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PROBLEM SOLVING STRATEGIES IN GRADES 3-5 Erie 1 BOCES May 22, 2013 Facilitators: Andrea Tamarazio & Steve Graser Pre-Assessment NY State Curriculum Updates K – 5 Module 1 is currently available 6 – 12 Overview of Module 1 is currently available Curriculum Maps for Grades 6 – 12 are available Changes have been made to the K – 5 Curriculum Map Grade 2 Module Titles Link to K – 5 Materials Link to 6 – 12 Materials K – 5 Modules Modules released during May NTI Kindergarten Module 1 Grade 1 Module 1 Grade 2 Modules 1 & 2 Grade 3 Module 1 Grade 4 Module 1 Grade 5 Module 1 Other Modules also available Kindergarten Module 5 Grade 2 Module 3 Grade 3 Module 5 Grade 5 Module 3 Recommended Instructional Minutes Elementary 60 minutes Fluency Application Problems (RDW) Concept Development (includes Problem Set) Math Models Student Debrief MS / HS 45 minutes Fluency Application Problems (RDW) Concept Development Math Models Student Debrief Primary Resource Districts have choices regarding the modules Adopt Adapt Delete (Ignore) If adapting or ignoring, it is highly recommended to implement a Balanced Math Program that will include the following: Daily Fluency Problem Solving Student Reflection Lessons within a Unit Activity Using your grade level knowledge, create a scope and sequence of lesson titles (6 – 10) for facilitation of instruction on multiplication. Title of the Unit is Multiplication Modify by grade level for hierarchy Lessons within a Unit Title: Units of Measure Lesson 1: Lesson 2: Lesson 3: Lesson 4: Lesson 5: Lesson 6: Lesson 7: Converting Customary Units of Length Converting Customary Units of Capacity Converting Customary Units of Weight Converting Metric Units of Length Converting Metric Units of Capacity Converting Metric Units of Weight Problem Solving: Multi-Step Problems What is Problem Solving? Solving problems is not only a goal of learning mathematics but also a major means of doing so… Problem solving is an integral part of all mathematics learning, and so it should not be an isolated part of mathematics program. Problem solving in mathematics should involve all the five content areas described in these standards … Good problems will integrate multiple topics and will involve significant mathematics. -NCTM, Principles and Standards for School Mathematics. (2000), p.52 Math SHIFTS Mathematical Practices Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning Questions…. How are you providing an opportunity for your students to apply and explain the mathematical practices? How are you including writing in your math program? Steal Time from ELA Steal Time from ELA Writing for Problem Solving in Math Class “When students write, their papers provide a window into their understandings, their misconceptions, and their feelings about the content.” M. Burns, “Writing in Math,” Education Leadership, 62(2) (October 2004), p.30 Rationale Organize and consolidate their mathematical thinking through communication Communicate mathematical thinking coherently and clearly to others Analyze and evaluate mathematical thinking and strategies of others Use the language of mathematics to express mathematical ideas precisely. NCTM, Principles and Standards for School Mathematics. (2000) Writing for Understanding Sentence 1 summarize in 15 words or less Summarize sentence 1 and 2 in 15 word or less Summarize sentence 1, 2 and 3 in 15 words or less Continue process for paragraph Problem: Writing for Understanding Activity As I watch the snow pile up outside, I’m dreaming of the sunny weather in California. Planning an imaginary trip across the country from Allentown, PA, to Los Angeles, CA, will help keep me warm. I could use your help. According to MapQuest, the total driving distance is 2,688.2 miles. With side trips and allowing for getting lost we will actually cover 2,800 miles. At times we will be on highways where we can travel from 50-70 miles per hour. At other times we will be on city streets with a speed limit of 35 miles per hour. Problem Continued To help with calculation use the data below: Travel 35 miles per hour for five hours Travel 50 miles per hour for fourteen hours Travel 65 miles per hour for fourteen hours Travel 70 miles per hour for the remaining distance If we spend 8 hours a day driving, how many days will the trip take? How long will we drive the last day? Bonus Following the MapQuest route, name the eleven states in order from Pennsylvania to California that you would travel through on this imaginary trip Selecting the Problem Solving Task Does this problem promote application of the mathematical ideas presented in the current instructional focus or unit of study? Does this problem match students’ current instructional level? Is this problem accessible to all students? Is the problem relevant and engaging to students? Does this problem require students to “stretch” their mathematical reasoning abilities? Selecting the Problem Solving Task (cont) Does this problem involve more than one strand or standard of mathematics? Is there more than one way to solve the problem? Could the problem be extended or enriched? Do I fully understand the mathematics in this problem, so that I can better facilitate student understanding? Goal for Problem Solving at the Intermediate Grade Levels Ultimate goal for Intermediate grade students is for them to be able - by the end of the school year – to solve a multistep problem and to communicate verbally and in writing the process they used. Scaffolds to Meet Goal Model the process for the whole class until familiar Student solve the selected problems in cooperative groups or selected teams Partner students to solve a given problem together We expect students to be able to complete the entire process independently Problem Solving Sequence Whole class problem solving at beginning of the year Gain experience and capacity for problem solving Learn the writing Interact with peers Communicate mathematically Transition to cooperative learning groups, partners, and individual practice Cooperative Teams Teacher arranges the students into small cooperative groups Guided by teachers, students attempt to solve a problem Using words, pictures, and/or numbers, the students complete the Data Sheet The students then complete then work onto Chart Paper Students share out to the rest of the class Benefits of Cooperative Teams Different teams will describe their process differently and thus add to everyone’s understanding of the problem Examples around the room will provide references for the next solving activity Math team posters are updated regularly which keeps student interest in the problem solving process Sample Task Find all the different ways you can divide equally 144 marbles into bags. Data Sheet: Show work in words, drawings, numbers ….. Write up: Paragraph 1: Problem Statement Paragraph 2: Work Write Up Paragraph 3: Answer Problem Solving Task Write Up Guide SAMPLE PROBLEM SOLVING TASK The total bill for Cassie and Brooke’s dinner was $18.40. They want to leave a 15% tip. How should they determine how much tip to leave? What is the total amount that Cassie and Brooke spent for dinner? Explain your answer. Problem Solving Task Write Up Guide Directions Write your name on a piece of paper Solve the problem using words, pictures, and / or numbers Number each step as you work to solve the problem Write a number sentence to match your problem Write your answer in a sentence under your solution Now write three paragraphs describing the problem, steps used to solve the problem, and explaining your answer. Use math vocabulary Assessing Student’s Problem Solving What are the…… Strengths Challenges of problem solving? Assessing: Elements to Consider… What particular elements do you want to see the students include in their problem solving? Issues to Think About … Correct Answer Wrong Answer, Right Process Calculation Errors Math Vocabulary Strategies used to solve Spelling and Conventions Fluency of Explanations Guidelines for Rubrics Performance levels – how many? Publish and distribute to students prior to them beginning the problem solving process Problem Solving Rubric Activity Problem: Mario has a wall in his room that measures 13 feet long and 8 ½ feet high and is freshly painted. He wants to hang his favorite posters on the wall. Each poster measures 3 feet long and 2 feet high. What is the greatest number of posters that he can hang on the wall so that the posters do not overlap? Problem Solving Rubric Activity (cont) Create a rubric or guidelines for scoring Include levels and criteria for each level (first draft) Problem Solving Rubric Activity (cont) Hints for Intermediate Grades 4 levels Exemplary Proficient Progressing Beginning Self Evaluation Teacher Evaluation Let’s Create Find or create a word problem that meets the criteria discussed Create an appropriate data sheet and write up sheet for the problem Create an appropriate rubric, include levels and criteria for each level Questions or Concerns If you have any questions or concerns, please feel free to contact us. Andrea Tamarazio [email protected] Steve Graser [email protected]