CVEDC CCSSM – HS Session # 1 Focus: Number & Quantity Content Domain and Applications of Practice Standards Monday, October 29, 2012

Introductions Share What feeds your soul personally? What is your professional role? What feeds your soul professionally?

Volunteers for Breaks I need volunteers to remind me when we need breaks! Every 20 minutes, we need a 2-minute “movement break” to help our blood circulate to our brains. Every hour we need a 5-minute bathroom break.

Formative Assessment How familiar are you with the CCSSM?

Goals for this Workshop You will leave with a deeper understanding of: The CCSSM HS Content Domain “Number and Quantity” The 8 Standards for Mathematical Practice How to find rich tasks that support student understanding of “Number and Quantity” and student practice of the Practice Standards

CCSSM Equally Focuses on… Standards for Mathematical Practice Standards for Mathematical Content Same for All Grade Levels Specific to Grade Level

Standards for Mathematical Practice Describe ways in which student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity

Standards for Mathematical Practice Provide a balanced combination of Procedure and Understanding Shift the focus to ensure mathematical understanding over computation skills

8 Practice Standards Go to Scroll down to the 8 links to Michelle Flaming’s Classroom Sneak Peek For each of the 8 practices, do the following activity in a small group.

8 Practice Standards Activity Individually read through the materials for each standard Discuss the standard with your group. How do you interpret the standard? What teacher moves do you envision using? What types of tasks will help to facilitate students to use these practices? After going through all 8 practices with small group, summarize in whole group discussion.

Standards for Mathematical Practice Students will be able to: 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.

4. Model with Mathematics Modeling is both a K - 12 Practice Standard and a 9 – 12 Content Standard.

Modeling Defined Modeling is the process of choosing and using appropriate mathematics and statistics to: analyze empirical situations understand them better improve decisions

Modeling Defined The word “modeling” in this context is used as a verb that describes the creative process of transforming a real situation into an abstract mathematical model.

Modeling Defined A model can be very simple, such as: writing total cost as a product of unit price and number bought, using a geometric shape to describe a physical object like a coin. Even such simple models involve making choices. It is up to us whether to model a coin as a three- dimensional cylinder, or whether a two-dimensional disk works well enough for our purposes.

Modeling Defined Other situations may need more elaborate models: modeling a delivery route, modeling a production schedule, modeling a comparison of loan amortizations Knowledge from other disciplines may be necessary Technology may or may not be needed

Modeling Defined Real-world situations are not organized and labeled for analysis. Formulating tractable models, representing such models, and analyzing them is a creative process. Like every such process, this depends on acquired expertise as well as creativity.

Modeling Defined There is no one correct model. The models students create increase in sophistication, elegance, and efficiency as they mature mathematically Modeling is best done as a collaborative activity

Modeling Defined The models devised depend on a number of factors: How precise an answer do we want or need? What aspects of the situation do we most need to understand, control, or optimize? What resources of time and tools do we have?

Modeling Activities Aligned with Numbers and Quantity Swimming Pool Task Having Kittens Task Choose one of these tasks to do with a partner or small group. To access tasks go to CVEDC CCSSM HS October 29, 2012 post on

Number and Quantity 4 of the 6 Complex Number System Standards are advanced topics (+) All of the Vector and Matrix Standards are advanced topics (+)

Number and Quantity Algebra I Extend the properties of exponents to rational exponents Use properties of rational and irrational numbers Algebra I Extend the properties of exponents to rational exponents Use properties of rational and irrational numbers Algebra I Reason quantitatively and use units to solve problems Foundation for work with expressions, equations, and functions Algebra I Reason quantitatively and use units to solve problems Foundation for work with expressions, equations, and functions

Number and Quantity Algebra II Perform arithmetic operations with complex numbers Algebra II Perform arithmetic operations with complex numbers Algebra II Honors Course (+) Use complex numbers in polynomial identities and equations Polynomials with real coefficients Algebra II Honors Course (+) Use complex numbers in polynomial identities and equations Polynomials with real coefficients

Number and Quantity Fourth Year Honors Course Vectors (+) Represent and model with vector quantities Perform operations on vectors Perform operations on matrices and use matrices in applications Fourth Year Honors Course Vectors (+) Represent and model with vector quantities Perform operations on vectors Perform operations on matrices and use matrices in applications Fourth Year Honors Course Complex Numbers (+) Perform arithmetic operations with complex numbers Represent complex numbers and their operations on the complex plane Fourth Year Honors Course Complex Numbers (+) Perform arithmetic operations with complex numbers Represent complex numbers and their operations on the complex plane

Number and Operation Activity Work with a partner and on your own laptop, go to Go to the HS Number and Quantity Domain and read through the standards Check out the illustrations. Which SMPs would they reinforce? Which illustrations would you use in your classroom? Check out the modeling standards (those with a star) Why do you think these standards were chosen as modeling standards?

Number and Operation Activity Work with a partner and on your own laptop, go to Extending the Definition of Exponents, Variation 2 Work through the problem What Practice Standards did you use when solving this task?