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Recommended prior knowledge
All of Core and particularly Core 6. Only those parts of the learning objectives or notes and exemplars not included in the core units are itemised, so this unit should be read alongside the Core document.
Context
There are five Core geometry units and this is the third of five Extension geometry units. Once the Core 6 and the other prior experience for Core 6 is completed this unit can be slotted in at any point. It is probably best taught as a whole but used to revise some of the Core 6. It may be useful to have 3 dimensional models both solid and skeleton framed to support the learning.
Outline
The unit extends the knowledge of Core 6 so be aware that examination questions that relate to aspects of Core 6 may have a greater degree of challenge as they combine with other areas of mathematics. This unit covers surface area and volume of pyramids and cones, areas and volumes of compound shapes.
Syllabus ref Learning objectives Suggested teaching activities
6.3
CCSS:
G-C5
6.4
CCSS:
G-GMD3
Same as core
Surface area and volume of pyramid (in particular, cone)
Surface area and volume of sphere
Notes and exemplars
From sector angles in degrees only – the phrase ‘simple examples only is removed.
Notes and exemplars
Formulae will be given for the curved surface area of cone, and the volume of pyramid and cone.
General guidance
As with other formula for surface area and volumes identifying the correct aspect of a figure to put into the formula is difficult for some students who find visualizing 3D shapes from 2D representations difficult. Making skeleton solids can help (Straws joined on vertices with inch long bent sections of pipe cleaner is a cheap way of avoiding the cost of commercial sets)
This can be linked to questions that use pythagorus and trigonometry to find
Learning resources www.bbc.co.uk/schools/gcsebitesize/math s/shapes/circles2hirev2.shtml
http://nrich.maths.org/4959 www.korthalsaltes.com/model.php?name_
en=three%20pyramids%20that%20form%
20a%20cube www.algebralab.org/lessons/lesson.aspx?f
ile=geometry_3dpyramidcone.xml
Past Paper 23 June 2011 Q21
(syllabus 0580)
Past Paper 42 June 2011 Q7
(syllabus 0580) v1 2Y01 Cambridge IGCSE Mathematics (US) 0444 1

Syllabus ref Learning objectives Suggested teaching activities the dimensions needed to solve a problem.
Teaching activities
The ‘korthalsaltes’ web site gives a net of a pyramid that if made three times can be turned into a cube – a nice way of looking at the formulae
6.5
CCSS:
G-GMD3
Areas and volumes of compound shapes
Notes and exemplars
Involving combinations of the shapes in section 6.4. core and extension
General guidance
Once again it is visualizing the separation of the shapes that will cause some pupils a problem.
This can also mean realising that a truncated solid is the whole solid minus the top of the solid to leave the truncated portion.
Teaching activities
Trying suggesting some shapes made from combinations of solids and ask students to draw a 2D representation with the measurements required to find the volume and surface area clearly identified – not as easier as it sounds.
Learning resources
Past Paper 31 June 2011 Q6
(syllabus 0580) www.ltscotland.org.uk/Images/ pythagora s 3d_tcm4-123382.ppt
http://nrich.maths.org/4979 v1 2Y01 Cambridge IGCSE Mathematics (US) 0444 2