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Integrating the Mathematical Practices in Problem Solving Grades 1 - 4 Monica Hartman August 28 and 29, 2012 Port Huron Back to School Professional Development Write Your Own Story Problem 1. Think of a story problem you would use with your students. 2. Write it down on a 3x5 card. 3. Place the card under your name tag. Pre & Post Teacher Survey Complete the left side “Before Attending Mathematical Practices Workshop” Learning Target I can integrate the Mathematical Practices in my teaching to develop deeper mathematical knowledge within my students. 8 Mathematical Practices From: Teaching Children Mathematics, March 2012, Getting Started in K – Grade 2, pg. 440-445. Solve and Discuss Structure • Some children go to board and solve a problem • Other children solve the problem at their desk. • Teacher asks two children at the board to explain their method. Solve and Discuss Structure The explaining student: • Relates solution to a math drawing • Asks if there are any questions • Responds to the questions The listening student: • Asks questions • Suggests edits to the explanation or solution Solve and Discuss Structure • The Solve and Discuss Structure is actually a Solve, Explain, Question, and Justify structure • Aspire to make your classroom a place where all children listen to understand each other, not just being quiet while someone else is talking. Mathematical Practice Rubric 3 min. Review Rubric (from: Institute for Advanced Study) http://www.ocf.berkeley.edu/~mimiyang/misc/rubric.pdf Pair Share 1. Look at Math Practice #3 and #6 2. Discuss what a classroom might look like where the teacher is using these practices during instruction. Implementing the Standards of Mathematical Practice In the Gum and Pretzel problem, we will focus of Mathematical Practices 3 and 6. MP3 – Construct viable arguments and critique the reasoning of others. MP6 – Attend to precision Review the Mathematics Classroom Visitation Recording Form Content Focus 1.OA and 2.OA Cluster Statements: Represent and solve problems involving addition and subtraction 2.OA.3 Standard: Determine whether a group of objects has an odd or even number of members; write an equation to express an even number as a sum of equal addends. Content Focus 3.OA Cluster Statement: Solve problems involving the four operations, and identify and explain patterns in arithmetic. 4.OA Cluster Statement: Use the four operations with whole numbers to solve problems. The Gum and Pretzel Problem gum 2¢ big pretzel 7¢ Mark has 30 cents in his pocket and he wants to spend it all and not have any change left in his pocket. What can he buy for 30 cents? What different choices does he have? Why? The Gum and Pretzel Problem gum 2¢ big pretzel 7¢ What can he buy for 30 cents? What different choices does he have? Why? Work independently (2-3 minutes) Share your strategies with your partner and with your group Each group should be ready to explain their method for solving this problem. Sharing Strategies Remember, the explaining student: • Relates solution to a math drawing • Asks if there are any questions • Responds to the questions The listening student: • Asks questions • Suggests edits to the explanation or solution Sean’s Numbers What mathematical practices do you observe in this video of a third grade class discussing odd and even numbers after doing the Gum and Pretzel problem? Video and Supporting Documents found at http://deepblue.lib.umich.edu/handle/2027.42/65013 Remodeling Tasks • Tasks can be remodeled to make them more intellectually challenging. • Look at the problem you wrote at the beginning of the session • Does it fit into one of the categories from Table 1, Common addition and subtraction situations? • Look at Remodeling Tasks in Mathematics Classroom Handout. • Use one of the suggestions listed, or another one, to remodel your task. Remodeling Tasks • Get into groups of 4. • Rewrite your original problem to make it more challenging, if needed • Share your original problem and revision with your group. • The group chooses one to remodel using the two page, Remodeling a Mathematical Task handout. • Groups will give a 2 minute report to class. 2 Minute Report • • • • • • Requirements Original Problem Remodeled Problem Mathematical Practice- refer to rubric Part 1: Setting up the mathematical task Part 2: Questions to supporting students’ during task Part 3: Questions to use during class discussion Bar Diagrams Watch Introduction Video http://www.mhschool.com/math/com mon/pd_video/mathconnects_bardi agram_p1/index.html http://www.mhschool.com/math/com mon/pd_video/mathconnects_bardi agram_p2/index.html Thinking Blocks http://www.mathplayground.com/think ingblocks.html Explore the site Learning Target I can integrate the Mathematical Practices in my teaching to develop deeper mathematical knowledge within my students. Exit Ticket On the back of your name tent write: What is your take-away from today’s session? Pre & Post Teacher Survey Complete the right side “After Attending Mathematical Practices Workshop” & Post Event Questions Thanks for another great session Monica