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

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Big and Small Numbers in the Living World

Age 11 to 16 Challenge Level:

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

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Global Warming

Age 14 to 16 Challenge Level:

How much energy has gone into warming the planet?

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Big and Small Numbers in Chemistry

Age 14 to 16 Challenge Level:

Get some practice using big and small numbers in chemistry.

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Big and Small Numbers in the Physical World

Age 14 to 16 Challenge Level:

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

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Big and Small Numbers in Physics

Age 14 to 16 Challenge Level:

Work out the numerical values for these physical quantities.

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Designing Table Mats

Age 11 to 16 Challenge Level:

Formulate and investigate a simple mathematical model for the design of a table mat.

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The Power of Dimensional Analysis

Age 14 to 18

An introduction to a useful tool to check the validity of an equation.

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Robot Camera

Age 14 to 16 Challenge Level:

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

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Witch's Hat

Age 11 to 16 Challenge Level:

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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9 Hole Light Golf

Age 5 to 18 Challenge Level:

We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?

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Trig-trig

Age 14 to 18 Challenge Level:

Explore the properties of combinations of trig functions in this open investigation.

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Chance of That

Age 14 to 18 Challenge Level:

What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?

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Carbon Footprints

Age 14 to 16 Challenge Level:

Is it really greener to go on the bus, or to buy local?

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The Invertible Trefoil

Age 14 to 16 Challenge Level:

When is a knot invertible ?

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So It's Times!

Age 7 to 14 Challenge Level:

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

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It's Times Again

Age 7 to 14 Challenge Level:

Numbers arranged in a square but some exceptional spatial awareness probably needed.

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Alternative Record Book

Age 14 to 18 Challenge Level:

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

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Advanced Investigations

Age 14 to 18 Challenge Level:

Some of our more advanced investigations

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Twizzles Venture Forth

Age 14 to 16 Challenge Level:

Where we follow twizzles to places that no number has been before.

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Eight Ratios

Age 14 to 16 Challenge Level:

Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.

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Two Regular Polygons

Age 14 to 16 Challenge Level:

Two polygons fit together so that the exterior angle at each end of their shared side is 81 degrees. If both shapes now have to be regular could the angle still be 81 degrees?

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Problem Solving: Opening up Problems

Age 5 to 16

All types of mathematical problems serve a useful purpose in mathematics teaching, but different types of problem will achieve different learning objectives. In generalmore open-ended problems have. . . .

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Peeling the Apple or the Cone That Lost Its Head

Age 14 to 16 Challenge Level:

How much peel does an apple have?

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Chocolate

Age 7 to 14 Challenge Level:

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

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Bent Out of Shape

Age 14 to 18 Challenge Level:

An introduction to bond angle geometry.

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Number Families

Age 11 to 14 Challenge Level:

How many different sets of numbers with at least four members can you find in the numbers in this box?

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Track Design

Age 14 to 16 Challenge Level:

Where should runners start the 200m race so that they have all run the same distance by the finish?

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A Rational Search

Age 14 to 18 Challenge Level:

Investigate constructible images which contain rational areas.

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Counting on Letters

Age 11 to 14 Challenge Level:

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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Steps to the Podium

Age 7 to 14 Challenge Level:

It starts quite simple but great opportunities for number discoveries and patterns!

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Squareo'scope Determines the Kind of Triangle

Age 11 to 14

A description of some experiments in which you can make discoveries about triangles.

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Snookered

Age 14 to 18 Challenge Level:

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

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Troublesome Triangles

Age 7 to 14 Challenge Level:

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

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There's Always One Isn't There

Age 14 to 16 Challenge Level:

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

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Pebbles

Age 7 to 14 Challenge Level:

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Few and Far Between?

Age 14 to 18 Challenge Level:

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

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Stacks of Maths!

Age 5 to 14

In this article for teachers, Bernard gives an example of taking an initial activity and getting questions going that lead to other explorations.

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Odd Stones

Age 14 to 16 Challenge Level:

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.

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Investigating Pascal's Triangle

Age 7 to 14 Challenge Level:

In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.

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Geometry and Gravity 1

Age 11 to 18

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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Take Ten Sticks

Age 11 to 16 Challenge Level:

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

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Perfect Eclipse

Age 14 to 16 Challenge Level:

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

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More Pebbles

Age 7 to 14 Challenge Level:

Have a go at this 3D extension to the Pebbles problem.

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2010: A Year of Investigations

Age 5 to 14

This article for teachers suggests ideas for activities built around 10 and 2010.

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Consecutive Numbers

Age 7 to 14 Challenge Level:

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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Building with Longer Rods

Age 7 to 14 Challenge Level:

A challenging activity focusing on finding all possible ways of stacking rods.

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More Plant Spaces

Age 7 to 14 Challenge Level:

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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Tea Cups

Age 7 to 14 Challenge Level:

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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Teddy Town

Age 5 to 14 Challenge Level:

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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More Children and Plants

Age 7 to 14 Challenge Level:

This challenge extends the Plants investigation so now four or more children are involved.