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Always, Sometimes or Never? Shape

Age 7 to 11 Challenge Level:
This challenge showed that there is some more thinking to be done - it was not straightforward!

In the solutions below, there are a few slip-ups. We think that some of the 'always true' should be 'sometimes true'.  Have a look for yourself - can you find out what is wrong and why?



Thomas and Miles from Holy Trinity in Halstead, Essex sent in this helpful diagram:



We think there might be two little mistakes ...

Lilly, Suzie and Poppy
 also from Holy Trinity Primary School,
 did the first six and wrote their response in a different way.  We have added in a few comments too:


Question...1. A hexagon has six equal length sides
2. Sometimes true
3. The reason that the question is sometimes true is because you can have an
irregular hexagon.

Question...1.   Triangles have a line of symmetry
2.  Sometimes true
3.  Because an equilateral and isosceles only have a line of symmetry. A right angle triangle and a scalene triangle do not have any lines of symmetry.  (Are you sure that is always the case?)

Question…1.   Squares have two diagonals that meet at right angles
2. Always true
3. Draw a square, then draw lines at each corner. Look at the corners and in the corners of the squares are right angles, which means it is always true. (How do you know?)

Question…1. Cutting a corner off a square makes a pentagon
2. Sometimes true
3. It wouldn't be a regular pentagon, it would be a irregular pentagon. (Could it be any other shape?)

Question…1.  The base of a pyramid is a square
2.  Sometimes true
3. Because you can have a triangular based pyramid.

Question…1. A cuboid has two square faces              
2. Always true
3. Because a cuboid is a 3d rectangle.  (Can a cuboid ever have a different number of square faces?)

 
5S Maths Group from Dulwich College Shanghai in China used a different way of recording their findings:



We think there is just one slip-up in the above.

Gabriella, Rosie, Ayana and Izzy from James Allen's Prep School showed their thinking in yet another way:

 
Again, we think there is just one slip-up.

There was some excellent thinking shown in these solutions, well done, but do see if you can spot the slight errors.