Other tags that relate to Cola Can
Pythagoras' theorem. Surface and surface area. Maths Supporting SET. Interactivities. Mathematical reasoning & proof. Volume and capacity. Spheres, cylinders & cones. Cubes & cuboids. Spreadsheets. Visualising.There are 36 results
Broad Topics > 3D Geometry, Shape and Space > Cubes & cuboids
Changing Areas, Changing Volumes
Age 11 to 14 Challenge Level:
How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?
Sending a Parcel
Age 11 to 14 Challenge Level:
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
All in the Mind
Age 11 to 14 Challenge Level:
Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?
Marbles in a Box
Age 11 to 16 Challenge Level:
How many winning lines can you make in a three-dimensional version of noughts and crosses?
All Tied Up
Age 14 to 16 Challenge Level:
A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
The Spider and the Fly
Age 14 to 16 Challenge Level:
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?
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.
Take Ten
Age 11 to 14 Challenge Level:
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?
Painted Cube
Age 14 to 16 Challenge Level:
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Nicola's Jigsaw
Age 11 to 14 Challenge Level:
Nicola has lost a piece of her 3D jigsaw. Can you work out the shape of the missing piece?
Boxed In
Age 11 to 14 Challenge Level:
A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?
Tic Tac Toe
Age 11 to 14 Challenge Level:
In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?
Counting Triangles
Age 11 to 14 Challenge Level:
Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
Which Solid?
Age 7 to 16 Challenge Level:
This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.
Cubic Conundrum
Age 7 to 16 Challenge Level:
Which of the following cubes can be made from these nets?
Which Face?
Age 14 to 16 Short Challenge Level:
Which faces are opposite each other when this net is folded into a cube?
Cubist Cuts
Age 11 to 14 Challenge Level:
A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?
Christmas Boxes
Age 11 to 14 Challenge Level:
Find all the ways to cut out a 'net' of six squares that can be folded into a cube.
Thinking 3D
Age 7 to 14
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?
Inside Out
Age 14 to 16 Challenge Level:
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .
Cuboids
Age 11 to 14 Challenge Level:
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Partly Painted Cube
Age 14 to 16 Challenge Level:
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
Troublesome Dice
Age 11 to 14 Challenge Level:
When dice land edge-up, we usually roll again. But what if we didn't...?
The Solid
Age 11 to 16 Challenge Level:
A task which depends on members of the group working collaboratively to reach a single goal.
Castles in the Middle
Age 7 to 14 Challenge Level:
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Solids
Age 11 to 16 Challenge Level:
A task which depends on members of the group working collaboratively to reach a single goal.
How Many Dice?
Age 11 to 14 Challenge Level:
A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .
Summing Squares
Age 14 to 16 Challenge Level:
Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
Nine Colours
Age 11 to 16 Challenge Level:
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?
Plutarch's Boxes
Age 11 to 14 Challenge Level:
According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have. . . .
Icosian Game
Age 11 to 14 Challenge Level:
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.
Painting Cubes
Age 11 to 14 Challenge Level:
Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
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. . . .
Paper Folding - Models of the Platonic Solids
Age 11 to 16
A description of how to make the five Platonic solids out of paper.
Classifying Solids Using Angle Deficiency
Age 11 to 16 Challenge Level:
Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
NRICH is part of the family of activities in the Millennium Mathematics Project.