# Resources tagged with: Visualising

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Broad Topics > Thinking Mathematically > Visualising ### Efficient Packing

##### Age 14 to 16 Challenge Level:

How efficiently can you pack together disks? ### Polygon Pictures

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge 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? ### Tied Up

##### Age 14 to 16 Short Challenge Level:

How much of the field can the animals graze? ### LOGO Challenge - Circles as Animals

##### Age 11 to 16 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star. ### Cube Paths

##### Age 11 to 14 Challenge 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? ### Efficient Cutting

##### Age 11 to 14 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. ### Rolling Around

##### Age 11 to 14 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? ### Like a Circle in a Spiral

##### Age 7 to 16 Challenge 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? ### Playground Snapshot

##### Age 7 to 14 Challenge 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? ### Semi-regular Tessellations

##### Age 11 to 16 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

Which hexagons tessellate? ### Polygon Rings

##### Age 11 to 14 Challenge Level:

Join pentagons together edge to edge. Will they form a ring? ### The Old Goats

##### Age 11 to 14 Challenge 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. . . . ### Counting Triangles

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge 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. . . . ### An Unusual Shape

##### Age 11 to 14 Challenge Level:

Can you maximise the area available to a grazing goat? ### Corridors

##### Age 14 to 16 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. ##### Age 11 to 14 Challenge Level:

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? ### Getting an Angle

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge 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? ### Dotty Triangles

##### Age 11 to 14 Challenge 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? ### All Tied Up

##### Age 14 to 16 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? ### Tilting Triangles

##### Age 14 to 16 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? ### Convex Polygons

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw? ##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge 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? ### Coloured Edges

##### Age 11 to 14 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? ### 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? ### Isosceles Triangles

##### Age 11 to 14 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? ### A Tilted Square

##### Age 14 to 16 Challenge Level:

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices? ### AMGM

##### Age 14 to 16 Challenge Level:

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

##### Age 11 to 14 Challenge 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? ### Tetra Square

##### Age 11 to 14 Challenge 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. ### Ten Hidden Squares

##### Age 7 to 14 Challenge Level:

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

##### Age 14 to 18 Challenge Level:

How can visual patterns be used to prove sums of series? ### The Farmers' Field Boundary

##### Age 11 to 14 Challenge Level:

The farmers want to redraw their field boundary but keep the area the same. Can you advise them? ### Auditorium Steps

##### Age 7 to 14 Challenge Level:

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

##### Age 11 to 18 Challenge Level:

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

##### Age 7 to 16 Challenge Level:

What can you see? What do you notice? What questions can you ask? ### Eight Hidden Squares

##### Age 7 to 14 Challenge 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? ### Sprouts

##### Age 7 to 18 Challenge Level:

A game for 2 people. Take turns joining two dots, until your opponent is unable to move. ### Something in Common

##### Age 14 to 16 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. ### Framed

##### Age 11 to 14 Challenge 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. . . . ### Khun Phaen Escapes to Freedom

##### Age 11 to 14 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. ### On the Edge

##### Age 11 to 14 Challenge Level:

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