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Broad Topics > 3D Geometry, Shape and Space > 2D representations of 3D shapes

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Building Blocks

Stage: 2 Challenge Level: Challenge Level:1

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

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The Third Dimension

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

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

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Nine Colours

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

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

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A City of Towers

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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Isometric Drawing

Stage: 3 Challenge Level: Challenge Level:1

Explore the properties of isometric drawings.

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Oblique Projection

Stage: 3 Challenge Level: Challenge Level:1

Explore the properties of oblique projection.

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Perspective Drawing

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

Explore the properties of perspective drawing.

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Bent Out of Shape

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

An introduction to bond angle geometry.

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Chopped Dice

Stage: 4 Challenge Level: Challenge Level:1

Can you make a new type of fair die with 14 faces by shaving the corners off a cube?

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Weekly Challenge 47: Weird Universes

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Consider these weird universes and ways in which the stick man can shoot the robot in the back.

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Torus Patterns

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How many different colours would be needed to colour these different patterns on a torus?

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Moving Squares

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

How can you represent the curvature of a cylinder on a flat piece of paper?

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Next Size Up

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

The challenge for you is to make a string of six (or more!) graded cubes.

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Stereoisomers

Stage: 5 Challenge Level: Challenge Level:1

Put your visualisation skills to the test by seeing which of these molecules can be rotated onto each other.

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Air Nets

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

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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The Perforated Cube

Stage: 4 Challenge Level: Challenge Level:1

A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?

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Shaping the Universe II - the Solar System

Stage: 3 and 4

The second in a series of articles on visualising and modelling shapes in the history of astronomy.

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Shaping the Universe I - Planet Earth

Stage: 3 and 4

This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.

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Pupils' Recording or Pupils Recording

Stage: 1, 2 and 3

This article, written for teachers, looks at the different kinds of recordings encountered in Primary Mathematics lessons and the importance of not jumping to conclusions!

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Euler's Formula

Stage: 5

Some simple ideas about graph theory with a discussion of a proof of Euler's formula relating the numbers of vertces, edges and faces of a graph.

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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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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. . . .

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Thinking 3D

Stage: 2 and 3

How can we as teachers begin to introduce 3D ideas to young children? Where do they start? How can we lay the foundations for a later enthusiasm for working in three dimensions?

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Geometry and Gravity 1

Stage: 3, 4 and 5

This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.

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Three Cubed

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

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

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Christmas Boxes

Stage: 3 Challenge Level: Challenge Level:1

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.

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Icosian Game

Stage: 3 Challenge Level: Challenge Level:1

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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Cutting a Cube

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

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?

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Take Ten

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

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .

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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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Tennis

Stage: 3 Challenge Level: Challenge Level:1

A tennis ball is served from directly above the baseline (assume the ball travels in a straight line). What is the minimum height that the ball can be hit at to ensure it lands in the service area?

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New House

Stage: 2 Challenge Level: Challenge Level:1

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?