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# Progression maps: Using and applying mathematics – Problem solving

Step 1
• Objective: Try different approaches to solve a problem.
Step 2
• Objective: Try different approaches and find ways of overcoming difficulties that arise when solving problems.
Step 3
• Objective: Use a range of strategies when solving problems.
Step 4
• Objective: Develop strategies for solving problems and use these strategies both in working within mathematics and in applying mathematics to practical contexts.
Step 5
• Objective: Begin to structure an approach when exploring a simple task or solving a problem. Generate and check the necessary information.
Step 6
• Objective: Identify the necessary information to carry through tasks and solve mathematical problems. Check results and consider whether they are sensible.
Step 7
• Objective: Solve more complex problems by breaking them into smaller steps or tasks, choosing and using efficient techniques for calculation, algebraic manipulation and graphical representation, and resources, including ICT.
Step 8
• Objective: Solve substantial problems by breaking them into simpler tasks, using a range of efficient techniques, methods and resources, including ICT.
Step 9
• Objective: Starting from given problems or contexts, progressively refine or extend the mathematics used to generate fuller solutions.
Step 10
• Objective: Solve increasingly demanding problems and evaluate solutions; explore connections in mathematics across a range of contexts: number, algebra, shape, space and measures, and handling data.