Implications for Teaching

Devising a Plan

**4 Part Problem Solving Model**

Carrying out the Plan

by Laura, Michele, Natalie, Sarah & Zahra

The Four-Step Problem-Solving Model was created by George Polya. This model is meant to help students apply their knowledge in a more organized manner, before they have completely internalized the problem-solving process. The four steps in this model are: Understand the Problem, Make a Plan, Carry out the Plan and Look Back to Check the Results.

Due to the depth of this model, it is typically not explicitly introduced until Grade 3. Students younger than this often get stuck on the model and forget the importance of the math concepts. Teachers, though, will often use this model with students implicitly to help guide his/her questions. It is also important to note that, although the model is taught in order, looking back at the steps may be required.

This model is meant to not only be used for mathematics, but to teach the student to think about problems before, during and after they occur, something that will transfer to other areas of their lives.

Resource: The Ontario Curriculum: Grades 1-8 Mathematics. (2005).

Understanding the Problem

Introduction

Student Strategies

* Can you state the problem in your own words?

* What are you trying to find or do?

* What is the main idea of the question?

* What are the unknowns?

* What information do you obtain from the problem?

* What information, if any, is missing or not needed?

Student Strategies Questioning

* Look for a pattern, and clues

* Examine related problems, and determine if the same technique can be applied

* Examine a simpler or special case of the problem to gain insight into the solution of the original problem

* Make a table

* Make a diagram

* Write an equation

* Use guess and check

* Work backward

* Identify a subgoal

Implications for teachers

Encourage students to think and talk about the problem and say it in their own words before going to get manipulatives and or paper and pencil.

Implications for Teachers

Teachers circulate and ask questions that elicit greater understanding.

Encourage perseverance.

Offer suggestions to help the student become "unstuck".

Looking Back/Reflecting

Implications for Teachers

Facilitate student sharing of work.

Encourage student discussion: what they have learned? (most efficient, easiest to use etc?

Pose new problems that are related.

Student Strategies

* Implement the strategy or strategies in step 2, and perform any necessary actions or computations

* Check each step of the plan as you proceed. This may be intuitive checking or a formal proof of each step

* Keep an accurate record of your work

* Don't be afraid to start over

An Overview:

Student Strategies

Step 1: Understand the Problem

Step 2: Make a Plan

Step 3: Carry Out the Plan

Step 4: Look Back at the

Solution

Source: The Ontario Curriculum, Grades 1-8, Mathematics, page 13

In this step, students identify the goal, decide what information in required, detect any missing information and break the problem down into smaller pieces.

Communication:

Talk about the problem to understand it better

In this step, students work to relate the problem to similar problems solved in the past, and consider other possible strategies. Together, they select a strategy or a combination of strategies to try.

Communication:

Discuss ideas with others to clarify to clarify which strategies would work best.

Communication:

- Draw pictures; use manipulatives to represent interim results

- Use words and symbols to represent the steps in carrying out the plan or doing the calculations

- Share results of computer or calculator operations

Communication:

Describe how the solution was reached, using the most suitable format, and explain the solution!

* Check the results in the original problem. (In some cases this will require a proof.)

* Interpret the solution in terms of the original problem. Does your answer make sense? Is it reasonable?

* Determine whether there is another method of finding the solution.

* If possible, determine other related or more general problems for which the techniques will work.

In this step, student implement the strategies they planned out in Step 2. Students should be given a reasonable amount of time to solve the problem and encouraged to seek hints if they hit a 'road block'.

Examples of

Clue words

Clue Words for Addition

* sum

* total

* in all

* perimeter

Clue Words for Multiplication

* product

* total

* area

* times

Clue Words for Subtraction

* difference

* how much more

* exceed

Clue Words for Division

* share

* distribute

* quotient

* average

In this step, students look back to the original question and check to see if the stated problem is satisfied, if it could have been approached differently and if plan can be extended for a general understanding.

**Resources & Other**

**S.O.L.V.E.**

**C.U.B.E.S.**

The first step is to highlight the question. The next step is to answer the question "What is the problem asking me to find?" Always start the answer to this question with the word "the."

O - Organize the Facts -

This step is referred to as "O" the problem. You must always "S" the problem first, then you may "O" the problem.

There are three steps to "O" :

1) Identify the facts by striking after each fact

2) Eliminate unnecessary facts by crossing them out

3) List the necessary facts

L - Line up a Plan -

Students must "S" and "O" the problem before they "L" the problem. In this step, students need to choose the operation or operations they will use to solve the problem. They must use the facts listed in "O" when writing their plan.

V - Verifying the Plan

with action -

The first step in this plan is to make an estimate of the answer and writing this estimate in a "thought bubble." Next, students will use the verbal expressions in the "L" step to write a numerical expression or equation that can be solved. This is where they actually do the math and find the answer.

S - Study the Problem -

E - Examine the Results -

In this step, students will ask the questions: "Did you answer what you were asked to find in S?" "Is my answer accurate?" "Is my answer reasonable?" The last step in "E" is to write the answer as a complete sentence.

www.cfisd.net/dept2/curricu/elmath/4step.htm

http://teacher.scholastic.com/lessonrepro/lessonplans/steppro.htm

http://faculty.salisbury.edu/~dccathcart/MathReasoning/Polya.html

www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf

http://eworkshop.on.ca/edu/resources/guides/Guide_Math_K_6_Volume_2.pdf

www.eworkshop.on.ca/edu/resources/numeracyProfessional_Development_Activities/Module2/Module2Slid...

**Images & Videos**

Solve me Maybe -

Problem Solving Strategies

How to use 4 step problem solving

Problem Solving song - UPSC

Problem Solving Steps