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Standards of Mathematical Practice http://thinkmath.blog.monroe.edu/ Today’s Goals • To explore the mathematical standards for Content and Practice • To discuss and learn strategies for getting students engaged in the Standards of Mathematical Practice • To explore how we can use existing resources to focus on the Practices Common Core State Standards Mathematics • Standards for Content • Standards for Practice Standards for Mathematical Practice 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 © Institute for Mathematics & Education 2011 SMP 1: Make sense of problems and persevere in solving them. Gather Information Continuously evaluate progress Anticipate possible solutions Make a plan Question sense of solutions Check results © Institute for Mathematics & Education 2011 SMP 2: Reason abstractly and quantitatively Decontextualize Represent as symbols, abstract the situation 5 ½ Mathematical Problem P x x x x Contextualize Pause as needed to refer back to situation © Institute for Mathematics & Education 2011 SMP 3: Construct viable arguments and critique the reasoning of others Make a conjecture Build a logical progression of statements to explore the conjecture Analyze situations by breaking them into cases Recognize and use counter examples © Institute for Mathematics & Education 2011 SMP 4: Model with mathematics Problems in everyday life… …reasoned using mathematical methods Images: http://tandrageemaths.wordpress.com, asiabcs.com, ehow.com, judsonmagnet.org, life123.com, teamuptutors.com, enwikipedia.org, © Institute for Mathematics & Education 2011 glennsasscer.com SMP 5: Use appropriate tools strategically © Institute for Mathematics & Education 2011 SMP 6: Attend to precision Comic: http://forums.xkcd.com/viewtopic.php?f=7&t=66819 © Institute for Mathematics & Education 2011 SMP 7: Look for and make use of structure © Institute for Mathematics & Education 2011 SMP 8: Look for and express regularity in repeated reasoning © Institute for Mathematics & Education 2011 Fraction Puzzles • On your own, write a fraction addition or subtraction equation. Fraction Puzzles • On your own, write a fraction addition or subtraction equation. • Rewrite your equation on an index card, replacing some numbers in the numerators or denominators with n or d. Fraction Puzzles • On your own, write a fraction addition or subtraction equation. • Rewrite your equation on an index card, replacing some numbers in the numerators or denominators with n or d. • Exchange with a partner to solve for the unknown numbers. Fraction Puzzles What Standards for Mathematical Practice were focused on in this task? Build a Fraction Build a Fraction What Standards for Mathematical Practice were focused on in this task? Subtraction with mixed numbers What Standards for Mathematical Practice were focused on in this task? Adding Unlike Fractions Adding Unlike Fractions What Standards for Mathematical Practice were focused on in this task? Strategies for Implementing the Practices Use Rich Tasks Where to find rich tasks. http://www.insidemathematics.org/ http://illustrativemathematics.org/ http://www.rda.aps.edu/mathtaskbank/start.htm http://www.galileo.org/math/MathProblems.html http://balancedassessment.concord.org/tasksalpha.html Rich Problems Worksheet • Read through the tasks on the Rich Problems worksheet • With a partner discuss what similarities you see in these problems Creating Open Ended Questions Creating open ended questions • With a partner choose an upcoming topic you will be teaching. • Create 3 open ended questions to engage your students? • For each questions what Math Practices would you expect your students to be engaged in? Additional Strategies Where do I find these opportunities in my resources? With a partner, pick an upcoming lesson and discuss how you are going to integrate the standards of Mathematical Practice. • Focus on 1 or 2 Practices • What will you see the students doing if they are engaging in the Practices? • How will you facilitate the Practices?