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5th Grade Problem Solving with8 Mathematical Practices Laura Chambless St. Clair RESA Consultant www.protopage.com/lchambess
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Pre & Post Teacher Survey Complete the left side “Before Attending Mathematical Practices Workshop”
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Write Your Own Story Problem1. 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.
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Learning TargetI can integrate the MathematicalPractices in my teaching todevelop deeper mathematicalknowledge within my students.
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8 Mathematical Practices CCSS for Mathematical Student-friendly Language Practice Make sense and persevere in I don’t mind trying many times to understand and solving problems. solve a math problem. Reason abstractly and I can think about the math problem in my head, first. quantitatively. Construct viable arguments and I can make a plan, called a strategy, to solve the critique the reasoning of others. problem and discuss other students’ strategies too. I can use pictures, objects, math symbols, and Model with mathematics. numbers to show how to solve a problem. Use appropriate tools I can choose the best math tool like calculators, strategically. rulers, pictures, or objects to solve the problem. I can check to see if my strategy and calculations are Attend to precision. correct. I use clear mathematical language. Look for and make use of I can use what I already know about math to solve structure. the problem. Look for and express regularity I can use different strategies or find a pattern from a in repeated reasoning. similar problem to solve a new math problem.From: Teaching Children Mathematics, March 2012, Getting Started in K – Grade 2, pg. 440-445. www.protopage.com/lchambless
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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.
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Solve and Discuss StructureThe explaining student:• Relates solution to a math drawing• Asks if there are any questions• Responds to the questionsThe listening student:• Asks questions• Suggests edits to the explanation or solution
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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.
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Content Focus 5.NF.65.OA.6 Standard:Solve real world problems involving multiplication of fractions and mixed numbers
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How Does MP Look in Action Your Story Problem Liz put 2/5 of her money in the bank and spent ½ of the remainder. If she had $30 left, how much money did Liz have at first? Write an equation.3 min. by yourself15 min. with a small group (2 or 3)Report out 2 min per group
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Mathematical Practice Rubric 3 min. Review Rubric (from: Institute for Advanced Study) http://www.ocf.berkeley.edu/~mimiyang/misc/rubric.pdf Pair Share1. Look at Math Practice #1 and #22. Discuss where your story problem fell on the rubric.3. Group Discussion
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Remodeling TasksOriginal ProblemLiz had $100. She put 2/5 in the bank and spends ½ of what is left. How much did she spend? Write an equation. How did I make it more intellectually challenging?*** Review Level of Cognitive Demand Handout
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Analysis of My TaskPart 1: Selecting and Setting up a Mathematical TaskGoals: 5.NF. 6 StandardSolve real world problems involving multiplication of fractionsAll Task Answers: $100 should see different representationsRepresentations Used: array drawings, fraction bars, comparison bars, …Record and Report work:Independently- 5 min. using whiteboardSmall Group– 5 to 15 min. - adding to each students whiteboardWhole Group Report: 2 min.
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Analysis of My TaskPart 2: Supporting Students’ Exploration of the TaskQuestions to help get started:1. Can you tell me what is happening in the story?2. Is there another ways can write the equation?3. Can you make a list of all the steps needed to solve the problem?4. What representation are you thinking about using?5. Which operation do you think you need to use?6. What are you being asked to find?7. How can you break apart the problem?Look at Common Errors pg. 126 to help think of questions.
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Analysis of My TaskPart 3: Sharing and Discussing the TaskWhat solution paths do you want shared during class discussion?*How many steps are in the problem, *Where to start in the problem,*Once you knew how much she spent, how did you figure out the missing 2/5s?Looking for different strategies and representations.Mathematical Ideas: fractions broken into equal partsExpand on, debate, and question the solutionsSolve and Discuss: (Solve-Explain-Question it- Justify it)EvidenceQuestions to build mathematical ideas connectionsWhy did you start where you did? Did anyone else start there?Can anyone retell what that group just said?How are _____’s pictures same/different than ____’s pictures?
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Your Story Problem1. Get into groups of 4.2. Everyone reads their story problem they wrote at beginning of session.3. The group chooses one to remodel.4. Each person fills in the Remodeling a Mathematical Task sheet while group is collaborating.5. Groups will give a 2 min. report to class.
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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
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Setting Up NormsWhat Norms do we need to have inplace?
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Problem Solving with Bar Diagrams1. Understand: Identify what is known and what is unknown. Draw the bar diagram to promote comprehension and demonstrates understanding. (Situation vs. Solution Equation)2. Plan: Decide how you will solve the problem (find the unknown). Analyze the bar diagram to find a solution plan.3. Solve: Execute the plan. Use the bar diagram to solve.4. Evaluate: Assess reasonableness using estimation or substitution. Substitute the solution for the unknown in the bar diagram.
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Bar DiagramsWatch Introduction Videohttp://www.mhschool.com/math/com mon/pd_video/mathconnects_bardi agram_p1/index.htmlhttp://www.mhschool.com/math/com mon/pd_video/mathconnects_bardi agram_p2/index.html
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Thinking Blockshttp://www.mathplayground.com/think ingblocks.html Explore the site When done exploring go to my Protopage and look at your grade level math tab.
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Other ResourcesCheck out my Protopage for content websites. How will you use the 8Mathematical Practices with them?www.protopage.com/lchambless
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Learning TargetI can integrate the MathematicalPractices in my teaching todevelop deeper mathematicalknowledge within my students.
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Exit TicketOn the back of your name tent write:What is your take-away from today’s session?
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Pre & Post Teacher Survey Complete the right side“After Attending Mathematical Practices Workshop” & Post Event Questions
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