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Resources tagged with Visualising similar to What Shape?:

Other tags that relate to What Shape?

Visualising. Pedagogy. Compound transformations. Shape, space & measures - generally. Questioning. Squares. Team-building. Circles. Mathematical reasoning & proof. Solids.

There are 262 results

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

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?

Baravelle

Stage: 2, 3 and 4 Challenge Level:

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

Chess

Stage: 3 Challenge Level:

What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?

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. . . .

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?

The Development of Spatial and Geometric Thinking: the Importance of Instruction.

Stage: 1 and 2

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

The Development of Spatial and Geometric Thinking: 5 to 18

Stage: 1, 2, 3 and 4

This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .

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.

Triangular Tantaliser

Stage: 3 Challenge Level:

Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.

Counting Triangles

Stage: 3 Challenge Level:

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?

Diagrams

Stage: 2 Challenge Level:

A group activity using visualisation of squares and triangles.

L-ateral Thinking

Stage: 1 and 2 Challenge Level:

Try this interactive strategy game for 2

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?

An Unusual Shape

Stage: 3 Challenge Level:

Can you maximise the area available to a grazing goat?

Square it for Two

Stage: 1 and 2 Challenge Level:

Square It game for an adult and child. Can you come up with a way of always winning this game?

Screwed-up

Stage: 3 Challenge Level:

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?

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.

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?

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?

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. . . .

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?

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.

On the Edge

Stage: 3 Challenge Level:

If you move the tiles around, can you make squares with different coloured edges?

Three Squares

Stage: 1 and 2 Challenge Level:

What is the greatest number of squares you can make by overlapping three squares?

Thinking Through, and By, Visualising

Stage: 2, 3 and 4

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. . . .

Circles, Circles

Stage: 1 and 2 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?

Conway's Chequerboard Army

Stage: 3 Challenge Level:

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

Ten Hidden Squares

Stage: 2 Challenge Level:

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

Christmas Boxes

Stage: 3 Challenge Level:

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.

LOGO Challenge - Circles as Animals

Stage: 3 and 4 Challenge Level:

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

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?

Flight of the Flibbins

Stage: 3 Challenge Level:

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

Take One Example

Stage: 1 and 2

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

Tied Up

Stage: 3 Challenge Level:

In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .

Framed

Stage: 3 Challenge Level:

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

Inside Seven Squares

Stage: 2 Challenge Level:

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Muggles Magic

Stage: 3 Challenge Level:

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

Take Ten

Stage: 3 Challenge Level:

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .

A Square in a Circle

Stage: 2 Challenge Level:

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

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.

Eight Hidden Squares

Stage: 2 and 3 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?

Squares, Squares and More Squares

Stage: 3 Challenge Level:

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

Painting Cubes

Stage: 3 Challenge Level:

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

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?

Intersecting Circles

Stage: 3 Challenge Level:

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

Matchsticks

Stage: 2 Challenge Level:

Reasoning about the number of matches needed to build squares that share their sides.

Put Yourself in a Box

Stage: 2 Challenge Level:

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

World of Tan 16 - Time Flies

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the candle and sundial?

World of Tan 18 - Soup

Stage: 2 Challenge Level:

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

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?