Dotty Grids


"Take a dotty grid. Draw a few lines. What can you draw? What can you discover? The more you explore, the deeper you are drawn in..."

The Dotty Grids pathway on wild.maths.org is filled with starting points to stimulate students' creativity. We hope students will be playful, pose their own questions, and make some unexpected discoveries.

The collection of related NRICH tasks below are ideal for teachers who want to promote creativity in the classroom. They are designed for classroom use, with accompanying Teachers' Notes and Resources.


Treasure Huntlive

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?

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?

Guess my Quad

Age 11 to 14 Challenge Level:

How many questions do you need to identify my quadrilateral?

Completing Quadrilaterals

Age 11 to 14 Challenge Level:

We started drawing some quadrilaterals - can you complete them?

Tilted Squares

Age 11 to 14 Challenge Level:

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Route to Infinity

Age 11 to 14 Challenge Level:

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

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?

Opposite Vertices

Age 11 to 14 Challenge Level:

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

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?

Square It

Age 11 to 16 Challenge Level:

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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?

Areas of Parallelograms

Age 14 to 16 Challenge Level:

Can you find the area of a parallelogram defined by two vectors?

Pick's Theorem

Age 14 to 16 Challenge Level:

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Doesn't Add Up

Age 14 to 16 Challenge Level:

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

Vector Journeys

Age 14 to 18 Challenge Level:

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

3D Treasure Huntlive

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?