MYP Standard Mathematics Patterns and Generalisations Notes

Patterns Turn Specific Examples Into Mathematical Structure

1. Mathematics often begins with noticing something repeats or grows in a regular way.
2. A pattern is an observable regularity (in numbers, shapes, or relationships).
3. When you describe that regularity in a way that works beyond the examples you started with, you are making a generalization.

1. In the IB MYP, generalizing is not just about "spotting the next term".
2. It is about using logic to create and validate rules that can become part of a mathematical model.
3. Done well, generalizations help you solve complicated problems by considering a more general case first.

Conjectures Are Testable Claims Suggested By Patterns

When you think you have found a rule, you usually express it first as a conjecture.

Conjectures are essential because they turn noticing into doing:

1. you predict what should happen for the next case,
2. you test the prediction on new cases,
3. you revise the conjecture or work toward a proof.

Representations Help You See And Communicate Relationships

1. In MYP mathematics, a key idea is that relationships are connections and associations between properties, objects, people, and ideas.
2. A pattern is one kind of relationship, and representation is how you show it clearly.

Different representations reveal different features:

1. A table is good for spotting changes from one step to the next.
2. A diagram can reveal geometric structure.
3. A graph highlights trends and rates of change.
4. An algebraic rule is compact and works for any input.

A Reliable Process For Generalizing Patterns

A disciplined approach reduces the risk of incorrect generalizations.