Problem Solving Strategies
Good mathematicians use systematic strategies to tackle unfamiliar problems. Learning these strategies builds persistence and mathematical reasoning that applies across all topics.
What You Need to Know
Key Concept Diagram
Understand the problem: identify what is given and what you need to find
Draw a diagram or make a table to organise information visually
Work backwards from the answer when the end result is known
Look for a pattern: find a rule and extend it
Break complex problems into smaller, manageable steps and check your answer
Key Vocabulary
Strategy
A planned method or approach for solving a problem
Logical Reasoning
Using known facts and rules to reach a conclusion step by step
Conjecture
An educated guess or prediction based on observed patterns
Verify
To check that a solution is correct by substituting back or testing it
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A farmer has hens and rabbits. There are 10 heads and 28 legs in total. How many rabbits are there?
Question 2
What strategy is most useful when you know the final answer and need to find the starting value?
Question 3
The pattern 3, 7, 11, 15 ... follows a rule. What is the 10th term?
Key Concepts Summary
- ●Understand the problem: identify what is given and what you need to find
- ●Draw a diagram or make a table to organise information visually
- ●Work backwards from the answer when the end result is known
- ●Look for a pattern: find a rule and extend it
- ●Break complex problems into smaller, manageable steps and check your answer