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.