INforM – Interactive Notebooks for Mathematics
Book 15 – Working in Three Dimensions
Working in 3D
This is the first of four `thematic’ Notebooks whose aim is to present some mathematics teaching ideas based on realistic problems and modelling which link to other subjects and which can be pursued in an open-ended and problem-solving manner.
The activities are related to work in Design & Technology and Art & Design. The mathematics covers 2D representations of 3D objects, nets, elevations and perspective.
Organisation of the materials
The Smart Notebook file is saved as `Book 15 ThreeD.notebook’.
It consists of 11 pages of which the first is the title page, shown above.
There are 8 pages to support the activity and its extension. Page 10 is a blank page.
Page 11 contains teacher notes which are amplified here.
The first activity
The title page shows a photograph of a stack of coloured cubes – a perspective view. The blue image of a cube is the stylised oblique view familiar from text books. Page 2 shows similar images of four simple solids. In each case the class are invited to make their own sketches of the nets of the objects – and for volunteers to come up and share them on the SMART Board.
Page 3 uses a Flash animation from the SMART Notebook gallery. The intention is to help pupils improve their powers of visualisation. Ask pupils to imagine folding each of the nets up to make the object. Then use the slider bar to slowly start forming a `3D’ representation of the emerging solid.
Page 4 shows an example activity from
the Standards Unit’s module SS6 on shape and space intended to be displayed for whole class discussion. Pupils have to imagine themselves viewing the stack of cubes (a) directly down from above (b) directly from in front and (c) directly from the right-hand side. The result will be a 2D plan view consisting of squares.
The correct images are concealed at the right-hand side where the coloured rectangles can be slid away.
Page 5 shows a still screen copy from one of the interactive files from the Standards Unit. Here the pupils should try and add and take away bricks mentally from the structure in a way which doesn’t change the plan and elevation – which is quite a challenging task!
Page 6 shows a flash video of the software being used to build up a structure and, at the same time, the plan and elevations for the structure. The link near the bottom of the page will open and run the software within a web-browser. The software is provided as an attachment to the Notebook. Dragging while holding a mouse button down allows the user to rotate the 3D scene.
Page 7 shows a screen created in the Cabri 3D software. In order to be able to spin the view you will need to open up one of the two files from the Attachments using the links shown. Ideally you will already have a full copy of this BETT 2007 Award winning software! In any case you download a free 30-day trial version of the software using the link from the Teacher Notes on page 11. Using the software you can add and delete cubes to change the configuration. As an alternative approach, the Cabri 3D file has been embedded in a Word document and then exported as a web-page. You will need to load the free plug-ins (from the same link) in order for your web-browser to be able to allow you to manipulate the object. Dragging with the right-mouse button you can spin the object. But also if any point has been constructed in a way which makes it draggable, then you can drag it on the web-page.
Page 8 shows a digital photograph of a bridge across the River Cam in Cambridge from Trinity College. It’s known as the Mathematical Bridge. Clearly there are lines in the image which should be parallel in space, which appear far from parallel in the image. The points where such lines meet are known as `vanishing points’ – how many can you locate in the picture?
Page 9 shows a building which is more or less formed from a cuboid base. Trace parallel sets of lines to find the vanishing points. Students can be encouraged to share their own photographs – or to search for interesting ones on the web.
Page 11 has the teacher notes which include the references and links to the sources of the materials used to support this activity. If you get interested in exploring Cabri 3D as a vehicle for motivating work in 3D you will find some materials to help you develop skills in its use, as well as a large number of pre-written files, at:
www.counton.org/cabri/index.htm
INforM Page 2 of 4 December 2006