Unit 2 – Logic and Reasoning

This unit walks students from the limits of inductive reasoning to the power of deductive argument, conditional statements, and axiomatic systems. It’s where they learn that patterns can fail, but well‑structured arguments—built on shared premises—can’t.

For the full story of how this unit is sequenced, what changed from Year 1, and how it prepares students for proof, read the complete Unit 2 overview and navigation instrument rubric.

Unit 2 Navigation Instrument

Track how students move from inductive hunches to deductive certainty. Use this instrument to see which reasoning habits and rows (2.1–2.6) are secure and which need more work.

Open Navigation Instrument

Unit 2 Lessons

Lesson 2.1 – Inductive Reasoning

Three tasks that push students to see the difference between “it seems true” and “we know why it’s true,” ending with the pattern‑fails moment that motivates the rest of the unit.

Open Lesson 2.1

Lesson 2.2a – Deductive Reasoning and Conditional Statements

Introduces deductive reasoning and the conditional as the answer to “what can we trust if patterns can fail?”, using puzzles to make the structure of “if…then…” feel concrete.

Open Lesson 2.2a

Lesson 2.2b – Converse, Inverse, Contrapositive, Biconditionals

Gives each form its own space: students discover how changing a conditional changes its truth, and why the contrapositive is the reliable partner for proof.

Open Lesson 2.2b

Mid‑Unit Quiz

Checks understanding of inductive vs. deductive reasoning, conditionals and their forms, and the early navigation instrument rows (1–3).

Lesson 2.3 Day 1 – Always / Sometimes / Never

Students sort statements and arguments, learning to distinguish valid, sound, and invalid reasoning before any formal fallacy names appear.

Open Lesson 2.3

Lesson 2.3 Day 2 – Fallacies and Monty Python

Uses a Monty Python clip and structured notes to name common fallacies and connect them back to conditional forms students already know.

Open Lesson 2.3

Lesson 2.4 Day 1 – Named Argument Forms

Students discover and name the core valid forms (like the law of syllogism) through a chain task, seeing how proof chains actually work. If you would like a copy of my quiz emil me from your school account at jay@thinkingthroughgeometry.com

Open Lesson 2.4

Lesson 2.4 Day 2 – Carroll Puzzle and Comparisons

Resolves the Lewis Carroll puzzle and builds a comparison table between valid forms and their fallacious look‑alikes.

Open Lesson 2.4

Lesson 2.5 – Transversal Angle Relationships

First time logical structures land directly on geometry diagrams: students conjecture angle relationships inductively, then derive them deductively from a shared premise.

Open Lesson 2.5

Lesson 2.6 – Axioms and Shared Premises

Uses a Sudoku task and disagreement questions to show why shared premises (axioms) matter, then names Euclid’s 10 axioms as the course’s foundation.

Open Lesson 2.6

Unit 2 Differentiation Day

A cumulative practice day where students use the navigation instrument to choose targeted problem sets and address specific reasoning gaps from Lessons 2.1–2.6.

Unit 2 Assessment

I’m happy to share my Unit 2 assessments and grading rubrics for teacher use, but I don’t want them publicly available on the internet. If you’d like a copy, please email me from your school account at jay@thinkingthroughgeometry.net and let me know which school and state you teach in.