Mathematics Knowledge & Skills - 8th Grade

| 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 site for teachers | a PowerPoint show | Adobe Acrobat document | a Word document sound | video format | interactive lesson | a quiz | lesson plan | to print

1. Compare and Order Numbers - explanation, examples and interactive applets
2. Comparing Exponential Expressions - select, <, >, or =
3. Comparing Integers - Comparing integers with absolute values - instruction and review, practice, and a quiz &
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!"
5. Comparing 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 &
7. Line Jumper - [this link opens on a new page] Click on the number line at the correct answer.
8. MathDrill lets your students practice <, >, or =.
9. Number Line Bounce - Instructions on how to play are included at the top of the window.
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.
11. Rational Numbers on a Number Line - [designed for 6th grade]
    1. Practice problems to go with the lesson
12. Rational Numbers on a Number Line - a 1 page document from Glencoe Publishers; with explanation, examples, and practice problems
13. Rational Numbers on a Number Line - a 13 page document with examples and sample problems
14. Rational 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
16. Visualizing Numbers on an Interactive Number Line - instructions for using this activity are included

1. All About Ratios - a Quiz
2. All About Ratios - links to several lessons by Cynthia Lanius
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
5. Determine the number based on the ratio - instruction and review, practice, and a quiz &
6. Determining the Ratio - instruction and review, practice, and a quiz &
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
10. Learning ratios and proportions through scale drawings - a text lesson plan
11. Math for Morons Like Us - a ThinkQuest entry on ratio
12. Nutshell Math: Ratios and Proportion - video lesson with examples and sample problems
    1. You Tube video of the same lesson - Instructor: Ms. Jenkins
13. Percentages and Proportions - online quiz
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 &
15. Percent with a Calculator - after the lesson there are problems to work
16. Practice with Ratios - online quiz
17. Proportion Practice Test - thirteen multiple choice questions
18. Proportions and Ratios - good explanation of means and extremes from Free Math
19. Rags to Riches: Ratio and Proportion Quiz - [this link opens on a new page] quiz at Quia
20. Rates, Ratios, and Proportions - [this link opens on a new page] a two person quiz from Quia
21. Ratio/Proportion Problems from Ask Dr. Math - three pages of links to real-world problems
22. Ratio & Proportion - math review practice exercises
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
26. Ratio and Proportion Quiz - play this game to practice writing ratios
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?
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.
29. Ratios - a six page module from Purple Math
30. Ratios and Proportions - explanation with four sample problems
31. Ratios and Proportions - an interactive lesson in a slide show format
32. Ratios and Proportions - an 18 slide PowerPoint show
33. Ratios 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
38. Teaching Ratios and Proportions - suggestion for teachers and parents
39. Using Proportions - online quiz

1. Estimating by Rounding - Addition with regrouping - instruction and review, practice, and a quiz &
2. Estimating by Rounding - Subtraction with regrouping - instruction and review, practice, and a quiz &
3. Estimate Square Roots - a 21 slide PowerPoint show
4. Round About - [this link opens in a new window] estimate by rounding. (Author - Sandi King)
5. Rounding Off - Three levels are available in this game from BBC Education
6. Spy Guys Interactive - Rounding Numbers - Lesson 9

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 &
3. Converting Standard Numbers to Scientific Notation - instruction and review, practice, and a quiz &
4. Converting from Scientific Notation to Standard Numbers - instruction and review, practice, and a quiz &
5. Comparing Scientific and Standard Notation Numbers - instruction and review, practice, and a quiz &
6. Converting Decimal Numbers to Scientific Notation - instruction and review, practice, and a quiz &
7. Converting from Scientific Notation to Decimal Numbers - instruction and review, practice, and a quiz &
8. Converting Fractions to Scientific Notation - instruction and review, practice, and a quiz &
9. Cube of a Number - AAA Math lesson and practice problems &
10. Division Using Scientific Notation - - two examples and seven practice problems
11. Evaluating Exponents of Negative Numbers - AAA Math lesson and practice problems &
12. Exponential Expressions - find the exponential expression that is equivalent to the number given
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.
14. Exponents - Unit 3 from Ms. Glosser's Math Goodies
15. Interactive Algebra Review on Integer Exponents
16. Multiplication and Division Problems Using Scientific Notation - two examples and seven practice problems
17. Multiplication in Scientific Notation - four examples and seven practice problems
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
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".
23. Scientific Notation Quiz - ten multiple choice questions
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.
25. Symbols of Inclusion - simplify each expression and choose the correct comparison symbol
26. What Is Scientific Notation And How Is It Used? - explanation and several practice problems, answers given on another page

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 - [this link opens on a new page] Students estimate by rounding. (Author - Sandi King)
8. Rounding Off - Three levels are available in this game from BBC Education
9. Spy Guys Interactive - Rounding Numbers - Lesson 9

1. Number & Operations (Grades 6 - 8)

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
4. Learning ratios and proportions through scale drawings - a text lesson plan
5. Math for Morons Like Us - a ThinkQuest entry on ratio
6. Nutshell Math: Ratios and Proportion - video lesson with examples and sample problems
   1. You Tube video of the same lesson - Instructor: Ms. Jenkins
7. Practice with Ratios - online quiz
8. Proportion Practice Test - thirteen multiple choice questions
9. Proportions and Ratios - good explanation of means and extremes from Free Math
10. Rags to Riches: Ratio and Proportion Quiz - [this link opens on a new page] quiz at Quia
11. Rates, Ratios, and Proportions - [this link opens on a new page] a two person quiz from Quia
12. Ratio/Proportion Problems from Ask Dr. Math - three pages of links to real-world problems
13. Ratio & Proportion - math review practice exercises
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
17. Ratio and Proportion Quiz - play this game to practice writing ratios
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?
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.
20. Ratios - a six page module from Purple Math
21. Ratios and Proportions - explanation with four sample problems
22. Ratios and Proportions - an interactive lesson in a slide show format
23. Ratios and Proportions - an 18 slide PowerPoint show
24. Ratios 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
29. Teaching Ratios and Proportions - suggestion for teachers and parents
30. Using Proportions - online quiz

1. Percentages and Proportions - online quiz
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 &
3. Percent with a Calculator - after the lesson there are problems to work

1. Algebra (Grades 6 - 8)

1. Geometry (Grades 6 - 8)

1. Demonstrate the Pythagorean Theorem - from NOVA
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.
3. Nineteen Pythagorean Theorem applets
4. Proof of the theorem is demonstrated through a Quicktime animation.
5. Pythagorean Explorer - Students find the length of a side of a right triangle by using the Pythagorean Theorem, and then check their answers.
6. Pythagorean theorem - Use this java applet to explore the Pythagorean theorem
7. Pythagorean Theorem - online quiz
8. Pythagorean Theorem - a java applet that allows students to investigate this theorem.
9. Pythagorean Theorem - This lesson will allow you to figure out the Pythagorean Theorem all by yourself.
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
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.
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.
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.

1. Alien Angles - estimate angles, without a protractor, ranging from 1-180 by dragging a movable line
2. Angles in a Triangle - interactive applet with several examples
3. Area Explorer - Students are shown shapes on a grid after setting the perimeter and asked to calculate areas of the shapes.
4. Banana Hunt -This game helps students practice the degrees of an angle
5. Calculate the Perimeter of the Rectangle - [this link opens on a new page] from FunBrain
6. Complementary Angles - [this link opens on a new page] Match the angles that are complementary. (a Quia game available in Matching, Flashcards, and Concentration format)
7. Finding the Third Angle of a Triangle - instruction, practice problems and a game
8. Geometric Terms - [this link opens on a new page] this Quia quiz contains four activities - matching, flash cards, concentration, and a word search puzzle - which reinforce students vocabulary concerning angles.
9. Introduction to Angles - [this link opens on a new page] Basic terms related to the classification of angles (a Quia game available in Matching, Flashcards, Word Search, and Concentration format)
10. Lesson on Perimeter of Polygons
11. Measuring Angles - online quiz with virtual protractor
12. Measuring Around - find circumferences, online quiz
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.
15. Perimeter of a Rectangle - Calculate the perimeter of a rectangle with given dimensions - instruction and review, practice, and a quiz &
16. Perimeter of a Square - Calculate the perimeter of a square with given dimensions - instruction and review, practice, and a quiz &
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
18. Ratio and Proportions: Similar Figures - a four part lesson including problems to work
19. Right Triangle Calculator - choose the known side then click on the calculate button
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
22. Triangle Calculator - four different calculators
23. Triangle Calculator - enter values three of the six sides and angles of the triangle and the other three values will be computed
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.
26. Working with Angles - Answer the questions which deal with angles

1. Measurement (Grades 6 - 8)

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.
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
3. Analyzing game probabilities - online quiz
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.
5. Describing 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
7. Graphing Skills - [this link opens on a new page] What's the point? Find the point on the grid
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.
9. Million Dollar Mission - a mathematics fantasy
10. Probability - online quiz
11. Probability Spinner - Check out your probabilities here!
12. Practice with Data - answer questions pertaining to collecting and organizing data
13. Two Colors - Students choose between three boxes and choose one marble from the box to look at conditional probabilities. Parameters: Number of trials.
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.
15. Using Graphs to Understand Data - online quiz
16. Vehicle Stopping Distance And Time - use data to reach conclusions - use their Vehicle Stopping Distance Calculator to do actual model calculations
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)

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
3. Displaying Data - [designed for 7th grade - use for remediation ] explanation, examples and several interactive practice activities
4. Displaying Data - [designed for 8th grade] explanation, examples and several interactive practice activities
5. How to Use Your TI-83 or 84 Calculator to Make a Scatter Plot - provided by MathBits
6. Interactive Scatter Plot - from Shodor
7. Interactive Scatterplot - students enter data and make their own scatterplot with this National Library of Virtual Manipulatives page
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 - [interactive] Students will construct box plots independently. Students identify the mean, median, mode, and range of a set of data
12. The Regression Line and Correlation - a lesson plan from Illuminations
13. Scatterplots - explanation and several good examples from Canada's National Statistical Agency
14. Scatterplots - a lesson plan from North Canton City Schools
    1. worksheet to use with the activity above
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
19. Scatter Plot: States in the US - an interesting example of a scatter plot
20. Scatter Plots - explanation, examples and several interactive practice activities
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. Using Excel to Display a Scatter Plot - an Internet4Classrooms step-by-step module on making your own scatter plots

1. Box Plot - the Wikipedia entry
2. Box Plot - [interactive] Use this tool to summarize data using a box plot graph
3. Box Plot - [interactive] This activity from Shodor allows the user to view box plots for either built-in or user-specified data, and experiment with outliers
4. Box Plot 2 - [interactive] This activity from Shodor allows the user to view box plots for either built-in or user-specified data, and experiment with outliers
5. Box Plot - an interactive online illustration of creating a box plot, includes an interactive illustration
6. Box Plot - [interactive] 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
7. Box Plotter - [interactive] This activity allows the user to explore maximum, minimum, median, upper quartile, lower quartile and outliers while learning how to draw box plots.
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
10. Box and Whisker Plot - [52 sec] a YouTube video
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 - [interactive] explanation and several good examples from Canada's National Statistical Agency
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
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
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

1. Class Interval - how to make the same data appear to support two different positions
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)
4. Junk Charts - several examples of using graphs to mislead
5. Misleading Graphs - a short YouTube video using one example graph
6. Misleading Graphs - from a BBC site on Data Handling
   1. Take a Practice Test on the subject - five questions
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
10. Misleading Graphs - lesson plan
11. Misleading Graphs - lesson in the form of a slide show with examples and questions
12. Misleading Graphs - lesson plan frolm Shodor
13. Misleading Graphs - how deaths from measles may be misrepresented
14. Misleading Graphs - sheet to print and use in class [from Glencoe]
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
16. The Treasury Department's Junk Chart - example and explanation
17. Vertical Scale Discussion - lesson plan from Shodor
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

1. Data Analysis & Probability (Grades 6 - 8)

1. Art, Geometry, and Abstract Sculpture - Computer Graphics, Art, Math, Geometry, and Abstract Sculpture are closely related.
2. Art & Geometry -
3. Geometry in Art and Architecture - many topics covered
4. Geometry Through Art - What children can learn about art and geometry

1. Button Beach - use logic to determine the value of rows of buttons, three levels of challenge
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
   1. Instructions on how to use this page in your classroom
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.
5. Number Cracker - [this link opens on a new page] guess what number comes next in the pattern
6. Patterns in Geometry - online quiz
7. Patterns - Figure out the patterns, if you can!
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
9. Writing Rules for Patterns - online quiz