# L,S&P Teaching Ideas

### Ideas, activities and resources

Here you should find a wealth of resources that can be used by you and your students for teaching this topic. The resources at the top of the page are activities and investigations aimed at creating a stimulating and engaging environment in the classroom. With these activities you can create opportunities for students to really explore the Mathematics they are studying and discover some of the ideas for themselves!

These lessons need to be backed up with practice activities and so below there are links to worksheets aimed at practicing the skills learned and to some short tests.

There is also a section called 'The Internet Guide' which provides a brief guide to some of the best related internet items that students could use to back up there studies.

### Web Venns

There are lots of venn diagrams out there that can be used to help understand the concept. For example, a venn diagram of films starring Denzel Washington, where the sets a 'films where he wore glasses, films where he wore hats and films where he had facial hair! This page contains links to diagrams and images with questions you could ask to go with them!

Check out this great Twitter application. Anyone can use it! Type in 2 or 3 different words. the engine checks statistics for 'daily tweets containing these words' then produces a venn diagram showing the stats with each set corresponding to one of the words you entered.

### Human Venn Diagrams

Help students get to grips with Venn diagrams by making a giant one with playground chalk, coming up with different ways of classifying themselves and jumping in to it! This can be done quickly with lots of different sets or more slowly with some considered sets and a bit of artistic impression. At the end students can draw themselves in the diagram and invite other students in the school to do the same!

All squares are rectangles, all rhombuses are parallelograms. how many of these statements can we make? Put all the sets of quadrilaterals on the same Venn diagram! Can it be done? These are a great context for exploring subsets and 'if then' statements

### Dopey Logic

Students fill out this questionnaire with true or false answers about the views on legalising marijuana. Collect and publish the results using a google form and then to a logical analysis of the results. Construct truth tables for some logical statements then see which students the argument holds for. A great way to bring context to truth tables and the subject matter is engaging!

### Fairground Games

The art of designing a fairground/carnival game that looks doable, is doable, but people are most likely not to be able to do! In this activity, students do just that, and then test each other out by collecting experimental data about their games. The practice is great fun and the analysis of the data helps familiarity with the difference between experimental and theoretical probability

### Probability Trees

This activity is about bridging the gap between the intuition of sample space diagrams and the efficiency of tree diagrams. Students will look at a problem from the two points of view, play with multiplying and adding fractions and hopefully see how tree diagrams are a more efficient way of doing the same thing! The activity is good for group work and physical manipulation, although it could be completed on computers by individuals if required.

### Monty Hall

This problem from the gameshow 'Lets Make a Deal' caused a real stir at the time and I never get tired of giving it to students! If you know the problem then you should find this activity helps bring the issues across to students. If you don't, then watch the videos and check out the links from the activity page - you wont be disappointed!

### False Positives

The False Positive Paradox is a good, if not somewhat alarming example of counterintuitive Probability. Very few tests are 100% effective and as such errors occur. What's surprising is the impact these errors can apparently have. In this exercise there are data and statistics to help understand this paradox along with some news articles and weblinks that demonstrate how and when this paradox appears, including a reference to the 'Prosecutors Fallacy'.

### The Great Elf Game

Have some seasonal fun with probability! That is really what this activity is all about. I wont pretend that it ticks lots of boxes for the syllabus but teachers can make as much of it as they want to. It goes down a treat though, year after year! I highly recommend saving a lesson to play this as Christmas approaches!

### Nerf Gun Roulette ​

I have now made an activity page and activity sheet to go with this activity. Get yourselves a Nerf Gun and get stuck in with the shooting. This is a great activity for thinking about conditional probability, using tree diagrams and solving a typical IB style problem in a fun context. There are also plenty of distracting extensions to pursue.

### Quick Ideas

The following is a list of ideas for teaching that are either quickly done or not yet fully developed in to resourced activities.

#### Sets of Countries

Use the CIA world factbook or otherwise choose 3 social indicators for countries. Decide on limits for these that help you define sets for a Venn diagram. Put the countries on the Venn. What does it show? Make a revealing display with this activity?

#### Making an Argument

Making arguments. Read an article from the BBC and follow the links to the sites on logical fallacies and the write a short essay summarising what you have learned! Why not, an essay in Mathematics? This topic lends itself to discussion and the study of logical fallacies helps to understand the symbolic logic that follows. Sound arguments are what Mathematics is often based on and so this topic really gets to the heart of the subject as well offering an engaging context!

#### The Biased Interview

Pick a poor unsuspecting student and subject them to a an interview in front of the class full of logical fallacies. Use their responses to make an unjustified conclusion and watch the others leap to their defense with logical counter arguments!

#### Monty Python's view

Watch these 2 clips from Monty Python. 'Shes a witch' and 'I've come for an argument' Enjoy the humour and then discuss with students the key points to come out. This need not take long but it is a good way of introducing some ideas.

#### The Internet Guide

This page is designed to be a brief guide to some of the best related Internet items on this topic that students could use to back up their studies.

This page contains a growing list of videos freely available on the internet that could be used to help the teaching of this module. Each video comes with a brief explanation of how and when it may be used. It may also link to an activity on the site

#### L, S & P Practice Questions

Worksheets

This page links to a series of focussed worksheets for this topic. The worksheets consist largely of 'Practise Questions' but most finish with more open ended questions to extend. Ultimately, students need to be able to answer questions from a variety of topics and contexts, but often it is necessary to spend some time focussing on particular skills whilst still in the process of learning them. The worksheets are clearly titled according to the particular sub-topic and come complete with answers.

Revision Notes

This is a series of 'Fill in the Gaps' notes that I have created to help students keep useful records of the course. The rationale is explained in more detail on the 'Exams and Revision pages. Essentially the aim is bridge the gap between Students making their own notes on a blank canvas and being given detailed notes that they did not create.

#### Tests/Assessments - Planned!

Short Tests

These are just a few short tests aimed at testing smaller subdivisions of the topic with IB style questions. The more exposed students are to past paper style questions, the more familiar they become with them and hopefully the more adept they become at handling them. The tests can be used for '30 minute quizzes' as the topic is taught.

#### End of Topic Test

Here is a 1 hour long end of topic test made up of 'IB style' questions that cover the syllabus items from this topic. This is a great opportunity to create a real IB exam experience.

#### Quick Test

There are hundreds of past paper questions and exercises available for this purpose and the challenge is trying not to reproduce questions and to put together collections of questions that serve your purpose. The 'Quick Test' series (there is one for every module) was written with an end of course revision day in mind but could be used at any other time as well. This page links to the quick test for Number and Algebra and there is a link to the document itself as well.

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