# Resources tagged with: Visualising

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### There are 255 results

Broad Topics > Thinking Mathematically > Visualising

### Like a Circle in a Spiral

##### Age 7 to 16Challenge Level

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

### LOGO Challenge - Circles as Animals

##### Age 11 to 16Challenge Level

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

### Trice

##### Age 11 to 14Challenge 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?

### An Unusual Shape

##### Age 11 to 14Challenge Level

Can you maximise the area available to a grazing goat?

### Polygon Pictures

##### Age 11 to 14Challenge Level

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

### The Old Goats

##### Age 11 to 14Challenge Level

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . .

### Cube Paths

##### Age 11 to 14Challenge Level

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

### Playground Snapshot

##### Age 7 to 14Challenge 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?

### Efficient Cutting

##### Age 11 to 14Challenge 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.

### Rolling Around

##### Age 11 to 14Challenge 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?

### Tetrahedra Tester

##### Age 11 to 14Challenge Level

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?

### Regular Rings 2

##### Age 7 to 11Challenge Level

What shape is made when you fold using this crease pattern? Can you make a ring design?

### Triangular Tantaliser

##### Age 11 to 14Challenge Level

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

### Constructing Triangles

##### Age 11 to 14Challenge Level

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

### Counting Triangles

##### Age 11 to 14Challenge Level

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?

### Convex Polygons

##### Age 11 to 14Challenge Level

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

### Hexagon Transformations

##### Age 7 to 11Challenge Level

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

### Semi-regular Tessellations

##### Age 11 to 16Challenge Level

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

### Polygon Rings

##### Age 11 to 14Challenge Level

Join pentagons together edge to edge. Will they form a ring?

### Cutting a Cube

##### Age 11 to 14Challenge Level

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?

### Weighty Problem

##### Age 11 to 14Challenge Level

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. . . .

### Tessellating Hexagons

##### Age 11 to 14Challenge Level

Which hexagons tessellate?

### Part the Polygons

##### Age 7 to 11 ShortChallenge Level

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

### Dotty Triangles

##### Age 11 to 14Challenge Level

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

### Tetra Square

##### Age 11 to 14Challenge Level

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.

### On the Edge

##### Age 11 to 14Challenge Level

If you move the tiles around, can you make squares with different coloured edges?

### Christmas Boxes

##### Age 11 to 14Challenge Level

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.

### Ten Hidden Squares

##### Age 7 to 14Challenge Level

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

### Marbles in a Box

##### Age 11 to 16Challenge Level

How many winning lines can you make in a three-dimensional version of noughts and crosses?

### Fred the Class Robot

##### Age 7 to 11Challenge Level

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

### Auditorium Steps

##### Age 7 to 14Challenge Level

What is the shape of wrapping paper that you would need to completely wrap this model?

### Overlapping Again

##### Age 7 to 11Challenge Level

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

### Triangles to Tetrahedra

##### Age 11 to 14Challenge Level

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

### Getting an Angle

##### Age 11 to 14Challenge Level

How can you make an angle of 60 degrees by folding a sheet of paper twice?

### Rati-o

##### Age 11 to 14Challenge 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?

### Isosceles Triangles

##### Age 11 to 14Challenge 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?

### Move Those Halves

##### Age 7 to 11Challenge Level

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

### Christmas Chocolates

##### Age 11 to 14Challenge Level

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

### Triangles in the Middle

##### Age 11 to 18Challenge Level

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

### Baravelle

##### Age 7 to 16Challenge Level

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

### Icosian Game

##### Age 11 to 14Challenge Level

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

### Shear Magic

##### Age 11 to 14Challenge Level

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

### Eight Hidden Squares

##### Age 7 to 14Challenge Level

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?

### Concrete Wheel

##### Age 11 to 14Challenge Level

A huge wheel is rolling past your window. What do you see?

### Tourism

##### Age 11 to 14Challenge 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.

### Take Ten

##### Age 11 to 14Challenge Level

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?

### Dissect

##### Age 11 to 14Challenge Level

What is the minimum number of squares a 13 by 13 square can be dissected into?

### Coloured Edges

##### Age 11 to 14Challenge 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?

### Framed

##### Age 11 to 14Challenge Level

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. . . .

### Zooming in on the Squares

##### Age 7 to 14

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?