ATOMIC Workshop 24/46: Teaching the CCSS using Problem Solving in a Workshop Environment Kristina Koprowski 3 rd Grade Teacher Woodstock Public Schools

Objectives: Participate in an introduction to division problem-solving lesson Receive an overview of the 5 Practices for Orchestrating Productive Mathematics Discussions Learn how to develop and support student thinking within the workshop format Learn how to pick/design “juicy” problems Learn about one math workshop format/design Obtain strategies for establishing routines and cultures for this type of teaching within your classroom

Sheet/Twitter! Please fill out the attendance sheet going around with your address. Within a couple of days, I will out a zip file with all the materials used today! OR go online to Twitter #CTmath13 and find my Click the link to download all the materials for today’s presentation!

The Problem: Teacher/Student Roles Teacher Role: Walking around to support, develop, and strengthen student thinking Gather information on student thinking for discussion Your (student) Role: Put yourself in the role of a 3 rd grade student who has had a lot of experience with addition and subtraction, two months of exposure to multiplication, but has barely heard the word “division.”

Instructions: 1. Individual Think Time: You will have 30 seconds to think before working with your group. During this time, draw/record anything you can think of on the paper in front of you. 2. Solve the Problem: You will then have 10 minutes to discuss the solution with your group and create a poster that explains your thinking. 3. Presentations: Some groups will be selected to present their thinking during the discussion. 4. Discussion: Presentations will be integrated within a whole-group discussion, reflecting and concluding on the task and learned mathematical ideas.

The Problem: You have 4 flowers that have 24 petals total. If each flower has the same number of petals, how many petals will each flower have? Extend Your Thinking: How would your answer change if you had 25 petals instead? Explain Why? How many more petals would you need to make each flower equal again? What conclusion can you draw about the number of petals you need to make each flower have the same amount?

Student Thinking Student 1: We would like put like 2 flowers, no… like like Ava said one, but like keep adding one more to each of them. Teacher: So what happens? Look at the picture. What happens if instead of that 24, you had one more – you had 25? Student 1: You would put um 7, and not um 6. Teacher: You would put 7 on each one? Student 1: Yea. Um… Student 2: I wouldn’t. You couldn’t do that because you only have 25. You can’t split that into 4. But you could do like split that into a little bit of a petal. Teacher: Hmm… Student 1: Wait like, we could like put 5 on each one and then that would be like 20. Teacher: Okay, but you have 25. Student 1: Oh… um… On the last one you could like um… Ugh I just lost it. Student 2: On the last one put umm…. Student 1: But that equals like 5 on each one, but on that last one put that many on that flower that makes it 25? Teacher: So you’re saying one flower would have an extra? Student 1: Yea Teacher: Hmm… Would that be fair? All students: Noooooooooo Teacher: Why not? Student 3: Because it wouldn’t be even. Student 2: It’s like, it’s sorta like it’s you’re birthday and you have 25 pieces of cake, but there’s 24 people. You wouldn’t want one person to have an extra. Teacher: So what would you do with it? What would you do with that extra piece? Student 2: You could split it…. into 4 different pieces. Teacher: Hmmm… (walks away to let students continue thinking)

Developing a Goal What is your goal? Examples: To build problem solving skills Exploration of a topic Develop an understanding of using the tools you have Using illustrations to help in problem solving Developing another strategy (guess and check, working backwards, making a table, etc.) Develop understanding that there are always multiple ways of solving problems

The 5 Practices Three Phases: “Launch” “Explore” “Discuss and Summarize” 1. Anticipating Think about the problem beforehand: How might students respond? 2. Monitoring Walk around during the task to monitor actual responses. 3. Selecting Which students should present their work during the discussion? (Which help meet your goals?) 4. Sequencing After selecting students, sequence the order they will present in 5. Connecting Connect different students’ responses to the key mathematical ideas, connecting back to your goal

Picking/Designing the Problems “Juicy” open-ended problems (sources at the end of this PowerPoint) Grouping students Grouping students by level encourages a challenge at every level and makes for multiple explanations Motivates students to share Leveling problems: Start in the middle! Easier to add in scaffolds and extensions Change the numbers, complexity, level of ambiguity, propose solutions, comingle different concepts within the same problem to make it harder or easier Use hint cards and additional tools to provide support

Timing of the Problem 2 minutes for independent thinking 20 minutes for the problem After 10 minutes, I announce start posters! 20 minutes for presentations, discussion, & closure

Math Workshop Timing & Roles Hoffer, Wendy Ward (2012). Minds on mathematics: Using math workshop to develop deep understanding in grades 4-8. Portsmouth, NH: Heinemann.

Minds on Math Workshop Teacher vs. Student Roles Train vs. Facilitate Teacher as coach Questioning: Teacher: “Does your answer make sense in the problem?” Allow students to struggle – this is SO important! Training Examples Model metacognition (Fist of 5) Model talk moves (I notice… and I wonder… statements)

Establishing Routine & Culture for Problem Solving Practice, Practice, Practice! Give realistic expectations Change groupings Value “guess & check” Utilize math notebooks Teambuilding & Communication challenges “I Notice, I Wonder” ALWAYS share your enthusiasm!

How Practical is this? It depends on how far you want to take it, what your goals are, what your curriculum is like, and how your classroom/time is set up at your school, etc. My food for thought: Opening/Mini-Lesson: Make time for it? Every day? If not, can I incorporate it in a different way the other days? And how often? 2 versions of Math Workshop used in my classroom Other version: 20 minute Mini-Lesson, 40 minutes student work time

Sources for Presentation Hoffer, Wendy Ward Minds on Mathematics: Using Math Workshop to Develop Deep Understanding in Grades 4-8. Portsmouth, NH: Heinemann.Minds on Mathematics: Using Math Workshop to Develop Deep Understanding in Grades 4-8 Ray, Max Powerful Problem Solving: Activities for Sense Making with the Mathematical Practices. Portsmouth, NH: HeinemannPowerful Problem Solving: Activities for Sense Making with the Mathematical Practices. Smith, Margaret S. and Stein, Mary Kay Practices for Orchestrating Productive Mathematics Discussions. Reston, VA: National Council of Teachers of Mathematics.5 Practices for Orchestrating Productive Mathematics Discussions.

“Juicy” Problems Inside Mathematics “Problems of the Month” The Math Forum at Drexel NRICH: Enriching Mathematics, University of Cambridge NRICH: Enriching Mathematics Yummy Math, Grades 3-12 Yummy Math “Implementing Standards-Based Mathematics Instruction” (Teachers College Press: 2009) “Implementing Standards-Based Mathematics Instruction

Thank You! Feel free to reach out to me with any questions! Thank you very much for coming!