# M/J Grade 6 Mathematics

## by Florida Association of School Administrators

This course material is only available in the iTunes U app on iPhone or iPad.

#### Course Description

This mathematics course provides resources to help teachers teach, students understand essential concepts and competencies, and parents the ability to support their child through the process.

In Grade 6, there are four critical areas of instruction:

- Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates.

- Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems. Students extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane.

- Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students construct and analyze tables, such as tables of quantities that are equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.

- Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different set of data can have the same mean and median yet be distinguished by their variability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected.

Students in Grade 6 also build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 by drawing polygons in the coordinate plane.

Name | Description | Time | Price | ||
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1 | Learn It Flashcards - Ratios and Percents | Become proficient in Ratios and Percents with Learn It Flashcards. Whether as a companion component to the Learn It Ratios and Percents Unit or as individualized skill building, Learn It Flashcards gives you experience in converting decimal numbers to percent, converting percent to decimal numbers, find percent change, determine ratios, equivalent ratios and proportions. | -- | $0.99 | View in iTunes |

2 | Khan Academy | Khan Academy allows you to learn almost anything for free. In our iPhone app: - You can learn anything – for free: Over 10,000 videos and explanations at your fingertips in math, science, economics, history, and much, much more - Sharpen your skills: over 40,000 interactive Common Core aligned practice questions are included with instant feedback and step-by-step hints. Follow along with what you’re learning in school or practice at your own pace - Quickly find what you need: Redesigned navigation and search make it faster to find what you want - Keep learning even when you’re offline: Bookmark your favorite content to “Your List” for easy access, and download it to keep learning even when you’re not connected to the internet. - Pick up where you left off: Your learning syncs between your iPhone and khanacademy.org, so your progress is always up-to-date In our iPad app, you can also: - Flex your muscles: the app adjusts to give you interactive exercise recommendations that are tailored just for you through the world of math. - Show your work: the app harnesses the power of writing down your thoughts as you problem-solve with a beautiful, expansive scratchpad. Once you have your answer, just write it in, and we’ll recognize your handwriting (powered by MyScript)! Learn using videos, interactive exercises, and in-depth articles in math (arithmetic, pre-algebra, algebra, geometry, trigonometry, statistics, calculus, linear algebra), science (biology, chemistry, physics), economics, and even the humanities with playlists on art history, civics, finance, and more. Spend an afternoon brushing up on statistics. Discover how the Krebs cycle works. Learn about the fundamentals of music notation. Prepare for the upcoming SAT, GMAT, or MCAT. Or, if you’re feeling particularly adventurous, learn how fire stick farming changed the landscape of Australia. It doesn't matter if you are a student, teacher, home-schooler, principal, adult returning to the classroom after 20 years, or a friendly alien just trying to get a leg up in earthly biology—Khan Academy's materials and resources are available to you completely free of charge. Head over to www.khanacademy.org to learn more."Khan Academy allows you to learn almost anything for free. | -- | Free | View in iTunes |

3 | Zeus vs Monster: Fun Math Game | Get your math drills and discover why users say Zeus vs Monsters – Fun Math Games for Kids is “better than Mathway”. It's been proven that kids learn math through games a lot faster than from math worksheets. Zeus vs. Monsters provides fun with maths for kindergarten, elementary level and adults. How? Math problems go gradually from very easy to extremely hard. - Voted #1 App of The Week by users - Easy to play - Guarantees both education and fun - Designed by educators - Top edutainment game - Educational tool for parents and teachers - Addition, Subtraction, Division and Multiplication from 0-1000 - Greek Mythology Learning Zeus vs. Monsters allows students to practice and develop general arithmetic at their own level, while providing increasing levels of difficulty as children master arithmetic skills. USERS: ****************************************************************************** + “I'm a mother of two - grade 5 and grade 7. Greek mythology and math in one game? Amazing!” +“Educational games like this shouldn't be free, but thanks!” + “A 1st grade kid I babysit isn't so good at math. I play the game with her and her addition and subtraction are improving! Magic...” ****************************************************************************** FOR EDUCATORS The feature “For educators” was created to offer different game settings for kids, depending on their age and level of math skills. Younger kids can choose to play the game only with addition and subtraction and only with numbers ranging from 0-50 at the ”easy” or “normal” level, whereas eight and nine-graders can choose to use all math operations and numbers between 0 and 1000 at the “hard” level. This feature is called “For educators” because parents, tutors or teachers can keep track of correct and wrong answers for each math operation and number range. TWO APPS IN ONE - 50 LEVELS OF MATH PROBLEMS AND GREEK MYTHOLOGY With 50 levels and 10 bosses to defeat, this is a real math adventure. The game is playable by kids of all ages with lots of positive encouragement, educational facts and catchy music. Game characters include Greek gods, Zeus and Athena, and mythical creatures/monsters such as Titans, Giants, Minotaur, Cerberus, Medusa, Typhon, Chimera, Centaur, Satyr and Hades. REVIEWERS: “Math Games – Zeus vs. Monsters has multiple goals, one of them is helping the kids sharpen their ability to stay focused for longer periods of time, change their perception of math, and see it like a fun way to spend time, and not just a boring and hard thing to do, also, kids will come in contact with some of the most common Greek symbols and mythology characters and stories…” “Zeus vs Monsters, a new educational math game from Peaksel, allows educators free use in order to help students do better in class. This kids' video game is designed to help educators determine weaknesses in a child’s math skills.” | -- | Free | View in iTunes |

4 | Fractions - by Brainingcamp | "The most comprehensive fractions app I've seen. This app should be in every classroom!" -- BestAppsForKids.org "If you have a student or child that has difficulty with fractions then this is the app for you." -- SmartAppsForKids.com Everything you need for teaching and learning: (1) Narrated lesson (2) Practice questions (3) Virtual manipulative (4) Challenging game TOPICS COVERED 1. Fractions Introduction 2. Equivalent Fractions 3. Common Denominator 4. Comparing and Ordering Fractions 5. Adding and Subtracting Fractions 6. Multiplying Fractions 7. Dividing Fractions FEATURES ▪ Lesson with visual models and audio narration to make abstract concepts concrete ▪ Questions to practice what was learned ▪ Virtual manipulative for hands-on discovery learning ▪ Challenge game to interactively apply understanding ▪ Alignment with state and Common Core standards ▪ Suitable for ages 9-14 | -- | Free | View in iTunes |

5 | Thinking Blocks Fractions | Thinking Blocks Fractions teaches children how to model and solve word problems involving fractions and whole numbers. In this interactive tutorial, children are introduced to 6 problem solving models. The models help children organize information and visualize number relationships. While Thinking Blocks Fractions may be used with any elementary math program, it is ideal for children who are learning model drawing strategies found in math books from Singapore. Thinking Blocks Fractions is best suited for children, ages 10+. | -- | Free | View in iTunes |

6 | Ratio Rumble | The battle is on in this game where you build your own potions! Create ratios to win this mixture mix-off! Ratio Rumble supports mathematical learning about equivalent ratios, and is relevant to Common Core topics such as: •Identifying ratios when used in a variety contextual situations •Providing visual representations of ratios •Solving common problems or communicating by using rate •Explaining why ratios and rates naturally relate to fractions and decimals. This app was developed as part of the Math Snacks initiative. Additional games, animations, and teacher support materials are available at http://mathsnacks.org. Developed by mathematics educators, researchers and game developers at the Learning Games Lab at New Mexico State University. Games developed by the Learning Games Lab undergo a rigorous instructional design process, extensive user testing, and input from learners, teachers, and researchers. For more information about the NMSU Learning Games Lab, visit http://learninggameslab.org. Math Snack materials were developed with support from the National Science Foundation (0918794). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Some materials were originally prototyped or discussed as part of a cooperative agreement from the U.S. Department of Education (U295A050004). | -- | $1.99 | View in iTunes |

7 | 4 Dice a Fractions Game | Multiplayer Fraction Game! Use two devices and play competitively or cooperatively with your classmates or parents. 4 Dice: Fraction Games hones the many concepts of fractions that include adding, subtracting, multiplying and dividing through a series of game mode options. The game also enhances analytical thinking by providing the answer and requiring students to determine the appropriate equation. KEY FEATURES: - Multiplayer Math Game! - High order thinking game to challenge students in a fun way - A built-in whiteboard to give students a place to work through problems 4 Dice: Fraction Games is a math app for middle school and upper elementary students. Common Core Mathematical Standard 4.NF Extend understanding of fractional equivalence and ordering. 5.NF Use equivalent fractions as a strategy to add and subtract fractions. 6 NF Apply and extend previous understandings of multiplication and division to divide fractions by fractions. "This is a fantastic app for 4th grade students and up. It reviews the procedures for adding, subtracting, multiplying, and dividing fractions in the instructions and gives the users challenges. The best part is probably the ability for users to challenge their friends and connect using different devices close by!" - Challenging App by M.L.I.S - Version 1.4 - Apr 14, 2013 Many classrooms don't have the resources for every student to have an iPad. Fortunately, there are ways to solve this problem and still get the most out of the 4 Dice game. 1. One Device with Multiple Players This is usually a situation where there is one device, which is probably owned by the teacher. Write the problem out on the board. Have each student get out a piece of paper and a pencil or use the printable version of the game. Set a time limit - one minute is recommended - to have each student try to solve the problem on the board. 2. A Few Devices with Multiple Players This is usually a situation where there are a few devices, but not enough for everyone to have their own. Let students work in small groups with one device. A blank piece of paper or the printable board can be used to record work. To do this: Create a multiplayer username (ex. Group 1) Use the numbers rolled on the device and solve the problem Input the information from the answer into the device to check it 3. Multiple Devices with Multiple Players If there are enough devices for everyone, there are four basic options: let students work individually, break students into small groups of two or three, split off into groups of two and compete as partners, or play as a classroom. | -- | Free | View in iTunes |

8 | Sixth Grade Learning Games SE | Learn important 6th Grade lessons with these 15 fun and interactive games! Teach them advanced 6th grade topics such as statistics, algebra, biology, science, geometry, rounding, language, vocabulary, reading, and more. Whether they are just starting Sixth Grade, or need to review and master the subjects, this is a perfect learning tool for kids aged 10-13. Math, language, science, STEM, reading, and critical thinking skills are all tested and practiced in these games. Every lesson and activity is designed using real sixth grade curriculums, so you can be sure these games will help give your child a boost in the classroom. And with helpful voice narration and exciting games, your 6th grade student will want to keep playing and learning! Improve your student's homework with these 6th grade teacher approved lessons, including STEM, science, language, and math. These learning games include dozens of important lessons for sixth grade, including: • Number Sense/Theory - Absolute Value, Roman Numerals, Number Lines, and More • Probability and Stats - Median, Mode, Range, and Probability • Geometry - Congruency, Symmetry, Angle Types, and Area • Consumer Math - Learn about sales, tax, tips, and other ways to calculate money • Algebra - Use the distributive property, evaluate expressions, and solve for x • Rounding - Round numbers to the nearest whole number, tenth, and hundredth • Synonyms and Antonyms - Identify different words that mean the same or opposite • Vocabulary - Learn the definitions of challenging words • Spelling - Hundreds of spelling words of varying difficulty • Reading Comprehension - Reading articles and then answer questions • Word Memory - Use clues to match words • Subject Verb Agreement - Pop balloons with verbs that match the subject • Laws of Motion - Use Newton's Laws of Motion in various experiments • Periodic Table - Learn about all the elements and how to use the periodic table • Biology - Advanced life science topics such as biology, evolution, and animal classifications Perfect for 6th grade kids and students who need a fun and entertaining educational game to play. This bundle of games helps your child learn important math, language, algebra, science, and STEM skills used in sixth grade all while having fun! 6th Grade teachers around the world use this app with their students to help reinforce math, language, and science subjects. Ages: 10, 11, 12, and 13 year old children and students. ===================================== PROBLEMS WITH THE GAME? If you are having any issues please email us at help@rosimosi.com and we will get it fixed for you ASAP. LEAVE US A REVIEW! If you're enjoying the game then we'd love for you to leave us a review! Reviews help small developers like us to keep improving the game. | -- | $3.99 | View in iTunes |

9 | FactorMan | This math game is played against the superhero FactorMan! You earn points by choosing numbers between 1 and 100. If you choose 5, you get 5 points; if you choose 18, you get 18 points. But FactorMan gets the sum of all of the factors of the number you have chosen (except for the number itself). If you choose 12, for example, you get 12 points, but FactorMan gets 1+2+3+4+6=16 points! Once a number has been used to gain points (by either you or FactorMan), it cannot be used again, and you may choose only numbers that have at least one other factor left on the board. To win you must have good arithmetic skills and develop a careful strategy. It is not as easy as it might sound! | -- | Free | View in iTunes |

10 | Coordinate Geometry | Explore Concepts Related to Coordinate Geometry with an Interactive Learning Tool The Coordinate Geometry app is a tool designed to help teachers introduce analytic geometry. It provides students with an interactive learning device to help them better understand the system of geometry where the positions of points on a plane are described using ordered pairs. Designed in California by Dr. Fred Ventura, Coordinate Geometry is one of the apps in the Math Power Series. Coordinate Geometry turns your iPad into a mathematical playground for introducing the coordinate plane, ordered pairs, reflection, rotation, translation, slope, y-intercept and other important mathematical concepts. Topics: • Coordinate Plane • x and y axes • Origin (0,0) • Coordinate Pairs • Quadrants • Points, Lines and Planes • Slope and y-intercept | -- | $1.99 | View in iTunes |

11 | Geoboard, by The Math Learning Center | Geoboard is a tool for exploring a variety of mathematical topics introduced in the elementary and middle grades. Learners stretch bands around the pegs to form line segments and polygons and make discoveries about perimeter, area, angles, congruence, fractions, and more. This virtual version of the manipulative is an open-ended educational tool, ideal for elementary classrooms and other learning environments that use iPod Touches, iPhones, or iPads. FEATURES • Create line segments and polygons by stretching bands around the Geoboard’s pegs. • Choose from 5 different band colors; 8 band colors on the iPad. • Fill individual shapes with a transparent color, or use the Fill All button to toggle all the bands between filled and unfilled. iPad only: • Switch between the standard 25-peg square board, a rectangular board with 150 pegs, or a circular board with 13 pegs. The circular board enables explorations with angles, fractions, and time measurement. • Duplicate shapes then move, rotate, or flip them to explore symmetry and congruency. • Change the color of selected bands. • Display grid lines with or without numbering to more easily calculate area and identify shape locations. • Use the drawing tools to annotate work and show understanding • Write equations and expressions with the text tool. MORE APPS For more Geoboard resources, a web and Windows version, and other apps, visit:www.mathlearningcenter.org/apps CURRICULUM To learn about Bridges in Mathematics, an elementary curriculum that employs visual models such as the geoboard, please visit: www.mathlearningcenter.org/bridges/overview ABOUT US This app is brought to you by The Math Learning Center, a nonprofit organization dedicated to K-12 math education since 1976. Visit us at: www.mathlearningcenter.org ACKNOWLEDGEMENTS The Geoboard app was made possible by a generous donation from Dr. David Moursund. This app was crafted by Clarity Innovations. We help improve teaching and learning by creating solutions that match promising technologies with the needs of education. Visit us at: www.clarity-innovations.com | -- | Free | View in iTunes |

12 | Math App - Geometry I | Building a strong foundation on basic geometry facts and the skill to quickly apply math formulas are important for young students to advance in their math skill. MathApp - Geometry I is to help young math students to understand and memorize the fundamental geometric facts and the basic set of geometric formulas through interactive displays and carefully selected quizzes and tests. Benefit of MathApp - Geometry I includes: 1. Quickly memorize Geometry facts with Answer On and Off switch right on the display. 2. Take a quick test on each subject, or challenge for the highest score to become a math master. 3. Answer each question as quickly as possible to earn higher score. Test timer will challenge students to memorize and apply geometric facts and formulas as quickly as possible, so they can achieve higher score in each game. 4. Masters test and quiz questions are combinations of both 'multiple choice' and 'put your own answer' questions. 5. Quiz and Test display has a button that brings up a full screen writing pad that helps students to apply geometric formulas to find the answer. 6. Adjustable question timer length. 7. Runs on iPhone, iPod Touch and iPad. Math App - Geometry I is primarily intended for students between 4th and 6th grades who are newly introduced to Geometry subject. We hope you enjoy our app, and improve on your math skill. ©2011 Digital Brainwash | -- | $1.99 | View in iTunes |

13 | 6th Grade Math Testing Prep | How do you know if your child is prepared for the state mandated math test? Get ready for standardized testing with hundreds of math questions covering a wide range of topics on a challenging 6th grade level. Topics covered include: addition advanced problem solving algebra critical thinking decimals division geometry logical calculation math with money multiple step procedures multiplication negative numbers percentages probability ratios statistics subtraction word problems 6th Grade Math Testing Prep was designed for the student and family looking for an advantage in solidifying their math skills: - Study anywhere and learn at your own pace - Specifically appropriate questions chosen at the 6th grade level - Practice with a quiz, then take the big final test to see how well you've learned - Email test results to a parent or teacher - Great for classrooms or at home - Increase your math knowledge and your scores! *With practice you can achieve your best score!* User reviews: - I’m an intervention math teacher and I love having my students take these tests after we have gone over the concepts and to get ready for our state exams! - Interactive and educational. I will definitely share this app with my students and their parents - This is a great app! It tests you on almost all the math subjects and then tells you what you can work on… I would recommend this app for anyone who wants to be a Straight "A" student in 6th grade We love to hear from you! Please send any feedback or questions to peekaboostudiosllc@gmail.com Teachers can use this app with their entire classroom: - Enter as many student names as you need - Set the number of questions you'd like on the test - Allow students to study and learn at their own pace - They can practice with a quiz, then take the big final test to see how well they've learned - Password-protected Administrator Section allows you to review scores, track student improvement, and zero in on topics where they could use extra help - Increase students' math knowledge and their scores! Peekaboo Studios is a member of Moms with Apps, a collaborative group of family-friendly developers seeking to promote quality apps for kids and families. Recommended Ages: 11-12 Categories: Math, Addition, Subtraction, Multiplication, Division, Algebra, Money | -- | $2.99 | View in iTunes |

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