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#### Resources tagged with Visualising similar to Stonehenge:

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### Stonehenge

##### Stage: 5 Challenge Level:

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

### Classic Cube

##### Stage: 5 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?

### Fitting Flat Shapes

##### Stage: 5 Challenge Level:

How efficiently can various flat shapes be fitted together?

### Problem Solving, Using and Applying and Functional Mathematics

##### Stage: 1, 2, 3, 4 and 5 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.

### Shaping the Universe I - Planet Earth

##### Stage: 3 and 4

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.

### Circuit Training

##### Stage: 4 Challenge Level:

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .

### Packing 3D Shapes

##### Stage: 4 Challenge Level:

What 3D shapes occur in nature. How efficiently can you pack these shapes together?

### Steel Cables

##### Stage: 4 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?

### Mach Attack

##### Stage: 5 Challenge Level:

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

### Efficient Packing

##### Stage: 4 Challenge Level:

How efficiently can you pack together disks?

### Shaping the Universe II - the Solar System

##### Stage: 3 and 4

The second in a series of articles on visualising and modelling shapes in the history of astronomy.

### Jam

##### Stage: 4 Challenge Level:

To avoid losing think of another very well known game where the patterns of play are similar.

### Mystic Rose

##### Stage: 4 Challenge Level:

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

### Around and Back

##### Stage: 4 Challenge Level:

A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .

### Escriptions

##### Stage: 5 Challenge Level:

For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.

### Hypotenuse Lattice Points

##### Stage: 4 Challenge Level:

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

### Triangles Within Squares

##### Stage: 4 Challenge Level:

Can you find a rule which relates triangular numbers to square numbers?

### Building Tetrahedra

##### Stage: 4 Challenge Level:

Can you make a tetrahedron whose faces all have the same perimeter?

### Air Nets

##### Stage: 2, 3, 4 and 5 Challenge Level:

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

### Fermat's Poser

##### Stage: 4 Challenge Level:

Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.

### LOGO Challenge - Triangles-squares-stars

##### Stage: 3 and 4 Challenge Level:

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

### Jam

##### Stage: 4 Challenge Level:

A game for 2 players

### LOGO Challenge - Circles as Animals

##### Stage: 3 and 4 Challenge Level:

See if you can anticipate successive 'generations' of the two animals shown here.

### Sliding Puzzle

##### Stage: 1, 2, 3 and 4 Challenge Level:

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

### Maximum Scattering

##### Stage: 5 Challenge Level:

Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?

### Building Gnomons

##### Stage: 4 Challenge Level:

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.

### One and Three

##### Stage: 4 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. . . .

### Triangles Within Pentagons

##### Stage: 4 Challenge Level:

Show that all pentagonal numbers are one third of a triangular number.

### Lost on Alpha Prime

##### Stage: 4 Challenge Level:

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

### Square It

##### Stage: 3 and 4 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.

### Changing Places

##### Stage: 4 Challenge Level:

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

### Sliced

##### Stage: 4 Challenge Level:

An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?

### Cubic Net

##### Stage: 4 and 5 Challenge Level:

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!

### Something in Common

##### Stage: 4 Challenge Level:

A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.

##### Stage: 5 Challenge Level:

A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?

### Proximity

##### Stage: 4 Challenge Level:

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

### Triangles Within Triangles

##### Stage: 4 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

### Contact

##### Stage: 4 Challenge Level:

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

### Bent Out of Shape

##### Stage: 4 and 5 Challenge Level:

An introduction to bond angle geometry.

### Triangles in the Middle

##### Stage: 3, 4 and 5 Challenge Level:

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

### Partly Painted Cube

##### Stage: 4 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?

### Rotating Triangle

##### Stage: 3 and 4 Challenge Level:

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

### Introducing NRICH TWILGO

##### Stage: 1, 2, 3, 4 and 5 Challenge Level:

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

### Charting Success

##### Stage: 3 and 4 Challenge Level:

Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?

### Charting More Success

##### Stage: 3 and 4 Challenge Level:

Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?

### Coke Machine

##### Stage: 4 Challenge Level:

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

### Speeding Boats

##### Stage: 4 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?

### Summing Squares

##### Stage: 4 Challenge Level:

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?

### Set Square

##### Stage: 5 Challenge Level:

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?