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### Big and Small Numbers in Chemistry

##### Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

### Big and Small Numbers in Physics

##### Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

### The Power of Dimensional Analysis

##### Stage: 4 and 5

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

### Big and Small Numbers in the Physical World

##### Stage: 4 Challenge Level:

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

### Global Warming

##### Stage: 4 Challenge Level:

How much energy has gone into warming the planet?

### Big and Small Numbers in the Living World

##### Stage: 3 and 4 Challenge Level:

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

### Trig-trig

##### Stage: 4 and 5 Challenge Level:

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

### The Invertible Trefoil

##### Stage: 4 Challenge Level:

When is a knot invertible ?

### Problem Solving: Opening up Problems

##### Stage: 1, 2, 3 and 4

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. . . .

### A Rational Search

##### Stage: 4 and 5 Challenge Level:

Investigate constructible images which contain rational areas.

### Few and Far Between?

##### Stage: 4 and 5 Challenge Level:

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

##### Stage: 4 and 5 Challenge Level:

Some of our more advanced investigations

### Chance of That

##### Stage: 4 and 5 Challenge Level:

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

### 9 Hole Light Golf

##### Stage: 1, 2, 3, 4 and 5 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?

### Peeling the Apple or the Cone That Lost Its Head

##### Stage: 4 Challenge Level:

How much peel does an apple have?

### 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.

### Eight Ratios

##### Stage: 4 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.

### Two Regular Polygons

##### Stage: 4 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?

### Odd Stones

##### Stage: 4 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.

### There's Always One Isn't There

##### Stage: 4 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.

### Robot Camera

##### Stage: 4 Challenge Level:

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

### Take Ten Sticks

##### Stage: 3 and 4 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?

### Twizzles Venture Forth

##### Stage: 4 Challenge Level:

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

### Perfect Eclipse

##### Stage: 4 Challenge Level:

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

### Designing Table Mats

##### Stage: 3 and 4 Challenge Level:

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

### Track Design

##### Stage: 4 Challenge Level:

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

### It's Times Again

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

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

### Number Families

##### Stage: 3 Challenge Level:

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

### Carbon Footprints

##### Stage: 4 Challenge Level:

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

### Chocolate

##### Stage: 2 and 3 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?

### Alternative Record Book

##### Stage: 4 and 5 Challenge Level:

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

### Snookered

##### Stage: 4 and 5 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?

### Squareo'scope Determines the Kind of Triangle

##### Stage: 3

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

### Tiling Into Slanted Rectangles

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

A follow-up activity to Tiles in the Garden.

### Crossing the Town Square

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

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

### Troublesome Triangles

##### Stage: 2 and 3 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. . . .

### Bent Out of Shape

##### Stage: 4 and 5 Challenge Level:

An introduction to bond angle geometry.

### Counting on Letters

##### Stage: 3 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?

### Witch's Hat

##### Stage: 3 and 4 Challenge Level:

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

### Stacks of Maths!

##### Stage: 1, 2 and 3

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

### Extending Great Squares

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

Explore one of these five pictures.

### Investigating Pascal's Triangle

##### Stage: 2 and 3 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.

### Steps to the Podium

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

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

### So It's Times!

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

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

### Building with Longer Rods

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

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

### Pebbles

##### Stage: 2 and 3 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?

### More Plant Spaces

##### Stage: 2 and 3 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.

### Great Squares

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

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

### Tea Cups

##### Stage: 2 and 3 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.

### Consecutive Numbers

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

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