# G & T Teaching Ideas

### Ideas, activities & 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 are 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.

### Crow Flies

This activity is about using Pythagoras theorem to work out the shortest distance between two points by using their coordinates. It invites students to start thinking about coordinate geometry.

### Stuck in the middle

Working out the coordinates of a mid-point can be wonderfully intuitive. This activity uses the context of some geometrical constructions using midpoints as a context for getting used to the idea. Students explore a bit of geometry in doing so.

### Steep

This activity gets at the heart of the concept! What is a gradient? How do we measure it? What's it got to do with anything? It is worth spending some time on here so its well understood for the study of calculus.

### Parallel & Perpendicular

Students explore some of the properties of parallel and perpendicular lines, ultimately discovering the relationships with the gradients.

### Two Ways

This is a short little reasoning puzzle aimed at helping students to understand why there are different forms for expressing the equations and straight lines and fluently converting between them

### Trig Calculator

Using dynamic geometry students set up a moving figure that calculates trig ratios between 0 and 90 degrees! This activity helps students to understand the very nature of trigonometry and can lend real meaning to and improve a students ability to calculate with it.

### Re-arranging relations

How to move from understanding trigonometry to solving problems with it. This activity aims to encourage a speculative approach to solving problems and relates right angled trig problems to a basic three way relationship.

### The Sine rule

This is a great chance to see Mathematics in action! Students speculate with what they know and understand about right - angled trigonometry to derive the sine rule for themselves (hopefully)

### Which Rule?

This one is based just around plotting a path through problems and helping students to work out quickly whether, the Sine rule, the Cosine, rule, SOHCAHTOA or Pythagoras's theorem is the most efficient way of solving a problem, without actually having to go on and solve it.

### 3D uncovered

This activity uses the 'Free' and 'Powerful' Google sketchup application to aid the visualisation of 3D geometry problems. Students 'orbit' the sketchup file to find the best view to solve a series of problems calculating lengths, angles and angles made between lines and planes!

### Making Cones

In this activity students are given minimal data about a cone and asked to build it from card. In doing so students have to consider Pythagoras theorem, arc lengths and sector areas as well as deducing the net of a cone. Having done this, students use their discoveries to deduce and prove algebraically the surface area of a cone. Its practise of skills in the context of problem solving and presents an engaging challenge!

### The Cuboid Challenge ​

This activity is really easy to describe, but difficult to carry out! It is a very hands on activity that should help develop a really good understanding of the geometry of pyramids. Making them is the very best way of finding out about them! You may be required to use Pythagoras’s theorem and trigonometry to work out some missing lengths.

### Quick Ideas

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

#### Spheres

This is a lovely little exercise to demonstrate the surface area of a sphere and some follow up investigations on spheres in general. Get an orange, cut in half and use the cross section to draw 4 circles that have the same radius as the sphere. Peel it as carefully as possible and then try to fill up the 4 circles with the peel!

#### Equable Cones & Sphere

How many cones can be made with the same volume as a given sphere? How do they vary in shape and size? These questions and more invite students to play with these shapes and become proficient with the associated formulae in doing so.

#### Impossible Triangles

This is an idea that is taking shape and coming soon. Here is the thought - draw a set of different triangles and label them with side lengths and angles such that some can exist and some are impossible! Students are then required to reason with each other using different geometrical theories to decide which can and which cannot exist! Watch this space...

### See Also

#### 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

#### G & T Practice

This page has a variety of tasks designed for practise and revision.

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 to 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!

This page will contains some assessments for use with this module

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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