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#### Resources tagged with Visualising similar to Weekly Problem 2 - 2008:

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### There are 187 results

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

### 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?

### 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?

### 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.

### 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?

### Efficient Packing

##### Stage: 4 Challenge Level:

How efficiently can you pack together disks?

### 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?

### 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?

### Making Tracks

##### Stage: 4 Challenge Level:

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?

### 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.

### Hidden Squares

##### Stage: 3 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?

### Königsberg

##### Stage: 3 Challenge Level:

Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?

### 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?

### Threesomes

##### Stage: 3 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?

### Qqq..cubed

##### Stage: 4 Challenge Level:

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. . . .

### Just Rolling Round

##### Stage: 4 Challenge Level:

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

### Concrete Wheel

##### Stage: 3 Challenge Level:

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

### Rolling Coins

##### Stage: 4 Challenge Level:

A blue coin rolls round two yellow coins which touch. The coins are the same size. How many revolutions does the blue coin make when it rolls all the way round the yellow coins? Investigate for a. . . .

### Around and Back

##### Stage: 4 Challenge Level:

A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .

### AMGM

##### Stage: 4 Challenge Level:

Choose any two numbers. Call them a and b. Work out the arithmetic mean and the geometric mean. Which is bigger? Repeat for other pairs of numbers. What do you notice?

### 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?

### Triangle Inequality

##### Stage: 3 Challenge Level:

ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.

### LOGO Challenge - Circles as Animals

##### Stage: 3 and 4 Challenge Level:

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

### 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.

### Frogs

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

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

### 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?

### 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?

### 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?

### 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?

### Convex Polygons

##### Stage: 3 Challenge Level:

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

### 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?

### A Tilted Square

##### Stage: 4 Challenge Level:

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

##### Stage: 4 Challenge Level:

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

### 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. . . .

### Triangles Within Pentagons

##### Stage: 4 Challenge Level:

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

### Triangles Within Triangles

##### Stage: 4 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

### How Many Dice?

##### Stage: 3 Challenge Level:

A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .

### 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.

### 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?

### Seven Squares

##### Stage: 3 and 4 Challenge Level:

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

### 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?

### Bent Out of Shape

##### Stage: 4 and 5 Challenge Level:

An introduction to bond angle geometry.

### 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?

### 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. . . .

### More Pebbles

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

Have a go at this 3D extension to the Pebbles problem.

### 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?

### 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?

### Steel Cables

##### Stage: 4 Challenge Level:

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

### Squares in Rectangles

##### Stage: 3 Challenge Level:

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

### Is There a Theorem?

##### Stage: 3 Challenge Level:

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?