ma201 dr byrne fall 2011 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
MA201 Dr. Byrne Fall 2011 PowerPoint Presentation
Download Presentation
MA201 Dr. Byrne Fall 2011

Loading in 2 Seconds...

play fullscreen
1 / 28

MA201 Dr. Byrne Fall 2011 - PowerPoint PPT Presentation


  • 120 Views
  • Uploaded on

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. .

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'MA201 Dr. Byrne Fall 2011' - mieko


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
problem solving
Problem Solving

Polya’s 4-step process:

  • Understand the problem.
  • Devise a plan.
  • Carry out the plan.
  • Look back.
problem solving1
Problem Solving

Polya’s 4-step process:

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

Understand

problem solving2
Problem Solving

Polya’s 4-step process:

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

Understand

Think

problem solving3
Problem Solving

Polya’s 4-step process:

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

Understand

Think

Do

problem solving4
Problem Solving

Polya’s 4-step process:

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

Understand

Think

Do

Check

problem solving5
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
Compare: NCSS Problem Solving Steps
  • Identify the problem.
  • Get the facts related to the problem.
  • Create a plan.
  • Carry out the plan.
  • Check your plan and adjust if needed.
slide10

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
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
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
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 problem1
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 problem2
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 problem3
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 problem4
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
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
Step 3: Carry out plan.

First, how many sizes of triangles are there?

step 3 carry out plan1
Step 3: Carry out plan.

First, how many sizes of triangles are there?

step 3 carry out plan2
Step 3: Carry out plan.

First, how many sizes of triangles are there?

‘big’

‘little’

step 3 carry out plan3
Step 3: Carry out plan.

Next, count how many of each size:

# little?

# big?

step 4 look back
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?

Answer: 8

4

4

step 4 look back1
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?

Answer: 8

4

4

problem solving in class
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
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.