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#### Resources tagged with Visualising similar to Rotating Triangle:

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### Rotating Triangle

##### Stage: 3 and 4 Challenge Level:

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

### Picture Story

##### Stage: 4 Challenge Level:

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

### The Triangle Game

##### Stage: 3 and 4 Challenge Level:

Can you discover whether this is a fair game?

### Natural Sum

##### Stage: 4 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. . . .

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

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

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. . . .

### Three Frogs

##### Stage: 4 Challenge Level:

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. . . .

### Rolling Coins

##### Stage: 4 Challenge Level:

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. . . .

### 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?

### Proximity

##### Stage: 4 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.

### Jam

##### Stage: 4 Challenge Level:

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

### Building Gnomons

##### Stage: 4 Challenge Level:

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

### Jam - a Game for Two Players

##### Stage: 4 Challenge Level:

A game for 2 players

### Route to Infinity

##### Stage: 3 and 4 Challenge Level:

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

### Hypotenuse Lattice Points

##### Stage: 4 Challenge Level:

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?

### 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.

### 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?

### 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?

### Triangles Within Squares

##### Stage: 4 Challenge Level:

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

### 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. . . .

### 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. . . .

### 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.

### Partially 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?

### 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?

### 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?

### Air Nets

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

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

### 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?

### Triangles Within Triangles

##### Stage: 4 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

### 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?

### Triangles Within Pentagons

##### Stage: 4 Challenge Level:

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

### Square It

##### Stage: 1, 2, 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.

### Problem Solving, Using and Applying and Functional Mathematics

##### Stage: 1, 2, 3, 4 and 5 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.

### 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. . . .

### 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?

### Square Coordinates

##### Stage: 3 Challenge Level:

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

### 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.

### 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?

### Reflecting Squarely

##### Stage: 3 Challenge Level:

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

##### Stage: 3 Challenge Level:

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

### Convex Polygons

##### Stage: 3 Challenge Level:

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

### Coloured Edges

##### Stage: 3 Challenge Level:

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

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

##### Stage: 3 Challenge Level:

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?

### There and Back Again

##### Stage: 3 Challenge Level:

Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?

### 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.

### 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.

### LOGO Challenge - Circles as Animals

##### Stage: 3 and 4 Challenge Level:

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

### 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.

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

##### Stage: 3 Challenge Level:

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?

### Bands and Bridges: Bringing Topology Back

##### Stage: 2 and 3

Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.

### 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?