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Broad Topics > Coordinates and Coordinate Geometry > Coordinates

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Attractive Rotations

Age 11 to 14 Challenge Level:

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

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Treasure Hunt

Age 7 to 14 Challenge Level:

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

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Eight Hidden Squares

Age 7 to 14 Challenge Level:

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?

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Route to Infinity

Age 11 to 14 Challenge Level:

Can you describe this route to infinity? Where will the arrows take you next?

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Square Coordinates

Age 11 to 14 Challenge Level:

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?

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Isosceles Triangles

Age 11 to 14 Challenge Level:

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?

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Ten Hidden Squares

Age 7 to 11 Challenge Level:

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

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Coordinate Patterns

Age 11 to 14 Challenge Level:

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

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A Cartesian Puzzle

Age 7 to 11 Challenge Level:

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

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Coordinate Tan

Age 7 to 11 Challenge Level:

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?

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Parabella

Age 16 to 18 Challenge Level:

This is a beautiful result involving a parabola and parallels.

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Beelines

Age 14 to 16 Challenge Level:

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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Ladder and Cube

Age 14 to 16 Challenge Level:

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?

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Being Resilient - Primary Geometry

Age 5 to 11 Challenge Level:

Geometry problems at primary level that may require resilience.

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Being Resourceful - Primary Geometry

Age 5 to 11 Challenge Level:

Geometry problems at primary level that require careful consideration.

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Being Collaborative - Primary Geometry

Age 5 to 11 Challenge Level:

Geometry problems for primary learners to work on with others.

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Being Curious - Primary Geometry

Age 5 to 11 Challenge Level:

Geometry problems for inquiring primary learners.

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Hidden Squares

Age 11 to 14 Challenge Level:

Can you find the squares hidden on these coordinate grids?

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Polar Bearings

Age 16 to 18 Challenge Level:

What on earth are polar coordinates, and why would you want to use them?

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Coordinate Designs

Age 11 to 14 Challenge Level:

This task requires learners to explain and help others, asking and answering questions.

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Two Number Lines

Age 7 to 11 Challenge Level:

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?

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Dotty Relationship

Age 7 to 11 Challenge Level:

Can you draw perpendicular lines without using a protractor? Investigate how this is possible.

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Parallel Parking

Age 14 to 16

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.

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Cartesian Isometric

Age 7 to 11 Challenge Level:

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?

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Fred the Class Robot

Age 7 to 11 Challenge Level:

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

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3D Treasure Hunt

Age 14 to 18 Challenge Level:

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

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Something in Common

Age 14 to 16 Challenge Level:

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.

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Coordinating Classroom Coordinates

Age 7 to 11

This article describes a practical approach to enhance the teaching and learning of coordinates.

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Going Places with Mathematicians

Age 7 to 14

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. . . .

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A Shade Crossed

Age 14 to 16 Challenge Level:

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

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Rational Round

Age 16 to 18 Challenge Level:

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.

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Corridors

Age 14 to 16 Challenge Level:

A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.

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Snookered

Age 14 to 18 Challenge Level:

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?

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Coordinate Cunning

Age 7 to 11 Challenge Level:

A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.

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Criss Cross Quiz

Age 7 to 11 Challenge Level:

A game for 2 players. Practises subtraction or other maths operations knowledge.

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What Are You Plotting?

Age 7 to 11 Challenge Level:

Investigate the positions of points which have particular x and y coordinates. What do you notice?

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Treasure Island

Age 7 to 11 Challenge Level:

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?

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Transformation Tease

Age 7 to 11 Challenge Level:

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?

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A Tilted Square

Age 14 to 16 Challenge Level:

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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Square Pair Circles

Age 16 to 18 Challenge Level:

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.

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Hypotenuse Lattice Points

Age 14 to 16 Challenge Level:

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?

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Napoleon's Hat

Age 16 to 18 Challenge Level:

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?

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Cushion Ball

Age 16 to 18 Challenge Level:

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?

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Just Opposite

Age 14 to 16 Challenge Level:

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?

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The Lily Pond

Age 7 to 11 Challenge Level:

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?