Related concepts (examples) flashcards

Topic 3: Related concepts (examples)

The twelve related concepts in MYP mathematics

Approximation, change, equivalence, generalization, models, patterns, quantity, representation, simplification, space, systems, validity. Teachers may add others.

Key concepts compared with related concepts

Key concepts are broad and shared across subjects. Related concepts belong to mathematics and look at a key concept more closely.

Equivalence: how do you show two expressions are (or are not) equivalent?

Expand and simplify until the forms match: 4(x − 1) + 2x = 6x − 4. One counterexample shows they are not equivalent. A matching test value supports equivalence but does not prove it.

Simplification compared with approximation

Simplifying rewrites an expression in an easier form and keeps its value exactly. Approximating changes the value slightly.

Pattern compared with generalization

A pattern is the ordered set of numbers or objects. A generalization is the rule you state about it, built from particular cases (4, 9, 14, 19 → 5n − 1).

Model compared with representation

A model depicts a real-life event through expressions, equations or graphs. A representation is the form something is shown in, such as a table or graph.

Validity, with an example

Sound, logical mathematics giving a true conclusion or a sensible interpretation. x² + 2x − 24 = 0 gives x = 4 or −6; for a length, reject −6.

Which related concepts appear in all four branches, and which in only one?

Equivalence, quantity and systems appear in all four branches. Space appears only in spatial reasoning.