CVEDCCCSSM – HS

Session # 1 Focus:

Number & Quantity Content Domain and Applications of Practice

StandardsMonday, October 29, 2012

IntroductionsShare • What feeds your soul personally?• What is your professional role?• What feeds your soul professionally?

Volunteers for BreaksI 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 AssessmentHow familiar are you with the CCSSM?

Goals for this WorkshopYou 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 PracticeDescribe 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 PracticeProvide a balanced combination of

Procedureand

UnderstandingShift the focus to ensure

mathematical understanding over

computation skills

8 Practice StandardsGo to http://www.watsonmath.com/?p=604

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 PracticeStudents 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 DefinedA 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 DefinedOther 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 DefinedReal-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 mathematicallyModeling is best done as a collaborative activity

Modeling DefinedThe 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 TaskHaving Kittens Task

Choose one of these tasks to do with a partner or small group.

To access tasks go to CVEDC CCSSM HSOctober 29, 2012 post on

www.watsonmath.com

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 IExtend the properties of exponents

to rational exponentsUse properties of rational and

irrational numbers

Algebra IReason quantitatively and use units

to solve problemsFoundation for work with

expressions, equations, and functions

Number and Quantity

Algebra IIPerform arithmetic operations

with complex numbers

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 Complex Numbers (+)

Perform arithmetic operations with complex

numbersRepresent complex numbers and their operations on the

complex plane

Number and Operation ActivityWork with a partner and on your own laptop, go to

http://illustrativemathematics.org/• 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 ActivityWork with a partner and on your own laptop, go to

Extending the Definition of Exponents, Variation 2

Work through the problemWhat Practice Standards did you use when solving this task?