MI-01: Ordering Your Operations

In a puzzle type format, these ten tasks ask students to complete the equations by adding in the arithmetic symbols which will make it work. These are great fun and ensure students get their order of operations both right and automatic. These is no method which will work every time. They will just have to play. Lots need brackets, and some even need factorials. By the end they can use any operations known to mathematics!

MI-02: Verbalising Mathematical Thinking I

It is much easier to get the right answer than explain why. For students who will go on to advanced mathematics, being able to verbalise their thinking is an invaluable skill. So let’s start young. This is the first of a number of units where tasks are designed to be fun, challenging and particularly suited to explaining their thinking.

MI-03: Verbalising Mathematical Thinking II

Puzzles are fun, explaining them is hard. So here are plenty more to verbalise about. For students who will go on to advanced mathematics, being able to verbalise their thinking is an invaluable skill. This is the second of a number of units where tasks are designed to be fun, challenging and particularly suited to explaining thinking.

MI-04: Playing With Integers

Using alphanumeric and other puzzles, this is a fun unit designed to have students play with numbers for the pure pleasure. They more they play with numbers, the more the numbers will talk to them and group themselves into patterns. So these tasks are for fun, but also serve to add to the familiarity and pleasure strong arithmetic skills can bring. The last two will really challenge their perseverance!

MI-05: Cunning Calculating

There are all sorts of tricks to make calculating easier. Or so they claim. These tasks introduce some of these tricks, from the familiar casting out of nines to the ways the Elizabethans and Russians used to do long multiplication. Exploring these techniques may not only provide useful tricks of the trade, but also lots of fun as the patterns embedded in our mathematical world show themselves to be very useful.

MI-06: Patterns, Patterns Everywhere

The patterns in mathematics are what make it so beautiful. In sequences and embedded in puzzles, the patterns appear when least expected. Sensitivity to the patterns in mathematics will help students toward solving problems when they have no path. Play and then look for the patterns, and they will guide the way. This unit is designed to make students far more conscious of the patterns they will find everywhere.

MI-07: Special Numbers

Prime, palindrome, square, cube, tetrahedral, Fibonacci, binary, triangular and perfect numbers – they are all special. They keep appearing in the most unexpected places. Recognising them and being able to use them is an invaluable skill. This unit introduces the students to these special numbers and lets them play with them.

MI-08: Tricks And Ciphers

Bright kids like to work fast. Very fast. So they jump to the obvious conclusions. These puzzles are designed to make them take the time to read the question and slow down a bit. The word ‘tricky’ is used to warn them: there is a trick in this. Then there are magic tricks, codes and  ciphers. They can trick others! Kids love these puzzles!

MI-09: Shapes And Spaces I

Playing around with shapes and spaces enhances students’ ability to work visually. These tasks are designed to have students play with the geometrical world. In a puzzle format, they ask students to get out pencil and paper and draw their shapes, cut them out, put them together and generally muck about with the geometrical world.

MM-01: The Nature Of Proof

There is a big difference between thinking the answer is correct and knowing it is. The difference is all to do with proof. Sometimes algebra proves, and sometimes it doesn’t. These tasks are designed to ask students to go beyond getting an answer they think is right and submitting one they are quite sure about. And proving they know the difference. The unit does not ask for formal proofs, but for students to explain in their own language why they are so sure.

MM-02: Geometric Proof

Proving things in space is a challenge. These tasks come from famous problems in geometry. They have intrigued the great mathematicians of the past and can do the same for the young mathematicians of the future. Famous problems in geometry are famous for very good reasons – they are interesting, challenging and good fun.

MM-03: Deception and proof

Proving things is fine when the mathematics works. But sometimes proofs can be deceptive, and the world a tad paradoxical. This is a fun unit which really challenges the mathematically able. It is hard enough to get your head around paradoxes, let alone explain them in words. Then there are proofs which look perfect, but they prove the impossible. These tasks will frustrate and inspire – at the same time!

MM-04: Verbalising mathematical thinking III

Verbalising mathematical thinking is a skill which will serve all students very well as they move to advanced mathematics in their senior years. This is another set of puzzles with answers that are challenging to explain. Students will use them to further polish their ability to express their thinking in their own language.

MM-05: Shapes and Spaces II

Playing around with shapes and spaces enhances the spatial ability of students. This unit includes tasks which look at patterns when multiple shapes are put together: pentominoes, other-ominoes, lots of triangles, lots of squares, lots of different shapes embedded in a single form. Then it looks at tessellations, tiling and the more complex reptiles. We end up exploring the very strange space of the Koch Curve. Students will be drawing and colouring and finding geometry everywhere!

MM-06: Pure Gold

Mathematics isn’t only intriguing, useful and heaps of fun, it is also an aesthetic delight. From optical illusions to the golden ratio to Pascal’s triangle, the incredible Mobius strip and the formulae which people find beautiful, these tasks take students into the world of beauty, the mathematical way. The unit circle and trigonometry is beautiful. The link is stunning and the patterns when iterating the trigonometric functions are totally weird. Some aspects of mathematics are so inspiring they can only be considered pure gold.

MM-07: Playing With Probability And Data

Probability appears in the news all the time. Statistics are used and abused. Gifted students are ready to play with probability long before they are ready for the formal calculations. This set of tasks asks students to explore probability and statistics from first principles, finishing up with the challenges of decoding bar codes and solving the famous Monty Hall problem.

MA-01: When Patterns Get Challenging

This unit is for students who are very advanced and willing to persevere and play and explore in depth. The tasks don’t depend on students having done advanced concepts as much as being really mathematically inclined. The mathematics isn’t sophisticated as much as beautiful and plentiful. If iterating endlessly or exploring the special world of Pythagorean triples, primes and transcendental numbers appeals, then this is the unit to set them on their way.

MA-02: Fractal Fascinations

Fractal geometry produces some of the most stunning images ever generated by computer. Some are unbelievable realistic. Is this the mathematics which underlies Nature and her processes? The mathematics of iteration is fascinating in its own right. This unit requires students to work autonomously, using with free software from the Internet to explore this new field of mathematics. It will extend even the most advanced mathematics student. Any mathematical theory, such as basic complex number theory, which is beyond year 9 level, is included with the unit.

MA-03: Games Theory – An Introduction

Games Theory is a pure strategic logic. Mathematicians enjoy the challenge of playing games where the rules are simple and the strategies complex. Explaining the strategies takes a strong command of clear language. Some mathematicians take it all the way to the Nobel prize. It was Games Theory which underpinned John Nash’s Nobel Prize for Economics. It was Games Theory which underpinned the 2005 prize again. The final game in this set is John Nash’s Hex. Books have been written on the strategies. Now we ask the same of the students! Don’t worry - they start simple!