5 Math Concepts Needed to Master Algebra
Many students seem do well in math until they reach the 8th and 9th grade and experience algebra. Algebra is a very different class compared to the type of math students have experienced before and requires a higher-level abstract thinking that many students initially struggle with. It may take some time for students to adjust to this level of thinking but if the students can master the 5 concepts below they will be able to breeze through algebra. Having a strong algebra foundation then will propel the students to be success in the higher-level math classes and into college. After the student masters these 5 concepts below they should have no problem acing their math class.
1) First and most important concept – Know the Basics
This is by far the most important skill need to be successful in algebra. Many students go into algebra without the imperative beginning skills that should of have been mastered in the lower in the graders. These skills include:
If a student starts an algebra class without these prerequisite skills it makes impossible to fully understand the new concepts. Many times these students are spending all of their effort trying to work through the arithmetic of the problem and are completely missing the algebra concept at hand. If a student is struggling with these prerequisite skills it is almost always advise that a student takes a remedial pre-algebra class before jumping into an Algebra I class. Read more about the dangers of algebra too soon.
2) Be able to solve linear equations and understand the reasoning and process.
Solving linear equations is an important skill that comes up in every subsequent math class and has many utilities to it. One important thing to note is that students must understand the process and reasoning and not just mimic what the steps. Many times students get in the habit of solving simple problems in their head by guess and check with reason but never take the time learn the process. Students then get stuck when they reach more complex problems, which become extremely more difficult to solve in their head. An example of this is 2x + 5 = 9, which many student are able to solve in their heads as x = 2. They do not take the time to learn the process of subtracting each side by 5 and then dividing all the terms by 2. Many students can make this guessing method work until they reach a problem like 7x – 4.5 = 20 where that answer is going to be a fraction. If the students did not learn the process there is a very little chance that the student is able to solve this problem. It is also very important for students to also understand the concept that when you apply the same action to both sides of the question it will not affect the value of the problem.
3) Know the different methods of solving a system of linear equations and know when to effectively apply each system.
In algebra class students are taught many different ways how to solve a system of linear equations but students often struggle knowing the advantages and disadvantages of the different methods and when to apply them. Students learn how to solve system of linear equations by graphing, elimination and substitution. It is important that students master all of these methods and understand that how they are all related and give the same solution to the problem. Even more important student should understand which method is most effective for the current application.
4) Master Exponential and Logarithmic functions and expressions
This is the first time many students experience exponents and logs. It is important for students to master all arithmetic operations when workingwith exponents and logs because this is the most important skill set that will come up in higher-level math. As well as mastering the arithmetic operations students should grasp a strong understanding of graphing these functions through transformations. Students most know how to graph the basic functions of and and be able to use transformations to graph more complex functions and their inverses. As well as being able to graph these functions students need to be able state the domain and range of each of the functions.
5) Understand everything there is about Polynomial and Quadratic Functions/Equations.
When working with polynomials students need to understand the algebraic representations of the functions. They need to be able to find the roots through factorization and rational roots theorem. In addition to understanding the algebraic representation they also need to understand graphic representation including graphing parabolas given its parameters and its x-intercepts. This is the most complex concept that students see in an algebra class because it requires a lot of prerequisite skills being put together at one time. If the student is just missing one of these prerequisite skills it makes the process extremely difficult to complete.
If the student is able to successful master these five skills they should have no problem with receiving an A in their algebra class and being prepared for higher-level math classes. If you student is having trouble in their math class you can visit one of our Mathnasium locations here to receive help from our expert math instructors.