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ÌÇÐÄVlog

Last updated

8 April 2026

zip, 71.14 KB
zip, 71.14 KB

This fully scripted 60-minute IB DP Theory of Knowledge (TOK) lesson explores the nature of mathematical knowledge, including proof, axioms, certainty, intuition, and infinity. It asks students to consider why mathematics often feels like the most certain form of knowledge, while also raising questions about formal systems, undecidable truths, and the relationship between mathematics and reality.

The lesson begins with two challenging statements about mathematics: that there are as many even numbers as whole numbers, and that there are true mathematical statements that cannot be proven. Students use these to start thinking about whether mathematics is discovered, constructed, or both. This leads into a teacher-guided introduction to axioms, theorems, proofs, formal systems, and Gödel’s limits.

The first main task is Activity 1: The Proof. Students work through a guided proof by contradiction showing that √2 is irrational. The focus is not just on reaching the conclusion, but on understanding what makes proof convincing and how mathematical certainty differs from scientific evidence.

The second main task is Activity 2: The 0.999… Debate. Students argue both sides of the claim that 0.999… = 1 and use algebraic, fractional, and series-based reasoning to explore the issue. This helps them examine the relationship between mathematical proof and intuition, and shows how formal reasoning can challenge common sense.

The lesson also includes Activity 3: Infinity Paradoxes, where students work with Hilbert’s Hotel, Zeno’s Arrow, and Cantor’s different infinities. These examples help students think about what happens when mathematical definitions conflict with everyday intuition and whether mathematics is describing reality or creating internally consistent systems.

The resource includes a full teacher walkthrough, proof worksheet, debate sheet, paradox activity sheets, TOK knowledge questions, and an exit ticket. It is useful for TOK lessons on mathematics, certainty, proof, intuition, infinity, and the relationship between formal systems and knowledge. It can also support TOK Exhibition planning and essay discussion.

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A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

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IB DP Theory of Knowledge (TOK): 19 Lesson Bundle - Part 2 - 2026

This bundle contains another 19 lessons covering the Areas of Knowledge and optional themes of the IB DP Theory of Knowledge course. There are multiple valid ways to sequence and teach these topics. This is not an exhaustive curriculum. These are just some ready-made lessons and activities for any teacher who needs something to use with their students, whether you follow this order or pick and choose what fits your context. Possible sequence and rationale This bundle picks up where the first 20 lessons left off, completing the Natural Sciences AOK before moving through Mathematics, History, Human Sciences, Ethics, Technology, Politics, the Arts, and Religious and Indigenous Knowledge Systems. The AOKs are ordered to build on each other: Natural Sciences and Mathematics sit together because both deal with formal knowledge and certainty, making comparison straightforward. History and Human Sciences follow because they raise similar questions about method, objectivity, and bias but in messier, more contested territory. Ethics comes next because the Human Sciences lessons, particularly the conformity material, lead naturally into questions of moral knowledge. The Technology and Politics optional themes close the AOK sequence because students are by then equipped to apply everything they have learned to the most current and contested knowledge contexts. The Arts and Religious and Indigenous Knowledge Systems sit last as a deliberate broadening; they challenge students to question the assumptions about knowledge they have built up across the rest of the course. What is included Paradigm Shifts Science Ethics and Values The Nature of Mathematical Knowledge Is Mathematics Invented or Discovered Mathematics Beauty and Intuition How Historians Know What They Know Perspective Bias and Revisionism in History History Language and Narrative Methods in the Human Sciences Ethics and Human Sciences Ethics and Conformity Moral Frameworks Applied Ethics and Knowledge Algorithms and the Architecture of Information AI and Knowledge Production Misinformation and the Digital Age Political Knowledge and Ideology Knowledge Through the Arts Religious and Indigenous Knowledge Systems Each lesson includes scripted teacher notes, student-facing materials, discussion questions, and at least one activity. Suitable for Grade 11 and 12 students in the IB DP TOK course. Aligns with the current IB TOK guide for 2026

£68.00

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