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Resources tagged with Visualising similar to Volume of a Pyramid and a Cone:

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

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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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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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Concrete Wheel

Stage: 3 Challenge Level: Challenge Level:1

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

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A Tilted Square

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

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

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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?

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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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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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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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Convex Polygons

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

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

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The Old Goats

Stage: 3 Challenge Level: Challenge Level:1

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. . . .

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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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Triangle Inequality

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

ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.

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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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Tessellating Hexagons

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

Which hexagons tessellate?

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Cuboid Challenge

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

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

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Triangles Within Pentagons

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

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

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Clocked

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

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

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Konigsberg Plus

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

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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Diagonal Dodge

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

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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Tourism

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

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.

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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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Khun Phaen Escapes to Freedom

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

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

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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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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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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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Triangles Within Triangles

Stage: 4 Challenge Level: Challenge Level:1

Can you find a rule which connects consecutive triangular numbers?

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More Pebbles

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

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

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Conway's Chequerboard Army

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

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

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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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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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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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How Many Dice?

Stage: 3 Challenge Level: Challenge Level:1

A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .

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Cogs

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

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. . . .

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Chess

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

What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?

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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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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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Tic Tac Toe

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

In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?

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3D Stacks

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

Can you find a way of representing these arrangements of balls?

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Dissect

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

It is possible to dissect any square into smaller squares. What is the minimum number of squares a 13 by 13 square can be dissected into?

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Muggles Magic

Stage: 3 Challenge Level: Challenge Level:1

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.

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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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Is There a Theorem?

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

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

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Buses

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

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?

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Intersecting Circles

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

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

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Threesomes

Stage: 3 Challenge Level: Challenge Level:1

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?

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Star Gazing

Stage: 4 Challenge Level: Challenge Level:1

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

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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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Turning Triangles

Stage: 3 Challenge Level: Challenge Level:1

A triangle ABC resting on a horizontal line is "rolled" along the line. Describe the paths of each of the vertices and the relationships between them and the original triangle.

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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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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?