Resources tagged with: Visualising

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There are 179 results

Broad Topics > Thinking Mathematically > Visualising

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. . . .

Hello Again

Age 11 to 14
Challenge Level

Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?

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.

Crossing the Atlantic

Age 11 to 14
Challenge Level

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?

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. . . .

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. . . .

Buses

Age 11 to 14
Challenge Level

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?

Efficient Packing

Age 14 to 16
Challenge Level

How efficiently can you pack together disks?

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.

Speeding Boats

Age 14 to 16
Challenge Level

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

Clocking Off

Age 7 to 16
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?

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?

Triangular Tantaliser

Age 11 to 14
Challenge Level

Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.

Trice

Age 11 to 14
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?

John's Train Is on Time

Age 11 to 14
Challenge Level

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

Königsberg

Age 11 to 14
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?

Flight of the Flibbins

Age 11 to 14
Challenge Level

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

Playground Snapshot

Age 7 to 14
Challenge Level

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

Konigsberg Plus

Age 11 to 14
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.

Rati-o

Age 11 to 14
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?

Problem Solving, Using and Applying and Functional Mathematics

Age 5 to 18
Challenge Level

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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?

Shear Magic

Age 11 to 14
Challenge Level

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

Seven Squares - Group-worthy Task

Age 11 to 14
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?

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.

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.

Changing Places

Age 14 to 16
Challenge Level

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

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. . . .

Dice, Routes and Pathways

Age 5 to 14

This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .

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?

Jam

Age 14 to 16
Challenge Level

A game for 2 players

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.

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?

Tourism

Age 11 to 14
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.

Squares in Rectangles

Age 11 to 14
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?

Frogs

Age 11 to 14
Challenge Level

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

The Cantor Set

Age 11 to 14
Challenge Level

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you picture it?

Painted Cube

Age 14 to 16
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?

Picturing Square Numbers

Age 11 to 14
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 Triangular Numbers

Age 11 to 14
Challenge Level

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

Rolling Around

Age 11 to 14
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?

Drilling Many Cubes

Age 7 to 14
Challenge Level

A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.

Is There a Theorem?

Age 11 to 14
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?

Tied Up

Age 14 to 16 Short
Challenge Level

How much of the field can the animals graze?

Linkage

Age 11 to 14
Challenge Level

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

Chess

Age 11 to 14
Challenge Level

What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?

AMGM

Age 14 to 16
Challenge Level

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

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.

Clocked

Age 11 to 14
Challenge Level

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

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?