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

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Baravelle

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

What can you see? What do you notice? What questions can you ask?

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Introducing NRICH TWILGO

Stage: 1, 2, 3, 4 and 5 Challenge Level: Challenge Level:1

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

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Folding, Cutting and Punching

Stage: 2 Challenge Level: Challenge Level:1

Exploring and predicting folding, cutting and punching holes and making spirals.

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Inside Seven Squares

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

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

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A Square in a Circle

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

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

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28 and It's Upward and Onward

Stage: 2 Challenge Level: Challenge Level:1

Can you find ways of joining cubes together so that 28 faces are visible?

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Like a Circle in a Spiral

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

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?

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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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Two Squared

Stage: 2 Challenge Level: Challenge Level:1

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

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Dodecamagic

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

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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Square Corners

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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Nine-pin Triangles

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

How many different triangles can you make on a circular pegboard that has nine pegs?

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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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Cubes Cut Into Four Pieces

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

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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?

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World of Tan 20 - Fractions

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

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

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Start Cube Drilling

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?

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Triangular Faces

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

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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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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World of Tan 19 - Working Men

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

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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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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Map Folding

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

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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Quadrilaterals

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

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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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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The Development of Spatial and Geometric Thinking: Co-ordinating Space in Drawings

Stage: 1

This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.

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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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Sea Defences

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

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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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 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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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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Fractional Triangles

Stage: 2 Challenge Level: Challenge Level:1

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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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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Counting Cards

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

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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World of Tan 1 - Granma T

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

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

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Putting Two and Two Together

Stage: 2 Challenge Level: Challenge Level:1

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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World of Tan 15 - Millennia

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

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

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World of Tan 14 - Celebrations

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

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

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World of Tan 6 - Junk

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

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

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Tangram Tangle

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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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World of Tan 5 - Rocket

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

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

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World of Tan 13 - A Storm in a Tea Cup

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

Can you fit the tangram pieces into the outline of these convex shapes?

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Square It

Stage: 1, 2, 3 and 4 Challenge Level: Challenge Level:1

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.

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

Stage: 1 and 2

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

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World of Tan 9 - Animals

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

Can you fit the tangram pieces into the outline of this goat and giraffe?

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Making Tangrams

Stage: 2 Challenge Level: Challenge Level:1

Here's a simple way to make a Tangram without any measuring or ruling lines.

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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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Ten Hidden Squares

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

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

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World of Tan 16 - Time Flies

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

Can you fit the tangram pieces into the outlines of the candle and sundial?

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World of Tan 18 - Soup

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

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

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World of Tan 4 - Monday Morning

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

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