Life To Math

The most important thing is that you think like a winner!

I will give you many problems, some easy, some hard. You must want to solve them all correctly. Have paper and pencil on your desk, next to your computer or tablet. After you read the statement of each problem, first understand what it says, and then solve the problem on paper. Many times you can find the solution immediately, but sometimes you cannot. If you cannot find the solution to a problem right away, do not be afraid, it is normal. Think for a while, imagine the real life situation described in the problem, be clever, be ingenious. If you still do not see the solution, take a break and return to the problem later. Give up only after you have worked hard. This is how you become better at solving problems. This is how you grow.

Keep in mind that the first problems are easy, but as you progress the problems become harder and harder. As you get better, hard problems become easy.

In order to start working on Life-to-Math you will need to  know a few  simple things:

• • how to represent numbers using decimals and fractions
  • how to add, subtract, multiply, and divide numbers written using decimals
  • how to add, subtract, multiply, and divide fractions,
  • have some real life experience with weights, distances, money.

You need to have a computer or tablet, paper and pencil, and a maybe a calculator that can perform addition, subtraction, multiplication, and division. I suggest that you try to do as many of the computations as possible without using a calculator in order to train your computational skills, and also because you want to get a better understanding of numbers.

Life-to-Math is divided into three chapters:

1. Some Methods of Reasoning, where I teach you how to reason mathematically.
2. Mathematics Everywhere, where I challenge you with various problems that are inspired from real life.
3. The Tools of Algebra, where I teach you the first skills of abstract mathematics.

Each of the three chapters is divided into several sections. A section is centered on one idea, which can be a method for solving problems or an area of application. For example one section can teach you how to use the graphical method, another section can ask you to solve problems about liquids. In each section you first see some explanation, followed by examples, and maybe a few instructions that you should follow. Read these carefully. After that you are given a sequence of problems, one at a time, that you have to solve by yourself. The material is to be followed in order.

You first see the statement of the problem.

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You are supposed to solve this problem by yourself and when you are done, you have to submit the answer. To solve the problem, sit at a table with paper and pencil and work on the solution. Most of the problems require both reasoning and computations, and might required time for thinking. Once you solve the problem, convince yourself that the answer is correct, for example by checking that it fulfills the situation described in the statement, then submit the answer by typing it in the gray box and then clicking the ``Check'' button.  Some problems have single choice or multiple choice answers, where you have to click one or more boxes.

Some problems are easy, but many are not easy. It is important for you to try hard to solve them all. Read the statements carefully, problems with similar statements might have different solutions. I try not to repeat ideas, so most problems require thinking. Work carefully, do not rush, make sure that you solved the problem correctly before entering the answer.

You can submit the answer as a number in the box. There are several types of answers:

• one numerical answer,
• several numerical answers,
• a multiple choice answer with only one correct choice,
• a multiple choice answer where several options should be selected simultaneously.

Most answers are numerical. In that case, the answer is a whole number, such as 1, 2, 25, or a number with decimals. Only the first two decimals are taken into account. Whole numbers should be entered as they are,  thus if your answer is 10, you should enter 10. If your answer is 4.5 you can enter 4.5 or 4.50, and if your answer is 7.259 you should enter 7.25.

Only after you have typed all answers in the grey boxes, click the ``Check" button.

All decimals appear when dividing numbers, but you are not supposed to enter the answer as a fraction, instead you have to give the result of the division. If the answer is 1/3, you are supposed to enter 0.33. However, in your computations we suggest that you work with fractions when you can, and only truncate numbers at the very end. For example, if at some point in the computation you have 1/6, and at the next step you are supposed to multiply it by 18, you obtain 3. But if you approximate 1/6 by 0.16, and then you multiply by 18, you get 2.88. So be careful, approximate only at the last step.

Each problem has its own score. This score is written in green  at the beginning of the statement of the problem. It is enclosed in brackets. Your score is announced at the end of every group of problems.

After you have submitted the answer, you will be told if you solved the problem correctly or not. You will also be told the correct answer.

After that you will be shown one or several complete solutions to the problem. It is important that you read my solutions. This way you can learn

• how I reason,
• new tricks that can be useful later,
• how to organize your thinking,
• how to write down a solution.

If my solution is different from your solution, it does not mean that my solution is correct and yours is wrong. There are many ways to solve a problem correctly.

After you read the solution, you can pass to the next problem, or to the next theoretical explanation.

At any time, if you want, you can take a look at:

• this page of instructions,
• all theoretical explanations that you have studied so far, but not the ones that you will study in the future.

My advice is that you should through Life-to-Math at a steady pace. You should not rush through the problems, think carefully about each questions before answering. Do not solve too many problems at once. It is better to set aside a time interval every week for working these problems. You should expect to have to solve over 300 problems. If working on a steady pace, Life-to-Math should take no longer than 1 year to complete.

When you decide to interrupt or stop working on Life-to-Math, just close your browser. To resume your work, just log in and you will be taken at the exact place where you have stopped.