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NEKSDC CCSSM – HS Session # 1 Focus:. Number & Quantity Content Domain and Applications of Practice Standards Tuesday, October 16, 2012 Presenter: Elaine Watson, Ed.D . Introductions. Share What feeds your soul personally? What is your professional role?

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Neksdc ccssm hs session 1 focus

NEKSDCCCSSM – HSSession # 1 Focus:

Number & Quantity Content Domain and Applications of Practice Standards

Tuesday, October 16, 2012

Presenter: Elaine Watson, Ed.D.




What feeds your soul personally?

What is your professional role?

What feeds your soul professionally?

Volunteers for breaks

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

Formative Assessment

How familiar are you with the CCSSM?

Goals for this workshop

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

CCSSM Equally Focuses on…

Standards for Mathematical Content

Standards for Mathematical Practice

Same for All Grade Levels

Specific to Grade Level

8 practice standards

8 Practice Standards

Click on the link for “Standards for Mathematical Practice Lesson Alignment Template”“October 16, 2012 NEKSDC High School Math: Numbers and Quantity”post

We will be referring to this template throughout today and the rest of the NEKSDC CCSSM series.

Standards for mathematical practice

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 practice1

Standards for Mathematical Practice

Provide a balanced combination of




Shift the focus to ensure

mathematical understanding


computation skills

Standards for mathematical practice2

Standards for Mathematical Practice

Students will be able to:

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.

4 model with mathematics

4. Model with Mathematics

Modeling is both a

K - 12 Practice Standard

and a

9 – 12 Content Standard.

Modeling defined

Modeling Defined

Modeling is the process of choosing and using appropriate mathematics and statistics to:

analyze empirical situations

understand them better

improve decisions

Modeling defined1

Modeling Defined

The word “modeling” in this context

is used as a verb that describes the creativeprocess of transforming a real situation into an abstract mathematical model.

Modeling defined2

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 defined3

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 defined4

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 defined5

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 defined6

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

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 NEKSDC October 16, 2012 post on

Number and quantity

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 quantity1

Algebra I

Extend the properties of exponents to rational exponents

Use properties of rational and irrational numbers

Number and Quantity

Algebra I

Reason quantitatively and use units to solve problems

Foundation for work with expressions, equations, and functions

Number and quantity2

Algebra II

Perform arithmetic operations with complex numbers

Number and Quantity

Algebra II Honors Course


Use complex numbers in polynomial identities and equations

Polynomials with real coefficients

Number and quantity3

Fourth Year Honors Course Complex Numbers (+)

Perform arithmetic operations with complex numbers

Represent complex numbers and their operations on the complex plane

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

Number and operation activity

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 activity1

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

Use the SMP Lesson Template to determine what Practice Standards you used when solving this task.



For resources used and/or discussed in this presentation, go to:

October 16, 2012 NEKSDC CCSSM High School: Number & Quantity Content Domain and Applications of Practice Standards

Check out other resources available on

archives of past posts

resource links in the right hand column

Contact Elaine at [email protected]