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8th Grade Mathematics Skills for Texas

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Standards listed on this page are from Texas Mathematics Knowledge & Skills - 8th Grade

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| Number, operation, and quantitative reasoning | Patterns, relationships, and algebraic thinking | Geometry and spatial reasoning |
| Measurement | Probability and statistics | Underlying processes and mathematical tools |

Page last edited 5/8/2009
Return to Grade Level Skills

A resource for the teacher to use in planning their lessons site for teachers | A PowerPoint show related to this standard PowerPoint show | An Adobe Acrobat document in .pdf format Acrobat document | A Microsoft Word document to be downloaded Word document | This interactive site would work well on an interactive whiteboard whiteboard resource | This resource includes voice instructions for students sound | A video is available through this link video format | This site is interactive and allows students to play a game or input or collect data interactive lesson | This site includes questions for your students to check their understanding a quiz | A lesson plan can be found at this site lesson plan | This link includes something for the teacher to print to print
(Texas Essential Knowledge and Skills)
Internet Resources
Number, Operations & Quantitave Reasoning
8.1 | 8.2

(8.1)   The student understands that different forms of numbers are appropriate for different situations.

(A)  compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals

  1. Compare and Order Numbers - explanation, examples and interactive applets
  2. Comparing Exponential Expressions - select, <, >, or = This site includes questions for your students to check their understanding
  3. Comparing Integers - Comparing integers with absolute values - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  4. Comparing two numbers on a number line from Web Math. Learn how to compare two numbers using a number line. Type each number into the boxes provided, then click "Show Me!" This site is interactive and allows students to play a game or input or collect data
  5. A resource for the teacher to use in planning their lessonsComparing Values - Create your own math facts worksheets for comparing values. Problems can include calculations using positive and negative numbers, and two-digit decimal values.
  6. Greater, Less Than, or the Same - Compare these decimals - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  7. Line Jumper - Click on the number line at the correct answer.
  8. MathDrill lets your students practice <, >, or =. This site is interactive and allows students to play a game or input or collect data
  9. Number Line Bounce - Instructions on how to play are included at the top of the window. This site is interactive and allows students to play a game or input or collect data
  10. Number Line: Comparing and Ordering Integers - practice with an Interactive Adventure with Deep Sea Carl - Carl is diving in the Great Barrier Reef off the coast of Australia. These waters are shark infested. Keep Carl safe by determining how many feet below sea level Jaws Daddy is. This site is interactive and allows students to play a game or input or collect data
  11. Rational Numbers on a Number Line - [designed for 6th grade]
    1. Practice problems to go with the lesson This site includes questions for your students to check their understanding
  12. A resource for the teacher to use in planning their lessonsRational Numbers on a Number Line - a 1 page document from Glencoe Publishers; with explanation, examples, and practice problems An Adobe Acrobat document in .pdf format This link includes something for the teacher to print
  13. A resource for the teacher to use in planning their lessonsRational Numbers on a Number Line - a 13 page document with examples and sample problems An Adobe Acrobat document in .pdf format This link includes something for the teacher to print
  14. A PowerPoint show related to this standardRational Numbers on a Number Line - a 22 slide PowerPoint show with good sample questions
  15. Review Rules for Working with Rational Numbers - two interactive sections are provided, look for the blue blocks This site is interactive and allows students to play a game or input or collect data
  16. Visualizing Numbers on an Interactive Number Line - instructions for using this activity are included This site is interactive and allows students to play a game or input or collect data
(B)  select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships
  1. All About Ratios - a Quiz This site includes questions for your students to check their understanding
  2. All About Ratios - links to several lessons by Cynthia Lanius A lesson plan can be found at this site
  3. All About Ratios: (Problem Solving) - A famous Texas chef has a secret recipe for her chili. When people ask her for it, she hands them a card with the complete recipe except for 1 detail. For the missing detail, she gives them a clue. Use ratios to discover the missing ingredient.
  4. Comparing Ratios and Rates - online quiz This site includes questions for your students to check their understanding
  5. Determine the number based on the ratio - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  6. Determining the Ratio - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  7. Figure This: Math Challenge for Families - proportional reasoning
  8. The Importance of Ratios and Proportions - this comes under the heading of a perfect answer to "Why do I have to learn this?" - how a stock market trader benefits from ratio and proportion
  9. Interpreting and Applying Proportions - online quiz This site includes questions for your students to check their understanding
  10. Learning ratios and proportions through scale drawings - a text lesson plan A lesson plan can be found at this site
  11. Math for Morons Like Us - a ThinkQuest entry on ratio
  12. Nutshell Math: Ratios and Proportion - video lesson with examples and sample problems A video is available through this link
    1. You Tube video of the same lesson - Instructor: Ms. Jenkins A video is available through this link
  13. Percentages and Proportions - online quiz This site includes questions for your students to check their understanding
  14. Percents and Ratios - an index of pages that teach percent and ratio skills covered in K8 math courses - Each page has an explanation, interactive practice and challenge games about percents and ratios. (from AAA math) - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  15. Percent with a Calculator - after the lesson there are problems to work This site includes questions for your students to check their understanding
  16. Practice with Ratios - online quiz This site includes questions for your students to check their understanding
  17. Proportion Practice Test - thirteen multiple choice questions This site includes questions for your students to check their understanding
  18. Proportions and Ratios - good explanation of means and extremes from Free Math
  19. Rags to Riches: Ratio and Proportion Quiz - quiz at Quia This site includes questions for your students to check their understanding
  20. Rates, Ratios, and Proportions - a two person quiz from Quia This site includes questions for your students to check their understanding
  21. Ratio/Proportion Problems from Ask Dr. Math - three pages of links to real-world problems
  22. Ratio & Proportion - math review practice exercises This site includes questions for your students to check their understanding
  23. Ratio & Proportion - A proportion is a name we give to a statement that two ratios are equal. (This is a 3 step lesson followed by a workout.)
  24. Ratio and Proportion - explanation and examples
  25. Ratio and Proportion - introduction, in depth explanation, examples and a workout of ten problems This site includes questions for your students to check their understanding
  26. Ratio and Proportion Quiz - play this game to practice writing ratios This site is interactive and allows students to play a game or input or collect data
  27. Ratio Exercises: Dolls : Camera] | Same ratio -- Fish : Atom | Different ratio -- Spider : Lizard | Different ratio -- Dots : Stars | 2 Dolls for every 1 Camera | 3 Atoms for every 2 Fish | [How Many Spiders do You Have? | Which Way Gives More Pizza? This site includes questions for your students to check their understanding
  28. Ratio Proportion Calculator - Enter the known and unknown values from your proportion problem. In classic algebraic format, place an x in the box where the value is unknown. Then select Calculate and click on it. This site is interactive and allows students to play a game or input or collect data
  29. Ratios - a six page module from Purple Math
  30. Ratios and Proportions - explanation with four sample problems This site includes questions for your students to check their understanding
  31. Ratios and Proportions - an interactive lesson in a slide show format This site is interactive and allows students to play a game or input or collect data
  32. A PowerPoint show related to this standardRatios and Proportions - an 18 slide PowerPoint show
  33. A PowerPoint show related to this standardRatios and Proportion Review - a 12 slide PowerPoint show
  34. Review of Proportion - examples and practice problems
  35. Review of Ratios - examples and practice problems
  36. Skillwise: Ratio and Proportion - five part module; fact sheet, game, quiz, activity and worksheet
  37. Spy Guys Interactive - Ratio - Lesson 3 A video is available through this link
  38. A resource for the teacher to use in planning their lessonsTeaching Ratios and Proportions - suggestion for teachers and parents
  39. Using Proportions - online quiz This site includes questions for your students to check their understanding

(C)  approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (such as pi, or the square root of 2)

  1. Estimating by Rounding - Addition with regrouping - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  2. Estimating by Rounding - Subtraction with regrouping - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  3. A PowerPoint show related to this standardEstimate Square Roots - a 21 slide PowerPoint show
  4. Round About - estimate by rounding. This site is interactive and allows students to play a game or input or collect data
  5. Rounding Off - Three levels are available in this game from BBC Education This site is interactive and allows students to play a game or input or collect data
  6. Spy Guys Interactive - Rounding Numbers - Lesson 9
(D)  express numbers in scientific notation, including negative exponents, in appropriate problem situations
  1. Calculating with Scientirfic Notation - explanation, several examples and links to a large number of worksheets at the bottom of the page
  2. Converting Numbers to Scientific Notation - AAA Math lesson and practice problems This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  3. Converting Standard Numbers to Scientific Notation - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  4. Converting from Scientific Notation to Standard Numbers - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  5. Comparing Scientific and Standard Notation Numbers - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  6. Converting Decimal Numbers to Scientific Notation - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  7. Converting from Scientific Notation to Decimal Numbers - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  8. Converting Fractions to Scientific Notation - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  9. Cube of a Number - AAA Math lesson and practice problems This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  10. Division Using Scientific Notation - - two examples and seven practice problems This site includes questions for your students to check their understanding
  11. Evaluating Exponents of Negative Numbers - AAA Math lesson and practice problems This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  12. Exponential Expressions - find the exponential expression that is equivalent to the number given This site is interactive and allows students to play a game or input or collect data
  13. Exponent Practice - Try a workout of 10 problems. If you get at least 8 correct on your first attempt, then you're ready to move on. If not, review "In Depth" and try again. This site is interactive and allows students to play a game or input or collect data
  14. Exponents - Unit 3 from Ms. Glosser's Math Goodies
  15. Interactive Algebra Review on Integer Exponents This site is interactive and allows students to play a game or input or collect data
  16. Multiplication and Division Problems Using Scientific Notation - two examples and seven practice problems This site includes questions for your students to check their understanding
  17. Multiplication in Scientific Notation - four examples and seven practice problems This site includes questions for your students to check their understanding
  18. Practice with Scientific Notation - Pencil and paper may be needed - (answers provided)
  19. Scientific Notation - explanation from New York University's MathMol page
  20. Scientific Notation - Why your wrist (or keyboard) will thank you for not writing all those zeros.
  21. Scientific Notation - interactive practice This site is interactive and allows students to play a game or input or collect data
  22. Scientific Notation Problem Generator - either the scientific notation or standard notation representation of a number will be shown. Put the corresponding value(s) in the empty cell(s) and press "Check Answer". This site includes questions for your students to check their understanding
  23. Scientific Notation Quiz - ten multiple choice questions This site includes questions for your students to check their understanding
  24. Simplifying - Expressions that have had their like terms combined. Match each expression on the left with an expression on the right. Type the letter of the correct expression in the box. This site is interactive and allows students to play a game or input or collect data
  25. Symbols of Inclusion - simplify each expression and choose the correct comparison symbol This site is interactive and allows students to play a game or input or collect data
  26. What Is Scientific Notation And How Is It Used? - explanation and several practice problems, answers given on another page This site includes questions for your students to check their understanding

(8.2)   The student selects and uses appropriate operations to solve problems and justify solutions.

(A)  select appropriate operations to solve problems involving rational numbers and justify the selections

 
(B)  use appropriate operations to solve problems involving rational numbers in problem situations
 

(C)  evaluate a solution for reasonableness

  1. Comparison Estimator - Similar to Estimator but compares two sets of objects.
  2. Estimating by Rounding - Addition with regrouping
  3. Estimating by Rounding - Subtraction with regrouping
  4. Estimating Sum - No hints or clues given
  5. Estimator - Practice estimation skills by determining the number of objects, length, or area. (parameters: error tolerance)
  6. More or Less Estimator - Similar to Estimator activity but states a quantity and asks the user to estimate whether the set of objects is more or less than the number given.
  7. Round About - Students estimate by rounding. This site is interactive and allows students to play a game or input or collect data
  8. Rounding Off - Three levels are available in this game from BBC Education
  9. Spy Guys Interactive - Rounding Numbers - Lesson 9
(D)  use multiplication by a constant factor (unit rate) to represent proportional relationships
 
National Library of Virtual Manipulatives
  1. Number & Operations (Grades 6 - 8) This site is interactive and allows students to play a game or input or collect data

Patterns, Relationships & Algebraic Thinking
8.3 | 8.4 | 8.5

(8.3)  The student identifies proportional or non-proportional linear relationships in problem situations and solves problems.

(A)  compare and contrast proportional and non-proportional linear relationships

  1. Figure This: Math Challenge for Families - proportional reasoning
  2. The Importance of Ratios and Proportions - this comes under the heading of a perfect answer to "Why do I have to learn this?" - how a stock market trader benefits from ratio and proportion
  3. Interpreting and Applying Proportions - online quiz This site includes questions for your students to check their understanding
  4. Learning ratios and proportions through scale drawings - a text lesson plan A lesson plan can be found at this site
  5. Math for Morons Like Us - a ThinkQuest entry on ratio
  6. Nutshell Math: Ratios and Proportion - video lesson with examples and sample problems A video is available through this link
    1. You Tube video of the same lesson - Instructor: Ms. Jenkins A video is available through this link
  7. Practice with Ratios - online quiz This site includes questions for your students to check their understanding
  8. Proportion Practice Test - thirteen multiple choice questions This site includes questions for your students to check their understanding
  9. Proportions and Ratios - good explanation of means and extremes from Free Math
  10. Rags to Riches: Ratio and Proportion Quiz - quiz at Quia This site includes questions for your students to check their understanding
  11. Rates, Ratios, and Proportions - a two person quiz from Quia This site includes questions for your students to check their understanding
  12. Ratio/Proportion Problems from Ask Dr. Math - three pages of links to real-world problems
  13. Ratio & Proportion - math review practice exercises This site includes questions for your students to check their understanding
  14. Ratio & Proportion - A proportion is a name we give to a statement that two ratios are equal. (This is a 3 step lesson followed by a workout.)
  15. Ratio and Proportion - explanation and examples
  16. Ratio and Proportion - introduction, in depth explanation, examples and a workout of ten problems This site includes questions for your students to check their understanding
  17. Ratio and Proportion Quiz - play this game to practice writing ratios This site is interactive and allows students to play a game or input or collect data
  18. Ratio Exercises: Dolls : Camera] | Same ratio -- Fish : Atom | Different ratio -- Spider : Lizard | Different ratio -- Dots : Stars | 2 Dolls for every 1 Camera | 3 Atoms for every 2 Fish | [How Many Spiders do You Have? | Which Way Gives More Pizza? This site includes questions for your students to check their understanding
  19. Ratio Proportion Calculator - Enter the known and unknown values from your proportion problem. In classic algebraic format, place an x in the box where the value is unknown. Then select Calculate and click on it. This site is interactive and allows students to play a game or input or collect data
  20. Ratios - a six page module from Purple Math
  21. Ratios and Proportions - explanation with four sample problems This site includes questions for your students to check their understanding
  22. Ratios and Proportions - an interactive lesson in a slide show format This site is interactive and allows students to play a game or input or collect data
  23. A PowerPoint show related to this standardRatios and Proportions - an 18 slide PowerPoint show
  24. A PowerPoint show related to this standardRatios and Proportion Review - a 12 slide PowerPoint show
  25. Review of Proportion - examples and practice problems
  26. Review of Ratios - examples and practice problems
  27. Skillwise: Ratio and Proportion - five part module; fact sheet, game, quiz, activity and worksheet
  28. Spy Guys Interactive - Ratio - Lesson 3 A video is available through this link
  29. A resource for the teacher to use in planning their lessonsTeaching Ratios and Proportions - suggestion for teachers and parents
  30. Using Proportions - online quiz This site includes questions for your students to check their understanding
(B)  estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates
  1. Percentages and Proportions - online quiz This site includes questions for your students to check their understanding
  2. Percents and Ratios - an index of pages that teach percent and ratio skills covered in K8 math courses - Each page has an explanation, interactive practice and challenge games about percents and ratios. (from AAA math) - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  3. Percent with a Calculator - after the lesson there are problems to work This site includes questions for your students to check their understanding

(8.4)   The student makes connections among various representations of a numerical relationship.

generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description)

 

(8.5)   The student uses graphs, tables, and algebraic representations to make predictions and solve problems.

(A)  predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations

 

(B)  find and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change)

 

National Library of Virtual Manipulatives
  1. Algebra (Grades 6 - 8) This site is interactive and allows students to play a game or input or collect data

Geometry & Spatial Reasoning
8.6 | 8.7

(8.6)   The student uses transformational geometry to develop spatial sense.

(A)  generate similar figures using dilations including enlargements and reductions

 

(B)  graph dilations, reflections, and translations on a coordinate plane

 

(8.7)   The student uses geometry to model and describe the physical world.

(A)  draw three-dimensional figures from different perspectives

 

(B)  use geometric concepts and properties to solve problems in fields such as art and architecture

 

(C)  use pictures or models to demonstrate the Pythagorean Theorem

 

(D)  locate and name points on a coordinate plane using ordered pairs of rational numbers

 

National Library of Virtual Manipulatives
  1. Geometry (Grades 6 - 8) This site is interactive and allows students to play a game or input or collect data

Measurement
8.8 | 8.9 | 8.10

(8.8)   The student uses procedures to determine measures of three-dimensional figures.

(A)  find lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (two-dimensional models)

 
(B)  connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects
 
(C)  estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume
 

(8.9)   The student uses indirect measurement to solve problems.

(A)  use the Pythagorean Theorem to solve real-life problems

  1. Demonstrate the Pythagorean Theorem - from NOVA This site is interactive and allows students to play a game or input or collect data
  2. Interactive Proof of Pythagoras' theorem - This Java applet was written by Jim Morey. It won grand prize in Sun Microsystem's Java programming contest in the Summer of 1995. This site is interactive and allows students to play a game or input or collect data
  3. Nineteen Pythagorean Theorem applets This site is interactive and allows students to play a game or input or collect data
  4. Proof of the theorem is demonstrated through a Quicktime animation. This site is interactive and allows students to play a game or input or collect data
  5. Pythagorean Explorer - Students find the length of a side of a right triangle by using the Pythagorean Theorem, and then check their answers. This site is interactive and allows students to play a game or input or collect data
  6. Pythagorean theorem - Use this java applet to explore the Pythagorean theorem This site is interactive and allows students to play a game or input or collect data
  7. Pythagorean Theorem - online quiz This site includes questions for your students to check their understanding
  8. Pythagorean Theorem - a java applet that allows students to investigate this theorem. This site is interactive and allows students to play a game or input or collect data
  9. Pythagorean Theorem - This lesson will allow you to figure out the Pythagorean Theorem all by yourself. A lesson plan can be found at this site
  10. Pythagorean Theorem and its many proofs (43 to be precise)
  11. Pythagorean theorem and right triangle facts - given the length of three sides, determine if a right triangle is being described This site is interactive and allows students to play a game or input or collect data
  12. The Pythagorean Theorem, Distance Formula and Intro to Trigonometry - other practice activities
  13. Solving a right triangle - This example illustrates how finding the height of the pyramid is equivalent to solving the right triangle. The virtual reality media can help students visualize the interrelation between the 3-dimensional pyramid and the 2-dimensional right triangle. This site is interactive and allows students to play a game or input or collect data
  14. Squaring the Triangle - Students learn about how the Pythagorean Theorem works, through investigating the standard geometric proof. Parameters: Sizes of the legs of the triangle. This site is interactive and allows students to play a game or input or collect data
  15. Using the Pythagorean Theorem Once you know the equation a2 + b2 = c2 is true, then you can use it to solve all kinds of problems. Try the Pythagorean theorem with two other examples given on this page. This site is interactive and allows students to play a game or input or collect data
(B)  use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements
  1. Alien Angles - estimate angles, without a protractor, ranging from 1-180 by dragging a movable line This site is interactive and allows students to play a game or input or collect data
  2. Angles in a Triangle - interactive applet with several examples This site is interactive and allows students to play a game or input or collect data
  3. Area Explorer - Students are shown shapes on a grid after setting the perimeter and asked to calculate areas of the shapes. This site is interactive and allows students to play a game or input or collect data
  4. Banana Hunt -This game helps students practice the degrees of an angle This site is interactive and allows students to play a game or input or collect data
  5. Calculate the Perimeter of the Rectangle - from FunBrain This site is interactive and allows students to play a game or input or collect data
  6. Complementary Angles - Match the angles that are complementary. (a Quia game available in Matching, Flashcards, and Concentration format) This site is interactive and allows students to play a game or input or collect data
  7. Finding the Third Angle of a Triangle - instruction, practice problems and a game This site is interactive and allows students to play a game or input or collect data
  8. Geometric Terms - this Quia quiz contains four activities - matching, flash cards, concentration, and a word search puzzle - which reinforce students vocabulary concerning angles. This site is interactive and allows students to play a game or input or collect data
  9. Introduction to Angles - Basic terms related to the classification of angles (a Quia game available in Matching, Flashcards, Word Search, and Concentration format) This site is interactive and allows students to play a game or input or collect data
  10. Lesson on Perimeter of Polygons This site includes questions for your students to check their understanding
  11. Measuring Angles - online quiz with virtual protractor This site includes questions for your students to check their understanding
  12. Measuring Around - find circumferences, online quiz This site includes questions for your students to check their understanding
  13. Oblique Triangles - from Dave's Short Trig Course
  14. Perimeter Explorer - Students are shown shapes on a grid after setting the area and asked to calculate perimeters of the shapes. This site is interactive and allows students to play a game or input or collect data
  15. Perimeter of a Rectangle - Calculate the perimeter of a rectangle with given dimensions - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  16. Perimeter of a Square - Calculate the perimeter of a square with given dimensions - instruction and review, practice, and a quiz This site is interactive and allows students to play a game or input or collect data & This site includes questions for your students to check their understanding
  17. Protractor - learn how to position and read a protractor in order to measure an angle, and how to use either scale on the protractor This site is interactive and allows students to play a game or input or collect data
  18. Ratio and Proportions: Similar Figures - a four part lesson including problems to work This site is interactive and allows students to play a game or input or collect data
  19. Right Triangle Calculator - choose the known side then click on the calculate button This site is interactive and allows students to play a game or input or collect data
  20. Right Triangles - from Dave's Short Trig Course
  21. Sum of Angles in a Triangle - students can explore this concept by moving the vertices of the triangle with pressed mouse button This site is interactive and allows students to play a game or input or collect data
  22. Triangle Calculator - four different calculators This site is interactive and allows students to play a game or input or collect data
  23. Triangle Calculator - enter values three of the six sides and angles of the triangle and the other three values will be computed This site is interactive and allows students to play a game or input or collect data
  24. Types of angles and pairs of angles - good illustrations
  25. Using Spreadsheets to Find Area and Perimeter - The cells of a spreadsheet are a useful way to represent area and perimeter. A lesson plan can be found at this site
  26. Working with Angles - Answer the questions which deal with angles

(8.10)   The student describes how changes in dimensions affect linear, area, and volume measures.

(A)  describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally

 
(B)  describe the resulting effect on volume when dimensions of a solid are changed proportionally
 
National Library of Virtual Manipulatives
  1. Measurement (Grades 6 - 8) This site is interactive and allows students to play a game or input or collect data
Probability & Statistics
8.11 | 8.12 | 8.13

(8.11)   The student applies concepts of theoretical and experimental probability to make predictions.

(A)  find the probabilities of dependent and independent events

  1. Adjustable Spinner - Students can create a game spinner with variable sized sectors to look at experimental and theoretical probabilities. Parameters: Sizes of sectors, number of sectors, number of trials. This site is interactive and allows students to play a game or input or collect data
  2. Adjustable Spinner - Change the number of sectors and increase or decrease their size to create any type of spinner. Then, conduct a probability experiment by spinning the spinner many times. How does the experimental probability compare with the theoretical probability This site is interactive and allows students to play a game or input or collect data
  3. Analyzing game probabilities - online quiz This site includes questions for your students to check their understanding
  4. Basic Spinner - Students can create a game spinner with one to twelve sectors to look at experimental and theoretical probabilities. Parameters: Number of sectors, number of trials. This site is interactive and allows students to play a game or input or collect data
  5. A PowerPoint show related to this standardDescribing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation - a 20 slide presentation
  6. Fun and Sun Rent-a-Car - students use tables, graphs, linear functions to solve a real-world problem A lesson plan can be found at this site
  7. Graphing Skills - What's the point? Find the point on the grid This site is interactive and allows students to play a game or input or collect data
  8. Marbles - Students learn about sampling with and without replacement by modeling drawing marbles from a bag. Parameters: Number and color of marbles in the bag, replacement rule. This site is interactive and allows students to play a game or input or collect data
  9. Million Dollar Mission - a mathematics fantasy
  10. Probability - online quiz This site includes questions for your students to check their understanding
  11. Probability Spinner - Check out your probabilities here! This site is interactive and allows students to play a game or input or collect data
  12. Practice with Data - answer questions pertaining to collecting and organizing data This site includes questions for your students to check their understanding
  13. Two Colors - Students choose between three boxes and choose one marble from the box to look at conditional probabilities. Parameters: Number of trials. This site is interactive and allows students to play a game or input or collect data
  14. Understanding Experimental Probability - Experiment with experimental probability using a fixed size section spinner, a variable section spinner, 2 regular 6-sided number cubes or design your own number cubes. This site is interactive and allows students to play a game or input or collect data
  15. Using Graphs to Understand Data - online quiz This site includes questions for your students to check their understanding
  16. Vehicle Stopping Distance And Time - use data to reach conclusions - use their Vehicle Stopping Distance Calculator to do actual model calculations This site is interactive and allows students to play a game or input or collect data
  17. The Winning Edge: Probability in Basketball - Time has run out in the big basketball game, and the score is tied. However, Up-State College has the ball with time out. You're the coach. Which players should you put into the game to give you the best chance of winning? (students collect data and make prediction based on the data) This site is interactive and allows students to play a game or input or collect data A lesson plan can be found at this site
(B)  use theoretical probabilities and experimental results to make predictions and decisions
 
(C)  select and use different models to simulate an event
 

(8.12)   The student uses statistical procedures to describe data.

(A)  select the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation

 
(B)  draw conclusions and make predictions by analyzing trends in scatterplots
  1. Creating a Scatter Plot in Excel - a long tutorial (27 pages if printed) on making your own scatter plot
  2. Creating an XY (Scatter) Plot in Excel - a seven page totorial on how to use Excel to make a scatter plot An Adobe Acrobat document in .pdf format
  3. Displaying Data - [designed for 7th grade - use for remediation ] explanation, examples and several interactive practice activities This site is interactive and allows students to play a game or input or collect data
  4. Displaying Data - [designed for 8th grade] explanation, examples and several interactive practice activities This site is interactive and allows students to play a game or input or collect data
  5. How to Use Your TI-83 or 84 Calculator to Make a Scatter Plot - provided by MathBits
  6. Interactive Scatter Plot - from Shodor This site is interactive and allows students to play a game or input or collect data
  7. Interactive Scatterplot - students enter data and make their own scatterplot with this National Library of Virtual Manipulatives page This site is interactive and allows students to play a game or input or collect data
  8. Introduction to Bivariate Data - several good examples of scatter plots are included
  9. Line Graphs and Scatter Plots - several good examples
  10. Linear Regression - an applet which allows your students to investigate a regression line, also known as a "line of best fit."
  11. Pizza Palace - Students will construct box plots independently. Students identify the mean, median, mode, and range of a set of data This site is interactive and allows students to play a game or input or collect data
  12. The Regression Line and Correlation - a lesson plan from Illuminations A lesson plan can be found at this site
  13. Scatterplots - explanation and several good examples from Canada's National Statistical Agency
  14. Scatterplots - a lesson plan from North Canton City Schools A lesson plan can be found at this site
    1. worksheet to use with the activity above an Excel file to downloasd
  15. Scatter Plot - includes examples of positive association, negative association, and no trend
  16. Scatter Plot - links to ten different examples are included with this Engineering Statistics Handbook entry
  17. Scatter Plot - the Wikipedia entry
  18. Scatter Plot and Line of Best Fit - four interactive applets to experiment with This site is interactive and allows students to play a game or input or collect data
  19. Scatter Plot: States in the US - an interesting example of a scatter plot
  20. Scatter Plots - explanation, examples and several interactive practice activities This site is interactive and allows students to play a game or input or collect data
  21. Scatter Plots - from the Business Knowledge Center
  22. Scatter Plots - includes examples of perfect correlation, high correlation, and low correlation
  23. Scatter Plots - from Oswego City School District Regents Exam Prep Center
  24. Scatterplot with Overlaid Linear Prediction Plot - includes links to other plots on the right
    1. Another version of the above information
  25. Internet4ClassroomsUsing Excel to Display a Scatter Plot - an Internet4Classrooms step-by-step module on making your own scatter plots
(C)  select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, stem and leaf plots, circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology
  1. Box Plot - the Wikipedia entry
  2. Box Plot - Use this tool to summarize data using a box plot graph This site is interactive and allows students to play a game or input or collect data
  3. Box Plot - This activity from Shodor allows the user to view box plots for either built-in or user-specified data, and experiment with outliers This site is interactive and allows students to play a game or input or collect data
  4. Box Plot 2 -This activity from Shodor allows the user to view box plots for either built-in or user-specified data, and experiment with outliers This site is interactive and allows students to play a game or input or collect data
  5. Box Plot - an interactive online illustration of creating a box plot, includes an interactive illustration This site is interactive and allows students to play a game or input or collect data
  6. Box Plot - Students can create box plots which use the median in calculating the interquartile ranges for either built in or user-specified data as well as experiment with outliers This site is interactive and allows students to play a game or input or collect data
  7. Box Plotter - This activity allows the user to explore maximum, minimum, median, upper quartile, lower quartile and outliers while learning how to draw box plots. This site is interactive and allows students to play a game or input or collect data
  8. Box-and-Whisker Plot - A box-and-whisker plot can be useful for handling many data values
  9. Box and Whisker Plot - [2:52 min] a video explaining this type of plot A video is available through this link
  10. Box and Whisker Plot - [52 sec] a YouTube video A video is available through this link
  11. Box-and-Whisker Plots - from Oswego City School District Regents Exam Prep Center
  12. Box-and-Whisker Plots - from the Worsley School
  13. Box-and-Whisker Plots - a large number of examples are provided
  14. Box Plot and Whisker Plots in Excel 2007 - step by step example on how to make them in Microsoft Excel 2007
  15. Constructing Box and Whisker Plots - explanation and several good examples from Canada's National Statistical Agency
  16. Create Your Own Graph - explanation and several good examples from Canada's National Statistical Agency This site is interactive and allows students to play a game or input or collect data
  17. Horizontal Box and Whisker Plots - a large number of examples are included
  18. How-To Activity for Your Graphing Calculator - a six page how to document An Adobe Acrobat document in .pdf format
  19. How to Use your TI-83 or 84 Calculator to Make a Scatter Plot - provided by MathBits
  20. Interactive Box Plot - [interactive] students enter data and make their own scatterplot with this National Library of Virtual Manipulatives page This site is interactive and allows students to play a game or input or collect data
  21. Mean and Median - this applet allows the user to investigate the mean, median, and box-and-whisker plot for a set of data that they create
  22. Measures of Spread: Box and Whisker Plots - from the Australian Bureau of Statistics
  23. Quartiles, Boxes, and Whiskers - from Purple Math
  24. Quartiles and Box and Whisker Plots - from Oswego City School District Regents Exam Prep Center
  25. Steppin' Out - a Middle School Math Project lesson plan An Adobe Acrobat document in .pdf format A lesson plan can be found at this site

(8.13)   The student evaluates predictions and conclusions based on statistical data.

(A)  evaluate methods of sampling to determine validity of an inference made from a set of data

 
(B)  recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis
  1. Class Interval - how to make the same data appear to support two different positions A lesson plan can be found at this site
  2. CNN posted misleading graph - poll results on Schiavo case - graph as presented and how it should have been shown
  3. Histograms and Bar Graphs - lesson plan on how data can be graphically represented (and mis-represented) A lesson plan can be found at this site
  4. Junk Charts - several examples of using graphs to mislead
  5. Misleading Graphs - a short YouTube video using one example graph A video is available through this link
  6. Misleading Graphs - from a BBC site on Data Handling
    1. Take a Practice Test on the subject - five questions This site includes questions for your students to check their understanding
  7. Misleading Graphs - comparison of two graphs
  8. Misleading Graphs - using only part of the data to misrepresent a point
  9. Misleading Graphs - [designed for grades 5-6] a worksheet to use in class An Adobe Acrobat document in .pdf format This link includes something for the teacher to print
  10. Misleading Graphs - lesson plan A lesson plan can be found at this site
  11. Misleading Graphs - lesson in the form of a slide show with examples and questions This site is interactive and allows students to play a game or input or collect data
  12. Misleading Graphs - lesson plan frolm Shodor A lesson plan can be found at this site
  13. Misleading Graphs - how deaths from measles may be misrepresented
  14. Misleading Graphs - sheet to print and use in class [from Glencoe] An Adobe Acrobat document in .pdf format This link includes something for the teacher to print
  15. Misleading Graphs - showing the relationship between asphalt use in Finland and asthma rates
    1. Excel file - use this spreadsheet to support the lesson plan above an Excel file to download
  16. The Treasury Department's Junk Chart - example and explanation
  17. Vertical Scale Discussion - lesson plan from Shodor A lesson plan can be found at this site
  18. Visual, as well as Statistical, Misunderstanding - examples of misleading presentation of data
    1. Context: Compared to What? - a graph must not show data out of context
    2. Goosed Up Graphics - making things appear to be `better' than they are by fiddling with the scales
    3. Have Something to Say - "Knowin' all the words in the dictionary ain't goonna help if you got nuttin' to say" - a quote from Blind Lemon Jefferson, the great blues musician
    4. The Lie Factor - the ratio of the size of an effect shown in the graphic is not proportional to the size of the effect in the data
    5. Missed Opportunities - some important information was there, but the graph maker missed it
  19. Wikipedia article on the Laffer Curve - showing possible misuse of data in economics
National Library of Virtual Manipulatives
  1. Data Analysis & Probability (Grades 6 - 8) This site is interactive and allows students to play a game or input or collect data

Underlying Processes & Mathematical Tools
8.14 | 8.15 | 8.16

(8.14)   The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school.

(A)  identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics

  1. Art, Geometry, and Abstract Sculpture - Computer Graphics, Art, Math, Geometry, and Abstract Sculpture are closely related.
  2. Art & Geometry -
  3. A resource for the teacher to use in planning their lessonsGeometry in Art and Architecture - many topics covered
  4. Geometry Through Art - What children can learn about art and geometry
(B)  use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness
 
(C)  select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem
 
(D)  select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems
 

(8.15)   The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models.

(A)  communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models

 
(B)  evaluate the effectiveness of different representations to communicate ideas
 

(8.16)   The student uses logical reasoning to make conjectures and verify conclusions.

(A)  make conjectures from patterns or sets of examples and nonexamples

  1. Button Beach - use logic to determine the value of rows of buttons, three levels of challenge This site is interactive and allows students to play a game or input or collect data
  2. Calculating the nth Term - how to develop a formula that can be used to calculate these terms
  3. Create your own pattern - drag shapes to create a pattern This site is interactive and allows students to play a game or input or collect data
    1. Instructions on how to use this page in your classroom A lesson plan can be found at this site
  4. Mystery Operations - In this activity the computer makes up a mystery operation, and you have to figure out what the operation is. You give the computer two numbers to calculate, and it tells you the answer. This site is interactive and allows students to play a game or input or collect data
  5. Number Cracker - uess what number comes next in the pattern This site is interactive and allows students to play a game or input or collect data
  6. Patterns in Geometry - online quizThis site includes questions for your students to check their understanding
  7. Patterns - Figure out the patterns, if you can! This site is interactive and allows students to play a game or input or collect data
  8. Power Lines - (math reasoning) Place numbers in the circles so all lines add to the same target number. You must get all correct to get the password to go on to the next level. level 2 | level 3 This site is interactive and allows students to play a game or input or collect data
  9. Writing Rules for Patterns - online quiz This site includes questions for your students to check their understanding
(B)  validate his/her conclusions using mathematical properties and relationships
 
Worksheet Generator - This web site will allow you to create printable math worksheets from your browser.
(addition, subtraction, multiplication, division, mixed problems, fractions, measurement, fractions, graphing, telling time, and a one-hundred chart)

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Internet4classrooms is a collaborative effort by Susan Brooks and Bill Byles.
 

  

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