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Resources tagged with Visualising similar to Got It! Article:

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Visualising. Properties of numbers. Addition & subtraction. Games. Generalising. Interactivities. Spreadsheets. Factors and multiples. Working systematically. Integers.

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Broad Topics > Using, Applying and Reasoning about Mathematics > Visualising

Tetrahedra Tester

Stage: 3 Challenge Level:

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

Triangles to Tetrahedra

Stage: 3 Challenge Level:

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

Tangram Paradox

Stage: 2 Challenge Level:

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

Cogs

Stage: 3 Challenge Level:

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

Domino Numbers

Stage: 2 Challenge Level:

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Travelling Salesman

Stage: 3 Challenge Level:

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?

Clocked

Stage: 3 Challenge Level:

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

Reflecting Squarely

Stage: 3 Challenge Level:

In how many ways can you fit all three pieces together to make shapes with line symmetry?

28 and It's Upward and Onward

Stage: 2 Challenge Level:

Can you find ways of joining cubes together so that 28 faces are visible?

Pattern Power

Stage: 1, 2 and 3

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

Christmas Chocolates

Stage: 3 Challenge Level:

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

Nine Colours

Stage: 3 Challenge Level:

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

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.

Picturing Triangle Numbers

Stage: 3 Challenge Level:

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

Twice as Big?

Stage: 2 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.

Endless Noughts and Crosses

Stage: 2 Challenge Level:

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

Frogs

Stage: 3 Challenge Level:

How many moves does it take to swap over some red and blue frogs? Do you have a method?

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?

Linkage

Stage: 3 Challenge Level:

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

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.

World of Tan 19 - Working Men

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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?

You Owe Me Five Farthings, Say the Bells of St Martin's

Stage: 3 Challenge Level:

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

Coloured Edges

Stage: 3 Challenge Level:

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

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?

More Pebbles

Stage: 2 and 3 Challenge Level:

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

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. . . .

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. . . .

Isosceles Triangles

Stage: 3 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?

World of Tan 29 - the Telephone

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this telephone?

World of Tan 28 - Concentrating on Coordinates

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

World of Tan 21 - Almost There Now

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Convex Polygons

Stage: 3 Challenge Level:

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

World of Tan 20 - Fractions

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the chairs?

World of Tan 24 - Clocks

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of these clocks?

World of Tan 25 - Pentominoes

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of these people?

World of Tan 27 - Sharing

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Little Fung at the table?

World of Tan 26 - Old Chestnut

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Right or Left?

Stage: 2 Challenge Level:

Which of these dice are right-handed and which are left-handed?

World of Tan 18 - Soup

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

Square Coordinates

Stage: 3 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?