Anyone can learn math, in depth at school or for a simple review of elementary basics. After discussing how to be a good mathematics student, in this article we will teach you the various levels in mathematics courses and the basic elements to learn in each course. Next, the article will cover the fundamentals for learning arithmetic, which will help both children in elementary school and those who need to review the basics.
Steps
Part 1 of 6: Key points for being a good math student
Step 1. Go to the lessons
If you miss lessons, you will need to learn the concepts from a classmate or from the textbook. Your friends or the textbook will not give you as good an overview as your teacher can.
- Don't be late for class. In fact, arrive a little early and open the notebook to the right page, prepare the textbook and the calculator. You will then be ready when your teacher starts the lesson.
- Skip classes only in case of illness. In case you miss a class, talk to a classmate to find out what the teacher has explained and what homework has given.
Step 2. Work with your teacher
If the teacher solves a problem on the board, you do the same in your notebook.
- Make sure you take clear and legible notes. Don't just write the exercises. Also write down anything the teacher says that can help you understand the concepts better.
- Do all the exercises that are assigned to you. As the teacher walks between desks while you work, answer the questions
- Participate when the teacher solves a problem. Don't wait for the teacher to call you. Offer to answer when you know the answer and raise your hand to ask when you don't understand what was explained.
Step 3. Do your homework the same day you receive it
If you do your homework the same day, the concepts will still be fresh in your mind. Sometimes, it's not possible to finish all homework in one day. But finish all your homework before you get to class.
Step 4. If you need help, work outside of class too
Go to your teacher during his breaks or during office hours.
- If your school has a math center, find out about opening hours and get help.
- Join a study group. Good study groups usually consist of 4 or 5 people with different skill levels. If you have enough, join a group that has 2 or 3 students with an excellent or distinguished one, in order to improve. Don't join students who are worse off than you.
Part 2 of 6: Learning math in school
Step 1. Start with Arithmetic
Generally, arithmetic is learned in elementary school. Arithmetic includes the basics of addition, subtraction, multiplication and division.
- Practice. Doing a lot of arithmetic exercises one after the other is the best way to get to know the fundamentals by heart. Get software with many different math problems. Also look for drills to be done in a specific time frame to increase speed.
- You can also find online tutorials and download math applications to your portable device.
Step 2. Switch to Pre-Algebra
This course will give you the basic elements you will need to solve all algebra problems.
- Study fractions and decimal numbers. You will learn how to add, subtract, multiply and divide with fractions and decimals. In fractions, you will learn how to reduce fractions and interpret mixed numbers. In decimals, you will understand what decimal places are, and you will be able to use decimals to solve problems.
- Study ratios, proportions, and percentages. These concepts will help you understand how to make comparisons.
- Familiarize yourself with the fundamentals of geometry. You will master what geometric figures and concepts of 3D are. In addition, you will learn the concepts of area, perimeter, volume and surface, along with what parallel and perpendicular lines and angles are.
- Understand the fundamentals of statistics. In pre-algebra, you will deal with plots, scatter plots, branch and leaf plots, and histograms.
- Learn the basics of algebra. This includes concepts such as solving simple equations containing unknowns, knowledge of some properties, such as the distributive one, representation of simple equations and solving inequalities.
Step 3. Switch to Algebra I
In the first year you will learn the basic symbols of algebra. You will also learn:
- How to solve equations and inequalities that contain unknowns. You will learn to solve these problems by doing the calculations or plotting them in a graph.
- Tackle math problems. You will be surprised to see how many everyday problems, which you will have to face in the future, have to do with the ability to solve algebraic problems. For example, you will need algebra to figure out the interest rate on your bank account or investments. Algebra also helps you calculate how many hours you will have to drive based on the speed of your car.
- Work with exponents. As you start solving equations with polynomials (expressions that contain both numbers and variables), you will need to understand how to use exponents. This could include the use of scientific notations. Once you understand the exponents, you will be able to add, subtract, multiply and divide polynomial expressions.
- Calculate the exponents to the second and the square roots. Once you are familiar with this topic, you will know the power to the second of different numbers by heart. You will also be able to work with equations that contain square roots.
- Learn what functions and graphs are. In algebra, you will be dealing with graphs of equations for sure. You will learn how to calculate the slope of a line, how to represent equations in the point-slope formula, and how to calculate the intersections of a line at points x and y using the slope-intersection formula.
- Solve systems of equations. Sometimes you will be given two distinct equations containing both variables x and y and you will have to solve both equations for x and y. Fortunately, you will learn several tricks to solve these equations, through graphing, substitution and addition.
Step 4. Dedicate to Geometry
In geometry, you learn the properties of lines, segments, angles and shapes.
- You will learn by heart the theorems and corollaries that will help you understand the rules of geometry.
- You will learn how to calculate the area of the circle, how to use the Pythagorean theorems and find the relationships between angles and sides of special triangles.
- Many of the exams you will face in the future will involve geometric problems.
Step 5. Take an Algebra II course
Algebra II builds on the concepts learned in Algebra I and adds other more complex topics, such as quadratic equations and matrices.
Step 6. Take on Trigonometry
You have already heard of sine, cosine, tangent, etc. Trigonometry will teach you many practical ways to calculate angles and lengths of lines. These notions will be very important for those studying construction, architecture, engineering and as a surveyor.
Step 7. Rely on some analytics
Analysis can be a little scary, but it is an excellent toolbox for understanding both the behavior of numbers and the world around you.
- The analysis will teach you what functions and limits are. You will observe the behavior of some useful functions, including e ^ x and logarithmic functions.
- Also you will learn how to calculate and work with derivatives. A first derivative provides information based on the slope of a tangent to an equation. For example, a derivative indicates how something changes in a non-linear situation. A second derivative will indicate whether a function is increasing or decreasing in a certain interval so that the concavity of that function can be determined.
- Integrals will show you how to calculate the area and volume delimited by a curve.
- Analysis taught in high school usually goes all the way down to sequences and series. Although students will not usually see many applications of series, they are important for those studying differential equations.
Part 3 of 6: The Fundamentals of Mathematics - Overcome some additions
Step 1. Start with the "+1" facts
Adding 1 to a number leads to the closest major number to that number on the number line. For example, 2 + 1 = 3.
Step 2. Learn the concept of zero
Any number added to zero is the same number because "zero" is the same as "nothing".
Step 3. Learn what double means
Duplicating means adding two equal numbers together. For example 3 + 3 = 6 is an equation that contains two doubles.
Step 4. Use the mapping to learn how to solve other additions
In the example below, using the mapping you can figure out what happens when you add 3 to 5, 2 and 1. Solve the "add 2" problems yourself.
Step 5. Go through 10
Learn to add 3 numbers to get a number greater than 10.
Step 6. Adding the largest numbers
Learn to group units in the tens place, tens in the hundreds place, etc.
- Column the numbers correctly. 8 + 4 = 12, it follows that you will have a ten and two units. Write 2 in the units column.
- Write 1 in the tens column.
- Add the tens column together.
Part 4 of 6: Mathematics Fundamentals - Subtraction Strategies
Step 1. Start with "1 backward"
Subtracting 1 from a number takes you back one number. For example, 4 - 1 = 3.
Step 2. Learn to subtract two double numbers
For example, the sum of 5 + 5 gives 10. Simply write the equation backwards and you will have 10 - 5 = 5.
- If 5 + 5 = 10, then 10 - 5 = 5.
- If 2 + 2 = 4, then 4 - 2 = 2.
Step 3. Memorize the families of facts
For instance:
- 3 + 1 = 4
- 1 + 3 = 4
- 4 - 1 = 3
- 4 - 3 = 1
Step 4. Find the missing number
For example, _ + 1 = 6 (the answer is 5).
Step 5. Learn the facts of subtraction up to 20
Step 6. Learn to subtract single digit numbers from two digit numbers without the loan
Subtract the numbers in the units column and write the number under the tens.
Step 7. Practice writing the values for the subtraction with the loan
- 32 = 3 tens and 2 ones.
- 64 = 6 tens and 4 ones.
- 96 = _ tens and _ units.
Step 8. Subtraction with the loan
- You want to subtract 42 - 37. You start by trying to subtract the 7 from the 2 in the units column. It is not possible!
- Borrow 10 from the tens and put it in the units column. Instead of 4 tens, you now have 3 tens. Instead of 2 units, you will now have 12 units.
- Subtract from the units first: 12 - 7 = 5. Then check the tens. Since 3 - 3 = 0, you don't have to write 0 to it. The result is 5.
Part 5 of 6: Math Fundamentals - Learn Multiplication
Step 1. Start with 1 and 0
Each number multiplied by 1 is equal to itself. Any number multiplied by zero gives zero.
Step 2. Memorize the multiplication table
Step 3. Practice single-digit multiplication problems
Step 4. Multiply two-digit numbers by single-digit numbers
- Multiply the lower right number by the upper right number.
- Multiply the lower right number by the upper left number.
Step 5. Multiply two two-digit numbers together
- Multiply the bottom right number by the top right and left numbers.
- Move the second row to the left one digit.
- Multiply the lower left number by the upper right and left numbers.
- Add the columns together.
Step 6. Multiply and group the columns
- Multiply 34 x 6. Start by multiplying the units (4 x 6); however, you cannot have 24 units in the units column.
- Keep the 4 in the unit column. Move the 2 tens to the tens column.
- Multiply 6 x 3, which gives 18. Add the 2 you moved to get 20.
Part 6 of 6: Mathematics Fundamentals - Discover the Division
Step 1. Think of division as the opposite of multiplication
If 4 x 4 = 16, then 16/4 = 4.
Step 2. Write your division
- Divide the number to the left of the division symbol, called the divisor, by the number under the division sign. Since 6/2 = 3, you will write 3 above the division sign.
- Multiply the number above the division sign by the divisor. Write the product under the first number under the division sign. Since 3 x 2 = 6, then you will write under 6.
- Subtract the two numbers you wrote. 6 - 6 = 0. You don't need to write 0, as you don't usually start writing a new number with 0.
- Write down the second number under the division sign.
- Divide the number you just wrote by the divisor. In this case, 8/2 = 4. Write 4 above the division sign.
- Multiply the number on the top right by the divisor and write it down. 4 x 2 = 8.
- Subtract the numbers. The last subtraction is zero, which means you are done with the problem. 68/2 = 34.
Step 3. Calculation of the remainders
Some divisors will not be contained in other numbers in an integer number of times. Once the last subtraction is calculated, if you have no more numbers to lower, the remaining number will be your remainder.
