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Resources tagged with Visualising similar to Always, Sometimes or Never?:

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

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Dice, Routes and Pathways

Age 5 to 14

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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Open Boxes

Age 7 to 11 Challenge Level:

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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Odd Squares

Age 7 to 11 Challenge Level:

Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?

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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.

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Drilling Many Cubes

Age 7 to 14 Challenge Level:

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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Single Track

Age 7 to 11 Challenge Level:

What is the best way to shunt these carriages so that each train can continue its journey?

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Circles, Circles

Age 5 to 11 Challenge Level:

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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Auditorium Steps

Age 7 to 14 Challenge Level:

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

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Problem Solving, Using and Applying and Functional Mathematics

Age 5 to 18 Challenge Level:

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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Shunting Puzzle

Age 7 to 11 Challenge Level:

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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Map Folding

Age 7 to 11 Challenge Level:

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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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?

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Sea Defences

Age 7 to 14 Challenge Level:

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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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?

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Take One Example

Age 5 to 11

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

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Tangram Tangle

Age 5 to 7 Challenge Level:

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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Cubes Within Cubes

Age 7 to 14 Challenge 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?

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Finding 3D Stacks

Age 7 to 11 Challenge Level:

Can you find a way of counting the spheres in these arrangements?

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Pattern Power

Age 5 to 14

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

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3D Stacks

Age 7 to 14 Challenge Level:

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

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World of Tan 10 - Butterflies

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of the butterfly?

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World of Tan 19 - A Circular Problem

Age 7 to 11 Challenge Level:

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

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Triple Cubes

Age 5 to 11 Challenge Level:

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

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Jigsaw Pieces

Age 7 to 11 Challenge Level:

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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World of Tan 17 - Weather

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of the house?

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Horizontal Vertical

Age 5 to 7 Challenge Level:

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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Domino Numbers

Age 7 to 11 Challenge Level:

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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World of Tan 13 - A Storm in a Tea Cup

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of the convex shapes?

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World of Tan 25 - Pentominoes

Age 7 to 11 Challenge Level:

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

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World of Tan 3 - Mah Ling

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of Mah Ling?

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Change Around

Age 5 to 7 Challenge Level:

Move just three of the circles so that the triangle faces in the opposite direction.

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Tessellate the Triominoes

Age 5 to 7 Challenge Level:

What happens when you try and fit the triomino pieces into these two grids?

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Cover the Camel

Age 5 to 7 Challenge Level:

Can you cover the camel with these pieces?

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Three Cubed

Age 7 to 11 Challenge Level:

Can you make a 3x3 cube with these shapes made from small cubes?

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Taking Steps

Age 7 to 11 Challenge Level:

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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Putting Two and Two Together

Age 7 to 11 Challenge Level:

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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Little Boxes

Age 7 to 11 Challenge Level:

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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Move Those Halves

Age 7 to 11 Challenge 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 ...

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World of Tan 21 - Almost There Now

Age 7 to 11 Challenge Level:

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

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Waiting for Blast Off

Age 7 to 11 Challenge Level:

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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Knight's Swap

Age 7 to 11 Challenge Level:

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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Music to My Ears

Age 7 to 11 Challenge Level:

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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World of Tan

Age 5 to 11 Challenge Level:

Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.

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World of Tan 4 - Monday Morning

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?

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World of Tan 26 - Old Chestnut

Age 7 to 11 Challenge Level:

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

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World of Tan 5 - Dragon

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of the dragon?

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World of Tan 20 - Fractions

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of the chairs?

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World of Tan 12 - All in a Fluff

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of the rabbits?

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World of Tan 1 - Granma T

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of Granma T?

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The Development of Spatial and Geometric Thinking: the Importance of Instruction.

Age 5 to 11

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.