#### Venn Diagrams and Set Notation Handout

Introduction to set notation and venn diragrams from the new GCSE, produced alongside AQA guidance documents (includes some snapshots of this). Handout has a PDF and editable PowerPoint format. Idea is that students fill in gaps on their version of the notes (printed as a booklet) as you talk through them on the board. Includes some basic examples, I then used questions from textbook and sourced from resourceaholic.

#### Introduction to set theory, Basic concepts

Power Point presentation, 12 slides, Explaining the meaning of the basic concepts used in set theory, based on IB Mathematical Studies Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlTTBZaDNtNUlfOTg/view?usp=sharing

#### Groups - teaching notes, examples and exercises (with solutions)

I have used this resource a few times with my classes to cover the whole topic of groups. This 24-page worksheet covers all the required knowledge and skills for FP3. Each section starts with introductory notes or examples, followed by an exercise for students to attempt. The sections are: 1. Sets, binary operations, closed/commutative/closed operations, identity elements and inverses. 2. Groups - definition of a group, order of a group, group tables 3. Multiplicative groups and cancellation laws 4. Groups using modular arithmetic 5.Symmetries of shapes 6. The order of an element 7. Cyclic groups and generators 8. Subgroups 9. Lagrange's theorem 10. Isomorphic groups The completed worksheet with all notes, examples and exercises completed (with fully-worked solutions) is also included.

#### OCR FP3 Isomorphism

A powerpoint presentation on Group Theory Isomorphism for OCR FP3

#### Sets theory and Venn diagrams

% Power point presentations on: Introduction to set theory The number sets Union and intersection of sets Shading regions in Venn diagrams Solving rpoblem using Venn diagrams

#### FP3 Group theory: Abstract algebra

Introduction to group theory followed by some worked example. This is for OCR FP3.

#### Edexcel 2017 Further Pure Maths 2 (FP2) Euclidean Algorithm Worksheet

SOLUTIONS ARE INCLUDED IN THE DOCUMENT! This is a resource for the 2017 Edexcel spec for Further Maths 2 regarding the number theory section (Euclidean Algorithm) It’s a 10Q worksheet where you are required to work out the GCD/HCF of a pair of numbers using the Euclidean Algorithm and the questions are worded in a couple of different ways - detailed solutions are at the end of the document This resource is also great for anyone who’s only just started a number theory course or studying number theory at University If you notice any mistakes at all please do notify me

#### Set Theory PowerPoint and Handouts

An extensive introduction to Set Theory, generally aimed at Computer Science A Level students, A Level Mathematicians or first year Undergraduate students in either Computer Science or Mathematics. It is intended to cover two lessons, extra examples and discussion may be required if aiming at a lower ability. Includes: A simple starter to encourage discussion on how to categorise numbers, as well as how many there may be e.g. how many natural numbers are there? A handout featuring all definitions given in the PowerPoint A PowerPoint covering set notation, intersections, unions, set comprehension and set compression. More resources can be added upon request. Please do give feedback/suggestions!

#### Closed, Commutative, Associative

A presentation that gives definitions for closed, commutative and associative in the context of group theory. Aimed at MEI FP3.

#### Logic & problem-solving saves wise man

An evil Emperor kidnapped the wisest man in the kingdom and said he was to be put to death. His family pleaded for his life, so the Emperor decided to have some evil fun and give the wise man a chance. The wise man is given 12 pills; 11 are poison and one is safe. The pills are identical except the safe one has a slightly differently weight. He is also given a balance on which he can weigh them. He can only make 3 weighings then he has to take one of the pills. Designed for G&amp;T years 9/10 this calls on all their logic and problem-solving skills. Ideally placed for collaborative working, where trial-and-error tests their ability to be wrong and yet try again. From a teaching perspective this is a real, practical, maths task, where the use of props such as Smarties or Tic-Tacs makes it more realistic than the static pencil and paper - or if you have access to some sort of ‘pod’, like those inside Kinder eggs, it’s very simple to make one slightly heavier than the rest to really bring it to life. We Solve Problems is a charity, founded by three PhD mathematicians, whose aim is to promote the use of advanced mathematics within secondary schools. We want to encourage creative mathematical thinking, to develop a skill within pupils for presenting their results clearly and coherently, as well as promoting personal problem-solving skills. Visit us at wesolveproblems.org.uk. We would very much appreciate it if you could take time to follow us, and hopefully review this resource as well, as this helps others to find us. Thank you.