"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 hunt
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
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?
Guess my quad
How many questions do you need to identify my quadrilateral?
Completing quadrilaterals
We started drawing some quadrilaterals - can you complete them?
Tilted squares
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Square it
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.
Opposite vertices
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
Coordinate patterns
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?
Route to infinity
Vector journeys
Beelines
Doesn't add up
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
Pick's theorem
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?
Areas of parallelograms