February 2003, All Stages

Problems

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Building with Solid Shapes

Stage: 1 Challenge Level: Challenge Level:1

We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

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Baked Bean Cans

Stage: 1 Challenge Level: Challenge Level:1

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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Skeleton Shapes

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

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

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Multilink Cubes

Stage: 2 Challenge Level: Challenge Level:1

If you had 36 cubes, what different cuboids could you make?

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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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Cereal Packets

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

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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Construct-o-straws

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

Make a cube out of straws and have a go at this practical challenge.

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Cubes Within Cubes

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

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?

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Cubic Conundrum

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

Which of the following cubes can be made from these nets?

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Lost in Space

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

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

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Squares

Stage: 3 Challenge Level: Challenge Level:1

Try making 3D patterns in two dimensions with LOGO

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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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Marbles in a Box

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

You have 27 transparent unit cubes arranged in a 3 by 3 by 3 array. Marbles are alternately placed into the cubes by two players. How many unique winning lines of three marbles are possible?

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All in the Mind

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

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .

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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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Cubist Cuts

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

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?

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Excel Technique: LOOKUP Functions

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

Learn how to use lookup functions to create exciting interactive Excel spreadsheets.

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Excel Interactive Resource: Equivalent Fraction Bars

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

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

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Excel Investigation: Happy Numbers

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

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Use a spreadsheet to investigate this sequence.

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In a Spin

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

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

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Plum Tree

Stage: 4 and 5 Challenge Level: Challenge Level:1

Label this plum tree graph to make it totally magic!

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Magic Caterpillars

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

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Golden Powers

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

You add 1 to the golden ratio to get its square. How do you find higher powers?

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Folium of Descartes

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

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

Elsewhere...