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Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
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?
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Can you make sense of these three proofs of Pythagoras' Theorem?
Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
Can you locate these values on this interactive logarithmic scale?
Can you work out which spinners were used to generate the frequency charts?
It would be nice to have a strategy for disentangling any tangled ropes...
The sine of an angle is equal to the cosine of its complement. Can you explain why and does this rule extend beyond angles of 90 degrees?
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?
Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?
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?
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?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Can you find an efficent way to mix paints in any ratio?
Can you work out the fraction of the original triangle that is covered by the inner triangle?
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.
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.
Quadratic graphs are very familiar, but what patterns can you explore with cubics?
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
Do you have enough information to work out the area of the shaded quadrilateral?
Complex numbers can be represented graphically using an Argand diagram. This problem explains more...
L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?
Can you find the link between these beautiful circle patterns and Farey Sequences?
Can you explain what is happening and account for the values being displayed?
An environment that enables you to investigate tessellations of regular polygons
Use your skill and judgement to match the sets of random data.
Move the point P to see how P' moves. Then use your insights to calculate a missing length.
Make different quadrilaterals on a nine-point pegboard, and work out their angles. What do you notice?
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.
Explain how to construct a regular pentagon accurately using a straight edge and compass.
Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.
Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.
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?
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?
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
A red square and a blue square overlap. Is the area of the overlap always the same?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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?
Kyle and his teacher disagree about his test score - who is right?
Can you find a way to turn a rectangle into a square?
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
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?
Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.
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?