6th Grade

Welcome to our Expressions and Equations 6th Grade Worksheets.

Here you will find a range of algebra worksheets to help you learn about basic algebra, including generating and calculating algebraic expressions and solving simple equations.

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Want to gain a basic understanding of algebra?

Looking for some simple algebra worksheets?

Do you need a bank of useful algebra resources?

Look no further! The pages you need are below!

Here is our selection of basic algebra sheets to try.

We have split the worksheets up into 3 different sections:

- Generate the algebra - and write your own algebraic expressions;
- Calculate the algebra - work out the value of different expressions;
- Solve the algebra - find the value of the term in the equation.
- Mixed questions involving all 3 of the above.

By splitting the algebra up into sections, you only need to concentrate on one aspect at a time!

Each question sheet comes with its own separate answer sheet.

Want to test yourself to see how well you have understood this skill?.

- Try our NEW quick quiz at the bottom of this page.

What is an algebraic expression?

An expression is a mathematical statement where variables and operations are combined.

Examples

- 2a + 5 is an expression involving the variable a
- 5(y
^{2}- 6) is another expression

What is an algebraic equation?

An equation is where an algebraic expression is equal to something, which might be a number, or another algebraic expression.

Examples

- 2a + 5 = 7 is an equation
- 5(y
^{2}- 6) = 3y + 8 is another equation

How to Generate an Expression

When we are generating an expression, we are taking a rule and turning it into algebra.

Examples

- Subtract 6 from n could be written as n - 6.
- Multiply d by 4 could be written as d x 4 or 4d.
- Add 5 to p and then double the result is written as (p + 5) x 2 or 2(p + 5)

How to Calculate an Expression

When we are calculating the value of an expression, we work out the value of the expression when we give a value to the variable.

Examples

- p + 5 has a value of 11 when p = 6 because 6 + 5 = 11
- 4 - q has a value of 1 ½ when q = 2 ½ because 4 - 2 ½ = 1 ½
- 4(n - 2) has a value of 32 when n = 10 because 4 x (10 - 2) = 4 x 8 = 32
- 4(n - 2) has a value of -8 when n = 0 because 4 x (0 - 2) = 4 x (-2) = -8

How to Solve a Simple Equation

When we are solving an equation, we are finding out the value(s) of the variable in the equation.

Examples

- If p + 5 = 9
- then p = 4 because 4 + 5 = 9
- Answer: p = 4

- If 7n = 56
- then n = 56 ÷ 7 = 8
- Answer: n = 8

- If 12 - f = 8
- means that f = 4 because 12 - 4 = 8
- Answer: f = 4

- If 0.6t = 3
- then t = 5 because 0.6 x 5 = 3
- Answer: t = 5

- If ½ r = 16
- then r = 32 because ½ x 32 = 16
- Answer: r = 32

These questions involve solving equations, working out the value of expressions and also generating expressions.

They are a combination of questions from all the above categories.

This short video walkthrough shows several problems from our Expressions and Equations Mixed Questions Worksheet 6:1 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, please check out the video below!

Take a look at some more of our worksheets similar to these.

The sheets on this page have been designed to factorize and expand a range of simple expressions using the distributive property..

We have a selection of basic algebra worksheets which are aimed at 6th and 7th graders and involve similar skills to the sheets here.

The Mathway Calculator is a great way to solve algebra problems that you can type into a calculator.

Try using this online calculator tool to solve one of your problems and watch it work!

There are a range of calculators to choose from to meet your needs.

The Mathway problem solver will answer your problem instantly and also give you a link to view each of the steps needed.

If you choose to 'View the steps' you will be directed to the Mathway website where you will be able to see in more detail each of the steps needed to solve the problem. Please note that Mathway may charge you a small fee for this!

Are you stuck on a quadratic equation and don't know what to do?

Are you looking for some worksheets on factorising quadratic equations to print out?

Take a look at our support pages on quadratic equations where you will hopefully find what you are looking for.

If you are looking for a fun printable algebra game to play then try out our algebra game page.

You will find a range of algebra games that make learning algebra fun and non-threatening.

The only equipment you need is a scientific calculator, some dice, and a few counters!

The sheets in this section involve using parentheses and exponents in simple calculations.

There are also lots of worksheets designed to practice and learn about PEMDAS.

Using these worksheets will help your child to:

- know and understand how parentheses works;
- understand how exponents work in simple calculations.
- understand and use PEMDAS to solve a range of problems.

This interactive equality explorer has been produced by PhET Interactive Simulations at the University of Colorado.

It is a useful tool for exploring different ideas including negative numbers and algebra equations and equality.

Probably the most useful part of the app is to use the 'Solve It' section once you are confident how it works.

You can then select your level of difficulty and start solving some algebraic equations by getting your variables onto one side of the equation and the numerical values on the other, and then multiplying or dividing the equation until you find the value of the required variable.

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

For more information on the information we collect, please take a look at our Privacy Policy

We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick expressions and equations 6th grade quiz tests your knowledge and skill at generating and calculating expressions, as well as solving equations.

How to Print or Save these sheets

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How to Print or Save these sheets

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Follow these 3 easy steps to get your worksheets printed out perfectly!

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The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

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We have updated and improved our fraction calculators to show you how to solve your fraction problems step-by-step!

Take a look and try them out!

Have a look at some of our most popular pages to see different Math activities and ideas you could use with your child

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- List of Geometric Shapes
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- Perimeter Worksheets

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