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Interactive mathematical sites
The star rating of some of these sites is purely my opinion. The more
interactive and enjoyable they are, then the higher the star rating. Many
sites have not yet been rated.
I hope these links make mathematics come alive for you!
Mrs M Murray.
Note: Many better activities from the
General section have been individually sorted under the following
categories:
General: The following
sites host many different interactive activities.
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Contains numerous interactive activities for all ages. |
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Scroll down and click on free flash films and
view 5 flash animations. |
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Double click the fast forward button to speed
up the intro. These two are the best: 1 : The regular hexagon
2: the two rectangles with the red arrow between them. |
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Play with these interactive geometrical
activities. |
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There is lots more on this site other than
these interactive applets. (University of Illinois - www.mste.uiuc.edu) |
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Unbelievable! This site contains over 700
interactive applets. (Some easy ones are picked out for you in links
below because some are very hard to understand.) |
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Contains a huge array of interactive learning
tools. (Teachers: look at the lessons and web links.) |
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Contains many questions about the world we
live in.
Choose a topic to see how mathematics surrounds us! |
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Right click any of the red boxes to pop-up
windows with different activities, questions and solutions. |
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Contains good student-friendly information
about functions. Also has graphing activities that help students
understand the key features of graphs. |
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Contains many interactive mathematical
activities from the University of Vienna |
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Many of these interactive activities need
teacher explanation. This site includes trigonometry, geometry,
calculus, complex numbers and conics. |
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Contains many geometric and solid shape
activities. |
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Contains many maths games. |
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Interactive shapes **** |
Contains a number of interactive activities
involving shape. |
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Interactive activites ***** |
The better activites are listed
individually in the categories below. Most of the others are very
good, but some of the activities on Number are just drill and practice and a
bit boring and frustrating if you are not good at number. |
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There are four parts to this video.
Similar Triangles in Radiation Therapy is excellent. |
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This website uses VRML to view mathematics in
3D. Some of the coordinate geometry and space geometry is great, but
others, like algebra, is really boring. |
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Contains good applets that demonstrate
aspects of measurement, geometry and trigonometry. |
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Many interactive activities - Data and
Probability |
Number:
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Click on the matching bottles to match the
picture with the fraction. |
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Help the dragon double his food using the
powers of 2. |
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This site converts numbers into Chinese characters. |
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These websites explore Egyptian hieroglyphs with imput from
you. |
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Contains an overview of many number systems. (not
interactive) |
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Contains a roman numeral calculator and a conversion test. |
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You can add and subtract on an empty number line.
Examples are given, then you can try some by yourself. |
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You can answer questions and then check your
answers. |
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This interactive site helps you understand
factor trees. |
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Write factors of numbers here and check out the
grid below by dragging out an area using these two factors. |
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This is an old puzzle of a convergent
sequence of numbers. |
Geometry: Many
of these activities are the easier ones from the website called 'Cut the knot',
above
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You can translate, reflect and rotate a square,
parallelogram and triangle in the coordinate plane. |
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Look at the animation and read the text.
Click on the menu at the bottom to see more animations and definitions.
Click and drag the red points to
rotate, translate and reflect these triangles onto each other. |
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Click on congruent triangles. Click SSS. Make a blue triangle then
make a red triangle. Why are they the same?
Repeat using SAS and AAS. |
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An interactive geometry activity. Can you see a
pattern? |
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Play with it then try to prove it using congruent triangles. |
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Drag point P to discover the size of each
angle of triangle ADE. |
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Click on the 'pop it up' button and explore
the drop-down menus of this interactive drawing program. Definitions
of some of the words in these menus are on the open web page behind this
drawing program. |
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Can you see the other 3 triangles? |
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Play with this applet. Click on 'Extra
construction', and play some more. After this, write the proofs, using
these constructions. |
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Easy to play with. More difficult to
understand. Click 'Have a go' and follow the instructions. |
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Drag A or B. Are the matching angles
equal? Are the sides proportional? |
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Click 'Play video' under the video called
Similar Triangles and Radiation Therapy.
(The other videos teach you a lot too.) |
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This geometry is different to Euclidean
geometry. Check out what a triangle looks like by following these
instructions: Scroll down to the large
button, 'NonEuclid 2005.12' and click on it, then click OK. Click
twice inside the black circle to make a 'line' segment. Click point B
and then click a different place inside the black circle to make
ÐABC. Click on C and then A to
complete the triangle. Use the menu to drag points, measure and do
other constructions. |
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(Harder) This website is interactive
but hard to understand if you do not read as you play. This geometry is not
Euclidean, so the rules are different. (Extension 2 students may like this.) |
Shape:
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Click on a colour, then click on a line to
draw these solids. |
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Slide your mouse over the picture to see the
solid shape outline. Read the name of each shape. |
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Click on the symmetry you want. You
draw and the computer creates the symmetry for you. |
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Click the squares each person sees.
They must also be in the correct position. |
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Click the correct view. |
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Click and drag these solids around to make them spin.
This will help you visualise these solids better. |
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Beautiful solids made by a dedicated
mathematician. |
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Scroll down to below the table. Click
on the 'Java Crystal pop-up' to spin its structure in 3D. Read to
learn more about minerals. |
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Click on a solid you want to make, then print
its net. |
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Click on an image to get more information about a solid. |
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Make a cup of tea. It takes a while to
download. (about two minutes.) |
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Help Pythagoras rotate patterns on tiles. |
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Just pretty and fun. |
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Colour a square. The computer rotates
this coloured square into the three other quadrants. |
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Change the square by dragging its vertices,
then click 'Tessellate' |
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Click on a few pictures so you get inspired
to draw your own. |
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Click and drag a shmuzzle to the play area.
Double click to rotate it. How many can you tesselate? |
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A fractal is a shape that has
self-similarity. Read more here. Change the
snowflake one step at a time.
Watch the snowflake and the carpet grow as you change
their colour.
This fractal shows you each iteration and describes each
one.
This website uses fractals to draw plants. You set
the parameters.
Create fractals here.
Click on the fractal art contests, under 'Mirrors' to see
some mathematical art.
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Measurement:
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Enter an angle to point the telescope at a
planet. |
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Drag squares onto the green screen.
Count the perimeter, then check your answer. |
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You can visualise and calculate the area of
different right-angled triangles with a grid background. |
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An animated proof of Pythagoras' theorem.
However, you need to first understand that if the base and height of a
triangle remains the same then its area is constant even if its shape
changes. |
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Follow the instructions, then drag all the coloured areas
(at their red point) into the larger square. |
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Use this to check your understanding of
Pythagoras's theorem. |
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This simply illustrates Pythagoras' Theorem with
a moving
triangle and three squares. |
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Click on 'left' and 'right'. Why does
the area stay the same? |
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Investigates the area of rectangles with the same
perimeter. (Click 'only draw rectangular shapes' and then adjust the
perimeter.)
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Investigates the perimeter of rectangles with
the same area. (Click 'only draw rectangular shapes' and then adjust the
area.) |
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Drag the mouse inside the graph paper until
the rectangle has a perimeter of 20 units. Click 'Trace', then drag it
to find its maximum area. What answer do you get? You can click
and read the answer. |
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This gives you a grid, so you can practise your
area and perimeter. |
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Click on the prism and drag it around to see
each side. Each rectangular and triangular prism has grid lines on it.
You can change their dimensions. |
Patterns and Algebra:
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Drag and drop bears and boxes to help you
understand grouping symbols in algebra. (You need Flash5 or higher) |
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A beautiful animation that helps you
understand equivalent expressions. |
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The computer gives you a number pattern.
Can you complete the next two? |
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A fun activity where a dog and a postman help
you understand substitution. |
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Balance the beam by dragging
x's and numbers to form the given
equation, then, rearrange them so that the correct number of
x's are on one side of the beam then
balance this with the correct whole numbers on the other side. Can you now
solve for x?
(Note: If the computer won't let you rearrange using the
number of blocks you want, try another equation that requires less blocks.) |
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Click on x, then click on x2.
Drag x so it is against one side of x2. Click on x again,
then click and drag one corner of the new x so it moves vertically.
Drag the sliders to get a better understanding of the meaning of x2,
y2, and xy with respect to area. |
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This is not interactive, but it gives an
easy-to-follow illustrated tutorial about balancing and solving equations. |
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Practise solving equations. Choose from
easy to hard. You get instant feedback. |
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Choose the correct operation then click
calculate to solve each step. |
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Match equations with the same solutions. |
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To download this free interactive
spreadsheet activity, you need to click on
PAS5 Patterns and Algebra/PAS5.2.2 Algebraic technq, then scroll down to
The rectangle problem. Click
on it to download. |
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To download this free interactive
spreadsheet activity, you need to click on
PAS5 Patterns and Algebra/PAS5.2.3 Coordinate Geometry, then scroll down to
the spreadsheet activity Equations of lines. Click
on it to download. |
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An exercise that gives computer generated
trinomials with instant feedback. Click 'Factorise' to start the first
question. This web site is just drill and practice,
and you may still need to use paper! However, you can use the sliders to
write your factors so the computer can check your answer. |
Coordinates, functions and graphs:
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Can you identify the coordinates of a point? |
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Plot and name points in the first quadrant
and other quadrants. When you are right you are given a diamond, when
you are wrong you get a lump of coal. |
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Use this game to become more familiar with
naming and plotting points in four quadrants. |
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Name and plot points in four quadrants. |
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Move your robot through a mine field that
uses all four quadrants of the coordinate plane. |
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Can you guess the rule that runs the machine? |
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A simple function machine for stage 2-4.
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Can you guess the function? Check your answer
with the computer. |
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Drag numbers into a machine, then try to
predict its output for other numbers. |
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To download these two free interactive
spreadsheet activities, you need to click on PAS4 Patterns and
Algebra/PAS4.5 Linear Rels, then scroll down to these two items. Click
on them to download. |
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See how the gradient, m, and y-intercept, b,
affect the graph. Change the values yourself. Use sliders to
change the gradient and y-intercept of a straight line, as you watch the
equation change. |
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Vertical line test
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Read this easy-to-understand definition of a
function. Draw lines
between points to make functions that pass the vertical line test. |
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See how a, b and c affect the graph of
y = ax2
+ bx + c |
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Not important. Just fun! Great
computer graphics. Click and drag to find out what it is. |
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Animation that shows how the
graph of y = sin x is related to a circle. |
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Helps you visualise families of graphs when
you change various pronumerals. Contains parabolas, circles,
hyperbolas and ellipses. |
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Scroll down to the bottom to
view the VRML. Click and drag the screen. |
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Right click on the red
rectangles to get a pop-up activity. (Left click the last one.) |
Data:
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Click on a student and
listen/read what they have to say, then tally their response in a table. |
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A really simple bar
graph for beginner students. |
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Enter your own data and the computer
calculates the median and quartiles and graphs it for you. |
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Enter your data and the computer draws the graph. |
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Click to
create different points on a dot plot and see how the mean, the median and
mode are affected. |
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Scatter plot
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Enter coordinates to draw a scatter plot. |
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Enter scores with commas between them and
click update plot. |
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What makes a distribution skewed? This
activity allows you to change the shape of a distribution when you drag the
median. Check out the position of the mean and mode as well. |
Probability:
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How many different ways can you dress bobby
bear? (You can also customise the data.) |
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This game allows you to spin two die.
The sum of the die determines which animal moves. The worksheets are
excellent. |
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Cars move along a track as you spin a die.
Results are recorded and graphed in a pie chart. |
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Keep on clicking 'spin'. Does
experimental probability slowly change to theoretical probability? Change the size of each sector of the
spinner. Is there an even chance of the spinner stopping on each
colour? Try a new experiment with a number of spins. Compare
experimental and theoretical data. |
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Throw some dice, use a spinner (biased or
unbiased) Tallies are recorded. |
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Stick or switch? |
Choose a door, then choose to stay with your
choice or switch doors. Column graphs of your choices are displayed. You win if you receive a good prize, like a
car, and lose if you get a bad prize, like a piece of rope. Which
strategy helps you win more often? |
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Choose a pair of spinners then select the
number of spins. After spinning you can compare your expected results
with actual results. |
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Toss coins then look at the column graph
change as the results for the number of heads grow. |
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Enter the number of rolls and click roll
dice. Watch the column graph grow. |
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Simulation of drawing marbles from a bag,
with (or without) replacement. |
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Roll dice and your results appear, with a
colourful column graph. |
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Enter the probabilities of throwing a die,
drawing a card or anything you like. Run the game and compare this
with your theoretical probabilities. |
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Santa takes toys out of his sack then
replaces them. How many times must he take toys out of his sack before
you can correctly predict the number of each toy from a sack of 10 or 20? |
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This program
simulates a bush fire. You can change wind direction, forest density
and size of forest. |
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A simulator of
the relationship between rabbit, wolf and forest populations. Could
prompt a useful environmental debate. |
Graphing programs:
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Click on
Winplot to download this free and powerful
graphing program. |
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Download Geogebra here. This is a free
graphing program that also allows you to drag points around just like the
program called Wingeom. |
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Enter an equation so you can graph it. |
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You can look at stage 6 graphs with this
machine. |
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Download this free software |
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This algebraic program is great, but it is only
a windows-based program. It
calculates derivatives and integrals and also draws these graphs. It
simplifies and factorises algebraic expressions as well. You must use
the usual keys such as * and ^ to make operations work. |
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Enter a function, then click 'set function'.
Move the sliders to see what happens to your graph when you change parts of
your equation. This graphing program also has a trace feature. You can also plot data here.
You must use the usual keys such as * and ^ to make operations work. |
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Type in an equation you want graphed.
Use the carat key to type exponents. Zoom in or out to change the
scale. |
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Type an equation and use the star key above
the 8 on your keyboard to multiply and the backslash to multiply. (Note: You
must use brackets for sin(x)) |
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Type an equation or coordinate points. |
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Choose one graph first. Click and drag the
man across the screen. Drag him slowly, forward or fast and backwards.
Watch the graph. (Choosing two or three graphs is more difficult to
understand.) |
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Select the power of the tap. Click the
pictures at the bottom of the bath. Watch the graph change as you play with
the water level. (This link is repeated below.) |
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An interactive maths program. You can
change equations and values of x and y of graphs and algebraic expressions.
Some of the instructions are in Greek, so it may take time to get your head
around this program. |
Time:
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Want to ring someone overseas? This webpage gives you
the time around the world. Daylight saving is indicated with a star. |
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View today's date in different calendars.
Enter your birth date. |
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A drill and practice activity that helps you
find the difference between two times using a clock face. |
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Adds or subtracts time from a given date. |
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Calculates the time between two dates. |
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Only for reading. This site is not interactive. |
Other interactive games:
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Many games to play! Choose one.
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Solve this virtual version of the classical 15-puzzle by
arranging its tiles. |
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Weigh coins to find the counterfeit coin. |
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Switch the positions of the coloured pegs.
Click 'instructions' to see the rules of the game. |
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Solve this virtual version of this classical
puzzle. |
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A fun game with real golf sounds.
A similar game with shapes. |
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Select a puzzle, then drag, and spin the
pieces to complete the puzzle. The computer lets you know when you are
correct. |
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You need to understand the 'clues' before you
begin this virtual mastermind game. |
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Click the correct scale factor to change the
size of each jigsaw piece. |
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Get the people across the other side of the
river. Click the people into and out of the boat. Click the
engine to move the boat. |
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Read the first page , then click on the game
at the end of the second page. Can you drop the water bomb on the man? |
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Select the power of the tap. Click the
pictures at the bottom of the bath. Watch the graph change as you play with
the water level. |
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You sort shapes and colours here. |
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Click on the screen and walk, fly, pan, turn
or roll until you see the xyz plane in 3D. Hint: Head for the
bottom of the screen.) |
Mathematical history:
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Contains a brief description of the life of some important
mathematicians. |
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Remember, these were written about 300BC. |
Printable materials for teachers:
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Print the first table and play with the
applet. It is about the simpler properties of quadrilaterals.
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