Cumberland County Schools Mathematics Common Core Leadership Institute High School Job Alike December 7, 2011

Intended Outcomes Participants will:  gain knowledge of Common Core State Standards attributes  engage in Critical Thinking skills activities to explore and discuss the 8 Mathematical Practices  recognize the relationships between the Common Core State Standards and the NCTM Standards.

Where to Find Information http://ccscandi.wikispaces.com/ Please go to the C&I wiki. Locate the Common Core Standards page in the blue bar on the left of the screen. Click on the page and open the PDF file titled ELA Common Core Standards. We will use this document in today’s presentation. The other documents used in today’s presentation are located here.

Common Core Attributes • Focus and coherence  Focus on key topics at each grade level  Coherent progression across grade level

Building Blocks and Leaning Progressions across K-12 Mathematics Domains 3 4 5 6 7 8 HS Counting and Cardinality Number and Operations in Base Ten Ratios and Proportional Relationships Number and Quantity Number and Operations in Fractions The Number System Operations and Algebraic Thinking Expressions and Equations Algebra Functions Geometry Measurements and Data Statistics and Probability

Common Core Attributes • Balance of concepts and skills Content standards require both conceptual understanding and procedural fluency

Common Core Attributes College and career readiness Level is ambitious but achievable

Design and Organization Standards Clusters Domains define what students should understand and be able to do. are groups of related standards are larger groups of related standards

Overview of the Structure of the Common Core State Standards for Mathematics K-8 High School Grade Conceptual Category Domain Cluster Standards

Design and Organization Standards define what students should understand and be able to do. Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject. Domains are larger groups of related standards. Standards from different domains may sometimes be closely related. Extend the properties of exponents to rational exponents. 1. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. 2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Conceptual Categories Domain The Real Number System N-RN Standards Cluster

HS Math Conceptual Categories Six Themes Algebra Functions Number and Quantity Statistics & Probability Geometry Modeling

Common Core Attributes Mathematical Practices  Fosters reasoning and sense-making in mathematics

How Does It Fit?

Standards for Mathematical Practices 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.

View of the Mathematical Practices

Who is doing the talking? Who is doing the math? Mathematical practices describe the habits of mathematically proficient students… Who is doing the talking? Who is doing the math?

Now Let’s Do Some Math

Question: A class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would they need each day for 12 caterpillars?

Turn and Talk How might students solve this problem correctly by finding the number of leaves needed for 1 caterpillar? A student gets an answer of 15. What questions could be asked to get to the correct answer? How might students solve this problem correctly by counting by 2’s and 5’s? How might students incorrectly use additive reasoning to solve this problem?

Solution Strategies

Table Top Discussion Standards for Mathematical Practices 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.

Mathematical Practices

Make sense of problems and persevere in solving them.

Mathematical Practices Activity “I Have….Who Has?”

Mathematical Practices

Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities The ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents The ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of: creating a coherent representation of the problem at hand considering the units involved attending to the meaning of quantities, not just how to compute knowing and flexibly using different properties of operations and objects

Write a complete sentence to describe what this sign is communicating. what does this mean? Write a complete sentence to describe what this sign is communicating.

The speed limit is 55 miles per hour The speed limit is 55 miles per hour. Now, write this sentence as a ratio.

55 miles : 1 hour 55 miles to 1 hour   55 miles to 1 hour 55 miles : 1 hour   What does the word “per” refer to in 55 mph? Express 55 mph as a maximum limit using an inequality.

Complete the following table. HOURS MILES 1 55 2 165 5 275 Estimate the quantity of miles traveled in 90 minutes and explain your reasoning. Predict the quantity of time in minutes if you traveled 440 miles.

Create a complete graph from the table Do you expect to have data in the third quadrant? Justify your response with complete sentences.

I don’t expect data in the third quadrant because time is not negative nor is distance traveled. Miles Hours

Find the rate of change between 2 and 5 hours.  

slope of a line  

Mathematical Practices

Construct viable arguments and critique the reasoning of others.

Mathematical Practices

Model with mathematics.

Mathematical Practices

Use appropriate tools strategically.

Mathematical Practices

Attend to precision.

Mathematical Practices Teacher Actions (Cause) Student Practices (Effect) 7. Look for and make use of structure. DO STUDENTS: Look closely to determine a pattern or structure? Utilize properties? Decompose and recombine numbers and expressions?

Mathematical Practices Teacher Actions (Cause) Student Practices (Effect) 8. Look for and express regularity in repeated reasoning. DO STUDENTS: Notice if calculations are repeated, and look for general methods and for shortcuts? Maintain oversight of the process, while attending to the details? Continually evaluate the reasonableness of their intermediate result?

Mathematical Practices Activity What Does it Weigh?

Common Core 9-12 Mathematics Updates

Updates Continued

--Jere Confrey Table Top Discussion The value of the Common Core is only as good as the implementation of the mathematical practices. --Jere Confrey

Take Aways Summary