This week I need some resources to demonstrate plans and elevations. There are several Wisweb applets from the Freudenthal Institute which are excellent for this topic. These work well on the interactive whiteboard for demonstrating to students, they are also ideal for students to explore themselves.
Cube houses shows several models with their elevations, select drawing then 3d-model to give a model you can rotate to generate different views.
Readers familiar with the excellent Improving Learning in Mathematics materials may recognise the applets for building houses; these are described in SS6 – Representing 3D shapes which has suggested lesson activities and describes the applets (see pages 4 and 5).
Building Houses allows you to create buildings and see the plan, front and side elevations as you build. (If that link does not work – try this).
You can add (build) or remove (break down) bricks and control the size of the square base.
Building houses with side views challenges students to construct 3D models given the plans and elevations; the task is made more challenging by specifying that as few cubes as possible should be used.
Note that in order to achieve the minimum number of cubes, ‘floating’ cubes are needed.
Note that these resources have been added to the ‘explore‘ series of pages on the companion blog for students.
Update - these resources worked well with my students – they particularly enjoyed the challenge of trying to build models using the minimum number of cubes!
Readers interested in the Improving Learning in Mathematics materials further may find IWB Resources useful as it has a flipchart and notebook file for each of the activities. This site is a result of the NCETM research project: Enabling enhanced mathematics teaching with some interactive whiteboards (September 2006- September 2008) and is supported by the IWB research team at Keele University and the www.iwbmaths.co.uk team. See also the link on the reading page to Malcolm Swan’s Improving Learning in Mathematics – Challenges and Strategies.
A collection of excellent free resources for demonstrating the various circle theorems:
Tim Devereux has created GeoGebra applets which allow exploration of the circle theorems. You can access each theorem from the menu on the left which includes a useful summary of all the theorems.
The 1000 Problems site is an excellent collection of resources organised into collections on Number, Algebra, Shape and Space and Statistics. Within each category problems are organised by age and key words and a clear description are given for each problem. For each problem a file can be downloaded which includes the solution.
I have been working on Surds with one of my classes recently, looking at the Extension problems on Number I can see there is a problem on ‘Friendly Surds’ which would make a good starter to review the work we have been doing and extend to generalise – what conditions do we need for surds to be ‘friendly’?
For other Starter ideas see the companion blog Mathematics – a variety of resources to start and end lessons.
John Page describes his ‘Math Open Reference‘ project as a free interactive textbook on the web, initially covering Geometry.
The tools include various function explorers. Younger students could explore linear functions for example, whilst older students could use the general Graphical Function Explorer to explore any functions, trigonometric for example.
GeoGebra is software for interactive geometry. Astonishingly is it free, astonishing as it is such of such high quality and is so well supported. There are many resources available on the Internet. I have created a Diigo list of resources which includes many examples and tutorials.
(Click on the green links for each item, then back on your browser if you wish to return to the list.)
Alternatively use the LiveBinders version.
Note that if you have not used GeoGebra before the Introductory book is very helpful. Also, see in particular Guillermo Bautista’s Mathematics and Multimedia Blog for numerous tutorials from beginner to advanced and the GeoGebra YouTube Channel.
I have included GeoGebra in my Top >10 Mathematics websites.