Can you work out which spinners were used to generate the frequency charts?
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
Engage in a little mathematical detective work to see if you can spot the fakes.
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
How good are you at estimating angles?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Move the point P to see how P' moves. Then use your insights to calculate a missing length.
How well can you estimate angles? Playing this game could improve your skills.
A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?
Move the corner of the rectangle. Can you work out what the purple number represents?
The farmers want to redraw their field boundary but keep the area the same. Can you advise them?
Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?
A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Quadratic graphs are very familiar, but what patterns can you explore with cubics?
What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
Can you work out the fraction of the original triangle that is covered by the inner triangle?
It would be nice to have a strategy for disentangling any tangled ropes...
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.
Can you find triangles on a 9-point circle? Can you work out their angles?
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Can you make sense of these three proofs of Pythagoras' Theorem?
Use the applet to explore the area of a parallelogram and how it relates to vectors.
Use the applet to make some squares. What patterns do you notice in the coordinates?
Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?
P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.
The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
In how many ways can you fit all three pieces together to make shapes with line symmetry?
An environment that enables you to investigate tessellations of regular polygons
Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
There are lots of ideas to explore in these sequences of ordered fractions.
We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
The length AM can be calculated using trigonometry in two different ways. Create this pair of equivalent calculations for different peg boards, notice a general result, and account for it.
Can you devise a system for making sense of complex multiplication?