transition to pa common core mathematical practices copyright ©2011 commonwealth of pennsylvania 1

Copyright ©2011 Commonwealth of Pennsylvania 1

Transition to PA Common CoreMathematical

Practices

PA Common

CoreRigor

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Practices

Assessm

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Toolbox

Local Curriculum


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• Place your name and school district/organization on your name tent

Your NameYour School District/Organization

Please Do the Following

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PA Common Core IntroductionEssential Questions

• What are the Standards for Mathematical Practices and how do they relate to the PA Common Core?

• Can the characteristics of a student and classroom that exemplify mathematical practices be identified and implemented?


Dan Meyer describes why we needto makeover math classrooms.

Math Class Makeover

http://www.youtube.com/watch?v=SjsfHTuZ14w


Explore

the Standards for Mathematical Practice.

Identify

characteristics of a student and classroom that exemplify mathematical practice.

Expected Outcomes


When all students are engaged in learning mathematics, what does a classroom...

Look Like Sound Like

Looks Like/Sounds Like


Standards for Mathematical Practice

The Standards for Mathematical Practice

describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest

on important ‘processes and proficiencies’ with longstanding importance in mathematics education.

(CCSS, 2010)


o Problem solving o Reasoning and proof o Connections o Communication o Representation

NCTM – Principles and Standards for School Mathematics


Adding It Up: Helping Children Learn MathematicsBy Jeremy Kilpatrick, Jane Swafford, & Bob Findell (Editors). (2001).Washington, DC: National Academy Press

p. 117

Standards of Proficiency of Mathematical Practice


1. Make sense of complex 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.



(McCallum, 2011)

Grouping the Standards for Mathematical Practice


1. Make sense of complex problems and persevere in solving them.

2. Reason abstractly and quantitatively3. 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. What implications might the standards of mathematical practice have on your classroom?



Rigor Iso approaching mathematics with

a disposition to accept challenge and apply effort;

o engaging in mathematical work that promotes deep knowledge of content, analytical reasoning, and use of appropriate tools; and

o emerging fluent in the language of mathematics, proficient with the tools of mathematics, and being empowered as mathematical thinkers.

Rigor Is Noto “difficult,” as in “AP calculus is

rigorous.”;

o enrichment activities for advanced students;

o Problem Solving Friday

o Adding two word problems to the end of a worksheet; and

o adding more numbers to a problem.

Mathematical Rigor


Buttons Task

Gita plays with her grandmother’s collection of black & white buttons. She arranges them in patterns. Her first 3 patterns are shown below.

Pattern #1 Pattern #2 Pattern #3 Pattern #4

1. Draw pattern 4 next to pattern 3.2. How many white buttons does Gita need for Pattern 5 and

Pattern 6? Explain how you figured this out.3. How many buttons in all does Gita need to make Pattern 11?

Explain how you figured this out.4. Gita thinks she needs 69 buttons in all to make Pattern 24.

How do you know that she is not correct?How many buttons does she need to make Pattern 24?

CTB/McGraw-Hill; Mathematics Assessment Resource Services, 2003


1. Individually complete parts 1 - 3.

2. Then work with a partner to compare your work and complete part 4. Look for as many ways to solve parts 3 and 4 as possible.

3. Consider each of the following questions and be prepared to share your thinking with the group:a) What mathematics content is needed to complete the task?b) Which mathematical practices are needed to complete the

task?

CTB/McGraw-Hill; Mathematics Assessment Resource Services, 2003

Buttons Task

National Council of Supervisors of MathematicsCCSS Standards of Mathematical Practice: Reasoning and Explaining


www.Inside Mathematics.org

• http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-numerical-patterning/218-numerical-patterning-lesson-planning?phpMyAdmin=NqJS1x3gaJqDM-1-8LXtX3WJ4e8

A reengagementlesson using the Button Task

Francis DickinsonSan Carlos ElementaryGrade 5

http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-numerical-patterning/218-numerical-patterning-lesson-planning?phpMyAdmin=NqJS1x3gaJqDM-1-8LXtX3WJ4e8







Learner A

Pictorial RepresentationWhat does Learner A see staying the same? What does Learner A see changing? Draw a picture to show how Learner A sees this pattern growing through the first 3 stages. Color coding and modeling with square tiles may come in handy.

Verbal RepresentationDescribe in your own words how Learner A sees this pattern growing. Be sure to mention what is staying the same and what is changing.


Pictorial RepresentationWhat does Learner B see staying the same? What does Learner B see changing? Draw a picture to show how Learner B sees this pattern growing through the first 3 stages. Color coding and modeling with square tiles may come in handy.

Verbal RepresentationDescribe in your own words how Learner B sees this pattern growing. Be sure to mention what is staying the same and what is changing.

Learner B


• Which of the Standards of Mathematical Practice did you see the students working with? Cite explicit examples to support your thinking.

• What value did Mr. Dickinson generate by using the same math task two days in a row, rather than switching to a different task(s)?

• How did the way the lesson was facilitated support the development of the Standards of Mathematical Practice for students?

• What classroom implications related to implementation of CCSS resonate?

Buttons Task Revisited


Standard 1: Make sense of problems and persevere in solving them.

4th Grade


http://insidemathematics.org/index.php/classroom-video-visits/public-lesson-number-operations/182-multiplication-a-divison-problem-4-part-c


Standard 4: Model with mathematics.9th Grade/10th Grade


http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-properties-of-quadrilaterals/300-properties-of-quadrilaterals-tuesday-group-work-part-a?


Traditional U.S. ProblemWhich fraction is closer to 1: 4/5 or 5/4?

Same problem integrating content and practice standards

4/5 is closer to 1 than is 5/4. Using a number line, explain why this is so.

(Daro, Feb 2011)

Standards for Mathematical Practice in a Classroom

Copyright ©2011 Commonwealth of Pennsylvania

1. Are there any aspects of your own thinking and/or practice that our work today has caused you to consider or reconsider? Explain.

2. Are there any aspects of your students’ mathematical learning that our work today has caused you to consider or reconsider? Explain.

End of the DayReflections

Slide 24


• Does our list of words/phrases describe a classroom where students are engaged in mathematical practice?

• Use the reflection sheet to capture key thoughts about the practice standards.

Reflection and Planning


• Jean HowardMathematics Curriculum Specialist(406) 444-0706; [email protected]

• Cynthia GreenELA Curriculum Specialist(406) 444-0729; [email protected]

• Judy SnowState Assessment Director (406) 444-3656; [email protected]

• http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-properties-of-quadrilaterals/300-properties-of-quadrilaterals-tuesday-group-work-part-a?

• http://insidemathematics.org/index.php/classroom-video-visits/public-lesson-number-operations/182-multiplication-a-divison-problem-4-part-c

• http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-numerical-patterning/218-numerical-patterning-lesson-planning?phpMyAdmin=NqJS1x3gaJqDM-1-8LXtX3WJ4e8

• National Council of Supervisors of Mathematics

• CCSS Standards of Mathematical Practice: Reasoning and Explaining

• www.mathedleadership.org

• http://www.youtube.com/watch?v=SjsfHTuZ14w

• Adding It Up: Helping Children Learn MathematicsBy Jeremy Kilpatrick,

Jane Swafford, & Bob Findell (Editors). (2001).Washington, DC: National Academy Press

References

mailto:[email protected]



http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-properties-of-quadrilaterals/300-properties-of-quadrilaterals-tuesday-group-work-part-a













http://www.mathedleadership.org/

transition to pa common core mathematical practices copyright ©2011 commonwealth of pennsylvania 1

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