# Algebra - Worksheets

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## Classifying Numbers - Level 2

This two-page worksheet covers real numbers. Students learn about rational and irrational numbers, and answer problems related to each set.

Key concept: Students know the difference between rational and irrational numbers, and understand patterns and structure.

## Understanding Data - Level 1

This one page worksheet introduces tables and graphs. Students need to finish a frequency table and histogram and use the information to answer a question.

Key concept: Students need to be able to create and understand tables and graphs and use the information to clarify data.

## Understanding Data - Level 2

This one page worksheet continues tables and graphs. Students fill in the frequency table and histogram and use the information to answer a question.

Key concept: Students need to be able to create and understand tables and graphs and use the information to clarify data.

## Understanding Data - Level 3

This one page worksheet covers tables and graphs. Students create a frequency table and histogram and use the information to answer questions.

Key concept: Students need to be able to create and understand tables and graphs and use the information to clarify data. They should also be able to recognize whether the data is important, related to the topic, and if it is a good resource to make decisions, especially when dealing with samples.

## Numerical and Verbal ExpressionsLevel 1

This one page worksheet introduces numerical and verbal expressions. It explains what are constants and expressions, and why expressions are important in mathematics.

Key concept: Students need to be able to express information into a mathematical problem and solution.

## Algebraic and Verbal ExpressionsLevel 1

This one page worksheet introduces algebraic and verbal expressions. It explains what are constants, variables, expressions, and why expressions are important in mathematics.

Key concept: Expressing information into a mathematical expression and solution, and understanding expressions is the key to algebra. An equation is two expressions that are the same.

## Order of Operations - Level 1

This two page worksheet introduces the Order of Operations. It covers multiplication and division, and addition and subtraction.

Helpful idea: Use an example like, 3 + 2 x 4, and solve it two different ways to show why we need the Order of Operations. If we do not use it our answers will vary.

## Order of Operations - Level 2

These one page worksheets cover the Order of Operations. They cover parentheses, multiplication and division, and addition and subtraction. There are two different versions.

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## Order of Operations - Level 2Free Sample Version

This three page worksheet covers the Order of Operations. It covers parentheses, multiplication and division, and addition and subtraction.

Student Misunderstanding: Multiplication does not come before division every time, and addition does not come before subtraction every time. They are considered equal in the Order of Operations, and we read from left to right.

## Order of Operations - Level 3

These one page worksheets cover the Order of Operations. They cover parentheses, exponents, multiplication and division, and addition and subtraction. There are two different versions.

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## Answer, Find, and ShadeOrder of Operations - Level 2

Students use the Order of Operations to solve expressions and shade in a picture. This art page is great for special occasions like Mother's Day, birthday, or thank you note.

Teacher misunderstanding: Many teachers like to use the phrase, "Please Excuse My Dear Aunt Sally," to help students remember the Order of Operations. This is helpful, but many students then think that multiplication comes before division and addition comes before subtraction.

## Answer, Find, and ShadeIntegers and Order of OperationsLevel 2

This one page art HALLOWEEN worksheet reviews integers and order of operations.

Key concept: Understanding positive and negative numbers and the order of operations.

## The Distributive Property of Multiplication Video

This video covers The Distributive Property of Multiplication. There are three different levels of worksheets to go with the video. Level 1 covers only addition, level 2 covers addition and subtraction, and level 3 covers algebraic expressions. Each worksheet includes basic practice and an Answer, Find, and Shade Activity, which can be used separately.

NOTE: The video link will take you to YouTube, where it is being hosted.

Video      The Distributive Property of Multiplication

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## The Distributive Property of Multiplication

These one page worksheets review the distributive property of multiplication. Each worksheet includes basic practice and an Answer, Find, and Shade Activity.

Important note: These handouts are designed to go with a Distributive Property of Multiplication Video which is currently located on VIMEO, but can also be used alone.

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## Multiplying Larger NumbersUsing the Distributive PropertyLevel 1

This one page worksheet uses the Distributive Property to multiply larger numbers.

Key concept: Students should know that a number can be taken apart and operations can be changed to create an easier problem that produces the same answer.

## The Distributive Propertyof MultiplicationWord Problems - Level 2

This one page worksheet uses the distributive property of multiplication to solve word problems.

Key concept: Students should know how to use the distributive property to help solve multiplication problems quicker.

These one page, art worksheets review the distributive property. Level one has students fill in the blanks, and level 2 and 3 has them solve equations. The drawing is the same but the questions are different for each level.

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## Associative Property - Level 2

This one page worksheet covers the associative property. It explains how we can change groups (move parentheses) in a problem to simplify it. Includes variables.

Key concept: Students need to understand that the order does not matter when adding or multiplying. Numbers and groups can be moved to help us simplify a problem or make it easier to solve.

## Simplifying Expressions - Level 1

This one page worksheet covers simplifying expressions. Students need to combine like terms using basic arithmetic and the associative, commutative, and distributive properties.

Student misunderstanding: To combine terms they need to have the same variable or no variable at all (constant).

## Simplifying Expressions - Level 2

This one page worksheet continues simplifying expressions. Students need to combine like terms using basic arithmetic and the associative, commutative, and distributive properties. It includes using the distributive property with fractions.

Student misunderstanding: If terms differ in at least one variable, then they are unlike terms and cannot be combined.

## Simplifying Expressions - Level 3

This one page worksheet finishes simplifying expressions. It includes using the distributive property with fractions and multiple variable and square terms. Students need to combine like terms using basic arithmetic and the associative, commutative, and distributive properties.

Student misunderstanding: After simplifying fractions don't forget to distribute any negative signs or numbers.

## Answer, Find, and ShadeThe Three Basic PropertiesLevel 2

These one page worksheets have students use the distributive, associative, and commutative properties to simplify expressions. The drawing is the same but the shading and questions are different for each worksheet.

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## Answer, Find, and ShadeArithmetic with Rational NumbersLevel 2

This one page art worksheet reviews arithmetic with rational numbers, positive and negative integers, fractions, and decimals.

Key concept: Students need to know and review their basics to progress through higher math.

## Exponents - Level 1

This one page worksheet covers basic exponents. It includes a short help section to help students better understand exponents.

Student misunderstanding: Students need to know that a number to the second power is the same as calling it squared and a number to the third power is the same as calling it cubed.

## Squares and Square Roots - Level 1

This one page worksheet introduces squaring a number and taking the square root of a number. All the square roots are perfect squares.

Key concept: Students need to be able to calculate perfect squares to help with estimating square roots of irrational numbers.

## Answer, Find, and Shade - Level 1Squares and Square Roots

This one page art worksheet reviews squares and square roots. The square roots are perfect squares so students will not have to estimate and no irrational numbers will be left over. Watch out for the decimals.

## Estimating Square Roots - Level 1

This one page worksheet introduces estimating squaring roots of irrational numbers (not perfect squares). Students estimate the square root to the nearest whole number.

Key concept: Students need to be able to estimate square roots of irrational numbers and know perfect squares.

## Absolute Value and Number LinesLevel 1

This one page worksheet introduces absolute value and reviews number lines. It explains what is the absolute value of a number and includes problems with number lines, greater than and less than, and solving simple expressions.

Student misunderstanding: The absolute value of a number is always positive not its opposite.
Example: | 3 | = 3 not -3.

## Stained GlassUnit Rate - Level 2

This art worksheet is a new idea we call Stained Glass. The picture is symmetrical and students choose their own colors to create a unique art project. The worksheet covers unit rate and students answer the problems, find the numbers in the picture, and color the shapes based on the colors they chose.

Key concept: Understand that rate is a measure of one quantity per unit value of another quantity.

## Input - Output Tables

These one page worksheets cover input-output tables. Students need to find the rules and complete the tables. Input-output tables help students recognize patterns and build a relationship between lines and equations. There is a different worksheet for each level.

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## Variable Puzzles - Level 1

These one page worksheets use puzzles to help kids practice their algebra skills. Students are given five variables (letters) and have to find what numbers they represent. They are given equations as clues and a grid to help solve the unknown variables. This can also be used to practice the process of elimination for test taking skills.

Upper level: Use their knowledge of algebra to solve for a variable and substitute it into another equation.

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## Substitution - Level 1

This two page worksheet introduces substitution. It has one page for addition and subtraction, and one page for multiplication and division.

Student misunderstanding: If v = 3 and z = 5, and students were given an expression: 4vz, most would think this means 435 instead of 4 x 3 x 5.

## Substitution - Level 2

These one page worksheets continue substitution. They cover basic arithmetic and alternative ways of showing multiplication and division.

Key concept: Letters (variables) can be used to represent numbers and they're interchangeable.

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## Substitution - Level 3

These one page worksheets finish up substitution. Students substitute numbers for variables to solve expressions.

Key concept: After substituting students use the Order of Operations to solve the expressions.

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## Substitution Puzzle - Level 2

This one page worksheet has students determine the value of three shapes and then substitute the values into expressions. It also reviews the order of operations.

Key concept: Students need to understand they can substitute numbers and variables into equations and expressions.

## Answer, Find, and Color - Level 1Fill in the Blank

This free winter holiday, one page art worksheet reviews basic order of operations by having students fill in the blanks to complete various equations.

Help idea: Allow students to choose their own colors so the art work becomes more personal and unique. Just shade in lightly.

## Answer, Find, and ShadeFill in the Blanks

These one page art worksheets use fill in the blank questions to review order of operations and solving equations. The drawing is the same but the questions are different for each level.

Helpful idea: Use the picture to help students see patterns. If they do the worksheet incorrectly than the shape will not look correct.

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## Answer, Find, and Shade - Level 1Substitution

This one page art worksheet reviews substitution, order of operations, and basic algebra. Students substitute the values into the expressions and solve.

Student misunderstanding:
1. Variables next to each other or a number next to
a variable is the same as multiplication.
For Example: abc = a x b x c or 2h = 2 x h

## Answer, Find, and Shade - Level 2Substitution

This one page art worksheet reviews substitution, order of operations, and basic algebra. Students substitute the values into the expressions and solve.

Student misunderstanding:
1. Variables next to each other mean multiplication.
For Example: abc = a x b x c
2. Be careful replacing the decimal after multiplying.
For Example: 0.6 x 0.6 = 0.36, but 0.6 x 6 = 3.6

## Answer, Find, and Shade - Level 3Substitution

This one page art worksheet reviews substitution, order of operations, and basic algebra. Students substitute the values into the expressions and solve.

Student misunderstanding: Variables next to each other mean multiplication.
For Example: abc = a x b x c.

## Answer, Find, and ShadeImportant Equations You Should Know

These one page art worksheets review solving equations, substitution, charts, and learning real world equations. Students are given a chart and must fill in the empty spaces. Level one and two include equations to help students, but the level 3 worksheet makes students research or use prior knowledge.

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## Solving One-Step Equations - Level 1Addition / Subtraction

This three page worksheet covers basic one step equations using the opposite operation method.

Student misunderstanding: Equals means the same, and we can alter an equation as long as we do the exact same thing to both sides.

## Solving One-Step Equations - Level 1Multiplication / Division

This two page worksheet covers basic one step equations using the opposite operation method.

Student misunderstanding: Equals means the same, and we can alter an equation as long as we do the exact same thing to both sides. Also, as problems become more complex students loose track of the negative signs.

## Solving One-Step EquationsLevel 2

This one page HALLOWEEN worksheet is a basic algebra practice page. Students use addition, subtraction, multiplication, and division to solve one step equations. After they answer the problems they shade in the corresponding shapes to create a scary picture.

Key concept: Solving variables and basic equations.

## One-Step EquationsLevel 2

This one page WINTER HOLIDAY worksheet covers solving one-step equations. It includes addition, subtraction, multiplication, and division. Students answer the problems and then shade in the corresponding shapes to create a picture.

## Answer, Find, and ShadeWord Sentences and Variables

These one page Halloween worksheets review verbal sentences and variables. Students read the sentences (equations) and find the missing number. The drawing is the same but the questions are different for each level.

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## Solving One-Step Equations - Level 1Add, Subtract with Decimals

This one page worksheet covers solving one-step equations with addition and subtraction of decimals. It does not have any negative variables.

Student misunderstanding: Whatever you do to one side of an equation you have to do to the other to keep them equal.

## Solving One-Step Equations - Level 1Multiply, Divide with Decimals

This one page worksheet covers solving one-step equations with multiplication and division of decimals. It does not have any negative variables or variables as the divisor.

Student misunderstanding: 4 x h is the same as 4h and b ÷ 4 is the same as b/4.

## Two-Step Fill in the Blanks

These one page art worksheets cover solving two-step equations. They help students visualize the process which should lead to solving equations faster.

Helpful idea: If students are confused change the blanks to a variable and solve the equation.

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## Two-Step Equations

These one page worksheets cover solving two-step equations. They include examples and review questions. Students perform operations to get the variable alone on one side of the equation.

Student misunderstanding: What to move first. Doing the Order of Operations backwards is a helpful guide.

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## Percent of a Number - Level 1

This two page worksheet begins the process of finding the percent of a number and what percent a number is of another number.

Key concept: Finding the percent of a number involves multiplication, but if you look at what percent a number is of another number you will notice it is backwards or in the opposite direction, which means division instead of multiplication

## Percent of a Number - Level 2

This two page worksheet continues finding the percent of a number and what percent a number is of another number. Students should be able to multiply and divide decimals.

Student misunderstanding: When changing a percent to a decimal or changing a decimal to a percent the decimal is ALWAYS moved two spaces.

## Percent of a Number - Level 3

This two page worksheet finishes finding the percent of a number and what percent a number is of another number.

Key concepts: Know how to change a percent to decimal and vise versa. Know how to multiply and divide decimals. Understand the relationship of 25%, 50%, 75%, and 100% to simple division (quarter, half, one).

## Answer, Find, and Shade (2 in 1)Percent of a Number

These one page art worksheets have two pictures hidden inside. Students need to use their knowledge of percent of numbers to solve various equations. Examples: 42.5% of 59 = ?, ? % of 85 = 10, or 40% of ? = 81. They must answer all the questions but for the shading students have the option to only shade in the odd numbered or even numbered problems to get one of the two different pictures.

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## Answer, Find, and ShadePercent of a Number - Level 3

These one page, art worksheets review percent of a number. Students need to find the percent of a number, what percent one number is of another, and find the original number when a percent is given.

Helpful idea: The two versions have the same questions, but in slightly different order and the pictures have been altered. Give half the class one version and the rest the other.

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## Answer, Find, and ShadePercent of Change

These one page art worksheets review percent of change. Students are given an original and new number and must figure out if the change is an increase or decrease and then calculate the percent of change. After solving, students find the answers in the picture and shade in the corresponding shapes.

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## Combining Like Terms ArtLevel 1

This one page art worksheet has students practice combining like terms. It includes using the Distributive Property to simplify the expressions.

Student misunderstanding: Even though a part of an expression or equation is surrounded by parenthesis, it can still be pulled apart using the Distributive Property. For example: 3(y + 4) = 3y + 12.

## Answer, Find, and ColorMulti-Step Equations

These one page art worksheets review multi-step equations. Level one includes combining like terms, Level two includes The Distributive Property, and Level three includes fractions.

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## Answer, Find, and ShadeMulti-Step Equations - Level 3

This one page art worksheet reviews solving equations. Students answer the problems, and then find and shade in the area that matches each answer.

Key concept: Understanding that we can change equations or "move numbers and variables" as long as we do the same to both sides.

## Answer, Find, and ColorFunctions

These one page Scary Halloween art worksheets review solving functions. Students need to substitute the given number into the function and solve. The picture and answers are the same but the problems are different for each level.

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## Multiplying Two Binomials (FOIL)Level 1

This two page worksheet introduces multiplying two binomials using the FOIL method. It uses the distributive property to help explain the process.

Key concept: The FOIL method helps keep Students organized when multiplying two binomials. FOIL stands for First-Outer-Inner-Last.

## Answer, Find, and ShadeSolving Inequalities - Level 2

This one page, art worksheet reviews solving inequalities. Students solve two inequalities and find the answer they have in common.

Student misunderstanding: Multiplying or dividing each side of an inequality by a negative number reverses the inequality sign. To prove this have students check their answers.

These one page art worksheets review proportions. Students find the missing value in each proportion. The drawing is the same but the questions are different for each level.

Helpful idea: The pattern is seen best from a distance.

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## Introduction to Coordinates - Video3

This is our third video and it covers coordinates. The video is meant to be used as an introduction or review video. It introduces coordinates and graphing, and how it is used in the real world. Use the handout as an additional resource for students while they watch the video.

NOTE: The video link below will take you to VIMEO. It is a website where the video is being hosted.

Video      Introduction to Coordinates

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## Graphing Linear Equations

These one page worksheets cover graphing linear equations. Students find points for each equation and graph the line on the given grid. There is a different worksheet for each level.

Key concept: Equations can describe real world objects like simple lines.

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## Finding the Slope from Two Points

These one page, help pages introduce the slope of a line and how to calculate the slope from two points.

Student misunderstanding: What goes on top? The ratio is rise-over-run or the change in y over the change in x.

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## Answer, Find, and ShadeFinding the Slope - Level 3

This one page, art worksheet reviews finding the slope from two points. Students calculate the slope using the change in x and y.

Helpful idea: When subtracting the coordinates, change the second point to its opposite.
Example: Given two points: (3 , 4);(2 , -2) - subtract
( 3 ,   4)
(-2 , +2) opposite of the numbers
( 1 ,   6) , answer: slope is 6.

## Pythagorean Theorem Video - All Levels

This video covers the pythagorean theorem. It explains what the theorem is and how it can be used. The video includes examples and additional review to help students better understand the theorem and how to use it in everyday life. In the Geometry Worksheets section there are four different handouts that can be used as additional resources for students while they watch the video.

NOTE: The video link below will take you to VIMEO. It is a website where the video is being hosted.

Pythagorean Theorem Video

## Introduction - Pythagorean TheoremAll Levels

This one page worksheet introduces the Pythagorean Theorem. Students should already know the square and square root of a number, solving basic equations, and triangles.

Key concept: It is a very important theorem in the real world. It is used in construction, drafting, measuring distance, calculating the height of large objects, etc. etc.

## Pythagorean Theorem - Level 1

This one page worksheet introduces the Pythagorean Theorem. Students should already know the square and square root of a number, solving basic equations, and triangles.

Key concept: It is a very important theorem in the real world. It is used in construction, drafting, measuring distance, calculating the height of large objects, etc. etc.

## Pythagorean Theorem - Level 2

This one page worksheet continues the Pythagorean Theorem. Students should already know the square and square root of rational and irrational numbers, solving basic equations, and triangles.

Help: If students do not know how to estimate irrational numbers (squares of not perfect squares) have them review Estimating Square Roots.

## Pythagorean Theorem - Level 3

This one page worksheet continues the Pythagorean Theorem. Students should already know the square and square root of rational and irrational numbers, solving basic equations, and triangles. Some of the problems have students using the theorem to find a missing side on a non-triangular shape.

Student misunderstanding: Some of the problems are not triangles but they need to use prior knowledge and the Pythagorean Theorem to solve.

## Intro to Distance of Line SegmentsLevel 1

This one page worksheet introduces finding the distance of a line segment using a graph. It uses the Pythagorean Theorem to help students better understand how to find the distance.

Prior Knowledge: Students should already know the Pythagorean Theorem which will lead into the Distance Formula.

## Distance Formula - Level 2

This one page worksheet covers the Distance Formula. Students are given two coordinates and a line segment and need to find the distance. Even though students can use the Pythagorean Theorem, they also need to understand and use the Distance Formula.

Key concept: Students should be able to use their prior knowledge of the Pythagorean Theorem to understand the Distance Formula.

## Distance of a Line Segment - Level 3

This one page worksheet allows students to use the Distance Formula or the Pythagorean Theorem to find the distance of a line segment. The problems include line segments on graphs and two coordinates with no graph.

Key concept: Students should be able to find the distance of a line segment, and understand the relationship between the Pythagorean Theorem and the Distance Formula.

## Answer, Find, and Shade - Level 3Distance of a Line Segment

This one page art worksheet reviews finding the distance of a line segment. Students will need to know the Distance Formula, but also can use the Pythagorean Theorem on most of the problems. The problems include line segments on graphs and two coordinates with no graph.

## Answer, Find, and ShadeDistance FormulaLevel 3

This one page art worksheet reviews the distance formula. Students find the distance between two points. All answers are rational numbers. This worksheet can also be used during Halloween.

Helpful idea: Students should be allowed to use a calculator.

## Introduction to Finding the MidpointLevel 1

This one page worksheet introduces the concept of midpoint and how to find it. It only covers basic number lines.

Prior knowledge: Students should already know how to find the average of a group of numbers. The midpoint formula is actually the same as finding the average of two numbers.

## Finding the MidpointLevel 2

This one page worksheet continues the concept of finding the midpoint and how to find it. It covers two-dimensional graphs.

Prior knowledge: Students should already know how to plot points on an x-axis and y-axis and be able to find the average of a group of numbers.