What's the difference between spotting a pattern and actually understanding it?
Think about your phone's battery draining at roughly the same rate every hour. You notice the pattern , but if you write a rule that lets you predict the percentage at any future hour, you've done something more powerful: you've made a generalisation. A pattern is just the observation. A generalisation is the rule that captures why it keeps happening and lets you apply it beyond the examples you started with.
In MYP Maths, the goal isn't just "what comes next?" , it's building a rule that works for any input, then defending why it must be true. That's what separates a lucky guess from actual mathematical reasoning.
Generalisation: A generalisation is a rule or statement built from specific examples that extends to cases you haven't yet seen.
A pattern you notice is your starting point, not your finish line. Every generalisation needs two things: a reason it should work, and evidence from testing it on new cases.
When you think you've found a rule, you express it as a conjecture , a claim that looks true based on what you've seen, but hasn't been fully proven yet. Your job is then to predict, test, and either confirm or revise it.
Conjecture: A conjecture is a statement that seems to hold based on observed examples, but still needs verification or proof before it can be trusted completely.
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