problem solving strategies in grades k - 2
DESCRIPTION
Problem solving strategies IN GRADES K - 2. Erie 1 BOCESMay 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 - PowerPoint PPT PresentationTRANSCRIPT
PROBLEM SOLVING STRATEGIES IN GRADES K - 2Erie 1 BOCES May 20, 2013Facilitators: 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]