Friday, 11 November 2011

Maths 2 (10-11-11)



Maths

Subject knowledge and teaching us to teach maths are 2 different things. Mark is teaching subject knowledge.
See Action Plan at the back of Maths Audit: Task no. 2. 
Ideas for Action Plan: Go to colleagues at school, e-mail Mark, go to BBC bitesize site and others, get a copy of LET’s guide
Nets
Looking at a net of a cube, making as many nets for a cube as possible (see handout).
- Refrain from saying, ‘We’re going to look at something really easy’- if a kid can’t do it, their confidence will take a knock.
Regular Shapes 
We call it ‘sides’ w/ 2-D shapes but ‘edges’ in 3-D shapes. Lots of problems- cannot just skim over these problems, must address the language used.
Blindfolded Activity
Lots of similar activities like this to get chn to start talking about shapes and using correct terminology. Chn will use a mixture of maths terminology (sides, angles, parallel lines) and informal language (it looks like a rabbit’s head / boat / tent). Use coloured cardboard and then place it face down (so there is a uniform colour, and say as soon as you touch it, you take it).
Multi link (bricks)- very manageable resources. Have a ready made 3D shape in a box and have one child come and describe it to other kids, who will make it with his instructions.
Make it harder: use different complexities of shape; instructor has or doesn’t have visual cues of seeing classmates correctly or incorrectly interpreted instructions, instructing kid only feels the shape rather than seeing it etc..
Do the same with whiteboards and have chn draw it.
Odd one out
4 kids stand shoulder to shoulder w/ hands behind back. Put shapes in their hands and give them time to describe the shape to each other. They find the odd one out (if there is one). Self-assessing; promotes kids talking and arguing about language of shapes.
Shapes leading onto Symmetry
2 kinds: Rotational (talking about order of symmetry) and reflective (talking about number of lines of axis of symmetry). 
Reflective is easy to prove, using shapes used for the blindfolded activities; so is rotational. Let the kids have a part to play in turning the shapes. Once you have put them altogether they make impressive displays. Putting in different colours to the shapes makes it more difficult (alters the symmetry)
Teaching rotational symmetry: don’t count the start point (think of the Merc badge and turning it around 360 degrees to prove rotational symmetry order 3).
Move away from regular shapes to weird ones.
Triangles
Look closely at vocab: ‘triangle’ indicates number of angles, rather than number of sides. So why do we describe a triangle as a three-sided shape? Kids will have encountered the word ‘tricycle’ so might have an idea about this.
Scalene, Isosceles, Equilateral. There is no such thing as right-angled triangle- it is either a right-angled scalene or a right-angled isosceles triangle. It is another term to further define the triangle (anaolgy of finding a girl in a class, and further defining who you’re looking for by adding hair colour etc).
Quadrilaterals
Attributes of 2D shapes are sides and angles. 
Organise by sides: can organise an average irregular quad. to a parallelogram, then onto a rhombus (all 4 sides are the same length), to diamond.
Organise by angles, and you turn a quad. into a parallelogram, to a rectangle/oblong.
Square is a very precise rhombus, parallelogram, and quadrilateral.
Quad.
    Parallelogram
Organise by Angle   Organise by Sides
(make the same) (make equal in length)
Oblong/Rectangle Rhombus
Organise by Sides Organise by Angle
Square
Trapezium (quad’s w/ 1 pair of parallel sides) and Kites (no parallel sides, 2 pairs of sides w/ equal length, but instead of being opposite and therefore parallel, they are adjacent) are the other 2 shapes.
Explaining parallel lines: two lines that will never meet (have kids line up, making sure they are exactly the same distance from a line like a football pitch line, then ask them what they notice about the lines- will they ever meet?).
Making Kites
Use different size paper to make smaller and smaller kites- then put them together to create larger shapes with the same lines of symmetry / angles (‘similarity’). Prove that angles are the same regardless of size. Congruent shapes are the opposite.
Tesselation
Kites ‘tesselate’. So do M.C. Escher’s drawings. Also see ‘Gift-wrapped by Artists’ for Tesselated sheets. 
Cut out bits from a square and add it to the other side. The new shape will tesselate as well. Mount the new shape on card and you have a template.
Making Shapes
 Use pre-made stencils, piled on top of each other to draw shapes. See Purple sheet.
Tangrams
(Making candlestick, E etc)
Task no. 3: Euler’s Law: Topology (e.g. Underground map- not accurate, not to scale, but you can still get where you want to go. Sometimes called rubber sheet geometry, where things are distorted)
Konnisburg Bridge Problem: two islands in the middle, can you cross all the bridges without crossing same one twice? Same as drawing an envelope without taking your pen off the paper. The bridge one, it can’ be done.
Important for people in Logistics: moving lorries tightly while minimising travel to make economic sense- or a newspaper round.
Platonic Solids (5 x):
Regular shape, equal angles inside (e.g. dodecahedron, cube, triangular based pyramid- the TetraPak)
Resources/Associations
Should be member of a society in English, Maths and Science. Lots of resources you can buy form them.
ATM (probably better for Primary School)
Maths Association
Skills Test
Get in, do it, then worry about passing it if you fail. You have to get on with it and try out so you’re at least up to speed with the format.
Mental part (first). These are harder questions. Only need to get 7 out of 12 right- so you can afford to ignore up to 5 questions.
Longer Qs (calculator allowed). Tend to be with Statistics. You can’t take your own calculator in- you have to use the one on the screen etc.
You are competing for slots with all student teachers- you will find it difficult to book them.

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