Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
Can you describe this route to infinity? Where will the arrows take you next?
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?
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?
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.
What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?
This is a beautiful result involving a parabola and parallels.
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
Geometry problems at primary level that may require resilience.
Geometry problems at primary level that require careful consideration.
Geometry problems for primary learners to work on with others.
Geometry problems for inquiring primary learners.
Can you find the squares hidden on these coordinate grids?
What on earth are polar coordinates, and why would you want to use them?
This task requires learners to explain and help others, asking and answering questions.
Max and Mandy put their number lines together to make a graph. How far had each of them moved along and up from 0 to get the counter to the place marked?
Can you draw perpendicular lines without using a protractor? Investigate how this is possible.
Scientist Bryan Rickett has a vision of the future - and it is one in which self-parking cars prowl the tarmac plains, hunting down suitable parking spots and manoeuvring elegantly into them.
The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form?
Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?
Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?
A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
This article describes a practical approach to enhance the teaching and learning of coordinates.
This article looks at the importance in mathematics of representing places and spaces mathematics. Many famous mathematicians have spent time working on problems that involve moving and mapping. . . .
Find the area of the shaded region created by the two overlapping triangles in terms of a and b?
Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.
A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.
In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?
A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.
A game for 2 players. Practises subtraction or other maths operations knowledge.
Investigate the positions of points which have particular x and y coordinates. What do you notice?
Write down what you can see at the coordinates of the treasure island map. The words can be used in a special way to find the buried treasure. Can you work out where it is?
What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Investigate the number of points with integer coordinates on circles with centres at the origin for which the square of the radius is a power of 5.
The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?
Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?
The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?
A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?
Freddie Frog visits as many of the leaves as he can on the way to see Sammy Snail but only visits each lily leaf once. Which is the best way for him to go?