Resources tagged with: Visualising

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There are 178 results

Broad Topics > Thinking Mathematically > Visualising

Polygon Pictures

Age 11 to 14 Challenge Level:

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

LOGO Challenge - Circles as Animals

Age 11 to 16 Challenge Level:

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

Getting an Angle

Age 11 to 14 Challenge Level:

How can you make an angle of 60 degrees by folding a sheet of paper twice?

Polygon Rings

Age 11 to 14 Challenge Level:

Join pentagons together edge to edge. Will they form a ring?

Trice

Age 11 to 14 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?

Tessellating Hexagons

Age 11 to 14 Challenge Level:

Which hexagons tessellate?

Playground Snapshot

Age 7 to 14 Challenge Level:

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

Efficient Cutting

Age 11 to 14 Challenge Level:

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

The Old Goats

Age 11 to 14 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. . . .

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.

Corridors

Age 14 to 16 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.

LOGO Challenge - Triangles-squares-stars

Age 11 to 16 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.

On Time

Age 11 to 14 Challenge Level:

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

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?

Star Gazing

Age 14 to 16 Challenge Level:

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

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.

Rolling Around

Age 11 to 14 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?

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?

Cube Paths

Age 11 to 14 Challenge Level:

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

Efficient Packing

Age 14 to 16 Challenge Level:

How efficiently can you pack together disks?

An Unusual Shape

Age 11 to 14 Challenge Level:

Can you maximise the area available to a grazing goat?

Weighty Problem

Age 11 to 14 Challenge Level:

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .

Tied Up

Age 14 to 16 Short Challenge Level:

How much of the field can the animals graze?

Convex Polygons

Age 11 to 14 Challenge Level:

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

There and Back Again

Age 11 to 14 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?

Sprouts

Age 7 to 18 Challenge Level:

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

Square Coordinates

Age 11 to 14 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?

Wari

Age 14 to 16 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?

Keep Your Distance

Age 11 to 14 Challenge Level:

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

Sea Defences

Age 7 to 14 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?

A Tilted Square

Age 14 to 16 Challenge Level:

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

Zooming in on the Squares

Age 7 to 14

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?

Coloured Edges

Age 11 to 14 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?

Squares, Squares and More Squares

Age 11 to 14 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?

Pattern Power

Age 5 to 14

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

Linkage

Age 11 to 14 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?

All Tied Up

Age 14 to 16 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?

Changing Places

Age 14 to 16 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. . . .

Khun Phaen Escapes to Freedom

Age 11 to 14 Challenge Level:

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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.

Alquerque

Age 5 to 18

This game for two, was played in ancient Egypt as far back as 1400 BC. The game was taken by the Moors to Spain, where it is mentioned in 13th century manuscripts, and the Spanish name Alquerque. . . .

Rolling Triangle

Age 11 to 14 Challenge Level:

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

Coordinate Patterns

Age 11 to 14 Challenge Level:

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

Framed

Age 11 to 14 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. . . .

Hypotenuse Lattice Points

Age 14 to 16 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?

Tetra Square

Age 11 to 14 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.

Something in Common

Age 14 to 16 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.

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?

Ten Hidden Squares

Age 7 to 14 Challenge Level:

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

Cubic Conundrum

Age 7 to 16 Challenge Level:

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