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Resources tagged with Visualising similar to Wrapping Gifts:

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Stage: 5 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?

Spotting the Loophole

Stage: 4 Challenge Level:

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?

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?

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?

Cheese Cutting

Stage: 5 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?

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.

Cubic Net

Stage: 4 and 5 Challenge Level:

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!

Platonic Planet

Stage: 4 Challenge Level:

Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?

Solving the Net

Stage: 5 Challenge Level:

Takes you through the systematic way in which you can begin to solve a mixed up Cubic Net. How close will you come to a solution?

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.

The Perforated Cube

Stage: 4 Challenge Level:

A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?

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?

Speeding Boats

Stage: 4 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?

Just Opposite

Stage: 4 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?

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?

Inside Out

Stage: 4 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. . . .

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.

Baravelle

Stage: 2, 3 and 4 Challenge Level:

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

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?

Jam

Stage: 4 Challenge Level:

A game for 2 players

Ding Dong Bell

Stage: 3, 4 and 5

The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.

A Rolling Disc - Periodic Motion

Stage: 5

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?

Fermat's Poser

Stage: 4 Challenge Level:

Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.

Classic Cube

Stage: 5 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?

Stage: 4 Challenge Level:

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

Instant Insanity

Stage: 3, 4 and 5 Challenge Level:

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

When the Angles of a Triangle Don't Add up to 180 Degrees

Stage: 4 and 5

This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the. . . .

Charting Success

Stage: 3 and 4 Challenge Level:

Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?

Something in Common

Stage: 4 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.

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?

One Out One Under

Stage: 4 Challenge Level:

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

Square It

Stage: 3 and 4 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.

Charting More Success

Stage: 3 and 4 Challenge Level:

Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?

Set Square

Stage: 5 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?

Sliced

Stage: 4 Challenge Level:

An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?

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. . . .

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.

Lost on Alpha Prime

Stage: 4 Challenge Level:

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

Cubic Conundrum

Stage: 2, 3 and 4 Challenge Level:

Which of the following cubes can be made from these nets?

Partly Painted Cube

Stage: 4 Challenge Level:

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Sliding Puzzle

Stage: 1, 2, 3 and 4 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

Stage: 4 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. . . .

Mystic Rose

Stage: 4 Challenge Level:

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

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?

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. . . .

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?

Escriptions

Stage: 5 Challenge Level:

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

Introducing NRICH TWILGO

Stage: 1, 2, 3, 4 and 5 Challenge Level:

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

Triangles Within Triangles

Stage: 4 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

Contact

Stage: 4 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?