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Resources tagged with Visualising similar to Out of the Window:

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Wari

Stage: 4 Challenge Level:

This is a simple version of an ancient game played all over the world. It is also called Mancala. What tactics will increase your chances of winning?

Baravelle

Stage: 2, 3 and 4 Challenge Level:

What can you see? What do you notice? What questions can you ask?

Making Tracks

Stage: 4 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?

Sprouts

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

A game for 2 people. Take turns joining two dots, until your opponent is unable to move.

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.

Like a Circle in a Spiral

Stage: 2, 3 and 4 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?

Star Gazing

Stage: 4 Challenge Level:

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

Clocking Off

Stage: 2, 3 and 4 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?

Corridors

Stage: 4 Challenge Level:

A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.

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!

Platonic Planet

Stage: 4 Challenge Level:

Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?

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?

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?

Spotting the Loophole

Stage: 4 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?

The Perforated Cube

Stage: 4 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 ?

Tilting Triangles

Stage: 4 Challenge Level:

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

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?

All Tied Up

Stage: 4 Challenge Level:

A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?

There and Back Again

Stage: 3 Challenge Level:

Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?

The Spider and the Fly

Stage: 4 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?

One Out One Under

Stage: 4 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?

Auditorium Steps

Stage: 2 and 3 Challenge Level:

What is the shape of wrapping paper that you would need to completely wrap this model?

Trice

Stage: 3 Challenge Level:

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

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?

Cutting a Cube

Stage: 3 Challenge Level:

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?

Just Opposite

Stage: 4 Challenge Level:

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

All in the Mind

Stage: 3 Challenge Level:

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .

Stage: 3 Challenge Level:

Can you mark 4 points on a flat surface so that there are only two different distances between them?

More Pebbles

Stage: 2 and 3 Challenge Level:

Have a go at this 3D extension to the Pebbles problem.

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?

Sea Defences

Stage: 2 and 3 Challenge Level:

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Ding Dong Bell

Stage: 3, 4 and 5

The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.

Diagonal Dodge

Stage: 2 and 3 Challenge Level:

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

Double Trouble

Stage: 4 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.

The Old Goats

Stage: 3 Challenge Level:

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . .

Stage: 4 Challenge Level:

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

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.

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. . . .

Tetra Square

Stage: 3 Challenge Level:

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

Zooming in on the Squares

Stage: 2 and 3

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?

LOGO Challenge - Circles as Animals

Stage: 3 and 4 Challenge Level:

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

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.

Picturing Triangular Numbers

Stage: 3 Challenge Level:

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Dissect

Stage: 3 Challenge Level:

It is possible to dissect any square into smaller squares. What is the minimum number of squares a 13 by 13 square can be dissected into?

Cubic Conundrum

Stage: 2, 3 and 4 Challenge Level:

Which of the following cubes can be made from these nets?

Rolling Around

Stage: 3 Challenge Level:

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

3D Stacks

Stage: 2 and 3 Challenge Level:

Can you find a way of representing these arrangements of balls?

Tic Tac Toe

Stage: 3 Challenge Level:

In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?

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?