Edges in a pyramid
A common problem in the NI transfer tests is one that describes a 3d shape in words, and asks how many faces / vertices / edges it has. I discovered that my son was answering these questions by sketching out the 3d shape  this inevitably led to a bad drawing and often to an incorrect answer. In some schools this is taught as an activity with midget gems and cocktail sticks so I gave that a try and it really helped. And we got to eat sweets  a great way to spend an hour on a rainy day. 

Hint: Vertices is the plural of vertex, which means the corner of a shape. This term is used in both 2d and 3d shapes.
2d shapes
 In these 2d shapes, sweets are vertices and sticks are sides 
The best way to begin the activity is to make some 2d shapes. We started with a triangle. Don't miss the opportunity as you go along to discuss things like how all the sides are the same size  this forces an equalateral triangle.
An Equalateral Triangle: All sides are equal and all angles are equal. Three sides and three verticesYou could shorten (by breaking) one of the sticks to make an isoceles triangle or shorten two of them by different amounts to make a rightangle triangle or a scalene triangle where all sides and angles are different.
Then we moved on to rectangles. Here we made a square and a rectangle, by shortening two sticks.
Rectangles: These are both rectangles  4 sides, 4 vertices and 2 pairs of parallel sides. One is also a square because all sides are of equal length.Finally, for 2d shapes, we looked at pentagons. We made one regular pentagon and then squeezed it to make a nonregular pentagon with eqaul sides but not equal angles.
A Regular pentagon  5 equal sides and five equal angles.  An irregular pentagon  the sides are still equal in length but the angles are no longer the same. 
3d shapes
 In these 3d shapes, sweets are still vertices, sticks are now egdes and 2d shapes are faces 
Now it gets interesting. We began discovering 3d shapes by changing our square into a squarebased pyramid.
Every pyramid has a base shape, and the number of sweets (vertices) required is always one more than number of vertices in the base. So add one more sweet.
The number of extra sticks (edges) required will be the same as the original number of sides in the base. So we added 4 more sticks.
Square based pyramid: 5 vertices (sweets), 8 edges (sticks) and 5 faces.
Continue changing your other 2d shapes into pyramids, and confirming each time that the pyramid's details are related to the base shape's details as follows:
Base Shape / Property  Vertices  Edges  Faces 
Triangle (3 sides)  3 + 1 = 4  3 + 3 = 6  3 + 1 = 4 
Square (4 sides)  4 + 1 = 5  4 + 4 = 8  4 + 1 = 5 
Pentagon (5 sides)  5 + 1 = 6  5 + 5 = 10  5 + 1 = 6 
Hexagon (6 sides)  6 + 1 = 7  6 + 6 = 12  6 + 1 = 7 
Just keep going with this. Think about cubes, prisms and other pyramids. Have fun and don't eat all the sweets.
Triangular Prism 
Cube 
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Good luck,
TransferReady.co.uk