLY Mathematically proficient students use available tools recognizing the strengths and limitations of each. Students consider available tools (including estimation and technology) when solving a mathematical problem and decide when certain tools might be helpful.

21. MP 6 ATTEND TO PRECISION Mathematically proficient students communicate precisely with others and try to use clear mathematical language when discussing their reasoning. They understand meanings of symbols used in mathematics and can label quantities appropriately.

22. MP 7 LOOK FOR AND MAKE USE OF STRUCTURE (DEDUCTIVE REASONING) Mathematically proficient students apply general mathematical rules to specific situations. They look for the overall structure and patterns in mathematics. Students routinely seek patterns or structures to model and solve problems. For instance, students recognize patterns that exist in ratio tables recognizing both the additive and multiplicative properties. Students apply properties to generate equivalent expressions (i.e. 6 + 2x = 2 (3 + x) by distributive property) and solve equations (i.e. 2c + 3 = 15, 2c = 12 by subtraction property of equality; c=6 by division property of equality). Students compose and decompose two- and three- dimensional figures to solve real world problems involving area and volume.

23. MP 8 LOOK FOR AND EXPRESS REGULARITY IN REPEATED REASONING (INDUCTIVE REASONING) Mathematically proficient students see repeated calculations and look for generalizations and shortcuts.

24. SMALL GROUP DISCUSSION What are some ways that we, as teachers, can ensure that our students are given the opportunity to utilize the mathematical practices?

25. 8 MATHEMATICS TEACHING PRACTICES 1.Establish mathematics goals to focus learning. Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions. 2.Implement tasks that promote reasoning and problem solving. Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies. 3.Use and connect mathematical representations. Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving. 4.Facilitate meaningful mathematical discourse. Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.

26. 5. Pose purposeful questions. Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships. 6.Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems. 7.Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships. 8.Elicit and use evidence of student thinking. Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.

27. THINK, WRITE, PAIR, SHARE Think about the teaching mathematics practices. Which one(s) do you currently use in your classroom? Write how this practice is used in your classroom. Pair up with a shoulder partner and discuss the teaching mathematic(s) practice that you wrote about. Share with the group.

28. 1 ST QUARTER STANDARDS (SUGGESTED PACING) Within your subject-specific groups, read each of the 1 st quarter suggested standards and discuss: What is it that the students are expected to understand and be able to do? Use the provided hand-out to write your notes. We, the iZone Mathematics team, have been working with C&I to write the curriculum guides. This is our suggested pacing, however C&I will make the ultimate decision. Either way, these standards will be taught sometime during the school year.

29. EXAMPLES Within your subject-specific groups, work through the examples provided. What is the math involved in this problem? Match the example to the standard it is assessing.

30. CHECK FOR UNDERSTANDING Now that you have done the following: Discussed the meaning of the standards Discussed the math involved in working through the examples Matched the examples to the standards Compare your interpretation of the standards to the unpacked document that gives more detailed explanations of the standards. Compare your solution paths to the provided answers and check to see if you aligned the example with the most appropriate standard.