Welcome to the Algebra worksheets page at Math-Drills.com, where unknowns are common and variables are the norm. On this page, you will find Algebra worksheets mostly for middle school students on algebra topics such as algebraic expressions, equations and graphing functions.
This page starts off with some missing numbers worksheets for younger students. We then get right into algebra by helping students recognize and understand the basic language related to algebra. The rest of the page covers some of the main topics you'll encounter in algebra units. Remember that by teaching students algebra, you are helping to create the future financial whizzes, engineers, and scientists that will solve all of our world's problems.
Algebra is much more interesting when things are more real. Solving linear equations is much more fun with a two pan balance, some mystery bags and a bunch of jelly beans. Algebra tiles are used by many teachers to help students understand a variety of algebra topics. And there is nothing like a set of co-ordinate axes to solve systems of linear equations.
Inverse Relationships Worksheets
Inverse relationships worksheets cover a pre-algebra skill meant to help students understand the relationship between multiplication and division and the relationship between addition and subtraction.
Inverse relationships with one blank
Inverse relationships with two blanks
Missing Numbers or Unknowns in Equations Worksheets
Missing numbers in equations worksheets in three types: blanks for unknowns, symbols for unknowns and variables for unknowns.
Missing numbers worksheets with blanks as unknowns (Blank Never in Answer Position)
In these worksheets, the unknown is limited to the question side of the equation which could be on the left or the right of equal sign.
Missing numbers worksheets with blanks as unknowns (Blank in Any Position)
In these worksheets, the unknown could be in any position in the equation including the answer.
Missing numbers worksheets with symbols as unknowns (Symbol Never in Answer Position)
Missing numbers worksheets with symbols as unknowns (Symbol in Any Position)
Missing numbers worksheets with variables as unknowns (Variable on Left; Answer on Right)
Missing numbers worksheets with variables as unknowns (Variable Never in Answer Position)
Missing numbers worksheets with variables as unknowns (Variable in Any Position)
Equalities with addition on both sides of the equation and symbols as unknowns
Algebraic Expressions Worksheets
Algebraic expressions worksheets including translating algebraic phrases, simplifying algebraic expressions and evaluating algebraic expressions.
Using the distributive property
Evaluating algebraic expressions
Exponent Rules and Properties
Practice with basic exponent rules
As the title says, these worksheets include only basic exponent rules questions. Each question only has two exponents to deal with; complicated mixed up terms and things that a more advanced student might work out are left alone. For example, 42 is (22)2 = 24, but these worksheets just leave it as 42, so students can focus on learning how to multiply and divide exponents more or less in isolation.
Linear Expressions & Equations
Linear equations worksheets including simplifying, graphing, evaluating and solving systems of linear equations.
Here is a recommended handout on translating English phrases into algebraic expressions. Please note that this is an external document found on Michael Bowen's Ventura College Start Page.
Translating algebraic phrases in words to algebraic expressions
Simplifying linear expressions (combining like terms)
Adding/Subtracting and Simplifying linear expressions
Rewriting linear equations
Determining linear equations from slopes, y-intercepts, and points
Graphing linear equations
Extracting information from linear equations graphs
You may have been intrigued by our comment above about solving linear equations with jelly beans. Here is how you might accomplish that. Ideally, you will want some opaque bags with no mass, but since that isn't quite possible (the no mass part), there is a bit of a condition here that will actually help students understand equations better. Any bags that you use have to be balanced on the other side of the equation with empty ones.
Probably the best way to illustrate this is through an example. Let's use 3x + 2 = 14. You may recognize the x as the unknown which is actually the number of jelly beans we put in each opaque bag. The 3 in the 3x means that we need three bags. It's best to fill the bags with the required number of jelly beans out of view of the students, so they actually have to solve the equation.
On one side of the two-pan balance, place the three bags with x jelly beans in each one and two loose jelly beans to represent the + 2 part of the equation. On the other side of the balance, place 14 jelly beans and three empty bags which you will note are required to "balance" the equation properly. Now comes the fun part... if students remove the two loose jelly beans from one side of the equation, things become unbalanced, so they need to remove two jelly beans from the other side of the balance to keep things even. Eating the jelly beans is optional. The goal is to isolate the bags on one side of the balance without any loose jelly beans while still balancing the equation.
The last step is to divide the loose jelly beans on one side of the equation into the same number of groups as there are bags. This will probably give you a good indication of how many jelly beans there are in each bag. If not, eat some and try again. Now, we realize this won't work for every linear equation as it is hard to have negative jelly beans, but it is another teaching strategy that you can use for algebra.
Solving linear equations
Despite all appearances, equations of the type a/x are not linear. Instead, they belong to a different kind of equations. They are good for combining them with linear equations, since they introduce the concept of valid and invalid answers for an equation (what will be later called the domain of a function). In this case, the invalid answers for equations in the form a/x, are those that make the denominator become 0.
Solving systems of linear equations
Solving systems of linear equations by graphing
Quadratic Expressions & Equations
Quadratic expressions and equations worksheets including multiplying factors, factoring, and solving quadratic equations.
Simplifying quadratic expressions (combining like terms)
Adding/Subtracting and Simplifying quadratic expressions
Multiplying factors of quadratic expressions
Factoring quadratic expressions
The factoring quadratic expressions worksheets below provide many practice questions for students to hone their factoring strategies. If you would rather worksheets with quadratic equations, please see the next section. These worksheets come in a variety of levels with the easier ones are at the beginning. The "a" coefficients referred to below are the coefficients of the x² term as in the general quadratic expression: ax² + bx + c.
Whether you use trial and error, completing the square or the general quadratic formula, these worksheets include a plethora of practice questions with answers. In the first section, the worksheets include questions where the quadratic expressions equal 0. This makes the process similar to factoring quadratic expressions, with the additional step of finding the values for x when the expression is equal to 0. In the second section, the expressions are generally equal to something other than x, so there is an additional step at the beginning to make the quadratic expression equal zero.
Solving Quadratic equations that Equal Zero (e.g. ax² + bx + c = 0)
Solving Quadratic equations that Equal an Integer (e.g. ax² + bx + c = d)
Other Polynomial and Monomial Expressions & Equations
Factoring non-quadratic expressions worksheets with various levels of complexity.
Simplifying polynomials that involve addition and subtraction
Simplifying polynomials that involve multiplication and division
Simplifying polynomials that involve addition, subtraction, multiplication and division
Factoring expressions that do not include a squared variable
Factoring expressions that always include a squared variable
Factoring expressions that sometimes include squared variables
Multiplying polynomials with two factors
Multiplying polynomials with three factors
Inequalities Including Graphs
Inequalities worksheets including writing the inequality that matches a graph and graphing inequalities on a number line.