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There are **52** NRICH Mathematical resources connected to **Coordinates**, you may find related items under Coordinates, functions and graphs.

Problem
Primary curriculum
Secondary curriculum
### Hidden Squares

Can you find the squares hidden on these coordinate grids?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Attractive Rotations

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Treasure Hunt

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

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Eight Hidden Squares

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?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Route to Infinity

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Coordinate Challenge

Use the clues about the symmetrical properties of these letters to place them on the grid.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cubestick

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Square Coordinates

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Isosceles Triangles

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ten Hidden Squares

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

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Coordinate Patterns

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Cartesian Puzzle

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Parabella

This is a beautiful result involving a parabola and parallels.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Beelines

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ladder and Cube

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?

Age 14 to 16

Challenge Level

List
Primary curriculum
Secondary curriculum
### Being Resourceful - Primary Geometry

Geometry problems at primary level that require careful consideration.

Age 5 to 11

Challenge Level

List
Primary curriculum
Secondary curriculum
### Being Collaborative - Primary Geometry

Geometry problems for primary learners to work on with others.

Age 5 to 11

Challenge Level

List
Primary curriculum
Secondary curriculum
### Being Curious - Primary Geometry

Geometry problems for inquiring primary learners.

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polar Bearings

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Coordinate Designs

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two Number Lines

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Flight Path

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dotty Relationship

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cartesian Isometric

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fred the Class Robot

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 3D Treasure Hunt

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

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Something in Common

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.

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Coordinates and Descartes

Have you ever wondered how maps are made? Or perhaps who first thought of the idea of designing maps? We're here to answer these questions for you.

Age 7 to 16

Article
Primary curriculum
Secondary curriculum
### Coordinating Classroom Coordinates

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

Age 7 to 11

Article
Primary curriculum
Secondary curriculum
### Going Places with Mathematicians

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 things.

Age 7 to 14

Problem
Primary curriculum
Secondary curriculum
### Mesh

A spherical balloon lies inside a wire frame. How much do you need to deflate it to remove it from the frame if it remains a sphere?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Shade Crossed

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rational Round

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Corridors

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Snookered

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?

Age 14 to 18

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Coordinate Cunning

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

Age 7 to 11

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Criss Cross Quiz

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What Are You Plotting?

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Treasure Island

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Transformation Tease

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Tilted Square

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Square Pair Circles

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Hypotenuse Lattice Points

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Four Points on a Cube

What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Plane to See

P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Napoleon's Hat

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cushion Ball

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Just Opposite

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cut Cube

Find the shape and symmetries of the two pieces of this cut cube.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Lily Pond

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?

Age 7 to 11

Challenge Level