MA201January 15th, 2010

Results of Paragraph: Explain the importance of elementary mathematics.

Generalized answer:• Needed for everyday life skills.

– To function independently.

• Develops problems solving skills.• Foundation for more complex math in high school (algebra and

calculus). • Young children are receptive to learning.

Some specific answers:• Math is a language developed to describe relationships between

things.• Math is needed as the foundation of careers that keep society going

(e.g., building houses).

Problem Solving

Polya’s 4-step process:

1. Understand the problem.

2. Devise a plan.

3. Carry out the plan.

4. Look back.

Problem Solving

Polya’s 4-step process:

1. Understand the problem.

2. Devise a plan.

3. Carry out the plan.

4. Look back.

Understand

Problem Solving

Polya’s 4-step process:

1. Understand the problem.

2. Devise a plan.

3. Carry out the plan.

4. Look back.

Understand

Think

Problem Solving

Polya’s 4-step process:

1. Understand the problem.

2. Devise a plan.

3. Carry out the plan.

4. Look back.

Understand

Think

Do

Problem Solving

Polya’s 4-step process:

1. Understand the problem.

2. Devise a plan.

3. Carry out the plan.

4. Look back.

Understand

Think

Do

Check

Problem Solving

Polya’s 4-step process:

1. Understand the problem.

2. Devise a plan.

3. Carry out the plan.

4. Look back.

Understand

Think

Do

Check

Compare: NCSS Problem Solving Steps

1. Identify the problem.

2. Get the facts related to the problem.

3. Create a plan.

4. Carry out the plan.

5. Check your plan and adjust if needed.

Polya’s 4-step process:

1. Understand the problem.

2. Devise a plan.

3. Carry out the plan.

4. 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.

HW: Section 1.1 / Problem Set A

1. 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?

‘little’ ‘big’

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?

Answer: 8

44

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

44

Problem Solving

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

Solve the problem using Polya’s 4 steps, then present your solution to the class.