Discussion in 'Mathematics' started by taspat, Jan 27, 2011.

1. ### taspat

Hi, could somebody please help me. I need to explain concave and convex to year 4 children. I'm a trainee teacher, shapes isn't my strong point and I want the children to be able to understand it. Is there anything I could say to help them explain it rather than simply saying and showing that the concave shapes cave in?

Thanks

2. ### taspat

Hi, could somebody please help me. I need to explain concave and convex to year 4 children. I'm a trainee teacher, shapes isn't my strong point and I want the children to be able to understand it. Is there anything I could say to help them explain it rather than simply saying and showing that the concave shapes cave in?

Thanks

3. ### NazardNew commenter

I teach secondary, not Y4, so I don't claim that this will be fantastic ...
Get your shape. Pick any two point inside the shape (or on the perimeter). Join them up with a straight line. If every single time you do this all the lines are completely inside the shape then it is convex. If some of the lines go off the edge of the shape and then back on again then it is concave.
Could you draw out some big shapes and ask them to try to draw two points and then a straight line joining them?
Or maybe use wool or string to join them?

4. ### DMNew commenter

My goodness - is this language really used in primary schools? Most A Level physicists struggle to remember the difference! A quick Google suggests they have given up using these terms in GCSE physics and have adopted converging and diverging lenses instead!

5. ### taspat

Thank you for the replies. I was never taught concave and convex at primary or high school! I don't think I understand it fully myself

6. ### pipipi

If you start with a shape and cut a bit out from the edge (like a bite from a donut), the hole will be concave. Like tunnelling into a cliff wold make a cave. to a shape it's conCAVE.

If you were doing a tessellation you could take a bit from one side of a square, that would leave a concave side, and if you stuck the bit you had cut out on the opposite side that would now havebe convex.

Picturse would help here i guess

7. ### weebecka

As a plenary, you could get the children to see if they can outwit each other.
Each draws a shape they think will confuse other students (as to whether it is convex or concave) and asks a friend.
If they manage to confuse their friend they are extra-clever. This should tease out any misconceptions which remain.

It's also worth extending into 3D. The imagery can help consolidate 2D.

8. ### DMNew commenter

Not 4D? You surprise me.

9. ### weebecka

Not with year 4. That's year 9. (See the BCME07 schedule).

10. ### weebecka

concave = inny bits. So in 2D you have one or more internal angles greater than 180 degrees.
So you can't have a concave triangle. Which makes sense if you think about triangles.
It also makes sense if you know that the internal angles in a triangle add up to 180 degrees!

11. ### florapost

i hadn't posted here yet as i planned to talk to the y4 class teachers tomorrow - i was as surprised as you - i introduce the idea with my y5 gat group and not before - though i thought the idea of joining vertices and matching or being outside the shape boundaries was amazing
so lovely to see yet another sensible thread hijacked by the blue butterfly

12. ### florapost

even by your standards, this is a load of c**p - that doesn't matter if you're flouncing about in a general thread, but it really does if someone who admits they are in technical difficulty is asking for serious advice

13. ### taspat

Hi

Many thanks for all your help. I explained it to the children by showing them lots of shapes which were concave and convex and pointing out that the shapes caved in. Most of the children seemed to understand it, I will be recapping it this week in the mental oral starter.
Am I right in assuming that polygons are 2d shapes with 3 or more sides? If yes then I am slightly confused because I was teaching the children about 2d plygons which are concave and convex but one of the posters who commented has mentioned something about extending it to 3d?
Please could I ask for some advice on regular and irregular shapes. I understand that a regular shape would be for example a pentagon with 5 sides which are of the same length and same sized angles. An irregular pentagon's sides would not be of the same length. Does regular and irregular only apply to 2d shapes?
I'm also going to be teaching the children a lesson on lines of symmetry. I was thinking of giving my LA and MA children images of regular and irregular concave and convex images and asking them to find the lines of symmetry using mirrors. For the HA children, I will get them to for example draw me a irregular concave hexagon that has 2 lines of symmetry. Do you think this activity sounds ok?

14. ### NazardNew commenter

Of course you can!
Yes. All the sides are the same length and all of the angles are equal.
This is one way to make an irregular pentagon. Another would be to have all the sides the same length but to make the angles different. A third would be to have angles different and sides different. One way of making the angles different while keeping the sides the same length would be to make a regular pentagon out of meccano and to push the sides around.
Sounds difficult to me. But do give it a go and let us know how you/they got on!

15. ### weebecka

3 or more straight sides.
If some of the sides are curved it is not a polygon.
Polygons are also dead parrots (joke).
At higher level maths we study hungry parrots (polynomials).

Polyhedra are like polygons but in 3D. The have flat faces instead of straight edges!
A concave polyhedron has at least one vertex (point/corner) which 'caves in'.
Here's one
You can get regular polyhedra.

Your activities sound lovely.
If you get a supersmart HA, you could get them to draw a table relating the number of sides on the concave polygon to the maximum number of lines of symmetry (and to illustrate that table with examples).

16. ### ian60New commenter

If I may just lower the tone a little here; I remember as a spotty 13 y/o trying to think of a way to rememer which was which.
My mate explained:
- 'Convex sounds a bit like sex, and what do you think of when you think of sex?'
-'****'
-'Yeah! And **** are convex, it's easy'

17. ### florapost

yeah - but a lad might think of something else which would be concave
oh - sorry! sorry! sorry!
polgons are 2D (ha - have my shift key back!!) shapes woith straight sides - having at least 3 sides is not part of their definition - it's just that it's impossible to have a polygon with fewer than 3 sides
sorry if any of this is repetitous - the alternative is backwards and forwards thro posts - regular polygons have all their sides and all their angles equal. equilateral polygons have sides but not angles equal (pentagon - think of a child's drawing of a house) and the equilateral triangle is so called because an equilateral triangle can only be regular
polyhedra are 3D shapes whose faces are polygons. the regular convex polyhedra are also called the platonic solids - their faces are all the same regular polygons, set at the same angles to each other
http://www.mathsisfun.com/platonic_solids.html -the net of the dodecahedron is a b**ger to score
archimedean solids (trub=ncated platonic solids, i think) - well. look for youself
http://www.uwgb.edu/dutchs/symmetry/archpol.htm
concave regular polyhedra are breathtakingly beautiful - i couldn't find a site which showed a selection - the maths gallery at the science museum is the best place to look, if you have the oppotunity to go to london

*truncated*

19. ### florapost

oh - and have no truck with old-fashioned textbookset al that call isosceles trapezia 'regular' as they fit no definition of regular polyhedra whatsoever