Mathematical Problem Solving
Mathematical problem solving involves choosing strategies, working systematically, and communicating reasoning clearly. Strong problem solvers are flexible thinkers who try multiple approaches.
What You Need to Know
Key Concept Diagram
Read problems carefully: identify what is given and what is unknown
Choose a strategy: draw a diagram, make a table, work backwards, look for a pattern
Check your answer makes sense in the context of the problem
Show working clearly so your reasoning can be followed
Key Vocabulary
Working backwards
Starting from the desired outcome and reasoning in reverse to find the starting value
Systematic approach
Organising work in a logical order to ensure nothing is missed
Conjecture
A mathematical statement that you believe is true but have not yet proven
Strategy
A planned method for solving a problem
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Anna thinks of a number, doubles it, adds 10, then halves the result to get 14. What was her number?
Question 2
Tiles are arranged in a pattern: 1, 5, 9, 13... How many tiles are in the 20th pattern?
Question 3
Three friends split a restaurant bill equally. Each pays $24.50. Then a discount of $7.50 is applied. How much should each person get back?
Key Concepts Summary
- ●Read problems carefully: identify what is given and what is unknown
- ●Choose a strategy: draw a diagram, make a table, work backwards, look for a pattern
- ●Check your answer makes sense in the context of the problem
- ●Show working clearly so your reasoning can be followed