"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.
problem
Favourite
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?
problem
Favourite
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?
problem
Favourite
Completing Quadrilaterals
Age
11 to 14
Challenge level
We started drawing some quadrilaterals - can you complete them?
problem
Favourite
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?
problem
Favourite
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.
problem
Favourite
Guess my Quad
Age
11 to 14
Challenge level
How many questions do you need to identify my quadrilateral?
problem
Favourite
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?
problem
Favourite
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?
problem
Favourite
Route to infinity
Age
11 to 14
Challenge level
Can you describe this route to infinity? Where will the arrows take you next?
problem
Favourite
Opposite vertices
Age
11 to 14
Challenge level
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
problem
Favourite
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?
problem
Favourite
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?
problem
Favourite
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?
problem
Favourite
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.
problem
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?
problem
Favourite
Areas of parallelograms
Age
14 to 16
Challenge level
Can you find the area of a parallelogram defined by two vectors?