This is one of those topics that comes in all varieties. We begin learning this in late elementary school and then turn up the heat as we transition out of middle school. This means that this skill most likely spans the most grade levels out of any topic that we offer. You will notice that we have a specific worksheet section for High School Algebra. This section highlights all of our algebra materials across all grade levels. This topic first shows up around grade 3 and follows students through high school. I am often adding topics to this section. If you can think of anything that I am missing, please let me know and I'll get it up quickly. The topics that you will find below all come with come complete with a healthy offering of worksheets, lessons, homework, and quizzes. We find this to be one of our most used areas.
- Adding and Subtracting Rational Expressions - These are values where a portion of the fraction is a polynomial.
- Adding, Multiplying, and Subtracting Monomials - Learn how to perform these operations with variables involved.
- Algebraic Expressions - We learn how to write them from math sentences.
- Applying the Remainder Theorem - This is a useful shortcut to use when a function is being divided by a linear polynomial.
- Binomial Theorem for Expansion - This will help you make sense of some unique expressions.
- Binary Operation Tables - We use our understanding of the property of operations to make sense of data sets.
- Combine Like Terms and Expand Terms - One of the fundamental skills that allow you to work with equations and expressions.
- Completing the Square in a Quadratic Expression - This technique is used to solve quadratic equations by adjusting equations to form perfect square trinomials.
- Complicated Expressions - We show you how to work through difficult algebraic tasks.
- Conditional Expressions - This is the foundation of most computer science applications.
- Creating Equations and Inequalities - Learn how to model your math behind a situation you are trying to better understand.
- Creating Equations with Two or More Variables - This is where students often get confused, but with a layered approach we show you how to handle these types of problems.
- Distance Formula - This is how we gauge the distance between two points pretty easily.
- Double Step Algebra - Students will begin to learn how rearrange equations or inequalities with ease.
- Explaining How to Solve Equations - We explore the essence of algebra with this skill.
- Finding and Using the Discriminant - In a quadratic formula, this is what resides beneath the square root symbol.
- Finding Points of Intersection for Complex Equations - If you do not have graph paper available, this will save you a great deal of frustration.
- Finding the Inverse of a Matrix - It is all about swapping position. You just need to know which data to focus on.
- Graphing Equations - We learn how to visualize an equation so that we can better understand the nature of it.
- Graphing Linear Inequalities as a Half-Plane - The goal here is to show where the solution could possibly reside.
- High School Algebra Posters - Great to post on your classroom walls.
- Identifying Zeros of Binomials - This helps you learn to solve binomial equations with a simple factoring trick.
- Interpret the Context of Expressions - It is all about making sense about what is happening in a system.
- Linear Equations as a Matrix Equation - How do we represent values in other ways?
- Multiplying Binomials - This will help you to accurately understand higher level applications of algebra.
- Multiplying Radical Expressions - I find that students need extra time with this specific operation.
- Multiplying and Dividing Rational Expressions - Learn how to process these operations.
- Parentheses, Brackets, and Braces in Math Expressions - What do they mean and how do we manipulate them to our advantage?
- Polynomial Addition and Subtraction - Simple operations that we show you how to set up.
- Polynomial Division - This is an intimidating topic, but we show you how to make it easy.
- Polynomial Multiplication - It is not as complicated as you would think to find the end values of the product of these expressions.
- Pre-Algebra Word Problems - Before you are ready to tackle tougher topics, this is a good place to start.
- Pre-Algebraic Number Sequences and Patterns - We learn how to organize sequences and make sense of them.
- Properties of Exponents - We look at how to evaluate them and understand how you can expand and condense values with them.
- Proving Polynomial Identities - We explore equations that are true for all values that are possible.
- Quadratic Equations: Completing the Square - We introduce you to this method from a different angle.
- Quadratics: Using Square Roots and Zero Property - This will help you learn how to manipulate and use quadratics.
- Rearranging and Understanding Formulas - We just simply learn that what ever we do to one side, we must do to other side.
- Rewriting Expressions - You will sometimes need to do this to help you solve them.
- Rewriting Rational Expressions - You will examine several different methods to get this done.
- Simple Algebra Word Problems - We show you how to spot the variables and write well develop equations for yourself.
- Simple Expressions That Record Calculations - We show you how to develop your own expressions.
- Single Step Algebra Equation Solving - It is all about getting that variable all by itself.
- Single Step Algebra Problems (Addition and Subtraction Based) - We show you how these operations can be used to cancel each other out.
- Single Step Algebra Problems (Division and Multiplication Based) - Another famous pair of operations that knock each other out of the picture.
- Solve Rational and Radical Equations - We explore how to set these up and then just knock them down.
- Solving Basic Function Tables - We learn how to follow and use operational rules.
- Solving Linear Equations and Inequalities in One Variable - This is a good starting point to help you compare the two.
- Solving Simple Equations With Fractions and Decimals - This is the second layer of math embedded in most equations.
- Solving Systems of Equations - Systems pop up when you two or more equations that share the same set of unknowns.
- Solving Systems Word Problems - We expand this skill to everyday situation-based problems.
- Solving Systems of Linear Equations by Graphing - This is a unique, but effective way to get the job done.
- Solving Simultaneous Equations (Linear and Quadratics) - We show you how to work within and off of both of the formats.
- Solving Quadratic Equations - Students will examine the basic problems they will run into with this topic.
- Solving Quadratic Equations By Factoring - If you get good with this technique it will always be your go to method.
- Using Graphs of Equations - Students will begin to use graphs to solve all types of different problems.
- Using the Quadratic Formula - This allows you to solve natural quadratic equations.
- Word Problems That Require Equations or Inequalities - These are some pretty complex word problems for some cool situations.
- Writing Expression for Geometric Sequences - These are sometimes referred to as geometric progressions.
What is Algebra?
There is no denying from the fact that most of the kids fear algebra. Yet despite this fear from students, algebra makes our lives and, especially equation solving easier. Algebra is something can tend to cause a great deal of anxiety for students. When you pace yourself and follow a simple trajectory, you will find that it is not only intuitive it is tremendously helpful in many different situations.
Algebra is essentially about solving for the unknowns or substituting real-life variables and then solving the equations for them. The most difficult portion of algebra is when we are applying this to the real world because there are countless variables that we come across. For most of us, algebra is the set of rules, formulas, and procedures employed to solve equations. But we often forget that real-life problems are being solved through the manipulation of variables and unknown factors.
To define it mathematically, algebra is the branch of mathematics that deals with symbols and the rules used to manipulate these symbols. In basic algebra, those symbols denote quantities without any fixed value, called variables. Algebraic equations are used to define the relationships between these variables in respect to all other factors that affect them.
Beyond giving us the solution to real-life problems, algebra is important for honing the reasoning skill of children. It enables them to state their ideas precisely and help them work in a systematic way. You find that if you have a good deal of success with this topic, most of the other higher level math topics will come easy to you as well.
Tips for Learning Algebra
While there is no skeleton code or hidden cheat code to solve every algebra problem you will come across, there are a number of things that can help you have a great deal more success. Here are some things that help many students achieve a greater level of success more quickly:
Remember PEMDAS - Understanding your order of operations is important. It becomes much more important as you get to the more advanced work. There are many times where you need to process an operation prior to beginning to balance equations that you come across. A quick review of the nature of operations is important. As the “P” indicates, always start with the parenthesis first. We should also remember that when we are working with our operations proceed in a left to right manner.
Get x alone - The goal of solving almost all algebra-based problems is to get the variable by itself. In most cases the variable is named x. We can just reverse engineer the equation. We need to remember that we can perform any operation, as long as we do it to both sides of the equal sign. You should focus on the side that has the variable and ask yourself, “What can I do to get it all by itself?” Just remember that addition and subtraction cancel one another out, as well as multiplication and division.
Remember Negatives - Negative numbers will often present as subtraction within most equations. Many students will often ignore the negative symbol and just solve away. That is not a good habit to get into. I recommend that you take another look at the rules for signed numbers before going full throttle with algebra. There are many times where this will become an issue for you.