PROBLEM SOLVING STRATEGIES IN GRADES 3-5Erie 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: 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?

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 SolvingWhat 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 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 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 Tamarazioatamarazio@e1b.org

Steve Graser sgraser@e1b.org