There are 102 NRICH Mathematical resources connected to Visualising, you may find related items under Thinking Mathematically.
Broad Topics > Thinking Mathematically > Visualising
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.
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?
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?
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?
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.
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?
Painted Cube
Age 14 to 16
Challenge Level
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Proofs with Pictures
Age 14 to 18
Some diagrammatic 'proofs' of algebraic identities and inequalities.
Marbles in a Box
Age 11 to 16
Challenge Level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Nine Colours
Age 11 to 16
Challenge Level
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
One and Three
Age 14 to 16
Challenge Level
Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .
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?
Picture Story
Age 14 to 16
Challenge Level
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
Bendy Quad
Age 14 to 16
Challenge Level
Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.
Circles Ad Infinitum
Age 16 to 18
Challenge Level
A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?
Steel Cables
Age 14 to 16
Challenge Level
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Charting More Success
Age 11 to 16
Challenge Level
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
Charting Success
Age 11 to 16
Challenge Level
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
Triangles in the Middle
Age 11 to 18
Challenge Level
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Mach Attack
Age 16 to 18
Challenge Level
Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.
Ford Circles
Age 16 to 18
Challenge Level
Can you find the link between these beautiful circle patterns and Farey Sequences?
Classical Means
Age 16 to 18
Challenge Level
Use the diagram to investigate the classical Pythagorean means.
Summing Squares
Age 14 to 16
Challenge Level
Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
Speeding Boats
Age 14 to 16
Challenge Level
Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?
Building Gnomons
Age 14 to 16
Challenge Level
Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.
Thinking Through, and By, Visualising
Age 7 to 16
This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view. . . .
Air Nets
Age 7 to 18
Challenge Level
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Packing 3D Shapes
Age 14 to 16
Challenge Level
What 3D shapes occur in nature. How efficiently can you pack these shapes together?
Fitting Flat Shapes
Age 16 to 18
Challenge Level
How efficiently can various flat shapes be fitted together?
The Perforated Cube
Age 14 to 16
Challenge Level
A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?
One Out One Under
Age 14 to 16
Challenge Level
Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?
Making Tracks
Age 14 to 16
Challenge Level
A bicycle passes along a path and leaves some tracks. Is it possible to say which track was made by the front wheel and which by the back wheel?
Cheese Cutting
Age 16 to 18
Challenge Level
In this problem we see how many pieces we can cut a cube of cheese into using a limited number of slices. How many pieces will you be able to make?
Shaping the Universe II - the Solar System
Age 11 to 16
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
Shaping the Universe I - Planet Earth
Age 11 to 16
This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.
Clocking Off
Age 7 to 16
Challenge Level
I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?
Like a Circle in a Spiral
Age 7 to 16
Challenge Level
A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?
Problem Solving, Using and Applying and Functional Mathematics
Age 5 to 18
Challenge Level
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
Maximum Scattering
Age 16 to 18
Challenge Level
Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?
Triangles Within Pentagons
Age 14 to 16
Challenge Level
Show that all pentagonal numbers are one third of a triangular number.
Triangles Within Squares
Age 14 to 16
Challenge Level
Can you find a rule which relates triangular numbers to square numbers?
Triangles Within Triangles
Age 14 to 16
Challenge Level
Can you find a rule which connects consecutive triangular numbers?
Classic Cube
Age 16 to 18
Challenge Level
The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?
NRICH is part of the family of activities in the Millennium Mathematics Project.