MA201 Dr. Byrne Fall 2011

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# MA201 Dr. Byrne Fall 2011 - PowerPoint PPT Presentation

MA201 Dr. Byrne Fall 2011. Chapter 1: Problem Solving. Problem Solving. Polya’s 4-step process: Understand the problem. Devise a plan. Carry out the plan. Look back. . Problem Solving. Polya’s 4-step process: Understand the problem. Devise a plan. Carry out the plan. Look back. .

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Presentation Transcript
Problem Solving

Polya’s 4-step process:

• Understand the problem.
• Devise a plan.
• Carry out the plan.
• Look back.
Problem Solving

Polya’s 4-step process:

• Understand the problem.
• Devise a plan.
• Carry out the plan.
• Look back.

Understand

Problem Solving

Polya’s 4-step process:

• Understand the problem.
• Devise a plan.
• Carry out the plan.
• Look back.

Understand

Think

Problem Solving

Polya’s 4-step process:

• Understand the problem.
• Devise a plan.
• Carry out the plan.
• Look back.

Understand

Think

Do

Problem Solving

Polya’s 4-step process:

• Understand the problem.
• Devise a plan.
• Carry out the plan.
• Look back.

Understand

Think

Do

Check

Problem Solving

Polya’s 4-step process:

• Understand the problem.
• Devise a plan.
• Carry out the plan.
• Look back.

Understand

Think

Do

Check

Compare: NCSS Problem Solving Steps
• Identify the problem.
• Get the facts related to the problem.
• Create a plan.
• Carry out the plan.

Polya’s 4-step process:

• Understand the problem.
• Devise a plan.
• Carry out the plan.
• Look back.

NCSS Problem Solving Steps

• Identify the problem.
• Get the facts related to the problem.
• Create a plan.
• Carry out the plan.
• Check the plan and adjust if needed.
Class Activity for Ch 1:Instructions and Example
• For a given word problem: (These instructions will be repeated.)
• Solve the problem with your group.
• Consider how you applied Polya’s 4 steps.
• If ‘trial and error’ was the strategy, is there another way you could have solved the problem?
• Include a careful diagram that you would provide to aid elementary students solving this problem.
• Compare your group’s solution with that of the other group working on the same question.
• Prepare a short 5 minute presentation comparing and contrasting the way groups worked on the problems and whether Polya’s 4 steps were useful for either group.
HW: Section 1.1 / Problem Set A
• a. If the diagonals of a square are drawn in, how many triangles of all sizes are formed?

b. Describe how Polya’s four steps were used to solve part a.

Step 1: Understand the problem.

If the diagonals of a square are drawn in, how many triangles of all sizes are formed?

• Draw a picture of a square with the diagonals drawn in.
• The question asks, “how many triangles?”
• “CLUE”: how many triangles of all sizes ?
Step 1: Understand the problem.

If the diagonals of a square are drawn in, how many triangles of all sizes are formed?

• Draw a picture of a square with the diagonals drawn in.
• The question asks, “how many triangles?”
• “CLUE”: how many triangles of all sizes ?
Step 1: Understand the problem.

If the diagonals of a square are drawn in, how many triangles of all sizes are formed?

• Draw a picture of a square with the diagonals drawn in.
• The question asks, “how many triangles?”
• “CLUE”: how many triangles of all sizes ?
Step 1: Understand the problem.

If the diagonals of a square are drawn in, how many triangles of all sizes are formed?

• Draw a picture of a square with the diagonals drawn in.
• The question asks, “how many triangles?”
• “CLUE”: how many triangles of all sizes ?
Step 1: Understand the problem.

If the diagonals of a square are drawn in, how many triangles of all sizes are formed?

• Draw a picture of a square with the diagonals drawn in.
• The question asks, “how many triangles?”
• “CLUE”: how many triangles of all sizes ?
Step 2: Devise a plan.

How to count the # of triangles of all sizes?

Plan: Figure out how many sizes there are and count them from smallest to largest.

Step 3: Carry out plan.

First, how many sizes of triangles are there?

Step 3: Carry out plan.

First, how many sizes of triangles are there?

Step 3: Carry out plan.

First, how many sizes of triangles are there?

‘big’

‘little’

Step 3: Carry out plan.

Next, count how many of each size:

# little?

# big?

Step 4: Look back.

We’ve counted 8 triangles:

If the diagonals of a square are drawn in, how many triangles of all sizes are formed?

4

4

Step 4: Look back.

We’ve counted 8 triangles:

If the diagonals of a square are drawn in, how many triangles of all sizes are formed?

4

4

Problem Solving – In Class

You will be assigned a chapter problem in small working groups.

• Small groups: Solve the problem as a group. As a group, consider how you applied Polya’s 4 steps by filling out the sheet.
• Individually: When the time is announced, spend one minute individually drawing a diagram, table or manipulative that could be used to explain the problem to a class of elementary students.
• Combined groups: Compare your group’s solution with that of the other group working on the same question. Prepare a short 5 minute presentation comparing and contrasting the way groups worked on the problems and whether Polya’s 4 steps were useful for either group.

-- pick one person to describe the problem and draw a diagram

-- pick one person to describe the solution (1 minute only)

-- pick one person to discuss the effectiveness of Polya’s 4 steps

Problem Solving – Homework

Choose 3 problems from Section 1.1 that were not assigned in class.

Solve the problem using Polya’s 4 steps, clearly dividing the steps of your solution and showing all your work.

Carefully make a diagram that you could use in a class to aid elementary students that were assigned this problem.