Angles - points, lines and parallel lines

problem
Arrowhead

Age

14 to 16

Challenge level

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?
problem
Quad in quad

Age

14 to 18

Challenge level

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
problem
A problem of time

Age

14 to 16

Challenge level

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?
problem
Flexi quads

Age

16 to 18

Challenge level

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?
problem
Square world

Age

16 to 18

Challenge level

P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?
problem
Clock hands

Age

7 to 11

Challenge level

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.
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Making maths: clinometer

You can use a clinometer to measure the height of tall things that you can't possibly reach to the top of, Make a clinometer and use it to help you estimate the heights of tall objects.
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Making maths: equilateral triangle folding

Make an equilateral triangle by folding paper and use it to make patterns of your own.
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Watch those wheels

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!
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Interacting with the geometry of the circle

Jennifer Piggott and Charlie Gilderdale describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions.