## 3D Uncovered

‘Use Google Sketchup to see 2D planes in 3D shapes and and literally look at 3D trigonometry from a different angle!’

This activity uses the ‘Free’ and ‘Powerful’ Google sketchup application to aid the visualisation of 3D geometry problems. The third dimension can really make problems more confusing and it is a really important skill to be able to see 2 dimensional planes within a 3 dimensional diagram. Then, it can easily be seen that 3D trigonometry is really only repeated 2 Dimensional trigonometry. ‘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!

Resources

The instructions for this activity are written here in the 3D uncovered worksheet. Teachers can read more about the activity in the 3D uncovered teacher notes. You will also need access to computers and the free design software Google Sketchup.

Orbiting

Watch the orbiting in action in the short screen cast below.

Part 1

For the first part of the activity you will need to use the Sketchup file – ‘Lines and planes’. The embedded file below gives you a preview of what the file does, but to use the file like it has been used in the screencast above you need to download the file in to google Sketchup.

Use the file above to…

Annotate and label the diagram above to show the information you would need to calculate the angle that is made between the lines and the planes.

Draw or copy and paste 2D diagrams on to your work that correspond to your labels

Part 2

For this part you will need to download the model rectangular based pyramid as above. The object below gives you a preview.

Use this model to tackle the tasks below

For this shape consider that the shape ABCDE is a rectangular based pyramid, P is the midpoint of BD and Q is the midpoint of DE, BC = 15cm, CE= 10cm, OA = 6cm.

For each of the following questions you should give justification for your answer. In some cases you should ‘orbit’ the sketchup file to a position that best shows the situation the question is asking and then take a screenshot and label it for your justification.

What are the lengths of the lines CD, OD and OP?
What are the lengths of the lines AB, AP and AQ?
What angle does the line AC make with the plane BCDE?
What angle does the line AQ make with the plane BCDE?
What angle does the triangle ACE make with plane BCDE?
What are the areas of triangles ADB and ABC?
What is the surface area and volume of the ‘closed shape’ (imagining all of the faces showing)?
What are the angles DAB and EAD?

### Description

Its important to make sure that students have access to computers and Google sketchup before starting.

• Students access the Google sketchup files and practise orbiting!
• Planes and Lines – part 1 of the activity as outlined above
• Rectangular based pyramid – part 2 of the activity as outlined above
• The teacher coordinates the sharing of solutions.
• Students correct and tidy up their records of what they have done.

#### I did it my way!

As a practising maths teacher I know that most us like to give activities our own little twist and do them ‘our way’. It would be great to add a little collect of ‘twists’ from users. You can either add your twist to the comments section below or e-mail them directly to me at jamesn@inthinlking.co.uk In time some of these twists may appear here….

# ‘Zoom around the Earth and discover just how far you have traveled’

Around the World in 3 years like Ferdinand Magellan, 80 days like Phileas Fogg or 23 hours like Concorde,…Discover how fast they traveled by making calculations about the Earth’s size using Google Earth. Measurement of distance and location using lines of longitude and latitude will make this possible.

Resources

Students will need computers with Google Earth installed and internet access.
Full instructions and the whole activity can be found here Around the World
A help video for instructions on how to use Google Earth for this activity is provided

The following Teacher instructions Around the World TN will help teachers find out how best to make the most of this activity in the classroom

Description

A great way to start this activity is to put it in context. Here is a short video from Vendée Globe yacht race from 2008-9 showing the route and the excitement of the race (the real action starts 1 minute in!)

The teacher may wish to demonstrate how to use Google Earth to make measurements or students could watch the short video tutorial.
Students should work through the activity worksheet and will be guided through the following sections

Longitude and Latitude – fly to different locations on the globe to learn about how we describe their positions.
How Big is The Earth? – estimate the distance around the world using angles of longitude and the line measuring ruler on Google Earth.
How Big is The Moon? – take the investigation a step further by using Goggle Moon to make calculations about our moon and making comparisons with Earth.
How Fast? – Many records have been set about circumnavigating the globe. Compare the speeds of Ferdinand Magellan, Phileas Fogg, Concorde and the rotation of the Earth.
Extension – The circumference of the Earth at different latitudes is related to the angle of latitude. Find the rule.

Students should be encouraged to record their results digitally.
They may wish to work individually or in pairs. It is important to encourage discussion so that students can share their findings.
Taking screenshots of the Google Earth images can really help provide a visual reminder of the learning experience.

‘Help Using Google Earth’

The functions required on Google Earth for this activity are very simple. However, if you have had little or no experience with this software you might find the following 3 ½ minute video tutorial useful.

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