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.

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

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.

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

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

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.

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

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

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

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

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.

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

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

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

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

Step One Understanding the Problem Paraphrase Visualize Analyze Information Graphic Organizers Highlight important information Determine question to be solved

Example Problem Name of School Female Students Male Students Lincoln Mason Washington Middle School Student Populations How many more students are at Lincoln Middle School than at Washington Middle School?

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

Example Problem Name of School Female Students Male Students Lincoln Mason Washington Middle School Student Populations How many more students are at Lincoln Middle School than at Washington Middle School?

Step Three Implementing 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

Example Problem Name of School Female Students Male Students Lincoln Mason Washington Middle School Student Populations How many more students are at Lincoln Middle School than at Washington Middle School?

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

Example Problem Name of School Female Students Male Students Lincoln Mason Washington Middle School Student Populations How many more students are at Lincoln Middle School than at Washington Middle School?

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?

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

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.

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?

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.

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

Literacy Connections Quick Writes Think-Write-Share Annotating Word Problems

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

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?

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.

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

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?

Your Math Instructional Advisors Christine Bingham Ashley Williams Elementary Math