MYP Standard Mathematics Problem-solving Strategies Notes

Why Problem-Solving Is A Skill (Not A Trick)

1. In mathematics, a problem is any task where the solution method is not immediately obvious.
2. That is why some questions feel easy to one student and challenging to another.
3. Often the difference is not "being good at math", it is having reliable strategies and knowing when to use them.

Pólya's Four-Step Framework Organizes Almost Any Problem

The mathematician George Pólya described a four-step approach that works in mathematics and many other subjects:

1. Understand the problem
2. Devise a plan
3. Carry out your plan
4. Look back

Step 1: Understand The Problem Before You Calculate

Understanding is active. Before you solve, you should be able to state:

1. What do I need to find (the unknown)?
2. What do I already know (the givens) and what are their units?
3. Are there conditions (whole number, positive, maximum, minimum)?
4. Can I draw a diagram, make a table, or label a sketch?
5. Can I restate the question in my own words?

Step 2: Devise A Plan Using A Strategy That Fits

1. A plan is a decision about which method to try first.
2. Common strategies include:
   1. Guess and check
   2. Look for a pattern
   3. Eliminate possibilities
   4. Use a formula
   5. Solve an equation

1. Choosing a plan is often the hardest part.
2. You can make it easier by asking: "What structure do I see?" For example:
   1. If an unknown is inside an expression, you may want to form an equation.
   2. If something changes repeatedly over time, look for a pattern.
   3. If a diagram is involved, draw and label it, then look for relationships.

Step 3: Carry Out The Plan Clearly And Monitor Your Work

When you execute the plan: