# Functions 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 their studies.

How many times will one by half the age of ones parents? This activity is about modelling the way we get older with some different types of functions. It is a simple idea, with one or two surprises and lots of possibilities.

### Meeting Functions

This is a matching activity where students have to match a set of input values with an equation and a set of output values. Its a great challenge and an excellent introduction to the functions topic.

Students are asked to match different pieces of information about quadratic functions to the graph. They then repeat the exercise with less information given each time until they are sketching graphs of the the quadratics alone! A good practical activity that really empowers students.

The axis of symmetry and the coordinates of the vertex are the key aims of this activity. Students are asked to plot different pairs of equations and describe what they have in common. They then need to start to generalise about such properties, ultimately working towards some 'Quadratic Art'!

Students are shown some animated videos of dynamic groups of quadratics and asked to figure out how they were made. In doing so they have to explore how quadratics in the completed square from are transformed. Students may then work on their own 'Dancing Quadratics' videos

### Exploring Exponentials

This activity is really a series of short activities and discussions to have to help think about what is meant by the term exponential as a lead into the study of exponential functions. We hear the word exponential regularly in discussion and in there is a sense of what it means, but it is actually quite important to be surprised by its actual meaning and the actual effect of exponential growth and decay.

### The Exponential function

Exponential functions break the mold by including the variable as a power. This makes them a completely different class of function and, as such, gives them a unique set of properties! Graphing software can really help us to discover and understand these properties and that is the aim of this investigation.

### The Tower of Hanoi

This is a great game and puzzle! What is the least number of moves? How does that vary with the number of discs? There is a lot of history in this puzzle and it is a lovely little model of an exponential sequence that can be both derived and understood!

### Which Wave

This is a simple matching activity. Students are given 15 different rig functions and 15 corresponding graphs. The object is simply to match each function with its graph. This can be either a test of their understanding or an investigation in to the properties of the functions. Simple, engaging and effective.

### Quick ideas

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

#### Angry Birds

An app that takes the world by storm for years and then becomes a physical game too! It seems a bit round about, but we have been having some fun shooting videos of real angry birds flying in parabolas and then using the Vernier physics app to model the path.....

#### Doubling time

Whilst thinking about exponential growth. How long will it take for an exponential function to double its value? This can be a great investigation and there are some interesting patterns. Start with y = ax and vary the value of a and take it from there!

#### The Internet Guide

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.

#### Functions 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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