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Resources tagged with Visualising similar to Diagonal Dodge:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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

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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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Soma - So Good

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

Can you mentally fit the 7 SOMA pieces together to make a cube? Can you do it in more than one way?

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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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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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Crossing the Atlantic

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

Every day at noon a boat leaves Le Havre for New York while another boat leaves New York for Le Havre. The ocean crossing takes seven days. How many boats will each boat cross during their journey?

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Triangular Tantaliser

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

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

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Linkage

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

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?

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Dice, Routes and Pathways

Stage: 1, 2 and 3

This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .

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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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Coordinate Patterns

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

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

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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.

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Screwed-up

Stage: 3 Challenge Level: Challenge Level:1

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?

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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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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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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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Keep Your Distance

Stage: 3 Challenge Level: Challenge Level:1

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

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Drilling Many Cubes

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

A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.

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Counting Triangles

Stage: 3 Challenge Level: Challenge Level:1

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

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World of Tan 2 - Little Ming

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

Can you fit the tangram pieces into the outline of Little Ming?

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Travelling Salesman

Stage: 3 Challenge Level: Challenge Level:1

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?

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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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Troublesome Dice

Stage: 3 Challenge Level: Challenge Level:1

When dice land edge-up, we usually roll again. But what if we didn't...?

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Counter Roundup

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

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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All in the Mind

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

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .

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Masterclass Ideas: Visualising

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

A package contains a set of resources designed to develop pupils' mathematical thinking. This package places a particular emphasis on “visualising” and is designed to meet the needs. . . .

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Cubist Cuts

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

A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?

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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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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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There and Back Again

Stage: 3 Challenge Level: Challenge Level:1

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

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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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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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Rolling Around

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

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?

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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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Tied Up

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

In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .

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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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Icosagram

Stage: 3 Challenge Level: Challenge Level:1

Draw a pentagon with all the diagonals. This is called a pentagram. How many diagonals are there? How many diagonals are there in a hexagram, heptagram, ... Does any pattern occur when looking at. . . .

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Rolling Triangle

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

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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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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Reflecting Squarely

Stage: 3 Challenge Level: Challenge Level:1

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

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World of Tan 25 - Pentominoes

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

Can you fit the tangram pieces into the outlines of these people?

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Cubes Within Cubes

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

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?

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World of Tan 24 - Clocks

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

Can you fit the tangram pieces into the outlines of these clocks?

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World of Tan 22 - an Appealing Stroll

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

Can you fit the tangram pieces into the outline of the child walking home from school?

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World of Tan 26 - Old Chestnut

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

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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World of Tan 27 - Sharing

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

Can you fit the tangram pieces into the outline of Little Fung at the table?

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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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Coloured Edges

Stage: 3 Challenge Level: Challenge Level:1

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?

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World of Tan 29 - the Telephone

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

Can you fit the tangram pieces into the outline of this telephone?

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World of Tan 28 - Concentrating on Coordinates

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

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

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World of Tan 21 - Almost There Now

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

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?