'Use a virtual world to explore the 2D representation of 3D shapes. Can you construct an object in 3D from a set of 2D drawings?'

The aim of this activity is to provide concrete experiences that develop the ability to visualise 3D shapes in the mind's eye, to look at them from different perspectives and to draw a series of 2D sketches that perfectly describe the object imagined. Einstein is famous for saying: "Imagination is more important than knowledge. For knowledge is limited to all we know and understand, while imagination embraces the entire world, and all there ever will be to know and understand". Imagination: the ability to see images in your mind and play with them. In the words of the late 1990s film, "The Matrix": "Your mind is your Dojo"!

A video overview of how to use the virtual manipulatives and draw plans and elevations using word (this video contains no audio):

Resources

The first activity on the worksheet is a whole class starter. The teacher may prefer to remove this page from the worksheet and show one question at a time to allow for whole class or team participation.

Sketch and name the solid given its 2D elevations: from Hardcourt online learning (www.harcourtschool.com)
"Rotating Houses" from the excellent Freudenthal Institute (www.fi.uu.nl/wisweb/)

"Building Houses": construct a 3D object from a set of 2D drawings (www.fi.uu.nl/wisweb/)

Plenary - Frontiers of Maths and Physics

Can you visualise the 11th dimension?

The study of quantum physics has resulted in mathematical equations that appear to imply the possibility of eleven dimensions to the universe. What is the fourth dimension? What do you think the fifth to eleventh dimensions might mean or look like . . . . . . ? Respected and serious scientists give their views, in the video below, as to some of the theories currently being proposed as to what these dimensions may look like, mean and/or imply (only click on this link to the different possible theories on what these dimensions may look like if instructed to do so by your teacher):

Description

• Use the Freundenthal institutes' excellent virtual reality: "Building and Rotating Houses" to experience how a 3D object can be represented using three 2D views or "elevations": front elevation, side elevation and plan.
• The first page is a teacher lead starting activity. The teacher asks students to sketch the 3D shape represented by the front, side and plan and elevations and then name it before moving onto the second question etc. This page can be cut from the worksheet if the teacher does not want students to race ahead, but rather complete each question as a whole class or in teams.
• Open and follow the tasks and activities on the above worksheet: first using the virtual manipulative to gain experience of what 3D shapes look like when see from the front or the side, then moving on to harder shapes that students can construct for themselves and/or draw the elevations for themselves.
• The video above gives an overview of how to add blocks, remove them, increase the number of cubes available and rotate a shape using this virtual manipulative.
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