# Calculus 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 practise activities and so below there are links to worksheets aimed at practising the skills learned and to some short tests. There also some IB style questions, some note taking tasks and an end of topic test!

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.

### Classifying Sequences

Starting with 'Carte Blanche' students are asked to look for common features of a number of sequences. The sequences have varied powers of x ranging from linear to quartic. The activity leads to using differences and differences of differences to determine the order of the sequence!

### Rates of Change

This activity involves looking at the distance, speed and acceleration of 8 cars all measured over a given time period. Students are asked to use these tables to describe the journeys and then match them with the appropriate graphs of the distance, speed and acceleration.

This activity follows on from classifying sequences or relies on students ability to determine the order of sequences. In this activity students 'not surprisingly' measure the gradients of different functions which leads to the discovery that the function that describes the gradient of a given function is one power of x less. Students use Autograph for its accuracy and ease so that they can concentrate on the observations!

### Optimal Jumble

This problem is all about the 9 steps of 3 different optimisation problems. These have been cut up in to 27 pieces and the name of the game is to put all this back together. The problem is really in two parts! You have to try and split them in to 3 different groups and then you have to try and put the steps of the problem in to a logical order. In practice you will find yourselves doing these simultaneously.

### Quick ideas

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

#### Max Box

For many maths teachers, this is a classic activity that has been around for a long time. Starting with a given rectangle, what size square should be cut out of the corner to leave a net for an open top box with the biggest volume? Don't miss the opportunity to build these and play with the results. This activity has lots to offer......

#### Speed!

How fast is Usain Bolt running when he runs the 100 metres? Students look at different speeds and convert them into different units in attempt to understand them. Use this  Split times link from speed endurance to look at how the speed varies over the course of the race. There are also results from previous winners.

#### 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

#### Calculus Practice

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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