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Table Dilemma: How Many People Can Sit at Multiple Square Tables?

This activity explores seating arrangements at square tables at Giovanni's Pizza. Students will determine how many people can sit at different numbers of tables. This lesson connects problem-solving to the TN Ready Assessment and emphasizes the use of mathematical practices.

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Table Dilemma: How Many People Can Sit at Multiple Square Tables?

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  1. Do Now Table Dilemma  Square tables at Giovanni’s Pizza seat 4 people each. For bigger groups, square tables can be joined. Tables can be pushed together so that they share a side. Part 1: One square table seats 4 people. Two square tables seat 8 people. How many people can sit at 3 tables? 4 tables? 5 tables? (www. http://3-5cctask.ncdpi.wikispaces.net/4.OA.5)

  2. CCR: Seeing is Believing:A Model Lesson using Problem Solving District Learning Day TBD Session 1 9:15-11:30 Thursday, August 6, 2015

  3. Norms • Be present and engaged. • Be respectful of differences in perspective while challenging each other productively and respectively. • Monitor “air time.” • Make the most of the time we have. • Stay focused on students.

  4. “When problem solving is interwoven with learning, students are learning mathematics by doing mathematics!”

  5. Agenda • Do Now • Objective • Mathematical Practices • The Importance of Problem-Solving • Connect problem solving to the TN Ready Assessment • The Problem-Solving Process • Practice with Problem-Solving • Reflecting and Connecting

  6. Objectives Know how using the mathematical practices encourages critical thinking and problem solving through written and verbal communication Understand the importance of teaching problem solving in order to ensure students’ College and Career Readiness Do Connect the problem solving process to the TN Ready Assessment Model and implement strategies connected to the four steps of the problem-solving process As a result of this PD we expect to see students engaged in problem solving activities as part of their daily math instruction so that they are proficient or advanced based on the TNReady Assessment.

  7. Mathematical Practices What are the mathematical practices and how are we currently utilizing them on our classrooms?

  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

  9. Teaching Mathematics Through Problem Solving Why should we teach mathematics through problem solving?

  10. Article Review: Mathematics Through Problem Solving • At each table/group count by 4’s. • Read the section that corresponds with your number. • Star items that resonate with you • ? Next to items that you may have a question about • Share your section with the table/group • Discuss your thoughts and be able to share one thing that resonated with your whole group

  11. Challenges • A significant number of K-5 students experience difficulty in understanding open-response problem-solving questions in mathematics. • Students also experience difficulty in explaining their thinking in mathematical terms. • Problem-solving is embedded in standards and mathematical practices across grade levels K-5 and beyond. • TN Ready Assessment requires students to use problem-solving skill in order to correctly answer test questions. • In order to become College and Career Ready, students must be provided with multiple opportunities to address complex problems and find solutions to those problems.

  12. TN Ready Sample Questions What type of questions can we expect on the TNReady assessment?

  13. Sample Questions • Look at the front of your packet • Find the sample question that matches your dot. • Work with your teammates to to answer the following questions: • What information do students need to know to successfully answer the question? • What strategies will help students solve the problem? • Group share – Make connections

  14. Problem Solving Process What methods can we use to help our students solve problems?

  15. Problem-Solving Process • Step 1: Understanding the Problem • Step 2: Devising a Plan to Solve the Problem • Step 3: Implementing a Solution Plan • Step 4: Reflecting on the Problem: Looking Back

  16. Step OneUnderstanding the Problem • Paraphrase • Visualize • Analyze Information • Graphic Organizers • Highlight important information • Determine question to be solved

  17. Example Problem Middle School Student Populations How many more students are at Lincoln Middle School than at Washington Middle School?

  18. Step Two Devising a Plan to Solve the Problem • Hypothesize • Estimate • Discuss/Share Strategies • Find a pattern • Work backwards • Draw a diagram • Write an equation • Decide what math operation(s) should be used • Explain the Plan

  19. Example Problem Middle School Student Populations How many more students are at Lincoln Middle School than at Washington Middle School?

  20. Step ThreeImplementing a Solution Plan • Experiment with different solution plans • Allow for mistakes/errors • Work collaboratively • Implement your own solution plan • Check your solution(s) to make sure they are reasonable

  21. Example Problem Middle School Student Populations How many more students are at Lincoln Middle School than at Washington Middle School?

  22. Step Four Reflecting on the Problem • Allow students to discuss similarities and differences between solution paths • Reflect on the plan • Involves risk-taking • Involves self-assurance • Involves independence

  23. Example Problem Middle School Student Populations How many more students are at Lincoln Middle School than at Washington Middle School?

  24. Reflection:MODELING • What resonated with you? • What is similar to your current practice? • What is different than your current practice? • What are you going to change as a result?

  25. Problem Solving in Action What will my students be doing as they problem solve?

  26. Sample Questions • Using the steps given, independently solve your problem. Make sure to show your work and be able to explain what you did to your partner/group. • Using “Talking Beans” Explain to your group how you solved your problem. • Reflect on what you learned/what you might do differently next time – how might this help you with future problems.

  27. Reflection:Application • What was easiest for you? • What was most difficult? • What else do you need to learn/do prior to applying to your classroom?

  28. Planning for Problem-Solving • Review the grade level task • Create a goal for the task • Plan a teacher model of this task using the problem solving process.

  29. Literacy Connections How can we include our district emphasis on literacy in our everyday math instruction?

  30. Literacy Connections • Quick Writes • Think-Write-Share • Annotating Word Problems

  31. Reflecting and Connecting What have we learned about problem solving? How can we share our understanding with others?

  32. Reflecting and Connecting • Your colleague teaches a problem-solving lesson and comes to debrief with you. • She is upset and disappointed that the lesson did not work. • How would you respond using what you have gained from this professional development session?

  33. Objectives Know how using the mathematical practices encourages critical thinking and problem solving through written and verbal communication Understand the importance of teaching problem solving in order to ensure students’ College and Career Readiness Do Connect the problem solving process to the TN Ready Assessment Model and implement strategies connected to the four steps of the problem-solving process As a result of this PD we expect to see students engaged in problem solving activities as part of their daily math instruction so that they are proficient or advanced based on the TNReady Assessment.

  34. Next Steps • Implement a problem solving process in your classroom. • Attend upcoming Professional Development that dive into the Mathematical Practices Challenge: • Use reflective practice to video a lesson on problem solving. • Reflect on your lesson • As a peer to watch the lesson and provide feedback

  35. Reflection: One minute paper on post-it • Jot down your “Take-Aways” • Consider what you need to know and be able to do to successfully implement what you have learned in this session. • What is still unclear? • What professional development or additional resources do you need?

  36. Your Math Instructional Advisors Christine Bingham Ashley Williams Elementary MathElementary Math binghamcl@scsk12.orgwilliamsa8@scsk12.org 416-7980 416-7983

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