Resources tagged with: Visualising

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There are 179 results

Broad Topics > Thinking Mathematically > Visualising

Tilting Triangles

Age 14 to 16
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?

Building Tetrahedra

Age 14 to 16
Challenge Level

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

Tied Up

Age 14 to 16 Short
Challenge Level

How much of the field can the animals graze?

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. . . .

Triangles Within Triangles

Age 14 to 16
Challenge Level

Can you find a rule which connects consecutive triangular numbers?

Triangles Within Pentagons

Age 14 to 16
Challenge Level

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

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.

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?

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?

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. . . .

Efficient Packing

Age 14 to 16
Challenge Level

How efficiently can you pack together disks?

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?

Vanishing Point

Age 14 to 18
Challenge Level

How can visual patterns be used to prove sums of series?

Tessellating Hexagons

Age 11 to 14
Challenge Level

Which hexagons tessellate?

Dotty Triangles

Age 11 to 14
Challenge Level

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

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?

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?

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.

Hidden Rectangles

Age 11 to 14
Challenge Level

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

Fermat's Poser

Age 14 to 16
Challenge Level

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

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.

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?

Jam

Age 14 to 16
Challenge Level

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

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?

Cutting a Cube

Age 11 to 14
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?

All in the Mind

Age 11 to 14
Challenge Level

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

Pattern Power

Age 5 to 14

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

Rati-o

Age 11 to 14
Challenge Level

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

Jam

Age 14 to 16
Challenge Level

A game for 2 players

An Unusual Shape

Age 11 to 14
Challenge Level

Can you maximise the area available to a grazing goat?

LOGO Challenge - Circles as Animals

Age 11 to 16
Challenge Level

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

Route to Infinity

Age 11 to 14
Challenge Level

Can you describe this route to infinity? Where will the arrows take you next?

3D Stacks

Age 7 to 14
Challenge Level

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

Polygon Rings

Age 11 to 14
Challenge Level

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

Partly Painted Cube

Age 14 to 16
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?

Christmas Chocolates

Age 11 to 14
Challenge Level

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

Speeding Boats

Age 14 to 16
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?

Clocking Off

Age 7 to 16
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?

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?

Cubes Within Cubes Revisited

Age 11 to 14
Challenge Level

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

Picturing Triangular Numbers

Age 11 to 14
Challenge Level

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

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?

Triangles Within Squares

Age 14 to 16
Challenge Level

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

Sliding Puzzle

Age 11 to 16
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.

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. . . .

Inside Out

Age 14 to 16
Challenge Level

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

Dice, Routes and Pathways

Age 5 to 14

This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .

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?

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?

Konigsberg Plus

Age 11 to 14
Challenge Level

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.