Pre-Alg · Unit 2

Irrational Numbers

√2 and the failure of ratios

Curriculum standard — Understand stage of the Thinking Ladder

Irrational Numbers begins with meaning — what it is and why it holds — before any procedure. The structure comes first; computation follows.

Definition

The precise meaning of this topic, stated in mathematical terms.

A plain-language restatement so the definition is understood, not just memorized.

Three pathways, one topic

Study irrational numbers at three depths

Grade/course-level problems with full understanding.

Parameters, multiple representations, proof, and modeling.

Non-routine problems and competition applications.