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There are **42** NRICH Mathematical resources connected to **2D representations of 3D shapes**, you may find related items under 3D geometry, shape and space.

Problem
Primary curriculum
Secondary curriculum
### Guess What?

Can you find out which 3D shape your partner has chosen before they work out your shape?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Next Size Up

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Spider and the Fly

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Building Blocks

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Third Dimension

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

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Nine Colours

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A City of Towers

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Nicola's Jigsaw

Nicola has lost a piece of her 3D jigsaw. Can you work out the shape of the missing piece?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Which Face?

Which faces are opposite each other when this net is folded into a cube?

Age 14 to 16

ShortChallenge Level

Article
Primary curriculum
Secondary curriculum
### 3D Drawing

The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.

Age 11 to 16

Problem
Primary curriculum
Secondary curriculum
### Stadium Sightline

How would you design the tiering of seats in a stadium so that all spectators have a good view?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Chopped Dice

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Weird Universes

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Construct the Solar System

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Torus Patterns

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Moving Squares

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Solids

A task which depends on members of the group working collaboratively to reach a single goal.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Solid

A task which depends on members of the group working collaboratively to reach a single goal.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 28 - Upward and Onward

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Perfect Eclipse

Use trigonometry to determine whether solar eclipses on earth can be perfect.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Stereoisomers

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Air Nets

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

Age 7 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Perforated Cube

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 ?

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Shaping the Universe II - the Solar System

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

Age 11 to 16

Article
Primary curriculum
Secondary curriculum
### Shaping the Universe I - Planet Earth

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.

Age 11 to 16

Article
Primary curriculum
Secondary curriculum
### Pupils' Recording or Pupils Recording

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!

Age 5 to 14

Article
Primary curriculum
Secondary curriculum
### Euler's Formula

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.

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### The Development of Spatial and Geometric Thinking: Co-ordinating Space in Drawings

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

Age 5 to 7

Article
Primary curriculum
Secondary curriculum
### The Development of Spatial and Geometric Thinking: 5 to 18

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 work of Piaget and Inhelder.

Age 5 to 16

Article
Primary curriculum
Secondary curriculum
### Thinking 3D

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?

Age 7 to 14

Article
Primary curriculum
Secondary curriculum
### Geometry and Gravity 1

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.

Age 11 to 18

Problem
Primary curriculum
Secondary curriculum
### Three Cubed

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Christmas Boxes

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Icosian Game

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cutting a Cube

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Take Ten

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Soma - So Good

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### New House

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?

Age 7 to 11

Challenge Level