First give me an interesting problem.

When mathematicians become interested in a problem they:

• Play with the problem to collect & organise data about it.
• Discuss & record notes and diagrams.
• Seek & see patterns or connections in the organised data.
• Make & test hypotheses based on the patterns or connections.
• Look in their strategy toolbox for problem solving strategies which could help.
• Look in their skill toolbox for mathematical skills which could help.
• Check their answer and think about what else they can learn from it.
• Publish their results.

Questions which help mathematicians learn more are:

• Can I check this another way?
• What happens if ...?
• How many solutions are there?
• How will I know when I have found them all?

When mathematicians have a problem they:

• Read & understand the problem.
• Plan a strategy to start the problem.
• Carry out their plan.
• Check the result.

A mathematician's strategy toolbox includes:

• Do I know a similar problem?
• Guess, check and improve
• Try a simpler problem
• Write an equation
• Make a list or table
• Work backwards
• Act it out
• Draw a picture or graph
• Make a model
• Look for a pattern
• Try all possibilities
• Seek an exception
• Break the problem into smaller parts
• ...

If one way doesn't work I just start again another way.