# COMMON CORE STATE STANDARDS MATHEMATICAL …

MARCH/APRIL 2013

VOLUME 1 ISSUE 2

COMMON CORE STATE STANDARDS

MATHEMATICAL PRACTICE #2

8 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

KEY DATES FOR COMMON CORE TEST

IMPLEMENTATION

DATE SPRING

2013

SPRING 2014

SPRING 2015

ACTIVITY PA STANDARDS ALIGNED PSSA TESTS GRADES 3 ? 8 PA STANDARDS ALIGNED PSSA TESTS GRADES 3 ? 8 COMMON CORE ALIGNED PSSA TESTS GRADES 3 ? 8

REASON ABSTRACTLY AND QUANTITATIVELY

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: 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--and 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 them; and knowing and flexibly using different properties of operations and objects.

-Common Core State Standards

PSSA TESTING CHANGE

The Pennsylvania Department of Education announced that the PSSA tests for next school year, 2013 ? 2014, will continue to assess Pennsylvania standards. The Common Core State Standards will be assessed on the 2014 ? 2015 PSSA in grades 3 ? 8.

NORRISTOWN AREA SCHOOL DISTRICT

CURRICULUM & INSTRUCTION

401 N. Whitehall Road Norristown, PA 19403

610.630.5000 office nasd.k12.pa.us

MARCH/APRIL 2013

VOLUME 1 ISSUE 2

MATHEMATICAL PRACTICE #2

- Jordan School District (2011)

KEY SHIFT: APPLICATION Use math and choose the appropriate

concept for application even when not prompted to do so. Provide opportunities at all grade levels for students to apply math concepts in "real world" situations. Teachers in content areas ensure students are using math to make meaning of and access content.

KEY SHIFT: COHERENCE

Begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.

Provide an opportunity for students to make connections between mathematical ideas.

-Barr, Blosveren, and O'Hara (2012) Implementing the Common Core Standards

WHAT DOES THE TASK LOOK LIKE? WHAT DOES THE TEACHER DO?

Task Has relevant realistic content. Requires students to frame solutions in a context. Have solutions that can be expressed with multiple representations.

Teacher Expects students to interpret, model, and connect multiple representations. Prompts students to articulate connections between algebraic procedures and contextual meaning. Links mathematical solution with a question's answer. Explains connections between procedures and meaning.

Modified from: Institute for Advanced Study/Park City Mathematics Institute

THESE STANDARDS STRESS NOT ONLY PROCEDURAL SKILL BUT ALSO CONCEPTUAL UNDERSTANDING, TO

MAKE SURE STUDENTS ARE LEARNING AND ABSORBING THE CRITICAL INFORMATION THEY NEED TO

SUCCEED AT HIGHER LEVELS. ?COMMON CORE STATE STANDARDS

"Mathematics instruction is not just a checklist of topics to cover, but a set of interrelated and powerful ideas." -Allison Barr, Kate Blosveren, and Marie O'Hara

MARCH/APRIL 2013

VOLUME 1 ISSUE 2

MATHEMATICAL PRACTICE #2

VIDEO EXAMPLE

Dan Meyer: TEDxNYED: h?v=BlvKWEvKSi8

HOW DOES A STUDENT USE MATHEMATICAL PRACTICE #2?

Act out and solve story

problems.

Represent the problem with

visuals or math tools.

Ask themselves how do these

tools represent the problem.

Consistently think about how

the problem and solution fit

together.

Explain their answers, not

just how they arrived at the

answer.

Use references and prior

knowledge to solve the

problem.

Visualize what the problem is

asking.

-Fleming (2012)

QUESTIONS TO

ASK STUDENTS What is a situation

that could be represented by this equation? What operation did you use to represent the situation? Why does that operation represent the situation? How do you know your answer is reasonable?

-GO Math! Houghton Mifflin Harcourt (2012)

- (2012)

WHAT DOES IT REALLY MEAN?

More generally, Mathematical Practice #2 asks students to be able to translate a problem situation into a number sentence (with or without blanks) and, after they solve the arithmetic part (any way), to be able to recognize the connection between all the elements of the sentence and the original problem. It involves making sure that the units (objects!) in problems make sense.

So, for example, in decontextualizing a problem that asks how many buses are needed for 99 children if each bus seats 44, a child might write 99?44. But after calculating 2r11 or 2? or 2.25, the student must recontextualize: the context requires a whole number answer, and not, in this case, just the nearest whole number. Successful recontextualization also means that the student knows that the answer is 3 buses, not 3 children or just 3.

-Understanding the Mathematical Practices (2012)

THESE STANDARDS STRESS NOT ONLY PROCEDURAL SKILL BUT ALSO CONCEPTUAL UNDERSTANDING, TO

MAKE SURE STUDENTS ARE LEARNING AND ABSORBING THE CRITICAL INFORMATION THEY NEED TO

SUCCEED AT HIGHER LEVELS. ?COMMON CORE STATE STANDARDS

"Mathematics instruction is not just a checklist of topics to cover, but a set of interrelated and powerful ideas." -Allison Barr, Kate Blosveren, and Marie O'Hara

MARCH/APRIL 2013

VOLUME 1 ISSUE 2

MATHEMATICAL PRACTICE #2

WHAT DO PROFICIENT STUDENTS DO?

Students Reason abstractly and quantitatively

Initial

Reason with models or pictorial representations to solve problems. (Grouping/Engaging)

Intermediate

Are able to transfer situations into symbols for solving problems. (Grouping/Engaging)

Advanced

Convert situations into symbols to appropriately solve problems as well as convert symbols into meaningful situations. (Encourage Reasoning)

-Hull, Balka, and Harbin Miles (2011)

WHAT ARE STUDENTS DOING? WHAT IS THE TEACHER DOING? Students Have the ability to contextualize and decontextualize (navigate between the concrete and the abstract). Fluently move between manipulatives pictures symbols. Understand and can explain the computation methods they use. Teachers Modeling and providing the appropriate tools. Facilitating conversations to connect models and symbols used in mathematical concepts. Make the connection betweWenritme caapntiiopnus lfoartithveesse,lepctiecdtpuhroetoss,. and symbols.

-Tompkins Seneca Tioga BOCES (2012)

-Lewis, Morgan, Wallen, and Younger (2012)

THESE STANDARDS STRESS NOT ONLY PROCEDURAL SKILL BUT ALSO CONCEPTUAL UNDERSTANDING, TO

MAKE SURE STUDENTS ARE LEARNING AND ABSORBING THE CRITICAL INFORMATION THEY NEED TO

SUCCEED AT HIGHER LEVELS. ?COMMON CORE STATE STANDARDS

"Mathematics instruction is not just a checklist of topics to cover, but a set of interrelated and powerful ideas." -Allison Barr, Kate Blosveren, and Marie O'Hara

MARCH/APRIL 2013

VOLUME 1 ISSUE 2

MATHEMATICAL PRACTICE #2

Norristown Area School District 401 N. Whitehall Road Norristown PA 19403

Administration Office: 610.630.5000

nasd.k12.pa.us

Are you integrating the Mathematical Practices in your

lessons? Please Share!

Send an email to:

sgardiner@nasd.k12.pa.us

References

Barr, Blosveren, and O'Hara (2012). Implementing the Common Core State Standards. Achieve: America Diploma Project. Available at

Big Ideas Learning (2012). Mathematical Practice #1 Video. Available at

Curriculum Institute (2013). Standards for Mathematical Practice Posters. Available at al%20Practice%20Student%20Posters.pdf

Fleming, Michelle (2012). Math Made Fun Blog. Available at

GO Math! Houghton Mifflin Harcourt (2012). Supporting Mathematical Practices Through Questioning. Orlando, FL: Houghton Mifflin Harcourt.

Hull, Balka, and Harbin Miles (2011). Standards of Student Practice in Mathematics Proficiency Matrix. Available at photos.

Institute for Advanced Study/Park City Mathematics Institute (2011). RubricImplementing Standards for Mathematical Practice. Available at

Jordan School District (2011). Mathematical Practices by Standard Posters. Available at

Lewis, S.; Morgan, T.; Wallen, K.; and Younger, J. (2012). Focusing on the Mathematical Practices of the Common Core Grades K ? 8. Available at

Meyer, Dan (2010). TEDXNYED Presents Dan Meyer. Available at

Tompkins Seneca Tioga BOCES (2012). Mathematical Practices and Indicators. Available at

Understanding the Mathematical Practices (2012). Practice Standard 2: Reason abstractly and quantitatively. Available at td2.pdf

THESE STANDARDS STRESS NOT ONLY PROCEDURAL SKILL BUT ALSO CONCEPTUAL UNDERSTANDING, TO

MAKE SURE STUDENTS ARE LEARNING AND ABSORBING THE CRITICAL INFORMATION THEY NEED TO

SUCCEED AT HIGHER LEVELS. ?COMMON CORE STATE STANDARDS

"Mathematics instruction is not just a checklist of topics to cover, but a set of interrelated and powerful ideas." -Allison Barr, Kate Blosveren, and Marie O'Hara

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