Math Worksheets
 

 

Middle School Internet Sites (6-8)

Eighth Grade

1. Number & Operations (N)

2.  Algebra (A)

3. Geometry (G)

4. Data and Probability (D)

Strand 2. Algebra (A)

  1. Understand the Concept of Non-Linear Functions Using Basic Examples
  2. Understand and Represent Quadratic Functions
  3. Recognize, Represent, and Apply Common Formulas
  4. Understand Solutions and Solve Equations, Simultaneous Equations, and Linear Inequalities

2. Algebra (A)

Eighth Grade

Understand the Concept of Non-linear Functions Using Basic Examples

  1. A.RP.08.01 Identify and represent linear functions, quadratic functions, and other simple functions including inversely proportional relationships (y = k/x); cubics (y = ax3); roots (y = √x ); and exponentials (y = ax , a > 0); using tables, graphs, and equations.*
    1. Bouncing Tennis Balls
      This is a lesson plan that has the students graph information found by bouncing a tennis ball.  They will use this information to determine the dependant and independent variables.
    2. Discovering Growth Patterns
      A web activity comparing linear and exponential growth.
    3. Dot Patterns and Sierpinski Gasket
      This site allows you to generate the Sierpanski Triangle.  You can enlarge the triangle one row at a time allowing you to see the changes at each stage of the triangle.
    4. Doubling Pennies
      This site poses a question relating to the doubling of pennies as opposed to receiving a set amount of money. It then goes through the solution using charts and a formula. This site also contains links to similar problems. This is a student activity.
    5. Functions Made Easy
      Students will explore the concept of functions as relationships, as machines, s equations, and as graphs.  This is a teacher resource site.
    6. Graphing and the Coordinate Plane
      This lesson is designed to introduce students to graphing ordered pairs of numbers on the coordinate plane.  Students will be able to give the rise over run for slope.
    7. Linking Length, Perimeter, Area, and Volume
      This is a lesson plan where students will work with 2-dimensional rectangles to focus on the relationship between the scale factor and ratio of perimeters or area of similar figures.   Graphs are drawn for students to visualize the linear and non-linear relationships of perimeter, area, and scale factor .
    8. Math Dictionary
      9. Nice, easy, and quick to use interactive lesson on Exponents. Students can see the lesson and practice exponents. When page loads select E on bottom of page and look for exponents. It's easy and fun!
    9. Math Files - Grid Game
      This is an intereactive game for students. Students need to find multiples, factors, squares, cubes, roots, evens, odds, triangular numbers, etc., and that meet the given condition (such as: find the multiples of 10 that are also multiples of 20.)
    10. Mathline: The Yo-Yo Problem
      Students explore linear patterns, write a pattern in symbolic form, and solve linear equations using algebra tiles, symbolic manipulation and the graphing calculator.
    11. Pattern Blocks
      This site allows the students to create their own patterns by manipulating the pattern block shapes onto the graph. It also gives a definition of each shape if the student needs the reference. Teachers can choose what type of pattern they want students to create. Also a possibility of using it for fractions.
    12. Play Pool on Different Sized Pool Tables
      In this interactive activity students will predict which pocket the pool ball will go into as well as the number of hits needed to sink the ball. By changing variables they will see patterns and generalizations to aide them in their predictions. Data will be represented by a model as well as a spreadsheet and a graph.
    13. Rectangle Pattern Challenges
      This site explores patterns in rectangles and then has students organizing the data they find into a table.  Also has discussion questions at the end. Use as whole class instruction or print off for inividual use.
    14. Tic Tac Toe Squares
      This site allows the student to play a tic tac toe game that is based on powers of 2 & 3. If the student is incorrect in his/her answer, the game will explain what the exponent should look like. This site can also do roots as well. In the upper right hand corner is the word "harder", use that to get to the power and root based exercises.
    15. Waldo's Interactive Math
      16. This interactive site allows students to manipulate triangles on a coordinate graph in order to explore their relationship. The site relies on Java applets.
  2. A.PA.08.02 For basic functions, e.g., simple quadratics, direct and indirect variation, and population growth, describe how changes in one variable affect the others.
    1. Best Practices of Technology Integration
      Students will use the Internet to find a car they would like to buy if they were old enough.  They would then compute monthly payments and the total amount of interest paid on a typical auto loan.  This is a teacher resource.
    2. Determining Ratios
      This is an interactive site where students can reduce the given ration into lowest form.  The student receives immediate feedback to their answer.  If the solution is correct you move on to a different problem.  If the solution is incorrect the students are told why there answer is wrong.
    3. Discovering Growth Patterns
      A web activity comparing linear and exponential growth.
    4. Dot Patterns and Sierpinski Gasket
      This site allows you to generate the Sierpanski Triangle.  You can enlarge the triangle one row at a time allowing you to see the changes at each stage of the triangle.
    5. Doubling Pennies
      This site poses a question relating to the doubling of pennies as opposed to receiving a set amount of money. It then goes through the solution using charts and a formula. This site also contains links to similar problems. This is a student activity.
    6. Functions Made Easy
      Students will explore the concept of functions as relationships, as machines, s equations, and as graphs.  This is a teacher resource site.
    7. Learning about Rate of Change in Linear Functions Using Interactive Graphs: Constant Cost per Minute
      This site allows students to manipulate a graph representing constant cost/minute of a phone contract.  There is also a link to a graph where the rate changes after a certain period of time ($.50/min for the first hour, $.10/minute thereafter).
    8. Lesson Plans: How Big is That Star?
      9. This site gives a complete lesson plan for using ratios to determine the size of a star based on observation.
       
    9. One False Move
      This is a game where students find their way out of a haunted house by  decimals in order (either from least to most or most to least).  This includes positive and negative integers with one decimal place and varying levels of difficulty.
    10. Paper Pool Games-Number and Operations-Number Sense and Numeration
      This site allows the student to interact directly with the activity. It encourages students to challenge themselves to go beyond just looking at a simple pattern. It requires the students to look for ratios that are created from the multiples and factors of the numbers. Students will be working on beginning skills on gathering data and looking for patterns.
    11. Pattern Blocks
      This site allows the students to create their own patterns by manipulating the pattern block shapes onto the graph. It also gives a definition of each shape if the student needs the reference. Teachers can choose what type of pattern they want students to create. Also a possibility of using it for fractions.
    12. Play Pool on Different Sized Pool Tables
      In this interactive activity students will predict which pocket the pool ball will go into as well as the number of hits needed to sink the ball. By changing variables they will see patterns and generalizations to aide them in their predictions. Data will be represented by a model as well as a spreadsheet and a graph.
    13. Population Ratios
      This site is an interdisciplinary project (mathematics, social studies) where students choose a county in the United States and using ratios convert the statistics into meaningful numbers. Students access web sites and record various population statistics pertaining to a county in the USA of their choice. Students then use this data to set up and solve ratios. Students compare data to make meaning of the numbers.
    14. Proportion Basics
      15. This is an interactive lesson on proportion which includes a good explanation along with examples. Practice problems which can be done interactively with step by step help available if necessary.
    15. Ratios
      This is an interactive math site where students solve for ratios.  The students are given a ratio and one part (either the numerator or denominator) of another ratio.  The students then have to solve for the missing expression.  They are given immediate feedback to their answers.
    16. Rectangle Pattern Challenges
      This site explores patterns in rectangles and then has students organizing the data they find into a table.  Also has discussion questions at the end. Use as whole class instruction or print off for inividual use.
    17. Sports and Math: Will Women Ever Surpass Their Male Counterparts?
      Students interpret numerical and graphical data about athletic performance, derive equations, and make statistical predictions.
    18. The Hand Shake
      A data collection and analysis class experiment. Use a table to show the number of handshakes when every person in the room shakes hands with everyone else.
    19. The Hot Tub
      This lesson uses the depth of water in a hot tub at various points.  Students need to describe the water level with positive or negative slope and function of depth of water over time.
    20. Waldo's Interactive Math
      21. This interactive site allows students to manipulate triangles on a coordinate graph in order to explore their relationship. The site relies on Java applets.
  3. A.PA.08.03 Recognize basic functions in problem context, e.g., area of a circle is πr2, volume of a sphere is ?? πr3, and represent them using tables, graphs, and formulas.
    1. Bouncing Tennis Balls
      This is a lesson plan that has the students graph information found by bouncing a tennis ball.  They will use this information to determine the dependant and independent variables.
    2. Function Machine
      Students are able to enter a number to represent the variables and then determine what functionis taking place. The activity explains linear functions and allows the students to ask how, what, and why for solving the problem.
    3. Functions Made Easy
      Students will explore the concept of functions as relationships, as machines, s equations, and as graphs.  This is a teacher resource site.
    4. Graphing and the Coordinate Plane
      This lesson is designed to introduce students to graphing ordered pairs of numbers on the coordinate plane.  Students will be able to give the rise over run for slope.
    5. Linking Length, Perimeter, Area, and Volume
      This is a lesson plan where students will work with 2-dimensional rectangles to focus on the relationship between the scale factor and ratio of perimeters or area of similar figures.   Graphs are drawn for students to visualize the linear and non-linear relationships of perimeter, area, and scale factor .
    6. Mathline: The Yo-Yo Problem
      Students explore linear patterns, write a pattern in symbolic form, and solve linear equations using algebra tiles, symbolic manipulation and the graphing calculator.
  4. A.RP.08.04 Use the vertical line test to determine if a graph represents a function in one variable.
    1. Interactivate - Vertical Line Test New
      2. Learn about the vertical line test for functions by trying to connect points in the plane to build a function.
    2. Vertical Line Test New
      3. A test use to determine if a relation is a function. A relation is a function if there are no vertical lines that intersect the graph at more than one point.
       
    3. The Vertical Line Test for Functions New
      4. The vertical Line test is a wy to determine whether or not a relation is a function. The vertical line test simply states that if a vertical line intersects the relation's graph in more than one place, then the relation is a NOT a function.
       

Understand and Represent Quadratic Functions

  1. A.RP.08.05 Relate quadratic functions in factored form and vertex form to their graphs, and vice versa; in particular, note that solutions of a quadratic equation are the x-intercepts of the corresponding quadratic function.
      Function Evaluator and Grapher
      Use of this system is pretty intuitive. Enter your function f(x) in graphing calculator format (press the "example" button to see some examples). Then specify some values of x, and press "Evaluate". To see a graph, enter a range of x-values (Xmin and xMax) and press "Graph." The graph will appear in a little window called "Your Graph."
    1. Chapter 1 Linear & Quadratic Functions! New
      2. This section is a basic review of lines and points and their relationship to graphing.
    2. Math for Morons Like Us - quadratic functions New
      3. On this page, we hope to clear up problems you might have with quadratic functions. We discuss and give examples of how changes in the equation y = f(x) affect the graph of the function.
       
  2. A.RP.08.06 Graph factorable quadratic functions, finding where the graph intersects the x-axis and the coordinates of the vertex; use words “parabola” and “roots”; include functions in vertex form and those with leading coefficient –1, e.g., y = x2 – 36, y = (x – 2)2 – 9; y = – x2; y = – (x – 3)2.
    1. Quadratic Functions New
      2. Quadratic functions and the properties of their graphs such as vertex and x and y intercepts are explored interactively using applets.
    2. Math for Morons Like Us - quadratic functions New
      3. On this page, we hope to clear up problems you might have with quadratic functions. We discuss and give examples of how changes in the equation y = f(x) affect the graph of the function.

Recognize, Represent, and Apply Common Formulas

  1. A.FO.08.07 Recognize and apply the common formulas:
    (a + b)2 = a2 + 2 ab + b2
    (a – b)2 = a2 – 2 ab + b2
    (a + b) (a – b) = a2 – b2 ; represent geometrically.
    1. QUADRATICS Polynomials of the 2nd degree NewThis site has a number of lessons on solving Quadratic equations.
      2.  
  2. A.FO.08.08 Factor simple quadratic expressions with integer coefficients, e.g.,
    x2 + 6x + 9, x2 + 2x – 3, and x2 – 4; solve simple quadratic equations, e.g., x2 = 16 or x2 = 5 (by taking square roots); x2 – x – 6 = 0, x2 – 2x = 15 (by factoring); verify solutions by evaluation.
    1. Solving Quadratic Equations by Factoring New
      2. Slide Share has a slide show that teaches how to solve quadratic equations by using interger coefficients.
  3. A.FO.08.09 Solve applied problems involving simple quadratic equations.
    1. QUADRATICS Polynomials of the 2nd degree New
      2. This site has a number of lessons on solving Quadratic equations.
       

Understand Solutions and Solve Equations, Simultaneous Equations, and Linear Inequalities

  1. A.FO.08.10 Understand that to solve the equation f(x) = g(x) means to find all values of x for which the equation is true, e.g., determine whether a given value, or values from a given set, is a solution of an equation (0 is a solution of 3x2 + 2 = 4x + 2, but 1 is not a solution).
    1. Algebra Balance Scales
      2. This interactive site allows student to solve simple linear equations through the use of a balance beam. Unit blocks (representing 1s) and X-boxes (for the unknown, X), are placed on the pans of a balance beam.
       
    2. E-Lab Grade 8 Activity 5- Modeling Like Terms
      This site allows students to use pictorial representations of algebraic tiles to mode algebraic expressions by combining like terms. They may generate their own problems or use computer generated problems. A work page is also available for students to review and practice algebraic concepts using positive and negative terms.
    3. I want a credit card - or do I?
      Students will pretend to borrow $1000.00 on a credit card. They will pretend to make minimum payments for a year. When they're done, they will make a pie chart showing how much of their payments reduced their debt, and how much was interest. A student worksheet, resources, and lesson extensions are included. Students will be writing and solving one-step linear equations in one variable. This includes a teacher lesson plan and is a student activity.
    4. It's Your Life
      This is a 3-part lesson utilizing census data of the mean income of workers 18 years or older by education attainment levels. Students will analyze census data to create graphs and take part in a simulation using this same data as a starting point to make financial decisions and budgets. Internet census links, student worksheets, and a log/journal are available to use with this site. Part of student problem solving process will include solving problems by using the correct order of operations. This includes a teacher lesson plan and is a student activity.
    5. Math Files - Equation Match
      This is an interactive game for students. They must find two equations that have the same solution. It is similar to a game of "Concentration". (Warning to teachers: Students may need a few minutes to play with the long arm.)
    6. Mrs Glossers Math Goodies
      7. Interactive Site that reviews Writing Algebraic Equations. Students can read questions and pick Equations that will answer the question.
    7. Multimedia Math Glossary
      8. Outstanding! Gives students a visual along with the definition. Some examples are animated, but all examples have the word and the definition is read to them. Grades K-8
    8. Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond
      This investigation illustrates the use of iteration, recursion and algebra to model and analyze a changing fish population. Graphs, equations, tables, and technological tools are used to investigate the effect of varying parameters on the long-term population. Students will complete a numerical analysis, a graphical analysis, and a symbolic analysis from the data.
    9. Waldo's Interactive Math
      10. This interactive sites includes an activity allowing students to manipulate a number line in order to solve equations. Students may choose the difficulty of the equations they wish to solve. Some teacher direction may be needed initially although the directions are clear. This site uses JAVA applets.
    10. Virtual Manipulatives Algebra Tiles
      11. Virtual Manipulatives Algebra Tiles - interactive.
       
  2. A.FO.08.11 Solve simultaneous linear equations in two variables by graphing, by substitution, and by linear combination; estimate solutions using graphs; include examples with no solutions and infinitely many solutions.
    1. Algebra Balance Scales
      2. This interactive site allows student to solve simple linear equations through the use of a balance beam. Unit blocks (representing 1s) and X-boxes (for the unknown, X), are placed on the pans of a balance beam.
    2. E-Lab Grade 8 Activity 5- Modeling Like Terms
      This site allows students to use pictorial representations of algebraic tiles to mode algebraic expressions by combining like terms. They may generate their own problems or use computer generated problems. A work page is also available for students to review and practice algebraic concepts using positive and negative terms.
    3. It's Your Life
      This is a 3-part lesson utilizing census data of the mean income of workers 18 years or older by education attainment levels. Students will analyze census data to create graphs and take part in a simulation using this same data as a starting point to make financial decisions and budgets. Internet census links, student worksheets, and a log/journal are available to use with this site. Part of student problem solving process will include solving problems by using the correct order of operations. This includes a teacher lesson plan and is a student activity.
    4. Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond
      This investigation illustrates the use of iteration, recursion and algebra to model and analyze a changing fish population. Graphs, equations, tables, and technological tools are used to investigate the effect of varying parameters on the long-term population. Students will complete a numerical analysis, a graphical analysis, and a symbolic analysis from the data.
    5. Waldo's Interactive Math
      6. This interactive sites includes an activity allowing students to manipulate a number line in order to solve equations. Students may choose the difficulty of the equations they wish to solve. Some teacher direction may be needed initially although the directions are clear. This site uses JAVA applets.
    6. Virtual Manipulatives Algebra Tiles
      7. Virtual Manipulatives Algebra Tiles - interactive.
  3. A.FO.08.12 Solve linear inequalities in one and two variables, and graph the solution sets.
    1. Algebra Balance Scales
      2. This interactive site allows student to solve simple linear equations through the use of a balance beam. Unit blocks (representing 1s) and X-boxes (for the unknown, X), are placed on the pans of a balance beam.
       
    2. E-Lab Grade 8 Activity 5- Modeling Like Terms
      This site allows students to use pictorial representations of algebraic tiles to mode algebraic expressions by combining like terms. They may generate their own problems or use computer generated problems. A work page is also available for students to review and practice algebraic concepts using positive and negative terms.
    3. I want a credit card - or do I?
      Students will pretend to borrow $1000.00 on a credit card. They will pretend to make minimum payments for a year. When they're done, they will make a pie chart showing how much of their payments reduced their debt, and how much was interest. A student worksheet, resources, and lesson extensions are included. Students will be writing and solving one-step linear equations in one variable. This includes a teacher lesson plan and is a student activity.
    4. It's Your Life
      This is a 3-part lesson utilizing census data of the mean income of workers 18 years or older by education attainment levels. Students will analyze census data to create graphs and take part in a simulation using this same data as a starting point to make financial decisions and budgets. Internet census links, student worksheets, and a log/journal are available to use with this site. Part of student problem solving process will include solving problems by using the correct order of operations. This includes a teacher lesson plan and is a student activity.
    5. Math Files - Equation Match
      This is an interactive game for students. They must find two equations that have the same solution. It is similar to a game of "Concentration". (Warning to teachers: Students may need a few minutes to play with the long arm.)
    6. Mrs Glossers Math Goodies
      7. Interactive Site that reviews Writing Algebraic Equations. Students can read questions and pick Equations that will answer the question.
    7. Multimedia Math Glossary
      8. Outstanding! Gives students a visual along with the definition. Some examples are animated, but all examples have the word and the definition is read to them. Grades K-8
    8. Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond
      This investigation illustrates the use of iteration, recursion and algebra to model and analyze a changing fish population. Graphs, equations, tables, and technological tools are used to investigate the effect of varying parameters on the long-term population. Students will complete a numerical analysis, a graphical analysis, and a symbolic analysis from the data.
    9. Waldo's Interactive Math
      10. This interactive sites includes an activity allowing students to manipulate a number line in order to solve equations. Students may choose the difficulty of the equations they wish to solve. Some teacher direction may be needed initially although the directions are clear. This site uses JAVA applets.
    10. Virtual Manipulatives Algebra Tiles
      11. Virtual Manipulatives Algebra Tiles - interactive.
       
  4. A.FO.08.13 Set up and solve applied problems involving simultaneous linear equations and linear inequalities.
    1. Algebra Balance Scales
      2. This interactive site allows student to solve simple linear equations through the use of a balance beam. Unit blocks (representing 1s) and X-boxes (for the unknown, X), are placed on the pans of a balance beam.
    2. E-Lab Grade 8 Activity 5- Modeling Like Terms -
      This site allows students to use pictorial representations of algebraic tiles to mode algebraic expressions by combining like terms. They may generate their own problems or use computer generated problems. A work page is also available for students to review and practice algebraic concepts using positive and negative terms.
    3. It's Your Life
      This is a 3-part lesson utilizing census data of the mean income of workers 18 years or older by education attainment levels. Students will analyze census data to create graphs and take part in a simulation using this same data as a starting point to make financial decisions and budgets. Internet census links, student worksheets, and a log/journal are available to use with this site. Part of student problem solving process will include solving problems by using the correct order of operations. This includes a teacher lesson plan and is a student activity.
    4. Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond
      This investigation illustrates the use of iteration, recursion and algebra to model and analyze a changing fish population. Graphs, equations, tables, and technological tools are used to investigate the effect of varying parameters on the long-term population. Students will complete a numerical analysis, a graphical analysis, and a symbolic analysis from the data.
    5. Waldo's Interactive Math
      6. This interactive sites includes an activity allowing students to manipulate a number line in order to solve equations. Students may choose the difficulty of the equations they wish to solve. Some teacher direction may be needed initially although the directions are clear. This site uses JAVA applets.
    6. Virtual Manipulatives Algebra Tiles
      7. Virtual Manipulatives Algebra Tiles - interactive.

 

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