There are many types of problems in mathematics. The answer or solution to a problem can often be obtained in several ways.
Solving problems in mathematics can be frustrating... but also very satisfying.
"How do you do this one?"  "That was easy!" 
Most problems can be solved by following a plan or strategy.
The following plan, which has four key steps, works well:
Step 1  Read the problem 
What information is given in the question? 
Step 2  Plan what to do 
What method shall we use? 
Step 3  Solve the problem  Make the calculations required. Show each step of your working. Write using full mathematical equations and statements 
Step 4  Give the answer  Does your answer make sense? Does your answer need rounding? Write the answer as a full sentence. 
This plan can be summarised:
READ > PLAN > SOLVE > ANSWER
Other Hints on Problem Solving
Every problem is different but there are several approaches you can take which may result in progress being made:
 Estimate the answer
 Use trial and error (guess and check) until you get the correct answer.
 Look for patterns
 Use algebra and form equations
 Make a table or list
 Draw a diagram, graph or make a model
 Break the problem up into parts.
Types of Problems
Example 1
A rectangle is twice as long as it is wide. Its perimeter is 24 cm, What is its area?
Step 1  Read the problem 
Key points: Shape is a rectangle, length = 2 x width, perimeter is 24 cm To find: Area of rectangle 

Step 2  Plan what to do 
We need to remember that the perimeter is the distance around the shape and the area is the length multiplied by the width. 

Step 3  Solve the problem 
Make a table of possible widths and lengths:


Alternatively, you can use algebra: L + L + W + W = 24 If the width = W, the length L = 2W Form an equation: W + W + 2W + 2W = 24 6W = 24 W = 4 Therefore the width = 4 cm and the height = 8 cm 

Step 4  Give the Answer  The area of the rectangle would be 32 cm^{2.} 
Example 2
What are the next 3 numbers in the sequence 2, 5, 10, 17,...?
Step 1  Read the problem 
The next three numbers are needed. 

Step 2  Plan what to do 
Look for a pattern 

Step 3  Solve the problem 
Method 1
You would expect the gap between 17 and the next number to be 9, so the next number is 26. Following this pattern the next numbers are 37 and 50. 

Method 2
Try to see a connection between the position of the number and the number itself. The connection is that if you SQUARE the first number and ADD ONE you get the sequence number. 

Method 3 The next three numbers (in blue) can be found from the graph . These sequence graphs are often straight lines. 

Step 4  Give the answer  The next three numbers are 26, 37 and 50. 