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Anyone can learn math whether they are at an advanced level or just want to practice basic skills. After discussing ways to become a good math student, this article will teach you the basic progression of math courses and tell you the basics to learn in each course. After that, the article will summarize the key issues when learning arithmetic, useful for elementary students and anyone who needs to improve the foundation of mathematics.
Steps
The key to being a good math student
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Go to class. After skipping class, you’ll have to learn concepts from your friends or self-study in textbooks. Information provided from friends or books is never as good as listening to lectures directly from teachers.
- Come to class on time. In fact, you should come to class a little early, open your notebook to the right page, open your textbook and take out your laptop, so that you are ready when the teacher starts to teach.
- Only skip class if you are sick. When skipping class, you should ask your friends to narrate what the teacher has taught and the homework assigned.
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Work together with teachers. When the teacher is doing the homework on the podium, you should also do the work in your own notebook.
- Remember to keep your notes clean and easy to read. Don’t just write the topic, you should write whatever the teacher says to help you understand the concepts better.
- Solve any sample problems written by the teacher on the board. Find the answer to the math problem while the teacher walks around the classroom waiting for the class to do the homework.
- Actively participate when the teacher solves the problem. Don’t wait for them to call you to answer. Volunteer to answer when you know the answer, and raise your hand to ask a question when you don’t understand what the teacher is saying.
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Do your homework on the assigned day. When you do your homework on the assigned day, the concepts are still etched in your mind. Sometimes you may not be able to finish your homework that day, but at the very least you should do it before class.
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Make an effort to study after class. Visit teachers during their free time or at work.
- If your school has a Math Center, it’s a good idea to know its hours so you can get help when you need it.
- Join a study group. The study group should have about 4 or 5 members of different levels. If you are a “C” student in math, you should join a group of 2 or 3 “A” or “B” students to improve your level. Avoid joining groups full of students who are weaker than you. [1] X Research Source
Learn math at school
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Start with arithmetic. Often students will begin with elementary school arithmetic. Arithmetic includes basic operations such as addition, subtraction, multiplication and division.
- Do homework. Doing a lot of arithmetic problems over and over is the best way to master the basics. Find software that gives you lots of exercises to solve. You should also look for timed exercises to speed up solving.
- Doing lots of exercises is the basis for being good at math. Not only do you learn concepts, you have to practice to remember them longer!
- You can find arithmetic problems online, and download arithmetic apps to your mobile device.
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Continue with pre-algebra. This course will provide the foundational knowledge needed to solve algebra problems later on.
- Learn about fractions and decimals. You will learn how to add, subtract, multiply, and divide both fractions and decimals. Regarding fractions, you will learn how to reduce and understand mixed numbers. Regarding decimals, you will learn how to find the row value of digits, and be able to use decimals in word problems.
- Learn about ratios, proportions and percentages. These concepts will help you learn how to make comparisons.
- Calculate the square and the square root. Once you’ve learned this topic well, you’ll remember the squares of many numbers. You can also solve equations with square roots.
- Start learning basic geometry. You will learn all shapes as well as holograms. The concepts you’ll learn are area, perimeter, volume, and surface area, and learn about parallel and perpendicular lines, and types of angles.
- Understand some basic concepts of statistics. In pre-algebra, the first part of statistics is mainly about histograms, scatterplots, leaf plots, and histograms.
- Learn basic algebra. Basic algebra covers things like solving simple equations containing variables, learning about properties like distributives, graphing simple equations, and solving inequalities.
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Continuing with Algebra I. In your first year of algebra, you will learn basic symbols related to algebra. You will also learn how to:
- Solve linear equations and inequalities containing 1-2 variables. You don’t just learn how to solve these problems on paper, but sometimes with a calculator.
- Solve word problems. You will be surprised how many problems in everyday life are related to the ability to solve algebraic problems with words. For example, you would use algebra to figure out the interest return on a bank account or on an investment. You can also use algebra to calculate how long it will take you to travel based on the speed of the car.
- Work with exponents. As you begin to solve equations containing polynomials (expressions with both numbers and variables), you will have to understand how to use exponents. To solve these equations you may also have to use mathematical notation. After mastering exponents, you can add, subtract, multiply, and divide polynomial expressions.
- Understand functions and graphs. In algebra, you will definitely have to learn graph equations. You must learn how to calculate the slope of a line, how to reduce the equation to a point-slope form, and how to calculate the coordinates of the intersection of the line with the x and y axes using the point-slope equation form.
- Solve the system of equations. Sometimes people give two separate equations with variables x and y, and you have to solve for x and y for both equations. Fortunately, you can learn many tricks for solving these equations, including graphing, substitution, and addition methods. [2] X Research Source
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Start learning geometry. In geometry, you will learn about the properties of lines, segments, angles, and shapes. [3] X Research Sources
- You must memorize a number of theorems and consequences in order to understand the principles of geometry.
- You will learn how to calculate the area of a circle, how to use the Pythagorean theorem, and find the relationship between the angles and sides of some special triangles.
- You will see later that geometry dominates in standardized tests like the SAT, ACT, and GRE.
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Study to Algebra II. Algebra II builds on the concepts you learned in Algebra I but adds more complex topics related to nonlinear functions and matrices.
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Learn trigonometry. Trigonometry has functions like sine, cos, tangent and so on. You will learn many practical ways to calculate angles and lengths, this skill is very useful for people who work in construction, architecture, and geodetic engineering.
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Apply some knowledge of calculus. Calculus sounds scary, but it’s a great toolbox to help you understand how numbers and the world around them work.
- With calculus, you will learn about functions and limits. You’ll see how some useful functions like the e^x and logarithmic functions work.
- You also learn how to calculate and work with derivatives. The first derivative gives you information based on the slope of the tangent to the graph of the equation. For example, the first derivative of a quantity tells the rate of change of something in the non-linear case. The second derivative shows whether a function is increasing or decreasing over a certain time frame, so you can determine the concavity of the function.
- Integral helps you calculate the area under a curve and also the volume.
- Calculus in high school usually ends with series and numbers. Although students do not see many applications of the topic of arithmetic, it is very important for those who will continue to study differential equations later.
- For some, calculus is still just the starting point. If you’re considering pursuing a career that involves a lot of math and science, like engineering, then go deeper into math! [4] X Research Sources
Basic math knowledge — Practice proficiently some additions
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Start with “+1” spell. Adding 1 to a number will result in the next number on the number line. For example, 2 + 1 = 3.
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Understanding zero. Any number plus zero equals itself, because “zero” is synonymous with “nothing”.
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Learn to add a number to itself. These problems require you to add two numbers that are the same. For example, 3 + 3 = 6 is an equation that adds a number to itself.
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Use the diagram to learn other ways of adding. In the example below, through the diagram you will know what the result is when adding 3 with 5, 2 and 1. Do the “add 2” problems yourself.
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Do math with numbers greater than 10. Learn to add 3s together to get a result greater than 10.
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Add larger numbers. Learn how to bring units to tens, and tens to hundreds etc..
- Add the digits in the right column first. 8 + 4 = 12, which means you have a 1 in the tens place and a 2 in the units row. Write the number 2 below the units column.
- Write the number 1 above the tens column.
- Add the numbers in the tens column together.
Basic math knowledge — How to do subtraction
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Start with the spell “-1”. Taking a number minus 1 takes you one unit back. For example, 4 – 1 = 3.
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Learn to subtract with two numbers that are the same. For example, you add two identical numbers 5 + 5 to get 10. Invert the equation to get 10 – 5 = 5.
- If 5 + 5 = 10 then 10 – 5 = 5.
- If 2 + 2 = 4 then 4 – 2 = 2.
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Memorize some related operations. For example:
- 3 + 1 = 4
- 1 + 3 = 4
- 4 – 1 = 3
- 4 – 3 = 1
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Find the missing number. For example, ___ + 1 = 6 (the answer is 5). This form of math lays the groundwork for algebra and beyond.
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Memorize subtraction operations up to 20.
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Subtract 2-digit numbers from 1-digit numbers without borrowing. Subtract the digits in the units column and bring down the number in the tens place.
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Set to find the row value of the digit to prepare to perform subtraction by borrowing.
- 32 = 3 in tens and 2 in units.
- 64 = 6 in tens and 4 in units.
- 96 = __ in the tens and __ in the units.
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Except by borrowing.
- You want to subtract 42 – 37. Start by subtracting 2 – 7 from the units column. However, this is not possible!
- Borrow 10 from the tens column and put it in the units column. Instead of having 4 in the tens place, you now only have 3. Instead of having 2 in the units row, you now have 12.
- Subtract the units column first: 12 – 7 = 5. Then check the tens column, since 3 – 3 = 0 you don’t need to write 0. The answer is 5. [5] X Research source
Basic math knowledge — Practice multiplication
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Start with multiplying by 1 and 0. Any number multiplied by 1 will equal itself. Any number multiplied by 0 will equal 0.
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Memorize the multiplication table.
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Practice multiplying by 1-digit numbers.
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Multiply a 2-digit number by a 1-digit number.
- Multiply the lower right digit by the upper right digit.
- Multiply the lower right digit by the upper left digit.
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Multiply two 2-digit numbers together.
- Multiply the lower right digit by the upper right digit followed by the upper left digit.
- Shift the second row to the left one digit.
- Multiply the lower left digit by the upper right digit followed by the upper left digit.
- Add the columns together.
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Multiply and group the columns.
- You want to multiply 34 x 6. Start by multiplying the units column (4 x 6), but you can’t write 24 in the units column.
- Retain 4 in the units column. Move the 2 in the tens to the tens column.
- Multiplying 6 x 3 gives you 18. Add the 2 you switched to and get 20.
Basic math — Learn division
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Think of division as the reverse operation of multiplication. If 4 x 4 = 16 then 16 / 4 = 4.
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Write down the division problem.
- Divide the number to the left of the divisor, also known as the divisor, by the first digit below the divisor. Since 6 / 2 = 3, you write 3 on top of the divider.
- Multiply the number on the top of the division by the divisor. Bring this product below the first digit below the division sign. Since 3 x 2 = 6 you will bring 6 down.
- Subtract the 2 numbers you just wrote. 6 – 6 = 0. You can leave the space 0 blank because a number usually doesn’t start with the digit 0.
- Bring down the second digit that is the year under the division sign.
- Divide the number you just brought down by the divisor. In this case, 8 / 2 = 4. Write 4 on top of the divider.
- Multiply the top right digit by the divisor and bring the number down. 4 x 2 = 8.
- Subtract numbers from each other. The final subtraction result is zero, which means you’ve completed the division problem. 68 / 2 = 34. [6] X Research Source
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Division with remainder. There are cases where the divisor is not divisible by other numbers. When you’ve done the last subtraction and have no more digits to put down, that last number is the remainder. [7] X Research Sources
Advice
- Learning math is not a passive activity. You can’t learn math just by reading textbooks. Use online tools and teacher-provided worksheets to work through until you understand the concepts.
- Concepts are a part of math that you can’t ignore. Sometimes it’s better to know the concepts and get it wrong, than to not know them but do the right thing.
- Practice each math topic. Study only one topic at a time so you can figure out your strengths and weaknesses. After going through all the topics, you begin to practice in the workbook. The more you practice, the better you get!
Warning
- Don’t depend on handheld computers. Learn how to solve math problems by hand so you can understand each step of the way. However, calculators may be needed for more advanced math courses in high school and college.
Things you need
- Writing instrument (pencil or ballpoint pen)
- Eraser
- Paper
- Ruler
- Pencil sharpener
- Laptop
- Notebook
- Geometry Toolkit
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Anyone can learn math whether they are at an advanced level or just want to practice basic skills. After discussing ways to become a good math student, this article will teach you the basic progression of math courses and tell you the basics to learn in each course. After that, the article will summarize the key issues when learning arithmetic, useful for elementary students and anyone who needs to improve the foundation of mathematics.
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