There are 355 NRICH Mathematical resources connected to Visualising, you may find related items under Thinking Mathematically.
Broad Topics > Thinking Mathematically > Visualising
Tumbling Down
Age 7 to 11
Challenge Level
Watch this animation. What do you see? Can you explain why this happens?
Finding 3D Stacks
Age 7 to 11
Challenge Level
Can you find a way of counting the spheres in these arrangements?
Seeing Squares
Age 5 to 11
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.
Paper Partners
Age 5 to 7
Challenge Level
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
Paper Patchwork 2
Age 5 to 7
Challenge Level
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Paper Patchwork 1
Age 5 to 7
Challenge Level
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
Polygon Pictures
Age 11 to 14
Challenge Level
Can you work out how these polygon pictures were drawn, and use that to figure out their angles?
Polygon Rings
Age 11 to 14
Challenge Level
Join pentagons together edge to edge. Will they form a ring?
Move Those Halves
Age 7 to 11
Challenge Level
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
Circles, Circles
Age 5 to 11
Challenge Level
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
How Would We Count?
Age 5 to 11
Challenge Level
An activity centred around observations of dots and how we visualise number arrangement patterns.
Seven Squares
Age 11 to 14
Challenge Level
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Poly Plug Pattern
Age 5 to 7
Challenge Level
Create a pattern on the small grid. How could you extend your pattern on the larger grid?
Triple Cubes
Age 5 to 11
Challenge Level
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Partly Painted Cube
Age 14 to 16
Challenge Level
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
Mystic Rose
Age 14 to 16
Challenge Level
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
Diminishing Returns
Age 11 to 14
Challenge Level
How much of the square is coloured blue? How will the pattern continue?
Tower of Hanoi
Age 11 to 14
Challenge Level
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Christmas Chocolates
Age 11 to 14
Challenge Level
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Coded Hundred Square
Age 7 to 11
Challenge Level
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Holes
Age 5 to 11
Challenge Level
I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?
Baravelle
Age 7 to 16
Challenge Level
What can you see? What do you notice? What questions can you ask?
Cuboid Challenge
Age 11 to 16
Challenge Level
What's the largest volume of box you can make from a square of paper?
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?
Overlapping Again
Age 7 to 11
Challenge Level
What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.
Overlaps
Age 5 to 7
Challenge Level
What does the overlap of these two shapes look like? Try picturing it in your head and then use some cut-out shapes to test your prediction.
Spotting the Loophole
Age 14 to 16
Challenge Level
A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?
Picture a Pyramid ...
Age 7 to 11
Challenge Level
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Twice as Big?
Age 7 to 11
Challenge Level
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Music to My Ears
Age 7 to 11
Challenge Level
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
Route to Infinity
Age 11 to 14
Challenge Level
Can you describe this route to infinity? Where will the arrows take you next?
Brush Loads
Age 7 to 11
Challenge Level
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Squares in Rectangles
Age 11 to 14
Challenge Level
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
Semi-regular Tessellations
Age 11 to 16
Challenge Level
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Stringy Quads
Age 7 to 11
Challenge Level
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Nine-pin Triangles
Age 7 to 11
Challenge Level
How many different triangles can you make on a circular pegboard that has nine pegs?
Cubes Within Cubes Revisited
Age 11 to 14
Challenge Level
Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
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?
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?
Efficient Cutting
Age 11 to 14
Challenge Level
Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
Fence It
Age 11 to 14
Challenge Level
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Ten Hidden Squares
Age 7 to 14
Challenge Level
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
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.
On the Edge
Age 11 to 14
Challenge Level
If you move the tiles around, can you make squares with different coloured edges?
Tangram Tangle
Age 5 to 7
Challenge Level
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Hundred Square
Age 5 to 7
Challenge Level
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
Cuboids
Age 11 to 14
Challenge Level
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
The Spider and the Fly
Age 14 to 16
Challenge Level
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
Shadow Play
Age 5 to 7
Challenge Level
Here are shadows of some 3D shapes. What shapes could have made them?
NRICH is part of the family of activities in the Millennium Mathematics Project.