Mathematics Knowledge & Skills - 6th 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 created 2/11/07
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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. Comparing Integers - Comparing integers with absolute values
2. 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.
3. Evaluating Expressions - a four step lesson
4. Evaluating Expressions - Get out your pencils and calculators and give these a try!
5. Greater, Less Than, or the Same - Compare these decimals
6. Put Whole Numbers in Order - Three or more numbers can be placed in order. A number may come before the other numbers or it may come between them or after them
7. Spy Guys Interactive - Understanding Integers - Lesson 6

1. Calculate percent - Discover relationships between fractions, percents, and decimals
2. Finding a percent of a quantity - online quiz
3. Fractions, Decimals or Percent - two are given, you supply the third
4. Percents and Wholes - online quiz
5. Percent Game - FunBrain site
6. Practice Solving Percent Problems - more percent practice
7. 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)
8. Percent Problems - a one-player, or two-player game from Quia
9. Solving Percent Problems Using a Pyramid Grid - an interactive lesson
10. Spy Guys Interactive - Solving Problems with Decimals - Lesson 5
11. Spy Guys Interactive - Improper Fractions & Mixed Numbers - Lesson 2
12. Spy Guys Interactive - Percent - Lesson 4
13. Using percents - online quiz
14. Using the Proportion Method to Solve Percent Problems - practice problems at the end
15. What's Your Name? - [this link opens on a new page] Students know the value of numbers when written in standard form or expanded notation. (Author - Sandi King)

1. Comparing Integers - Comparing integers with absolute values
2. Spy Guys Interactive - Understanding Integers - Lesson 6

1. Spy Guys Interactive - Factors, Multiples, and Prime Factorization - Lesson 7

1. Simple Fractions - An instructional site that reviews terms, factoring, reducing, addition and subtraction of fractions
2. Using Number Patterns, Fractions, and Ratios - use a Quia quiz to practice greatest common factor, simplify fractions, least common multiple, and divisibility rules [Who Wants to be a Millionaire format]

1. Adding Fractions - with the same denominator
2. Adding Fractions - mixed denominators
3. Adding Fractions - using circle graphs - Mixed numbers
4. Multiply fractions - with circles,mixed number times a whole number
5. Multiplying Rational Fractions - online quiz - (answers provided)
6. Multiplying Fractions - Soccer Shootout - (FunBrain activity)
7. Subtracting Fractions - with same denominator

1. Count the Goodies - This multiplication activity from Harcourt School’s Mighty Math Calculating Crew asks you to multiply using regrouping. Three problems at a time are presented.
2. Decifractator - convert fractions to decimal equivalents
3. EZ Fractions - Add, Subtract, Multiply and Divide fractions - Help tools are on the site to give students every tool necessary for performing operations with fractions as easy as it has ever been!.
4. Math Baseball - Complete the Number Sentence - (Fun Brain) - All Operations - Numbers less than 100 | All Operations - Numbers less than 1000 | Division - Numbers less than 100 | Division - Numbers less than 1000 | Division - Numbers less than 10,000 | Multiplication - Numbers less than 1000 | Multiplication - Numbers less than 10,000
5. Math Facts -Timed math facts, or select practice mode without the timer
6. Math Mayhem - A fast paced program where student can select addition problems. (most are two digit problems) - warning: turn sound to mute; this activity gets very loud!
7. Mental Math - Select an operation to practice your skills
8. Mixed Review - Addition and subtraction of three numbers - find answer to reveal mystery picture (warning: very difficult, will need pencil and paper)
9. Timed Facts - at end of 60 seconds shows the score and answers to problems
10. Decimals
    1. Adding with decimals - Addition of numbers with three decimal digits
    2. Comparing fractions and decimals - interactive game
    3. Complete the number sentence - All operations with decimals
    4. Decimal addition - Push the green blocks into the holes to make the target number.
    5. Dividing Decimals - Complete the number sentence\
    6. Division of Decimals - Divide with 2 decimals
    7. Division of Decimals - Divide with 3 decimals
    8. Multiplying and Dividing with Decimals - online quiz
    9. Multiplying with decimals - Multiplying numbers with two decimals
    10. Rounding off - Round numbers to significant decimal places - (interactive game)
    11. Subtracting with decimals - Subtraction with three decimal digits
11. Fractions
    1. Divide fractions - (using circles) this will show graphically how the divisor will fit into the dividend a whole number of times
    2. Dividing fractions - Fraction Bar -This is a very versatile tool that can be used to illustrate a variety of number operations.
    3. Fractional Distances - find Grampy by entering a fractional distance - (includes mixed numbers and various fractions)
    4. Fraction Practice - All operations, mixed practice - (explanations given for wrong answers)
    5. Multiplying and Dividing Fractions - online quiz
    6. Worksheet Generator - Reducing Fractions to Lowest Terms - You decide on the number of problems, the difficulty and whether or not to include improper fractions

1. All About Ratios - a Quiz
2. 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.
3. Comparing Ratios and Rates - online quiz
4. Determine the number based on the ratio - online quiz
5. Determining the Ratio - online quiz
6. Interpreting and Applying Proportions - online quiz
7. Percentages and Proportions - online quiz
8. Percent Calculators
   1. Percent Calculator
   2. Percent Calculator - three possible calculations
   3. Percent Calculator - calculate amount, percent amount or percent rate if you know two of the three
   4. Percent Change Calculator
9. Percent with a Calculator - after the lesson there are problems to work
10. Percent Problems - a one-player, or two-player game from Quia
11. Practice with Ratios - online quiz
12. 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)
13. 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.)
14. Ratio & Proportion - math review practice exercises
15. 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.
16. 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?
17. Solving Percent Problems Using a Pyramid Grid - an interactive lesson
18. Spy Guys Interactive - Ratio - Lesson 3
19. Using Proportions - online quiz

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. An order of operations game from Funbrain.com (easier levels are available)
2. Evaluating Algebraic Expressions - Order of Operations/P.E.M.D.A.S.
3. Evaluating Algebraic Expressions - from Regents Prep
4. Order of Operations - tutorial and quiz
5. Order of Operations - 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.
6. Order of Operations - lesson
7. Order of Operations - practice problems
8. Order of Operations - a matching grid pattern game
9. Practice with Order of Operations - Get out your pencils and calculators and give these a try!

1. Number & Operations (Grades 6 - 8)

1. Comparing Ratios and Rates - online quiz
2. Determining the Ratio - online quiz
3. Determine the number based on the ratio - online quiz
4. Interpreting and Applying Proportions - online quiz
5. Percentages and Proportions - online quiz
6. Percent with a Calculator - after the lesson there are problems to work
7. Practice with Ratios - online quiz
8. 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)
9. 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.)
10. Ratio & Proportion - math review practice exercises
11. 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.
12. Spy Guys Interactive - Ratio - Lesson 3
13. Using Proportions - online quiz

1. 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?
2. All About Ratios - a Quiz
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.

1. Spy Guys Interactive - Decimals - Lesson 1

1. Algebra (Grades 6 - 8)

1. Angles - Students practice their knowledge of acute, obtuse and alternate angles.
2. Angles - Interactive game to help recognize angles.
3. Classifying Angles - online quiz
4. Giraffe Angles - Draw, and label as many angles as you can that are formed by their bodies, or are parts of their bodies. Also try Shark Angles.
5. Measuring Angles - use a virtual protractor
6. Protractor - learn how to position and read a protractor in order to measure an angle, and how to use either scale on the protractor
7. Triangle Explorer - Students learn about areas of triangles and about the Cartesian coordinate system through experimenting with triangles drawn on a grid.
8. Triangles Side-By-Side - [this link opens on a new page] Students use geometric vocabulary to describe properties of triangles. (Author - Carolyn Garner)
9. Spy Guys Interactive - Working with Angles - Lesson 16

1. Identify Polygons - Names of polygons by number of sides and angles
2. Identify Shapes - Recognize properties and names of shapes
3. Name that Polygon - Identify name of given polygon components
4. Pete's Polygons - [this link opens on a new page] Students learn about closed figures called polygons. (Author - Paulette Boggs)
5. Polygon Playground - arrange designs with online movable polygons - hundreds of polygons to drag anywhere you want
6. Quad Squad - [this link opens on a new page] Students describe various quadrilaterals. (Author - Sandi King)
7. Sam's Similar Shapes - [this link opens on a new page] Students learn about shapes that are different sizes but the same shape. (Author - Paulette Boggs)
8. Triangle Identification - identify the triangle given its angles
9. Triangle Identification - identify the triangle given its number of sides

1. Billy Bug - Guide Billy to the coordinates hiding the food. coordinates 0-10 | coordinates 0-5
2. Catch the Fly - [all 4 quadrants are used] Use the keyboard to enter the x and y values of an ordered pair to help the fly catch a bug. No score is kept, each question is essentially a one question game.
3. Graphing Skills - What's the point? find the point on the grid (choose Easy for Quadrant 1 problems)
4. Grid Graph - [this link opens on a new page] Students identify and plot points on a grid. (Author - Paulette Boggs)
5. Reading a Grid - Find Hurkle behind the grid. Type ordered pairs to find him
6. Simple Coordinates Game - Students investigate the first quadrant of the Cartesian coordinate system through identifying the coordinates of points, or requesting that a particular point be plotted.
7. Simple Maze Game - Students investigate the first Quadrant of the Cartesian coordinate system by directing a robot through a mine field laid out on the plane.
8. Spy Guys Interactive - Using Ordered Pairs - Lesson 18
9. What's the Point? - Find the x-y point on a grid
10. Worksheet Generator - Print your own blank coordinate plane worksheets, you determine the number of grids on a sheet and whether the grids are numbered or not.
11. Advanced (all 4 Quadrants used)
    1. General Coordinates Game - Students investigate the Cartesian coordinate system through identifying the coordinates of points, or requesting that a particular point be plotted. (all 4 quadrants utilized)
    2. Maze Game - Students use their knowledge of points on a graph to move a robot to the target, while avoiding mines. (all 4 quadrants utilized)

1. Geometry (Grades 6 - 8)

1. Banana Hunt -This game helps students practice the degrees of an angle
2. Measuring Angles - Investigating angles and the use of a protractor

1. Measurement Equivalents - Match game with standard equivalent measurements, such as pounds, ounces, pints, cups, etc.
2. Practice converting from one metric unit to another with this java applet (length, area, volume, mass, or time units)
3. Teaching Measures – Choose from three modules; length, mass, and capacity. Each category offers several activities for your large screen display as well as supporting worksheets.

1. Measurement (Grades 6 - 8)

1. Heads Up Probability - [this link opens on a new page] Students use tree diagrams as models for predicting outcomes and the likelihood of events using coins. (Author - Michaél Dunnivant)
2. Leap Frog - [this link opens on a new page] Students design an experiment to answer a question, collect information, and interpret the results using charts. (Author - Michaél Dunnivant)
3. Me Too Probability - [this link opens on a new page] Students use a tree diagram to display possible outcomes of who will come to the party. (Author - Michaél Dunnivant)
4. On Stage Probability - [this link opens on a new page] Students use tree diagrams to display the possible outcomes of casting a play. (Author - Michaél Dunnivant)
5. What are Your Chances - What many people refer to as 'good luck' can actually be explained by a little knowledge about probability and statistics. Our dice game allows you to see how increasing or decreasing the number of dice rolls effects an outcome.
6. Who Will Probably? - [this link opens on a new page] Students use problem-solving steps and a tree diagram to display possible outcomes and make predictions. (Author - Michaél Dunnivant)

1. The Random Ball-Picking Machine - experiment with a random generator at a BBC site to collect data to make decisions about probability.
   1. After you finish working through the ball-picking activity, take a ten-question quiz

1. A lesson designed to introduce students to stem-and-leaf plots
2. An overview of stem-and-leaf plot - a display that organizes data to show its shape and distribution
3. An Overview of Mean, Median, and Mode
4. Box Plot - explanation from the Engineering Statistics Handbook
5. Box Plot - comparing the average height of singers
6. Box Plot - interactive
7. Box and Whisker Plots
8. Box and Whisker Plot - use your TI-83+ graphing calculator with box and whisker plots
9. Interpreting Data - survey a small group by clicking on each of the children, turn the tally marks into two types of graphs and then go back and take a different survey
   1. Interpreting Data Quiz - after you finish the lesson above, take this quiz
   Interpreting Data - survey a small group by clicking on each of the children, turn the tally marks into two types of graphs and then go back and take a different survey
10. Let the Games Begin: Olympic Trials in Data Analysis
11. Long Distance Airplanes - a stem-and-leaf plot lesson from Iluminations (rated 3rd-5th grade, but quite useful)
12. Make a Stem-and-Leaf plot of the data you enter into the text area (ignore the warning about Internet Explorer, it works fine).
13. Organizing Data in a Stem and Leaf Plot - a lesson plan from Annenberg CPB
    1. Making a Stem and Leaf Plot - An excellent interactive assignment can be found at the bottom of this page.
    2. Ordering a Stem and Leaf Plot - An excellent interactive assignment can be found at the bottom of this page.
    3. Grouping by Fives - An excellent interactive assignment can be found at the bottom of this page.
14. Overview of a Stem-and-leaf plot by Nicole Carroll followed by a practice quiz
15. Stem-and-Leaf Plots - Their Construction and Use - an overview followed by several suggested assignments
16. Stem and Leaf Plotter - an interactive applet that allow students to input data
17. Stem-and-Leaf plots - from Purple Math
18. Worksheet to accompany a "Stem-and-Leaf Plots" Lesson

1. All That Data - [this link opens on a new page] Students use range, mean, median, and mode. (Author - Kristy Rousseau)
2. All That Data Two - [this link opens on a new page] Students describe graphs in terms of range, measures of central tendency, and distribution. (Author - Kristy Rousseau)
3. An Overview of Mean, Median, and Mode
4. Basketball Debate - [this link opens on a new page] Students explore the meaning of average (or mean) and relate these concepts to real world experiences. (Author - Michael Naylor)
5. Bicycles Ala Mode - [this link opens on a new page] Students understand and apply the concepts of mean, median and mode. (Author - Michael Naylor)
6. Jupiter Is Average - Using data from our solar system, students explore median, mode, mean, and range. Students learn to use an on-line calculator to determine the mean and range. (Author - Sandi King)
7. Mean Green Machine - [this link opens on a new page] Students use a calculator to find and use the average, or mean, of a set of data. (Author - Kristy Rousseau) (designed for 5th grade)
8. Mode, Mean, Median - calculate mode, median and mode of a set of buildings, then repeat the activity with a different set - (metric measurements)
   1. Quiz following the Mode, Mean, Median activity
9. Mean, Median, and Mode Calculator - enter numbers separated by comma and then calculate
10. Medians - [this link opens on a new page] Students understand and apply the concepts of median and mean. (Author - Michael Naylor)
11. Range, Mean, Median and Mode of a set of numbers - from Dr. Howard Ufigure's Math Tutorials
12. Party Comedian - [this link opens on a new page] Students find and use the median of a set of data. (Author - Kristy Rousseau)
13. Party Mode - [this link opens on a new page] Students find and use the mode of a set of data. (Author - Kristy Rousseau)

1. Circle Graph - Enter data categories and the value of each category to create a circle graph (similar to "Pie Chart" but the user can define the data set)
2. Data Interpretation Games - Numerous activities on using and interpreting data - Activities include bar, pie and line graphs, data collecting and much more
3. Data Picking - students collect data, enter tally marks or numbers and then select which graph is appropriate
4. Interpreting Circle (Pie) Graphs - students practice by answering eight questions about the graph
5. Overview of a Circle Graph by Nicole Carroll followed by a practice quiz
6. Pie Chart - Students view pie charts (parameters: number of sectors, size of sector as a percent)
7. Piece Of Pie - [this link opens on a new page] Students display data using a circle graph. (Author - Sandi King)

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