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Resources tagged with Visualising similar to Advent Calendar 2011 - Secondary:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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

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Yih or Luk Tsut K'i or Three Men's Morris

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

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .

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Picture Story

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Natural Sum

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

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Rotating Triangle

Stage: 3 and 4 Challenge Level: Challenge Level:1

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

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The Triangle Game

Stage: 3 and 4 Challenge Level: Challenge Level:1

Can you discover whether this is a fair game?

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AMGM

Stage: 4 Challenge Level: Challenge Level:1

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?

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Rolling Coins

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

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Proximity

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Three Frogs

Stage: 4 Challenge Level: Challenge Level:1

Three frogs hopped onto the table. A red frog on the left a green in the middle and a blue frog on the right. Then frogs started jumping randomly over any adjacent frog. Is it possible for them to. . . .

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Sliding Puzzle

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

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.

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Jam

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A game for 2 players

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Problem Solving, Using and Applying and Functional Mathematics

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

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.

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Hypotenuse Lattice Points

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

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Steel Cables

Stage: 4 Challenge Level: Challenge Level:1

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

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Cubes Within Cubes Revisited

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Icosagram

Stage: 3 Challenge Level: Challenge Level:1

Draw a pentagon with all the diagonals. This is called a pentagram. How many diagonals are there? How many diagonals are there in a hexagram, heptagram, ... Does any pattern occur when looking at. . . .

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Dice, Routes and Pathways

Stage: 1, 2 and 3

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. . . .

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Pattern Power

Stage: 1, 2 and 3

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

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Building Gnomons

Stage: 4 Challenge Level: Challenge Level:1

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

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Air Nets

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

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

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You Owe Me Five Farthings, Say the Bells of St Martin's

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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Route to Infinity

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you describe this route to infinity? Where will the arrows take you next?

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Jam

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

To avoid losing think of another very well known game where the patterns of play are similar.

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When Will You Pay Me? Say the Bells of Old Bailey

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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Playground Snapshot

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

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?

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Reflecting Squarely

Stage: 3 Challenge Level: Challenge Level:1

In how many ways can you fit all three pieces together to make shapes with line symmetry?

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Cutting a Cube

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Flight of the Flibbins

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Picturing Triangle Numbers

Stage: 3 Challenge Level: Challenge Level:1

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

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Painted Cube

Stage: 3 Challenge Level: Challenge Level:1

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?

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Shady Symmetry

Stage: 3 Challenge Level: Challenge Level:1

How many different symmetrical shapes can you make by shading triangles or squares?

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Picturing Square Numbers

Stage: 3 Challenge Level: Challenge Level:1

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

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Tilting Triangles

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Rolling Triangle

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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Framed

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Tetra Square

Stage: 3 Challenge Level: Challenge Level:1

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

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Tetrahedra Tester

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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Nine Colours

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

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Trice

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Linkage

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Around and Back

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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. . . .

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Königsberg

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Weighty Problem

Stage: 3 Challenge Level: Challenge Level:1

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. . . .

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Tied Up

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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An Unusual Shape

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you maximise the area available to a grazing goat?

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On the Edge

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try. . . .

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Christmas Chocolates

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Partially Painted Cube

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Mystic Rose

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Eight Hidden Squares

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

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?