Resources tagged with: Visualising

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There are 179 results

Broad Topics > Thinking Mathematically > Visualising

Picturing Triangular Numbers

Age 11 to 14Challenge Level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

AMGM

Age 14 to 16Challenge Level

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

Steel Cables

Age 14 to 16Challenge Level

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

Age 11 to 14Challenge Level

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

Clocked

Age 11 to 14Challenge Level

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?

Tower of Hanoi

Age 11 to 14Challenge Level

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Mystic Rose

Age 14 to 16Challenge Level

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

Christmas Chocolates

Age 11 to 14Challenge Level

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

Partly Painted Cube

Age 14 to 16Challenge 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?

Painting Cubes

Age 11 to 14Challenge Level

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

Frogs

Age 11 to 14Challenge Level

How many moves does it take to swap over some red and blue frogs? Do you have a method?

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?

The Triangle Game

Age 11 to 16Challenge Level

Can you discover whether this is a fair game?

Painted Cube

Age 14 to 16Challenge Level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Picturing Square Numbers

Age 11 to 14Challenge Level

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Seven Squares

Age 11 to 14Challenge Level

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

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?

Cubes Within Cubes Revisited

Age 11 to 14Challenge 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?

Jam

Age 14 to 16Challenge Level

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

One Out One Under

Age 14 to 16Challenge Level

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

Paving Paths

Age 11 to 14Challenge Level

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

Hidden Rectangles

Age 11 to 14Challenge Level

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

Flight of the Flibbins

Age 11 to 14Challenge Level

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

Cubes Within Cubes

Age 7 to 14Challenge 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?

Building Gnomons

Age 14 to 16Challenge Level

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

Pattern Power

Age 5 to 14

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

Hypotenuse Lattice Points

Age 14 to 16Challenge 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?

Squares, Squares and More Squares

Age 11 to 14Challenge Level

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

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.

Route to Infinity

Age 11 to 14Challenge Level

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

Changing Places

Age 14 to 16Challenge 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. . . .

Sliding Puzzle

Age 11 to 16Challenge 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

Age 14 to 16Challenge Level

A game for 2 players

Coordinate Patterns

Age 11 to 14Challenge Level

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

Triangles Within Pentagons

Age 14 to 16Challenge Level

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

Triangles Within Squares

Age 14 to 16Challenge Level

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

Cogs

Age 11 to 14Challenge 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. . . .

Triangles Within Triangles

Age 14 to 16Challenge Level

Can you find a rule which connects consecutive triangular numbers?

Euromaths

Age 11 to 14Challenge Level

How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5x5 array?

Squares in Rectangles

Age 11 to 14Challenge Level

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Cuboids

Age 11 to 14Challenge Level

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Bands and Bridges: Bringing Topology Back

Age 7 to 14

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

John's Train Is on Time

Age 11 to 14Challenge Level

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

KÃ¶nigsberg

Age 11 to 14Challenge Level

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?

Age 11 to 14Challenge Level

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

Something in Common

Age 14 to 16Challenge 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.

There and Back Again

Age 11 to 14Challenge Level

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

Buses

Age 11 to 14Challenge 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?

Reflecting Squarely

Age 11 to 14Challenge Level

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

Square It

Age 11 to 16Challenge 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.