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Resources tagged with Visualising similar to Towers:

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

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?

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. . . .

The Spider and the Fly

Stage: 4 Challenge Level:

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?

An Unusual Shape

Stage: 3 Challenge Level:

Can you maximise the area available to a grazing goat?

All Tied Up

Stage: 4 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?

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. . . .

Star Gazing

Stage: 4 Challenge Level:

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

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.

Efficient Packing

Stage: 4 Challenge Level:

How efficiently can you pack together disks?

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?

Marbles in a Box

Stage: 3 and 4 Challenge Level:

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

Summing Squares

Stage: 4 Challenge Level:

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?

Seven Squares - Group-worthy Task

Stage: 3 Challenge Level:

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

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. . . .

Rati-o

Stage: 3 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?

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?

Corridors

Stage: 4 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.

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?

Frogs

Stage: 3 Challenge Level:

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

Paving Paths

Stage: 3 Challenge Level:

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

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?

Triangles Within Triangles

Stage: 4 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

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?

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.

Cuboids

Stage: 3 Challenge Level:

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

All in the Mind

Stage: 3 Challenge Level:

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. . . .

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?

Triangles Within Squares

Stage: 4 Challenge Level:

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

Doesn't Add Up

Stage: 4 Challenge Level:

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

Konigsberg Plus

Stage: 3 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.

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.

Cubes Within Cubes Revisited

Stage: 3 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?

Efficient Cutting

Stage: 4 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.

Triangles Within Pentagons

Stage: 4 Challenge Level:

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

Fence It

Stage: 3 Challenge Level:

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

Tilting Triangles

Stage: 4 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?

Three Frogs

Stage: 4 Challenge Level:

Three frogs hopped onto the table. A red frog on the left a green in the middle and a blue frog on the right. Then frogs started jumping randomly over any adjacent frog. Is it possible for them to. . . .

Picturing Square Numbers

Stage: 3 Challenge Level:

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Painted Cube

Stage: 3 Challenge Level:

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Wari

Stage: 4 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?

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?

Weighty Problem

Stage: 3 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. . . .

Floating in Space

Stage: 4 Challenge Level:

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

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?

On the Edge

Stage: 3 Challenge Level:

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. . . .

Concrete Wheel

Stage: 3 Challenge Level:

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

Tourism

Stage: 3 Challenge Level:

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

Cutting a Cube

Stage: 3 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?

One and Three

Stage: 4 Challenge Level:

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .