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#### Resources tagged with Visualising similar to Hypotenuse Lattice Points:

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### 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?

### 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.

### 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?

### Building Gnomons

##### Stage: 4 Challenge Level:

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

### Jam

##### Stage: 4 Challenge Level:

A game for 2 players

### 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.

### Jam

##### Stage: 4 Challenge Level:

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

### 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.

### Building Tetrahedra

##### Stage: 4 Challenge Level:

Can you make a tetrahedron whose faces all have the same perimeter?

### Cogs

##### Stage: 3 Challenge Level:

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

### 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?

### Picture Story

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

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

### 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?

### 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. . . .

### 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. . . .

### Triangles Within Triangles

##### Stage: 4 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

### 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. . . .

### The Triangle Game

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

Can you discover whether this is a fair game?

### Triangles Within Squares

##### Stage: 4 Challenge Level:

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

### Triangles Within Pentagons

##### Stage: 4 Challenge Level:

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

### Proofs with Pictures

##### Stage: 4 and 5

Some diagrammatic 'proofs' of algebraic identities and inequalities.

### Baravelle

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

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

### 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?

### 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?

### 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?

### Christmas Chocolates

##### Stage: 3 Challenge Level:

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

### 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.

### Sea Defences

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

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

### 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.

### More Pebbles

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

Have a go at this 3D extension to the Pebbles problem.

### 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?

### Zooming in on the Squares

##### Stage: 2 and 3

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?

### 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?

### AMGM

##### Stage: 4 Challenge Level:

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

### Convex Polygons

##### Stage: 3 Challenge Level:

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

### Cubes Within Cubes

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

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

### 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?

### 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.

### 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?

### 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!

### Coordinate Patterns

##### Stage: 3 Challenge Level:

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

### 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.

### Khun Phaen Escapes to Freedom

##### Stage: 3 Challenge Level:

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

##### Stage: 3 Challenge Level:

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

### 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.

### 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.

### Conway's Chequerboard Army

##### Stage: 3 Challenge Level:

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

### 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.

### Buses

##### Stage: 3 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?

### LOGO Challenge - Triangles-squares-stars

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

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.