Resources tagged with: Visualising

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There are 101 results

Broad Topics > Thinking Mathematically > Visualising

Escriptions

Age 16 to 18
Challenge Level

For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.

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.

Circles Ad Infinitum

Age 16 to 18
Challenge Level

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

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?

Tied Up

Age 14 to 16 Short
Challenge Level

How much of the field can the animals graze?

Set Square

Age 16 to 18
Challenge Level

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

Efficient Packing

Age 14 to 16
Challenge Level

How efficiently can you pack together disks?

Ford Circles

Age 16 to 18
Challenge Level

Can you find the link between these beautiful circle patterns and Farey Sequences?

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?

LOGO Challenge - Circles as Animals

Age 11 to 16
Challenge Level

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

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?

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.

One and Three

Age 14 to 16
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. . . .

The Spider and the Fly

Age 14 to 16
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?

AMGM

Age 14 to 16
Challenge Level

Can you use the diagram to prove the AM-GM inequality?

Classic Cube

Age 16 to 18
Challenge Level

The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?

A Rolling Disc - Periodic Motion

Age 16 to 18

Imagine a rectangular tray lying flat on a table. Suppose that a plate lies on the tray and rolls around, in contact with the sides as it rolls. What can we say about the motion?

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?

Doesn't Add Up

Age 14 to 16
Challenge Level

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

Classical Means

Age 16 to 18
Challenge Level

Use the diagram to investigate the classical Pythagorean means.

Semi-regular Tessellations

Age 11 to 16
Challenge Level

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Three Cubes

Age 14 to 16
Challenge Level

Can you work out the dimensions of the three cubes?

Natural Sum

Age 14 to 16
Challenge Level

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .

Picture Story

Age 14 to 16
Challenge Level

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

Around and Back

Age 14 to 16
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. . . .

A Problem of Time

Age 14 to 16
Challenge Level

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

Proximity

Age 14 to 16
Challenge Level

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

Coke Machine

Age 14 to 16
Challenge Level

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

Marbles in a Box

Age 11 to 16
Challenge Level

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Cheese Cutting

Age 16 to 18
Challenge Level

In this problem we see how many pieces we can cut a cube of cheese into using a limited number of slices. How many pieces will you be able to make?

Circuit Training

Age 14 to 16
Challenge Level

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .

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.

Square It

Age 11 to 16
Challenge Level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Sprouts

Age 7 to 18
Challenge Level

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

The Triangle Game

Age 11 to 16
Challenge Level

Can you discover whether this is a fair game?

Wrapping Gifts

Age 16 to 18
Challenge Level

A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?

Triangles Within Triangles

Age 14 to 16
Challenge Level

Can you find a rule which connects consecutive triangular numbers?

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. . . .

Triangles Within Squares

Age 14 to 16
Challenge Level

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

Triangles Within Pentagons

Age 14 to 16
Challenge Level

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

Building Gnomons

Age 14 to 16
Challenge Level

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.

Something in Common

Age 14 to 16
Challenge Level

A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.

Vanishing Point

Age 14 to 18
Challenge Level

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

Contact

Age 14 to 16
Challenge Level

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?

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?

Air Nets

Age 7 to 18
Challenge Level

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Cuboid Challenge

Age 11 to 16
Challenge Level

What's the largest volume of box you can make from a square of paper?

Baravelle

Age 7 to 16
Challenge Level

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

Just Opposite

Age 14 to 16
Challenge Level

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?

Summing Squares

Age 14 to 16
Challenge Level

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