Algebra Worksheets

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.

Most Popular Algebra Worksheets this Week

Properties and Laws of Numbers Worksheets

The Commutative Law

The commutative law or commutative property states that you can change the order of the numbers in an arithmetic problem and still get the same results. In the context of arithmetic, it only works with addition or multiplication operations, but not mixed addition and multiplication. For example, 3 + 5 = 5 + 3 and 9 × 5 = 5 × 9. A fun activity that you can use in the classroom is to brainstorm non-numerical things from everyday life that are commutative and noncommutative. Putting on socks, for example, is commutative because you can put on the right sock then the left sock or you can put on the left sock then the right sock and you will end up with the same result. Putting on underwear and pants, however, is noncommutative.

The Associative Law

The associative law or associative property allows you to change the grouping of the operations in an arithmetic problem with two or more steps without changing the result. The order of the numbers stays the same in the associative law. As with the commutative law, it applies to addition-only or multiplication-only problems. It is best thought of in the context of order of operations as it requires that parentheses must be dealt with first. An example of the associative law is: (9 + 5) + 6 = 9 + (5 + 6). In this case, it doesn't matter if you add 9 + 5 first or 5 + 6 first, you will end up with the same result. Students might think of some examples from their experience such as putting items on a tray at lunch. They could put the milk and vegetables on their tray first then the sandwich or they could start with the vegetables and sandwich then put on the milk. If their tray looks the same both times, they will have modeled the associative law. Reading a book could be argued as either associative or nonassociative as one could potentially read the final chapters first and still understand the book as well as someone who read the book the normal way.

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.

Algebraic Expressions Worksheets

Using the distributive property

The distributive property is an important skill to have in algebra. In simple terms, it means that you can split one of the factors in multiplication into addends, multiply each addend separately, add the results, and you will end up with the same answer. It is also useful in mental math, and example of which should help illustrate the definition. Consider the question, 35 × 12. Splitting the 12 into 10 + 2 gives us an opportunity to complete the question mentally using the distributive property. First multiply 35 × 10 to get 350. Second, multiply 35 × 2 to get 70. Lastly, add 350 + 70 to get 420. In algebra, the distributive property becomes useful in cases where one cannot easily add the other factor before multiplying. For example, in the expression, 3(x + 5), x + 5 cannot be added without knowing the value of x. Instead, the distributive property can be used to multiply 3 × x and 3 × 5 to get 3x + 15.

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.

Translating algebraic phrases in words to algebraic expressions

Knowing the language of algebra can help to extract meaning from word problems and to situations outside of school. In these worksheets, students are challenged to convert phrases into algebraic expressions.

Solving linear equations with jelly beans is a fun activity to try with students first learning algebraic concepts. 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.

Linear Systems

Quadratic Expressions & Equations

Quadratic expressions and equations worksheets including multiplying factors, factoring, and solving quadratic equations.

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.

Other Polynomial and Monomial Expressions & Equations

Factoring non-quadratic expressions worksheets with various levels of complexity.

Inequalities Including Graphs

Inequalities worksheets including writing the inequality that matches a graph and graphing inequalities on a number line.

Writing the inequality that matches the graph

Graphing inequalities on number lines

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