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PROBLEM SOLVING STRATEGIES IN GRADES K - 2Erie 1 BOCES May 20, 2013
Facilitators: Andrea Tamarazio & Steve Graser
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 addition.
Title of the Unit is Addition Modify by grade level for hierarchy
Lessons within a Unit
Title: Units of Measure Lesson 1: Converting Customary Units of
Length Lesson 2: Converting Customary Units of
Capacity Lesson 3: Converting Customary Units of
Weight Lesson 4: Converting Metric Units of
Length Lesson 5: Converting Metric Units of
Capacity Lesson 6: Converting Metric Units of
Weight Lesson 7: 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?
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 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.
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 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.
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
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
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
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
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
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 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
Assessing Student’s Problem Solving How are you currently assessing student
problem solving in your classroom?
Strengths
Challenges
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 ActivityProblem: 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 Primary Grades 3 or 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 [email protected]
Steve Graser [email protected]