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Resources tagged with Visualising similar to Warmsnug Double Glazing:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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

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The Spider and the Fly

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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An Unusual Shape

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you maximise the area available to a grazing goat?

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Trice

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Like a Circle in a Spiral

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

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?

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Star Gazing

Stage: 4 Challenge Level: Challenge Level:1

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

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Marbles in a Box

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

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

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Isosceles Triangles

Stage: 3 Challenge Level: Challenge Level:1

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?

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Corridors

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Framed

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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All Tied Up

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Sprouts

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

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

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Efficient Cutting

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Conway's Chequerboard Army

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Buses

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A bus route has a total duration of 40 minutes. Every 10 minutes, two buses set out, one from each end. How many buses will one bus meet on its way from one end to the other end?

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Fence It

Stage: 3 Challenge Level: Challenge Level:1

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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Spotting the Loophole

Stage: 4 Challenge Level: Challenge Level:1

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?

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Qqq..cubed

Stage: 4 Challenge Level: Challenge Level:1

It is known that the area of the largest equilateral triangular section of a cube is 140sq cm. What is the side length of the cube? The distances between the centres of two adjacent faces of. . . .

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Cubist Cuts

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?

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Keep Your Distance

Stage: 3 Challenge Level: Challenge Level:1

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

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The Perforated Cube

Stage: 4 Challenge Level: Challenge Level:1

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 ?

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Picturing Triangle Numbers

Stage: 3 Challenge Level: Challenge Level:1

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

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Triangles to Tetrahedra

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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The Old Goats

Stage: 3 Challenge Level: Challenge Level:1

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. . . .

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On the Edge

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try to. . . .

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All in the Mind

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Sea Defences

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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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?

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Floating in Space

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Two angles ABC and PQR are floating in a box so that AB//PQ and BC//QR. Prove that the two angles are equal.

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Wari

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Khun Phaen Escapes to Freedom

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Tilting Triangles

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Making Tracks

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Tetrahedra Tester

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Diagonal Dodge

Stage: 2 and 3 Challenge Level: Challenge Level:1

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.

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Doesn't Add Up

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Frogs

Stage: 3 Challenge Level: Challenge Level:1

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

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Bands and Bridges: Bringing Topology Back

Stage: 2 and 3

Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.

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Concrete Wheel

Stage: 3 Challenge Level: Challenge Level:1

A huge wheel is rolling past your window. What do you see?

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There and Back Again

Stage: 3 Challenge Level: Challenge Level:1

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

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Tic Tac Toe

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Troublesome Dice

Stage: 3 Challenge Level: Challenge Level:1

When dice land edge-up, we usually roll again. But what if we didn't...?

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Intersecting Circles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Crossing the Atlantic

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Every day at noon a boat leaves Le Havre for New York while another boat leaves New York for Le Havre. The ocean crossing takes seven days. How many boats will each boat cross during their journey?

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Triangles in the Middle

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

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Clocking Off

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

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?

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Dissect

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Just Opposite

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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3D Stacks

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Contact

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

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When the Angles of a Triangle Don't Add up to 180 Degrees

Stage: 4 and 5

This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the. . . .