google sketchup

Google SketchUp version 8 is now available, for free.

There are booklets from 3Dvinci which look to be a good buy - available for a reasonable cost each as a pdf download and with heaps of good tasks utilising SketchUp. Every student should have a play with this!

You can obtain some free instructions in YouTube, by looking for 'bonnie roskes' (author of 3Dvinci). For example, there are videos on drawing tesselations, an octahedron, an icosahedron (from three orthogonal golden rectangles) and creating the conic sections (very simply).

quadratic graph

There are several programmes that enable the three parameters of a quadratic expression to be varied. This one seems clear and can be expanded to a whole screen.

Varying 'b' seems to trace a quadratic (with the lowest graph points). Establish that the equation is y = -1/4 b^2 when c = 0 and a = 1.

There is also a completed square version.

circle pi

Archimedes' method for calculating pi is fairly well demonstrated using this programme. It is best to open the 'pi graphics' box to a full screen and then the 'pi controlling' box within it.

Note that to close these two screens you have to click inside the given box (as it explains).

fractals etc

This website has some fascinating pictures, mostly of a fractal nature. Not too much by way of classroom activity (that I can see anyway) but interesting never the less. Has a link to fractal producing software.

shooting at a target

Several variables to play around with and some neat quadratic curves.
Virtual laboratory: cannon

vector addition - waldomaths

vector addition - change the two base vectors by dragging and use a slider to obtain linear combinations of these, to show how the parallelogram for vector addition works.

NLVM: shifting columns, add/subtract numbers

This is helpful for those students who have not quite appreciated that ten somethings in one column make one in the column to the left of it.

The blocks group into tens as you move them to the left.

This does a similar job for subtraction - with the rods splitting into ten as you move to the right

eManipulatives: directed number

This site shows positive and negative counters (use the rubber stamp to include counters and the hand to move them).

It can be useful to show, for example, that taking away a negative counter results in a positive counter being added to the top pile.

To make the picture larger use Ctrl and your mouse wheel

illuminations NCTM pi and visualising equation solving

Computing pi - the Archimedean 'squeezing' a circle between polygons method; compares accurate to approximate areas and circumferences

Pan balance-expressions - set up equations with an expression in each pan balance (one could be a constant or zero) and use a slider to see where the two expressions have the same value. Especially good for seeing how the solution fits two linear expressions (i.e unknown on both sides of an equation, viewed as line graphs).

illuminations NCTM: symmetry

cyclic figures: rotational - vary the original shape for different orders of symmetry

dihedral figures: line - change the start shape and see what happens with several mirror lines

shape tool : Pattern blocks - put shapes together and then reflect or rotate them

illuminations NCTM: 3D

geometric solids they spin; you can colour the faces (using the shift key and palette) - how many do you need for each Platonic solid so that adjoining faces are different colours?

cube nets which nets can be folded to make a cube? Students choose - if they are a net they go brown and if not it tells you.

the isometric drawing tool is a good all-purpose tool for creating isometric drawings and exploring these.

illuminations NCTM dynamic paper

This software enables you to create graph paper, number grids, nets, number lines, shapes and spinners.

These can be outputted as either a JPEG or pdf file

3D representation websites

The Freudenthal 'Wisweb' site is also very good for various tasks, especially building solids out of blocks and twirling them around so that you can see a plan and various elevations.

Malcolm Swan's (excellent purple and blue 'standards' box of resources, gathering dust somewhere) disk in the pack includes a programme that does similar things.

formulator (tarsia)

formulator's tarsia software (available as a download)

[Hermitech Laboratory]

cumbria and lancashire grid for learning

cleo.net maths, KS3, digital whiteboard has a version of filling different shaped jugs and the associated graphs ('bottles')

subtangent.com Duncan Keith

subtangent.com

has the novel and engaging 'transformation golf' (go for the improved version: in resources, then in miscellaneous)


diagonal differences investigation on a number grid is probably helped by this programme

keymath.com

keymath.com (in the dynamic explorations)

has 'the eliminator' which is not easy to see in a classroom but is a great way to visualise solving simultaneous equations

the multipliers are shown as sliders

when a variable is eliminated the sum of the two linear graphs is either a vertical or horizontal line

Peter Grabarchuk's puzzle site

Peter Grabarchuk's puzzle site is well designed and helpful

the net puzzles are found here and solid visualisation here

cutting shapes into 4 congruent parts is here

fitting pentominoes is here (click the shape to rotate it)

and much more...

free websites I like

These are some of the websites I like. Apologies for missing out some other good ones - I'll collect these together later (for myself at least):

• 'ptolemy' (Alec Mc Eachran) is a fine site ('primitives' being an excellent way to view an image of numbers - with their factor properties); it has links to Mandelbrot (great zooming in to a Mandelbrot set on Vimeo) and a Utah genetics site, for visualising tiny things (and powers of 10)

• 'teacherled' (Spencer Riley) has many excellent and very well presented whiteboard resources, leaving teaching - rightly - up to the teacher. Particularly like (most of it but, at the moment): reptiles (fitting 4 similar shapes together to form an enlarged version); shape exploder (making it easy to count the number of cubes in a cuboidal (invented word) solid); dice (roll up to 3 dice, in space (which could get irritating...)); rotating around a point (I like sliders... and this shows a rotation beautifully)   

• the Primary, national strategy ITPs are good and are easily viewed and used from this index

• the Cymru ngfl site has many good (and some not so good) resources, I particularly like the resources produced by Dr Iestyn Jones (of 'eChalk') for 3D investigation and geometrical transformations and some of the investigative software (e.g. painted cube). The 'geoboard' for Pick's theorem etc is lovely (go to the 'develop' section/tab for DIY shapes).

• NLVM has a really good collection of virtual manipulatives - saves picking pattern blocks up from the floor

• pedagoguery software has poly (1.11) as a download which creates foldable nets of polyhedra

• mathspig (blog) (Kerry Cue) contains a healthy look at maths in the media with applications of maths that are actually interesting (as opposed to functional maths efforts that take some reading and then only evoke yawns)

• Matt Dunbar's 'estarters downloads' is a fantastic use of Excel (how does he do it?) with quite a few free downloads (including fine demonstrations of Pythagoras)

• the 'geometry toolbox' is good for simple constructions

NLVM

(from the fractals iterative programme)

Fill and pour - the 'jugs' problem: given two jugs of various capacities, how can you create a third amount?

How high? - pour liquid from one container to another, how high will it go? Can involve volumes of cuboids.

Could involve volumes of cuboids, cylinders and cones (illustrating that a cone is a third of a surrounding cylinder)




Grapher -set up a general quadratic ax^2 + bx + c and see the effect of changing each parameter (with a slider)

Line plotter -given a point and the gradient of the line, construct and check the line's position.

Platonic solids - what's the minimum numbers of colours needed to colour faces of the platonic solids so that adjacent faces are different colours?

nrich resources

nrich helpfully give a 4 digit code to their resources
ou can find these resources by searching for nrich then the code










4348 cuisenaire rods

5618 dotty circle sine function, from a point going round a circle

2883 virtual geobaords (square, circle, isometric)

4901 large pinboard

2667 tilted square (coordinates of skew squares)

6703 mystic rose drawing tool, for various divisions of a circle, useful for creating a rule for the numbers of diagonals - with a focus on proving a generalisation
(you can also download an Excel tool for this from Bodmas.)

5528 tangram (square)