The rugby secret which helps ace your exams.

In 2019, England almost won a rugby world cup. 

They outmuscled Australia in the quarterfinals, and outplayed New Zealand, the favourites, in the semifinals. They played some of the best rugby the modern era has ever seen. 

Yet only four years prior, on home soil, the same team couldn’t even manage to get out of the group stages. A remarkable performance improvement occurred in only a four year period. How was this possible?

After England’s disappointing performance in 2015, a new manager, Eddie Jones, was chosen. Jones is a rugby genius, and improved the team in many ways. But one part of his philosophy stands out. One simple thing helps his players maximise their in-game performance, while also minimising their stress. 

This same insight can be used in other sports. It can even be used to prepare for exams. In fact, we think it might be the secret to preparing for any type of assessment!
He trains his players above match intensity.

In the run-up to big tournaments, Jones trains his players hard. They leave training shattered, sweat dripping from every pore. They train at a higher level than their opponents will be able to meet. On game day, when the whistle blows, the England players are calm. They don’t have to get out of third gear. It feels easy.


The secret to acing exams is to practice above exam intensity.

At nedandtom.com, we teach our students to solve problems from first principles, asking them questions above and beyond those expected on exams. 

We don’t force students to learn how to ‘hack’ practice tests. We don’t fill their heads full of formulas, either. Instead, we help our students work things out for themselves. This builds a lasting understanding of maths, which they can use to answer questions in other areas. 

Our students don’t cram one week, only to forget the next. They learn maths problem solving for their whole life.

Like England rugby, we practice with intensity, but unlike sports practice, our classes are fun and encouraging. Students leave our sessions with aching brains, but also the satisfaction that they are mastering a new skill.

This is not just the best way to smash exams. It teaches basic problem solving skills which are important in every part of life. Because our students have seen so many tough problems, by the time they get to exams, they are relaxed. They know they can do them. Like England beating Australia at rugby, it feels easy.

Holiday Maths: Cruel or Kind?

In the classic film “Recess: School’s Out”, 10 year-old T.J. finds himself left alone all holiday as his friends are sent off to camps dedicated to their interests. Meanwhile, supervillain (and former hippie) Dr. Phillium Benedict plans to end holidays forever to boost test-scores.

Outside the animated world, the line between school-time and free-time is increasingly becoming blurred as the holidays are seen as a chance to ‘get ahead’ with school work. Is it fair to do this to students, or should holidays be holidays?

Term-time is hectic and the holidays can be a great opportunity to supplement areas which students haven’t had time to focus on. This can mean exploring a subject in which a student excels or building more confidence in an area where they’ve been lagging behind.

So what extra work can students do? The blunt tool is to get students to revise during their holiday – the last thing any student wants. The other option is to do activity courses and work-experience which help students decide what they want to do and be. Neither of these options are ideal. Spending the holidays doing homework seems unfair, whilst activities simply don’t address the academic blindspots students need to fill in.

The third option is to do nothing. This can be great, as it gives students the chance to be creative with what they already know, rather than forcing their brains to take in more information. The only problem is that the distractions of a holiday environment: Minecraft, Snapchat – dare I say it – siblings, don’t facilitate this.

In the end, the kids in Recess escape their holiday camps and use their existing skills  to defeat the supervillain (all to a tubthumping 1960s soundtrack). Students can surprise themselves with what they already know…

Students learn a lot at school, but the relentless march through the syllabus, the judgement of peers, and the weight of textbooks can stifle their ability to do exciting things with their knowledge. Their heads are filled with powerful mathematical tools, but they haven’t had the chance to use them. What if over the holidays they got the chance to push what they already know to the limit?  The ideal holiday activity would be a bridge between their existing skills and the real world. It would show how the humdrum of school is helping students build their future. This would avoid boring revision, whilst still contextualising schoolwork.

Giving students the opportunity to see how far their knowledge can take them is far from cruel, it’s the kindest thing you can do.

Ned and Tom are running a Maths For Future Leaders bootcamp from Jan 2-5. If you’re interested you can get in touch here.

Are you smarter than a politician?

We all like feeling smarter than other people. Especially when those people are politicians.

With the general election coming up, we want to cover some maths mistakes made by politicians all the time. Can you succeed where they failed?

A few years ago, several MPs were given a maths quiz. More than half of them couldn’t answer the following question:

If I toss two coins, what is the probability of heads coming up both times?

If you know the answer, scroll to the bottom and leave a comment below! If you want to see how we’d work it out, read on…

Working:
Assuming the coins are unbiased, any one flip is equally likely to show heads or tails.
So if we flip one coin, there is a 50% (or 1-in-2) chance that it shows heads. If we flip another coin afterwards, then there is another 50% chance it lands heads-up. Since there is a 1-in-2 chance the first coin shows heads, and another 1-in-2 chance the second coin shows heads, the chances that both coins show heads is one-half times one-half, or 1-in-4.

We can see this illustrated in the picture below.

The first fork corresponds to flipping the first coin. We get heads with probability one-half. Then we flip the second coin. To get heads again we travel along the top line, again with probability one-half. We multiply these probabilities together to obtain one quarter.

Now it seems simple.
But if you can answer this question, you know probability better than 60% of surveyed MPs! Quite worrying, as the job of an MP is to weigh up the likelihood of different policy scenarios…

If you or your child want to get better at questions like these, Ned and Tom offer private maths tutoring. They teach maths which is useful in real-life, not just exams.

Stuck? 3 Tips for starting a maths problem

The clock strikes 10. Then 11. The rest of the world is falling asleep, while you’re still at your desk, staring blankly at a maths problem. Stuck. 

As midnight arrives, you search your mind desperately for a solution. But you’re still out of ideas.

For many problems, the hardest part is knowing where to start.
To make your life easier, we at Ned & Tom are sharing our 3 top tips for starting tough questions.

1. Restate the problem in your own words.

Imagine you want to visit a friend, but you don’t know her address.
It doesn’t make sense to start walking without finding out where she lives. You might walk in the wrong direction.

This is like starting a problem without understanding what the question is asking.  Understanding what the questioner wants can be hard, because frankly, mathematicians are awkward. 

Rephrasing the question in your own words helps you understand what it wants from you. Sometimes this helps you work out every step to the answer – like knowing the exact route to your friends house.

Other times, you can only work out vaguely what the question wants. This is still better than nothing! This is like knowing the neighbourhood where your friend lives. You can at least walk there. Maybe when you get there you’ll see a familiar house and know where to go.

2. Find a related problem you know how to solve.

Sometimes, a question is so hard that we feel we have no hope of solving it. 

For example:
How would you find the volume of a four-dimensional hyper-cube?

At first, this question seems impossible.
I can’t even imagine a 4-d cube! How on earth could I find its volume?

The trick is to find an easier, related problem. It helps to start small. Find a problem which you know how to solve, and work your way up from there. In this case, a simpler problem is to find the volume of a 3-d cube.

We can go even simpler. A 3-d volume is analogous to an area in 2-d. An even easier problem is to find the area of a 2-d square.

The area of a square is the product of both its side lengths. Since both sides have the same length (call it a), the area of a square with side-length a is , a2, a squared. Similarly, the volume of a cube with side length a is a3, a cubed.

Working this out gives us courage to tackle our original problem. 

By analogy, it is reasonable to state that in 4 dimensions, the volume of a 4-d cube is a4

The question seemed difficult, but by finding a simpler problem and working our way up, we made it easy.

3. Build it and the ideas will come.

Doing maths is like building with Legos.
The building blocks are the information given in the question. When we understand the problem clearly, we know exactly what we want to make. Solving the problem is like following the instructions on the box. 

Sometimes, we find a problem unlike any we’ve done before.
We can’t find a related problem. We try to restate it, but we still don’t understand what it wants from us. In this case, the best thing to do is start using the information given in the question.

Solving a problem we don’t fully understand is like building Legos without instructions.

We can’t initially see the finished Lego on the box. But we can start by using the Legos we have. We can build these up into something useful, like a wall, or a doorway. These parts suggest the idea to build a house. We can combine our useful pieces further, eventually ending up with the finished article.

We can start with the information given in the question.
Try and work something useful out from it. After finding something useful, maybe we can use it to get closer to the answer to our original problem.

If you can’t restate the question, and you can’t find an easier one to solve, the best thing to do is start. Put the information in your question together like Legos, and often you’ll build something useful.

If you or your child wants to learn useful problem solving techniques like these, Ned and Tom offer private 1-to-1 and small group tutoring. We teach your children the maths you wish you’d learnt. Sign-up here.

What’s the point of maths?

It’s a beautiful Spring afternoon.
The sun is shining, flowers are blooming, and you’re stuck inside a stuffy classroom, being forced to memorise the quadratic formula. All of the sudden, a question strikes your bored mind. The same question a thousand students have asked before you:

What is the point of maths?

We have all wondered about this question. I know I did.

Many students ask their teachers, and often get an unsatisfying reply. “Maths is important”, some say, rarely explaining why. “You need it for your taxes”, partially true, but mostly false. Or my personal favourite: “You just do”. 

These reasons all suck. But there are good reasons to study maths. Three of them, in fact.

1.
Maths is the best tool humans have to describe the world around us.

Put simply, maths works! Planes fly, buildings stand tall, and social networks connect. All of these things were designed and built using mathematics. Maths lets us work stuff out. It helps us understand the world, which means we can make useful things.

2.
Maths is the most useful skill taught in school today.

Technology is changing faster and faster. Machines are learning better every year.

Soon there will be two types of people: People who tell computers what to do, or people who are told what to do by computers.

Millions of people, from Uber drivers to Amazon employees, already have a computer as their boss. In a world of increasing change, the biggest opportunities will go to those who understand technology instead of fearing it. And to understand technology, you need to understand maths.

3.
Learning maths teaches you how to think.

Other subjects teach you facts which you can easily Google, but maths teaches you methods for solving problems.

A good maths education teaches you general problem solving. You learn how to work out what you want to know from the information you already know. A problems-based maths education doesn’t just force you to hack exams. It gives you skills which apply beyond the classroom.

Ned & Tom help their students understand maths. 

We base our teaching on real problems, not some formula book. We use these problems to teach our students how to think for themselves. Our students go on to study at the best universities, and are in prime position to take advantage of technology, instead of having technology take advantage of them. And they never have to memorise the quadratic formula.


To learn more, please reach out here.