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Problem solving. Learning mathematics. Visualising. Games. Enrichment. Addition & subtraction. Rich Tasks. Interactivities. Pedagogy. Mathematical Thinking.

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

Thinking Through, and By, Visualising

Stage: 2, 3 and 4

This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view. . . .

The Development of Spatial and Geometric Thinking: 5 to 18

Stage: 1, 2, 3 and 4

This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .

Cover the Camel

Stage: 1 Challenge Level:

Can you cover the camel with these pieces?

Tangram Paradox

Stage: 2 Challenge Level:

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

Overlaps

Stage: 1 Challenge Level:

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

Tetrafit

Stage: 2 Challenge Level:

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Go Moku

Stage: 1 Challenge Level:

A game for two players on a large squared space.

Counters

Stage: 2 Challenge Level:

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Alquerque II

Stage: 1 Challenge Level:

A variant on the game Alquerque

One Big Triangle

Stage: 1 Challenge Level:

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Change Around

Stage: 1 Challenge Level:

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

Red Even

Stage: 2 Challenge Level:

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Dragons and Swans a Game for Two Players

Stage: 1 Challenge Level:

A game for two players. You'll need some counters.

Tessellate the Triominoes

Stage: 1 Challenge Level:

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

Posting Triangles

Stage: 1 Challenge Level:

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

Makeover

Stage: 1 Challenge Level:

Exchange the positions of the two sets of counters in the least possible number of moves

Domino Numbers

Stage: 2 Challenge Level:

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

Horizontal Vertical

Stage: 1 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?

Four Triangles Puzzle

Stage: 1 and 2 Challenge Level:

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Penta Play

Stage: 2 Challenge Level:

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

Diagonal Dodge

Stage: 2 and 3 Challenge Level:

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.

Tricky Triangles

Stage: 1 Challenge Level:

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

Making Maths: Rolypoly

Stage: 1 and 2 Challenge Level:

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

World of Tan 25 - Pentominoes

Stage: 2 Challenge Level:

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

Twice as Big?

Stage: 2 Challenge Level:

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Shadow Play

Stage: 1 Challenge Level:

Here are shadows of some 3D shapes. What shapes could have made them?

World of Tan 16 - Time Flies

Stage: 2 Challenge Level:

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

World of Tan 18 - Soup

Stage: 2 Challenge Level:

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

World of Tan 17 - Weather

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

Right or Left?

Stage: 2 Challenge Level:

Which of these dice are right-handed and which are left-handed?

Cubes Within Cubes

Stage: 2 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?

World of Tan 24 - Clocks

Stage: 2 Challenge Level:

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

Endless Noughts and Crosses

Stage: 2 Challenge Level:

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

Routes 1 and 5

Stage: 1 Challenge Level:

Find your way through the grid starting at 2 and following these operations. What number do you end on?

Coded Hundred Square

Stage: 2 Challenge Level:

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Counting Cards

Stage: 2 Challenge Level:

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?

World of Tan 19 - Working Men

Stage: 2 Challenge Level:

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

World of Tan 20 - Fractions

Stage: 2 Challenge Level:

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

Skeleton Shapes

Stage: 1 Challenge Level:

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

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.

World of Tan 22 - an Appealing Stroll

Stage: 2 Challenge Level:

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

World of Tan 21 - Almost There Now

Stage: 2 Challenge Level:

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

Redblue

Stage: 2 Challenge Level:

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?