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Resources tagged with Visualising similar to Weekly Problem 28 - 2008:

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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?

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.

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.

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?

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?

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.

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. . . .

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?

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?

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.

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?

More Pebbles

Stage: 2 and 3 Challenge Level:

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

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. . . .

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?

Bent Out of Shape

Stage: 4 and 5 Challenge Level:

An introduction to bond angle geometry.

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. . . .

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?

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?

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?

An Unusual Shape

Stage: 3 Challenge Level:

Can you maximise the area available to a grazing goat?

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. . . .

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. . . .

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?

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?

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?

Convex Polygons

Stage: 3 Challenge Level:

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

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?

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?

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?

Triangles in the Middle

Stage: 3, 4 and 5 Challenge Level:

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

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. . . .

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?

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?

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?

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?

LOGO Challenge - Circles as Animals

Stage: 3 and 4 Challenge Level:

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

Mystic Rose

Stage: 3 Challenge Level:

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

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?

Christmas Chocolates

Stage: 3 Challenge Level:

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

Stage: 3 Challenge Level:

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

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?

Baravelle

Stage: 2, 3 and 4 Challenge Level:

What can you see? What do you notice? What questions can you ask?

Eight Hidden Squares

Stage: 2 and 3 Challenge Level:

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Masterclass Ideas: Visualising

Stage: 2 and 3 Challenge Level:

A package contains a set of resources designed to develop pupils' mathematical thinking. This package places a particular emphasis on “visualising” and is designed to meet the needs. . . .

Clocking Off

Stage: 2, 3 and 4 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?

Triangles Within Pentagons

Stage: 4 Challenge Level:

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