1. Problem solving strategies IN GRADES K - 2
November 8, 2013 Erie 1 BOCES
Facilitators: Andrea Tamarazio & Steve Graser

2. Pre-Assessment

3. Balanced Math Instruction
Computational Skills / Math Review / Mental Math
Problem Solving
Conceptual Understanding
Mastery of Math Facts
Common Formative Assessments
Jan Christinson

4. 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 addition.
Title of the Unit is Addition
Modify by grade level for hierarchy
Chart paper and markers will be needed. Teachers will need to post their responses in the room.

5. Lessons within a Unit Title: Adding with Tens and Ones
Lesson 1: Adding Groups of 10
Lesson 2: Adding Tens on a Hundred Chart
Lesson 3: Adding Tens to Two-Digit Numbers
Lesson 4: Using Mental Math to Add Tens
Lesson 5: Adding to a Two Digit Number
Lesson 6: Problem Solving: Draw a Picture and Write a Number Sentence
Compare and Contrast teacher unit and sample textbook unit
Envision Grade 1 list of lessons within a unit. Only one day of problem solving when we are promoting problem solving daily

6. 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
From 5 Easy Steps to a Balanced Math Program

7. Math SHIFTS
Provide copies of the mathematical shifts to participants

8. 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

9. 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?
Teacher answer these questions in writing. show teachers anchor writing standards and discuss
Need copies of information text reading and writing standards

10. Reading Anchor CCLS
Give participants copies of anchor standards

11. Steal Time from ELA …
Grade 1 RI standards

12. Writing Anchor CCLS

13. Steal Time from ELA

14. 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

15. 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)

16. Writing for Understanding Activity
Freddie has $250 in ten dollar bills. How many ten dollar bills does Freddie have?
He gave 6 ten dollar bills to his brother. How many ten dollar bills does he have left?
Summarize sentence one in 15words or less. Then summarize sentence one and two in 15 words or less. Summarize sentences one, two, and three in 15 words or less. Summarize all of the sentences in 15 words or less.
Andrea to facilitate – use the graphic organizer to complete the writing tasks.

17. 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?
Give teachers a math problem and see if it aligns to the questions listed on slides 12 & 13

18. 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?

19. Goal for Problem Solving at the Primary Grade Levels
Ultimate goal for primary 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.

20. 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

21. Whole Class Instruction
Teacher and students read the problem together. The teacher makes sure the student understands what the problem is asking
Students work 5 to 10 minutes to solve the problem individually, with manipulatives (recording work on paper)
Students share possible strategies for solving the problem
Teacher and students decide on a solution(s) to the problem

22. Whole Class Instruction (cont)
Teacher creates a class Data Sheet
Students copy the Data Sheet
Teacher and students compose a few sentences to describe how the problem was solved
Teacher records the sentences on chart paper to be posted in the classroom
Students copy the class-written explanation
Data Sheet is a chart showing all the work done to solve the problem, usually represented in words, pictures, and/ or numbers)

23. Cooperative Teams
Teacher arranges the students into small cooperative groups
Guided by teachers, students attempt to solve a new 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

24. 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
Let’s talk about grouping and DI

25. Problem Solving Task Write Up Guide
SAMPLE PROBLEM SOLVING TASK Curious George collected bicycle and tricycle wheels. He already found 6 wheels and then he found 3 more. Draw a picture of how many bicycles and tricycles George could make using all the wheels he collected. Include a math sentence that matches your drawing. Can you draw a picture to show that there might be more than one answer and explain why.
Create a data sheet for primary students (page 58 of book). Create a problem for teachers to work through the data sheet
Use the Problem Solving Task Write Up Guide to solve this problem.

26. 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 a short paragraph that explains, step by step, how you solved the problem
Use math vocabulary
Use this write-up guide to help you write your paragraph

27. Assessing Student’s Problem Solving
How are you currently assessing student problem solving in your classroom?
Strengths
Challenges

28. Elements to Consider…
What particular elements do you want to see the students include in their problem solving?

29. Issues to Think About … Correct Answer Wrong Answer, Right Process
Calculation Errors
Math Vocabulary
Strategies used to solve
Spelling and Conventions
Fluency of Explanations

30. Guidelines for Rubrics
Performance levels – how many?
Publish and distribute to students prior to them beginning the problem solving process
Page 49 of book, 54 of book

31. Problem Solving Rubric Activity
Use the previous Problem Solving problem with bicycles and tricycles to create the rubric.
Give teachers a problem

32. Problem Solving Rubric Activity (cont)
Create a rubric or guidelines for scoring
Include levels and criteria for each level (first draft)
Have teachers complete the first draft then share with peers

33. Problem Solving Rubric Activity (cont)
Hints for Primary Grades
3 or 4 levels
Exemplary
Proficient
Progressing
Beginning
Self Evaluation
Teacher Evaluation

34. 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
Look at curriculum between and the end of the year – create problems that can be implemented for the remainder of the year

35. Questions or Concerns
If you have any questions or concerns, please feel free to contact us.
Andrea Tamarazio
Steve Graser