Start Your Day With Math

Every morning before I start work I tackle a math problem. I schedule 30 minutes to solve this problem, and if I don’t succeed I stick with it the next morning and subsequent mornings until I have solved it and I am ready to move on to the next.

Why do I do this? Well, because I enjoy it, but also because it offers me these very important benefits:

• Solving math problems trains your brain to be organized, logical and systematic, which is incredibly important in order to be successful in the most chaotic situations in work and life
• Solving math problems exercises a muscle in your brain where you can relate seemingly separate concepts and see important connections between them. This is also another critically important transferable problem-solving skill.
• You can learn math more effectively through solving problems. Your learning is more likely to stay in your brain because you found it useful in a specific situation.
• Successfully solving a problem generates an endorphin hit and provides you with a confidence to start your day. The impact of this on your daily performance should not be underestimated. Think about it as a sparring session before the real deal.

I get these problems from various sources, but mostly from math exams written for high school students. As a trained mathematician, I take on some of the most challenging problems, but the benefits are available to everyone as long as they choose a level of difficulty that suits their current level of experience and knowledge.

Where to source interesting math problems

Your source will depend on your current level of knowledge and interest in math. Examination questions at various stages of high school will provide a challenge for a wide range of abilities — it’s just a matter of working out a level where you are comfortable to start. Here are a few things to consider:

• Avoid multi-choice math problems in favor of problems where you need to fully write your solutions. Multi-choice problems are really just a cost-efficient way of testing skills, and can often be solved by process of elimination, which does not encourage the problem solver to explore why the correct solution is, in fact, correct. It’s through deriving a correct solution that the real learning and skill-building is to be found.
• This website contains a vast array of exam papers from the UK. GCSE papers focus on a general curriculum for lower high school students at various levels of challenge, while A-levels focus on upper high school students who have chosen to specialize in math. I’m sure there are many other free resources like this out there in different countries.
• Try a mix of different disciplines to stretch your brain as widely as possible: algebra, trigonometry, numbers, mechanics, statistics.

Some examples of what I mean

Here are a few examples of the kinds of questions which form great morning math material, according to your starting point.

Basic (very rusty, forgotten most of my high school math). This question is taken from a Higher tier GCSE paper for 16 years olds.

Intermediate (Loved math at high school but have not really used it since). A more challenging problem taken from a Higher tier GCSE paper for 16 year olds.

Advanced (Did some math at college/university). This problem is taken from an A level examination for 18 year old high school students who have chosen to specialize in math.

Very advanced (Studied and currently work in a highly math-related field). This problem is taken from a Sixth Term Examination Paper (STEP), which some of the top universities in the UK use to select the best high school applicants.

These are just examples of what is a huge array of resources out there to give your brain a proper math workout. Start wherever suits you best, practice regularly, look up the definition of concepts you have forgotten about or are not familiar with. You’ll be surprised how much you can improve your knowledge and capabilities, and you’ll see the benefits pretty quickly in how you solve other problems in life and work. Good luck.

If you have good suggested sources for interesting practice math problems, please do suggest them in the comments.