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6th grade (Illustrative Mathematics)

Unit 1: area and surface area, unit 2: introducing ratios, unit 3: unit rates and percentages, unit 4: dividing fractions, unit 5: arithmetic in base ten, unit 6: expressions and equations, unit 7: rational numbers, unit 8: data sets and distribution.

6 th Grade Math Worksheets

Free, Printable Math Worksheets for at-home Practice

A Parent’s Guide to Sixth Grade Math + Practice Worksheets

Download this informative guide to learn how to best support your sixth grader as they learn and master important sixth grade math concepts.

Free Practice Worksheets

Choose a Grade

Click on a concept below to try a sample question

Measurement & Data

Number representation.

Ratio & Proportion

Probability, number relation, factors & multiples, why 6th grade math worksheets are important.

A stated objective of Common Core State Standards (CCSS) is to standardize academic guidelines nationwide. In other words, what sixth graders learn in math in one state should be the same as what students of the same age are learning in another state. The curricula may vary between these two states, but the general concepts behind them are similar. This approach is intended to replace wildly differing guidelines among different states, thus eliminating (in theory) inconsistent test scores and other metrics that gauge student success.

An increased focus on math would seem to include a wider variety of topics and concepts being taught at every grade level, including sixth grade. However, CCSS actually calls for fewer topics at each grade level. The Common Core approach (which is clearly influenced by “Singapore Math”—an educational initiative that promotes mastery instead of memorization) goes against many state standards. Many states mandate a “mile-wide, inch-deep” curriculum in which children are taught so much in a relatively short time span, that they aren’t effectively becoming proficient in the concepts they truly need to understand to succeed at the next level. Hence, CCSS works to establish an incredibly thorough foundation not only for the math concepts in future grades, but also toward practical application for a lifetime.

For sixth grade, Common Core’s focus is on addition and subtraction— the basic math facts they will use throughout their education and beyond—as well as learning how to measure without necessarily using a ruler, and how to understand shapes. Ultimately, this focus will enable children to develop rigor in real life situations by developing a base of conceptual understanding and procedural fluency.

How Our Sixth Grade Math Worksheets Reflect Common Core Standards

Our sixth grade worksheets focus on the four critical areas outlined by CCSS:

• Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems
• Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers
• Writing, interpreting, and using expressions and equations
• Developing understanding of statistical thinking

6th Grade Math Worksheets: Critical Areas of Focus

Fasten your seatbelts: Sixth graders are in for a wild ride this year in math. Many new concepts, such as negative numbers and variables, are introduced, but students’ previous learning will set them up nicely for learning these topics. Furthermore, much of what debuts in sixth grade provides some foundation for the algebra in the near future. Here are the four critical areas that Common Core brings to sixth grade math:

Students not only apply their proficiency of multiplication and division that they learned in earlier grades, they also use fractions extensively to solve problems about ratios and rates (e.g, if a recipe uses 4 cups of flour to make 20 cookies, how many cups are needed to make 5 cookies?).

Division of Fractions, Negative Numbers

Negative numbers are introduced, with an emphasis on negative rational numbers, negative integers, and absolute value. In the last of the four basic operations they will apply to fractional equations, students learn to divide fractions by fractions. The graph system, on which students previously were working with only one quadrant, is expanded to include all four quadrants on the coordinate plane.

Expressions and Equations

In what may be the strongest preview of future algebra, students will learn to solve one-step equations using variables (e.g, x+10=17, solve for x). Sixth graders will also rewrite equations in equivalent forms and understand that a solution is the values of the variables that make an equation true.

Statistical Thinking

As they develop their ability to think statistically, sixth graders will learn about mean, median, and mode, and they will start describing data distributions. They will also learn about measures and variability and the effect of outliers.

6th Grade Math Worksheet - A Parent's Guide

Many educators, politicians, and parents believe the instruction of mathematics in the United States is in crisis mode, and has been for some time. Indeed, recent test results show that American 15-year-olds were outperformed by 29 other countries on math testing scores. 1 To help counter this crisis, educational, civic, and business leaders worked together to develop the Common Core State Standards (CCSS).

The goal of Common Core is to establish consistent, nationwide guidelines of what children should be learning each school year, from kindergarten all the way through high school, in English and math. Though CCSS sets forth these criteria, states and school districts are tasked with developing curricula to meet the standards.

The 2014-15 school year will be important for Common Core as the standards are fully implemented in many remaining states of the 43 (and the District of Columbia) that have embraced their adoption. CCSS has its advocates as well as its critics, and the debate on its merits has become more pronounced in recent months. Irrespective of the political differences with Common Core, its concepts are critical for students because the standards help with understanding the foundational principles of how math works. This guide steers clear of most of the controversy surrounding CCSS and primarily focuses upon the math your sixthgrader will encounter.

1 U.S. Students Slide in Global Ranking on Math, Reading, Science; NPR.org; Dec. 13, 2013

Common Core Standards

A stated objective of Common Core is to standardize academic guidelines nationwide. In other words, what sixth-graders are learning in math in one state should be the same as what students of the same age are learning in another state. The curricula may vary between these two states, but the general concepts behind them are similar. This approach is intended to replace wildly differing guidelines among different states, thus eliminating (in theory) inconsistent test scores and other metrics that gauge student success.

An increased focus on math would seem to include a wider variety of topics and concepts being taught at every grade level, including sixth grade. However, CCSS actually calls for fewer topics at each grade level. The Common Core approach (which is clearly influenced by so-called “Singapore Math”—an educational initiative that promotes mastery instead of memorization) goes against many state standards, which mandate a “mile-wide, inch-deep” curriculum in which children are being taught so much in a relatively short span of time that they aren’t effectively becoming proficient in the concepts they truly need to succeed at the next level. Hence, CCSS works to establish an incredibly thorough foundation not only for the math concepts in future grades, but also toward practical application for a lifetime.

For sixth grade, Common Core’s focus includes ratios, division of fractions, negative numbers, and variables. Ultimately, this focus will enable children to develop rigor in reallife situations by developing a base of conceptual understanding and procedural fluency.

Overview of Sixth Grade Math Topics

From the four critical areas of focus discussed in the previous section, Common Core also further clarifies the skills sixth graders should know by the end of the school year. For example, the fluency requirement at this level is multi-digit division and multi-digit operations with decimals. The five topics presented here, taken directly from CCSS itself, include some specifics on what kids will be taught in 6th Grade.

Ratios and Proportional Relationships

• Understand ratio concepts and use ratio reasoning to solve problems. The concept of ratios will be taught; for example, every soccer team in the league has 12 players, so the ratio of players to teams is 12:1. From this concept is introduced the idea that a unit rate of a ratio a:b is the same as a/b (e.g., if the soccer team has 2 goalkeepers out of its 12 players, 1/6 of the team are goalies). Once ratios are understood, students will solve real-world math problems including ratios of time and speed, unit pricing, percentages, and measurement.

• Gain familiarity with factors and multiples. Prime numbers are also introduced.

• Generate and analyze patterns. The idea here is that sixth graders will recognize the patterns apparent in the four basic math operations, as well as create patterns based on a given rule.

Number Operations in Base 10

• Use place value understanding and properties of operations to perform multi-digit arithmetic. Students will strive toward fluently adding or subtracting numbers within a 1,000. They will master rounding numbers to the nearest 10 or 100, and they will also learn to multiply one-digit numbers by multiples of 10 but less than 100 (e.g., 6 × 40).

The Number System

• Apply and extend previous understandings of multiplication and division to divide fractions by fractions. This is exactly how it sounds: Students will become proficient in dividing fractions by fractions. Then, they will apply this concept to word problems.

• Compute fluently with multi-digit numbers and find common factors and multiples. By the end of sixth grade, students complete their fluency of the four basic operations and will be able to add, subtract, multiply, or divide any multi-digit number, either whole or including decimals. Also, they will learn to find the greatest common factor (GCF) of two numbers of 100 or less and the least common multiple (LCM) of two numbers not greater than 12.

• Apply and extend previous understandings of numbers to the system of rational numbers. The concept of negative numbers are emphasized, particularly in real-world quantities (e.g., temperature, budgets, and so on). Rational numbers and absolute value are introduced, as well as the role of 0 on the number line. Finally, word problems will include graphing points in all four quadrants of a coordinate plane.

• Apply and extend previous understandings of arithmetic to algebraic expressions. Among the subjects taught:.

• Students will begin to identify and evaluate expressions that replace letters for numbers (e.g., add x to 8 to get x + 8).
• They will identify parts of an expression using the terms they have learned from previous grades (e.g., quotient, factor, sum, and so on).
• They will create and evaluate expressions using whole-number exponents.
• They will apply the order of operations to equations, especially those without parentheses.
• They will apply the distributive property to reach equivalent equations. For example, 2 (x + 4) is the same as 2x + 8.
• They will be able to identify when equations are equivalent. For example, x + x + 2x is equivalent to 5x - x.

• Reason about and solve one-variable equations and inequalities. With these algebraic concepts down, sixth graders will begin to solve simple equations and inequalities that include one variable. They will also use substitution to determine if an equation is true.

• Represent and analyze quantitative relationships between dependent and independent variables. Students will solve problems that use variables to represent two quantities that change in relationship to one another. For example, how far would a train that goes 50 miles per hour travel in a certain number of hours? If d represents distance and t equals time, then d = 50t. The equation can change if the train goes faster or slower.

• Solve real-world problems involving area, surface area, and volume. Concepts taught in sixth grade include:

• Students will solve for the area of right triangles, special quadrilaterals, and other polygons by composing the shapes into rectangles or decomposing them into triangles and other shapes.
• The will learn how to find the volume of a right prism.
• They will draw polygons in the coordinate plane based on given vertices, and they will apply this concept to word problems.
• They will represent three-dimensional problems using nets of rectangles and triangles to find surface area.

Statistics and Probability

• Develop understanding of statistical variability. Students will be taught the definition of a statistical question as one that anticipates variability (for example, asking someone’s age with the knowledge the answer could be within a range of numbers). Also, they will learn that data collected to answer a statistical question has a center (mean, median, and mode), a spread (interquartile range, mean absolute deviation, and outliers), and an overall shape.

• RSummarize and describe distributions. Sixth graders will display data on a number line, including dot plots, histograms, and box plots. Furthermore, they will summarize data sets in relation to context, including by reporting the number of observations, describing the nature of the attribute (e.g., how it was measured), by mean and median, and by identifying patterns in relation to the center.

Tips for Helping Your Sixth Grader with These Sixth Grade Math Worksheets

Some of parents’ trepidation with Common Core isn’t so much with the guidelines themselves, but with the testing now aligned with CCSS via local math curricula. Standardized testing was stressful for students and parents before; with the ongoing Common Core implementation, many families simply don’t know what to expect.

Fortunately, CCSS does not have to be that stressful, for you or your sixth grader. Here are some tips to help your children succeed with Common Core math:

Be informed; be involved

If Common Core concerns you, intrigues you, or confuses you, don’t hesitate to learn as much about it—in your child’s classroom, at your kids’ school, and on a national level. Talk with teachers, principals, and other parents. Seek advice on how you can help your kids, and yourself, navigate CCSS math. If you want to take further action, become involved with PTA or other organizations and committees that deal with your school’s curriculum. The more you know, the more, ultimately, you can help your child.

Give them some real-world math

A basic tenet of Common Core is to apply math principles to real-world situations. Why not start now? Give your child math problems when you are out and about— the grocery store, in traffic, the park, and so on. For example, if you are putting gasoline into your car, before you start dispensing the fuel, ask your sixth grader how much money will be required to fill up your 15-gallon tank. Without a pencil and notebook to compute the answer, he or she might have to fall back on alternative math processes—processes that Common Core encourages—for a solution.

Take time to learn what they are learning

You might look at a worksheet your child brings home and think, “This isn’t the math I’m used to.” Because Common Core emphasizes understanding the process of arriving at an answer, your child may be taught additional ways to fry a mathematical egg, so to speak. Instead of shunning these approaches, learn them for yourself. Once you comprehend these additional methods, you will be better able to help your child comprehend them as well.

Encourage them to show their work

This suggestion can be read two ways. First, students will be encouraged to show how they arrived at an answer (and beginning with sixth grade math, some answers can be self-checked to see if they are correct), especially within Common Core. Second, ask your children to show you their homework, particularly the challenging stuff. Explaining how a problem is solved is a basic CCSS tenet, so if your kids can be confident in explaining their work to you, they will carry that confidence into the classroom when the teacher asks for those same explanations.

Seek more help if necessary

If your sixth grader is struggling with the new math standards, talk with his or her teacher first. You then might want to seek outside resources to help your child. Several online resources provide math help, including worksheets and sample tests that conform to Common Core standards. Tutoring might be an option you consider as well. Innovative iPad-based math programs have emerged that combine the personalized approach of a tutor with today’s technology. This revolutionary approach also may feature a curriculum based on Common Core, thus ensuring your child’s learning at home is aligned with what he or she is learning at school.

The Truth About CCSS and Performance

Common Core aims to improve educational performance and standardize what students should learn at every grade in preparation for a lifetime of application, but it does not set curricula, nor does it direct how teachers should teach. As with any educational reform, some teachers, schools, and school districts will struggle with CCSS, some will seamlessly adapt, and some will thrive. As a parent, your responsibility is to monitor what your sixth-grader is learning, discover what is working or isn’t working for your child, and to communicate with his or her teacher—and to accept that your children’s math instruction does differ from what you learned when you were younger, or even what they might have learned last year. The transition can be a little daunting for parent and student alike, but that’s not a product of the standard itself. Common Core simply takes a new, more pointed approach to improving the quality of math instruction in this country.

The Benefits

As previously mentioned, CCSS decreases the number of topics students learn at each grade. However, the remaining topics are covered so extensively that the chances a child will master the corresponding skills increase. An analogy to this approach is comparing two restaurants. One restaurant has a varied menu with dozens of items; the other only serves hamburgers, fries, and milk shakes. The quality of the food at the first restaurant may vary upon the cooks’ experience, the multitude of ingredients required for so many offerings, and the efficiency (or lack thereof) of the staff. Because the second restaurant only serves three items, mastering those three items efficiently should result in an excellent customer experience. That’s not to say the first restaurant won’t succeed (because many do), but there’s always a chance that something on the menu won’t live up to the business’s own expectations.

By reducing the number of math topics taught, Common Core helps ensure students are truly ready for what comes next. Given the attention given to the included concepts, more practical applications and alternate operations of the math can be explored.

Coinciding with the reduction of topics is an emphasis on vigor—achieving a “deep command” of the math being taught. Students will be challenged to understand the concepts behind mathematical operations rather than just resorting to rote memorization and processes to get a right answer. Speed and accuracy are still important; kids won’t be getting away that easily from flash cards and quizzes that increase fluency. Moreover, Common Core places even additional emphasis on practical application—after all, the math kids learn now will be important when they become adults, even if they never have to think about prime numbers or symmetrical lines in their day-to-day lives.

Finally, CCSS links standards from grade to grade so that the skills learned at one level translate into the tools they need to learn at the next level. This coherence would seem an obvious educational approach, but often, there is no link—students are taught a skill in sixth grade that might not be used (and might have to be re-taught) until eighth. Each new concept in Common Core is an extension of a previous, already learned concept.

2 Grade 4: Introduction, Common Core State Standards Initiative

Math Practices to Help Improve Performance

In addition to the grade-specific standards it sets forth, Common Core also emphasizes eight “Standards of Mathematical Practice” that teachers at all levels are encouraged to develop in their students.3 These eight practices, designed to improve student performance, are described here, with added information on how they apply to sixth-graders.

• Make sense of problems and persevere in solving them. Students explain the problem to themselves and determine ways they can reach a solution. Then, they work at the problem until it’s solved. This CCSS math practice encourages students to take their time to read and try understanding the problem, emphasizing that the process is ultimately important even if it doesn’t result in a correct answer. Sixth-graders, for example, might create a table of numbered pairs to better understand a ratio. Students this age will also be encouraged to visualize the problem in order to better reach a solution.

• Construct viable arguments and critique the reasoning of others Students use their acquired math knowledge and previous results to explain or critique their work or the work of others. Sixth-graders may be asked to work in teams to solve a problem or set of problems, then present their work to the class.
• Model with mathematics This is just like it sounds: Students use math to solve real-world problems. Sixth-graders can be challenged to take the math skills they have learned into their own lives. For example, a student may use ratios and variable equations to determine how many lawns could be mowed in 30 hours if it takes 6 hours to mow 4 lawns.
• Use appropriate tools strategically Another self-explanatory practice: Students learn and determine which tools are best for the math problem at hand. Fourth-graders might be directed to fgure out the perimeter of their classroom and be given a choice of a yardstick, a 6-inch ruler, or a tape measurer to achieve that goal. They then decide which will work best toward a solution.
• Attend to precision Students strive to be exact and meticulous—period. A great thing about ratios and variable equations: Answers can be easily and efficiently double-checked, and sixth-graders will be expected to review an answer to ensure they were correct. Here’s another example of the importance of precision: Students can use the distributive property to express the sum of two whole numbers between 1 and 100 with a common factor as a multiple of a sum of two whole numbers with no common factor—e.g., 36+8 can also be expressed as 4 (9+2).
• Look for and make use of structure Students will look for patterns and structures within math and apply these discoveries to subsequent problems. For example, solving for x in an equation might be as simple as adding or subtracting the variable from each side—a basic algebraic principle that will help sixth-graders with variable expressions. Another example: The smaller number in negative inequality (e.g., -7
• Look for and express regularity in repeated reasoning Students come to realizations—“a-ha” moments is a good term for these realizations—about the math operations that they are performing and use this knowledge in subsequent problems. For example, a fourth-grader may realize that whenever an odd number is divided by an even number, there will be a remainder, which is something he or she can look for in future division problems.
• Look for and express regularity in repeated reasoning Students come to realizations—“aha” moments is a good term for these realizations—about the math operations that they are performing and use this knowledge in subsequent problems. For example, a sixth-grader might realize that 30 percent of a quantity is the same as 30/100 times the quantity. He or she can then use that knowledge when solving other problems involving percentages.

How to Help Your Children Succeed Beyond CCSS

Fortunately, CCSS does not have to be that stressful, for you or your fourth-grader. Here are some tips to help your children succeed with Common Core math:

A basic tenet of Common Core is to apply math principles to real-world situations. Why not start now? Give your child math problems when you are out and about— the grocery store, in traffic, the park, and so on. For example, if you are putting gasoline into your car, before you start dispensing the fuel, ask your fourth-grader how much money will be required to fill up your 15-gallon tank. Without a pencil and notebook to compute the answer, he or she might have to fall back on alternative math processes—processes that Common Core encourages—for a solution.

This suggestion can be read two ways. First, students will be encouraged to show how they arrived at an answer (and beginning with fourth-grade math, some answers can be self-checked to see if they are correct), especially within Common Core. Second, ask your children to show you their homework, particularly the challenging stuff. Explaining how a problem is solved is a basic CCSS tenet, so if your kids can be confident in explaining their work to you, they will carry that confidence into the classroom when the teacher asks for those same explanations.

If your fourth-grader is struggling with the new math standards, talk with his or her teacher first. You then might want to seek outside resources to help your child. Several online resources provide math help, including worksheets and sample tests that conform to Common Core standards. Tutoring might be an option you consider as well. Innovative iPad-based math programs have emerged that combine the personalized approach of a tutor with today’s technology. This revolutionary approach also may feature a curriculum based on Common Core, thus ensuring your child’s learning at home is aligned with what he or she is learning at school.

Math Practice Worksheets

Ratio and proportion.

Enter the ratio of number of boxes to number of cupcakes as a fraction in its simplest form: 3 boxes for 15 cupcakes

Identify all the equivalent ratios: For every 4 students who like Math in Victoria Public School, 8 like Chemistry.

12 laps in 3 hours = _ laps per hour

Steven saved $54 in 3 days. If he saved the same amount each day, how much money did he save in a day?

Which is a better buy?

• 7 items for $50
• 10 items for $61

Use a 2x multiplication table to write two equivalent ratios, a/c and b/d. Fill in the missing numbers. a/c = _ / _ b/d = _ / _

Are these ratios equivalent? 42 books for every 6 notepads 126 books for every 18 notepads

Write unit rate as a fraction in its simplest form Mason traveled 164 miles in 8 hours. If he traveled the same number of miles each hour, how many miles did he travel per hour?

Select the car that is the most efficient

Fill in the missing numbers a = _ b = _ c = _

If the value of x is 10, the value of y is _ .

Select the even number smaller than 5 and greater than -18.

Identify the coordinates of the point Z.

If the cross is reflected over the y-axis, give the coordinates of its reflected position.

When the point B is reflected over the y-axis, in which quadrant will the reflected point, B’, lie?

• Quadrant II
• Quadrant III
• Quadrant IV

Fill in the missing number The distance between (4, -2) and (4, 3) is _ units.

On the map of Jack’s neighborhood, Jack’s home is located at (5, 2). The park is located 3 units right of Jack’s home. What are the coordinates of the park?

Which is the farthest from Myra’s home?

T4 2/5 ÷ 3 7/9

The Highest Common Factor of 24 and 36 is _.

A set of tiles are put as a border of a room. Every third tile in the border is green and every fifth tile is checked. Which would be the first checked green tile?

Express in an equation form: If 8 is subtracted from a number, the answer is 14.

If a = -14 and b = 6, what is a x b?

Find the value of the expression, when x = 15. (6 ÷ 2)x - 4

Identify all the equivalent expressions

• p + p + p + p + p

If (30+20) is expressed as 10(2+3), where 10 is the greatest common factor of 30 and 20, how can you express (24+28)?

Study the table and define a rule for the output

Mason bought toffees for $3 and z candies costing $0.25 each. Which expression gives the total amount spent by Mason?

• 0.25 × z - 3
• 0.25 × z × 3
• 3 × z + 0.25
• 0.25 × z + 3

Select all the correct options: A shop sells a DVD for $8 and a CD for $4. Select the correct combinations that Mia would be able to buy if she has $40 dollars in hand.

• 3 DVDs and 5 CDs
• 2 DVDs and 6 CDs
• 4 DVDs and 2 CDs
• 5 DVDs and 1 CD

Is this statement true or false? When n is an integer less than 0, 10n > 1.

Select all the values that would make the inequality true: 15 - 4z > 6

Robert painted the walls and ceiling of two of his rooms. Each room measures 15 ft × 20 ft × 12 ft. How many rectangular faces did he paint?

Does the net match the solid figure of a triangular pyramid?

Which solid figure does the net represent?

Scroll down to see all the options: Which other faces have the same area as B? Select all the correct options.

What is the surface area of the net, in square inches, if each small square measures 1 square inch?

A rectangular pyramid and its net are given. Fill in the missing number. The area of the net is _ cm².

The area of one of the faces of a closed rectangular prism is 90 cm². The area of another face is 126 cm². If the area of the base is 35 cm², what is the surface area of the prism in cm²?

Emily is building a tent in the shape of a square pyramid. The area of the base is 25 ft² and the side and height of each of the triangular faces is 5 ft. How much material, in ft², does Emily need to build the tent?

Perimeter of a rectangle is 58 cm and one side is 14 cm. Calculate the area in sq. cm.

A cube and its net are given. Fill in the missing number. The area of the net is _ ft².

50 students of grade 5 are asked their ages. In which of these statements can you anticipate more variability?

• What is your age in months?

Stella collected the price of DVDs sold at the neighborhood store. The dot plot represents the data she collected. Describe the shape of data distribution.

• The distribution is symmetrical
• The data is clustered
• The data has an outlier.
• The distribution is skewed to the left

Identify the sampling method that the statement conveys: Andrew asks five members of every age group attending the gym about the number of hours in a week they exercise.

• Representative

The Basketball team of Brentwood High School played 5 games in a tournament and their scores are depicted in the Box and Whisker plot. What was their highest score?

The sizes of farms (in acres) in Sonoma County and Ben Hill County are depicted in the histograms. There are _ more 50-acre farms in Sonoma County than in Ben Hill County.

An ice-cream store recorded the different types of icecreams sold in a day. The table shows the data. How many Vanilla ice-creams were sold?

Holdings Inc. launched a new website. The number of hits on the first 5 days are listed here: 35, 95, 120, 115, 110 What is the effect of the outlier on the mean?

• The outlier increases the mean
• The outlier decreases the mean.
• The outlier has no effect on the mean.

Fill in the missing number The time (in seconds) taken by 10 contestants to complete a puzzle was recorded.

52, 48, 59, 62, 54, 135, 51, 59, 62, 58

The mean increases by _ seconds when outlier is included.

The line graph represents the price of stationery items at a departmental store.

Eva is taking French classes. The following are the number of new words learned by her over a period of 10 days.

5, 8, 7, 10, 6, 3, 12, 7, 8, 15

The range of the of the data is _ .

• (2) A), B), C)
• (6) 6, 10, 12, 20
• (10) 3, 5, 7, 10
• (3) (-8, -8)
• (8) 1 14/85
• (10) A, B, C, D

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grade 6, 7, 8 math

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Grade 6, 7, 8 math

Algebra, Geometry, and Middle School Math Grade 6 , 7 , & 8 - Anchor Chart BUNDLE

Math Word Walls - Grade 6 , 7 , 8 , Algebra, and Geometry Bundle

Grades 6 - 7 - 8 CCSS Math Self-Assessment BUNDLE | Pretests, Posttests, Tutoring

3rd Grade enVision Math Topics 3, 5, 6 , 7 , 8 , 9, & 15 Review Bundle!

Math Test Prep Math - MAP Attack Grades 6 - 7 - 8

Grade 6 , 7 , & 8 MATH BEST Standards BUNDLE I Can Posters & Checklists Florida

Grades 4, 5, 6 , 7 , 8 Coordinate Grids (New Ontario Math Curriculum 2020)

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BUNDLE First Grade iReady Math Lessons 5, 6 , 7 , 8 , 9, and 10 - 2024

2nd grade , I - Ready Math Lesson 6 , 7 , 8 , 9, 10 study guides regrouping add sub

Escape Rooms - Math Revision- Grades 6 , 7 , 8

Math Worksheets Bundle Grades 6 , 7 , 8 Over 1900 pages of activities

Math Fact Practice (Adding 6 , 7 , 8 , 9) for Second Grade - Common Core Aligned

Integer Operations - Unit 6 of 3-Part Grade 7 / 8 Ontario Math (2020)

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Decimal Enrichment Packets: Printable Tasks for grades 4,5, 6 , 7 , 8 Mental Math Fun

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Based on IM Grade 8 Math ™, unit 8 lessons 6 / 7 guided notes

Based on IM Grade 8 Math ™ Unit 7 lessons 6 / 7 guided notes

Based on IM Grade 8 Math ™ Unit 6 lessons 6 / 7

2nd Grade Go Math Bundle: Chapters 5, 6 , 7 , 8

Grade 6 / 7 Probability, Algebra Financial Unit 8 (Ontario Math Curriculum 2020)

Linear Equations Two Variables | Escape Room | Valentines Day | 6 / 7 / 8 Grade Math

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Based on IM Grade 8 Math ™, unit 5 lessons 6 / 7 guided notes

Based on IM Grade 8 Math ™, unit 6 / 7 guided notes

Grades 6 , 7 , 8 Math Common Core Checklist Multiple Grades

Based on IM Grade 8 Math ™, unit 2 lesson 6 / 7 guided notes

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Daily Assignments: title

Weekly Assignments: 10/1/12-10/5/12

Monday: Chapter 3, Lesson 1

Tuesday: Chapter 3, Lesson 2

Wednesday: Chapter 3, Lesson 3 

Thursday: BENCHMARK REVIEW

Friday: BENCHMARK ASSESSMENT

*If in doubt of which problems to do, ALWAYS do the Independent Practice section AND the Spiral Review section.

Course Syllabus title

Welcome to 6 th Grade Math !! J

• My Main Goal:

Every student will be proficient or advanced on the Math STAR test this school year. Failure is NOT an option.  

  …And we'll even have some fun while we're at it! J

• Course Overview

The 6 th grade mathematics program will include the development of logical reasoning skills, effective communications skills, and real-life problem solving.   The students will build on prior mathematical knowledge through increasingly challenging situations. The content will also include a strong introduction to the fundamental concepts of algebra and geometry.   Calculators will be used when appropriate.  

The course content will include: algebraic reasoning, integers, number theory and fractions, operations with rational numbers, proportional relationships, percents, collecting and analyzing data, probability, geometric figures, measurement and geometry, and multi-step equations and inequalities.  

• Suggested Supplies

Students are expected to have the following items daily :

1.        Backpack/book bag

2.       Binder (or a labeled section of a large binder for Math- this binder will be checked often to ensure proper note-taking is occurring)

3.       2 correcting pens (RED)

4.       A compass

5.       A protractor

6.       Lined paper

7.       Graph paper

8.       Pencil (homework will not be accepted if done in pen)

9.       School Planner

10.   Highlighters

11.    Expo dry erase markers

• Daily Assignment/HW Policy

Daily Assignments/Homework are assigned daily to reinforce skills learned in class and is due the following day.   It prepares students for upcoming lessons, teaches responsibility, and helps students develop positive study habits.   Homework will be assigned Monday through Thursday during a regular school week. I expect students to do their personal best on each assignment.   Homework should not take more than 45 minutes to complete and should be ready to turn in the following day for full credit.   Homework must always be done in PENCIL .   Students MUST SHOW THEIR WORK, or they will not get full credit. ***Homework Club is offered every Tuesday, Wednesday, and Thursday from 3-4pm in my classroom for all 6 th grade students!

It is the student's responsibility to record daily assignments in their Student Planner each day as a procedure while in class.   The Planner should be checked daily by the parent to make sure your child is being responsible and staying organized.   The Planner allows you to stay informed of your child's tasks that need to be completed and it can also be used a communicative tool from parent to teacher or vice versa.   If your child does not do their homework, they will write, "I did not do my homework last night" in red pen inside their planner.

• Make-Up Work/Absences

Absences may occur. (Please refer to the student handbook regarding the district tardy/absence policy).   If the absence is excused, students will have as many days to make-up the work as the number of days they missed.   If this period is more than three days, parents need to contact the office for information on school policy.   If the students has an unexcused absence, it may be necessary for them to do their make-up work during their free time (break time, lunch) until the work is completed.   I will accept late work under the following conditions :

1.        1 School day late = ½ credit

2.       After 1 School day= No credit

Parents and students can stay informed of their grades by checking the assignments and grades online and by viewing the district progress reports and report cards.

• Grading Scale and Grading Calculation

A+= 100%                           A=99-93%                           A-=92-90%

B+=89-88%                         B=87-83%                           B-=82-80%

C+=79-78%                        C=77-73%                           C-=72-70%

D+=69-68%                        D=67-63%                           D-=62-60%

• Participation 10%
• Homework/Classwork 30%
• Tests/Quizzes/Projects 60%
• Classroom Rules and Expectations

To guarantee every student in my classroom the excellent learning climate he/she deserves, it is necessary to have classroom rules/expectations.   I believe that all students can and should behave appropriately in our classroom.   I will tolerate no student preventing me from teaching and/or another student from learning .   Students will:

• Show Respect
• Make Good Decisions
• Solve Problems

Positive Consequences include, but are not limited to: intrinsic rewards, classroom freedoms, first in line, classroom helper, class points, phone call/note home, etc.

Negative Consequences include, but are not limited to: warning, removal from classroom for a timeout in another teacher's classroom, phone call/note home, detention, referral to administration, etc.

• Communication

I believe it is important that parents, students, and teachers work together.   Therefore, I encourage open communication.   If at any time you have questions, feel free to call, email, or send me a quick note.   (Email is the best way to get in touch with me.   It allows me to respond quicker).   In any situation, I will do my very best to get back with you within 24 hours.

Amanda Garceau                          [email protected]                                 530.743.1271

Daily Assignments title

Weekly Assignments 10/8-10/12

Monday: Chapter 3 Lesson 2 & 3 Review Worksheet

Tuesday: Chapter 3 Quiz (In Class) and Review Worksheet

Wednesday: Chapter 3 Lesson 4

Thursday: Chapter 3 Lesson 5

Friday: NO MATH

Tuesday: Chapter 3 Quiz (In class) and Benchmark Review

Friday: No Homework

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enVision Math Answer Key for Class 8, 7, 6, 5, 4, 3, 2, 1, and K | enVisionmath 2.0 Common Core Grades K-8

Envision math common core answer key for grade 8, 7, 6, 5, 4, 3, 2, 1, and kindergarten.

• envision Math Common Core Grade Kindergarten Answer Key
• envision Math Common Core Grade 1 Answer Key
• envision Math Common Core Grade 2 Answer Key
• envision Math Common Core Grade 3 Answer Key
• envision Math Common Core Grade 4 Answer Key
• envision Math Common Core Grade 5 Answer Key
• envision Math Common Core Grade 6 Answer Key
• envision Math Common Core Grade 7 Answer Key
• envision Math Common Core Grade 8 Answer Key

enVision Math Common Core Grade 8 Answer Key

• Topic 1 Real Numbers
• Topic 2 Analyze and Solve Linear Equations
• Topic 3 Use Functions to Model Relationships
• Topic 4 Investigate Bivariate Data
• Topic 5 Analyze and Solve Systems of Linear Equations
• Topic 6 Congruence and Similarity
• Topic 7 Understand and Apply the Pythagorean Theorem
• Topic 8 Solve Problems Involving Surface Area and Volume

enVision Math Common Core Grade 7 Answer Key

• Topic 1 Rational Number Operations
• Topic 2 Analyze and Use Proportional Relationships
• Topic 3 Analyze and Solve Percent Problems
• Topic 4 Generate Equivalent Expressions
• Topic 5 Solve Problems Using Equations and Inequalities
• Topic 6 Use Sampling to Draw Inferences About Populations
• Topic 7 Probability
• Topic 8 Solve Problems Involving Geometry

enVision Math Common Core Grade 6 Answer Key

• Topic 1 Use Positive Rational Numbers
• Topic 2 Integers and Rational Numbers
• Topic 3 Numeric and Algebraic Expressions
• Topic 4 Represent and Solve Equations and Inequalities
• Topic 5 Understand and Use Ratio and Rate
• Topic 6 Understand and Use Percent
• Topic 7 Solve Area, Surface Area, and Volume Problems
• Topic 8 Display, Describe and Summarize Data

enVision Math Common Core Grade 5 Answer Key

• Topic 1 Understand Place Value
• Topic 2 Use Models and Strategies to Add and Subtract Decimals
• Topic 3 Fluently Multiply Multi-Digit Whole Numbers
• Topic 4 Use Models and Strategies to Multiply Decimals
• Topic 5 Use Models and Strategies to Divide Whole Numbers
• Topic 6 Use Models and Strategies to Divide Decimals
• Topic 7 Use Equivalent Fractions to Add and Subtract Fractions
• Topic 8 Apply Understanding of Multiplication to Multiply Fractions
• Topic 9 Apply Understanding of Division to Divide Fractions
• Topic 10 Represent and Interpret Data
• Topic 11 Understand Volume Concepts
• Topic 12 Convert Measurements
• Topic 13 Write and Interpret Numerical Expressions
• Topic 14 Graph Points on the Coordinate Plane
• Topic 15 Algebra: Analyze Patterns and Relationships
• Topic 16 Geometric Measurement: Classify Two-Dimensional Figures

enVision Math Common Core Grade 4 Answer Key

• Topic 1 Generalize Place Value Understanding
• Topic 2 Fluently Add and Subtract Multi-Digit Whole Numbers
• Topic 3 Use Strategies and Properties to Multiply by 1-Digit Numbers
• Topic 4 Use Strategies and Properties to Multiply by 2-Digit Numbers
• Topic 5 Use Strategies and Properties to Divide by 1-Digit Numbers
• Topic 6 Use Operations with Whole Numbers to Solve Problems
• Topic 7 Factors and Multiples
• Topic 8 Extend Understanding of Fraction Equivalence and Ordering
• Topic 9 Understand Addition and Subtraction of Fractions
• Topic 10 Extend Multiplication Concepts to Fractions
• Topic 11 Represent and Interpret Data on Line Plots
• Topic 12 Understand and Compare Decimals
• Topic 13 Measurement: Find Equivalence in Units of Measure
• Topic 14 Algebra: Generate and Analyze Patterns
• Topic 15 Geometric Measurement: Understand Concepts of Angles and Angle Measurement
• Topic 16 Lines, Angles, and Shapes

enVision Math Common Core Grade 3 Answer Key

• Topic 1 Understand Multiplication and Division of Whole Numbers
• Topic 2 Multiplication Facts: Use Patterns
• Topic 3 Apply Properties: Multiplication Facts for 3, 4, 6, 7, 8
• Topic 4 Use Multiplication to Divide: Division Facts
• Topic 5 Fluently Multiply and Divide within 100
• Topic 6 Connect Area to Multiplication and Addition
• Topic 7 Represent and Interpret Data
• Topic 8 Use Strategies and Properties to Add and Subtract
• Topic 9 Fluently Add and Subtract within 1,000
• Topic 10 Multiply by Multiples of 10
• Topic 11 Use Operations with Whole Numbers to Solve Problems
• Topic 12 Understand Fractions as Numbers
• Topic 13 Fraction Equivalence and Comparison
• Topic 14 Solve Time, Capacity, and Mass Problems
• Topic 15 Attributes of Two-Dimensional Shapes
• Topic 16 Solve Perimeter Problems

enVision Math Common Core Grade 2 Answer Key

• Topic 1 Fluently Add and Subtract Within 20
• Topic 2 Work with Equal Groups
• Topic 3 Add Within 100 Using Strategies
• Topic 4 Fluently Add Within 100
• Topic 5 Subtract Within 100 Using Strategies
• Topic 6 Fluently Subtract Within 100
• Topic 7 More Solving Problems Involving Addition and Subtraction
• Topic 8 Work with Time and Money
• Topic 9 Numbers to 1,000
• Topic 10 Add Within 1,000 Using Models and Strategies
• Topic 11 Subtract Within 1,000 Using Models and Strategies
• Topic 12 Measuring Length
• Topic 13 Shapes and Their Attributes
• Topic 14 More Addition, Subtraction, and Length
• Topic 15 Graphs and Data

enVision Math Common Core Grade 1 Answer Key

• Topic 1 Understand Addition and Subtraction
• Topic 2 Fluently Add and Subtract Within 10
• Topic 3 Addition Facts to 20: Use Strategies
• Topic 4 Subtraction Facts to 20: Use Strategies
• Topic 5 Work with Addition and Subtraction Equations
• Topic 6 Represent and Interpret Data
• Topic 7 Extend the Counting Sequence
• Topic 8 Understand Place Value
• Topic 9 Compare Two-Digit Numbers
• Topic 10 Use Models and Strategies to Add Tens and Ones
• Topic 11 Use Models and Strategies to Subtract Tens
• Topic 12 Measure Lengths
• Topic 13 Time and Money
• Topic 14 Reason with Shapes and Their Attributes
• Topic 15 Equal Shares of Circles and Rectangles

enVision Math Common Core Grade K Answer Key

• Topic 1 Numbers 0 to 5
• Topic 2 Compare Numbers 0 to 5
• Topic 3 Numbers 6 to 10
• Topic 4 Compare Numbers 0 to 10
• Topic 5 Classify and Count Data
• Topic 6 Understand Addition
• Topic 7 Understand Subtraction
• Topic 8 More Addition and Subtraction
• Topic 9 Count Numbers to 20
• Topic 10 Compose and Decompose Numbers 11 to 19
• Topic 11 Count Numbers to 100
• Topic 12 Identify and Describe Shapes
• Topic 13 Analyze, Compare, and Create Shapes
• Topic 14 Describe and Compare Measurable Attributes

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Grade Calculator

Use this calculator to find out the grade of a course based on weighted averages. This calculator accepts both numerical as well as letter grades. It also can calculate the grade needed for the remaining assignments in order to get a desired grade for an ongoing course.

Final Grade Calculator

Use this calculator to find out the grade needed on the final exam in order to get a desired grade in a course. It accepts letter grades, percentage grades, and other numerical inputs.

Related GPA Calculator

The calculators above use the following letter grades and their typical corresponding numerical equivalents based on grade points.

Brief history of different grading systems

In 1785, students at Yale were ranked based on "optimi" being the highest rank, followed by second optimi, inferiore (lower), and pejores (worse). At William and Mary, students were ranked as either No. 1, or No. 2, where No. 1 represented students that were first in their class, while No. 2 represented those who were "orderly, correct and attentive." Meanwhile at Harvard, students were graded based on a numerical system from 1-200 (except for math and philosophy where 1-100 was used). Later, shortly after 1883, Harvard used a system of "Classes" where students were either Class I, II, III, IV, or V, with V representing a failing grade. All of these examples show the subjective, arbitrary, and inconsistent nature with which different institutions graded their students, demonstrating the need for a more standardized, albeit equally arbitrary grading system.

In 1887, Mount Holyoke College became the first college to use letter grades similar to those commonly used today. The college used a grading scale with the letters A, B, C, D, and E, where E represented a failing grade. This grading system however, was far stricter than those commonly used today, with a failing grade being defined as anything below 75%. The college later re-defined their grading system, adding the letter F for a failing grade (still below 75%). This system of using a letter grading scale became increasingly popular within colleges and high schools, eventually leading to the letter grading systems typically used today. However, there is still significant variation regarding what may constitute an A, or whether a system uses plusses or minuses (i.e. A+ or B-), among other differences.

An alternative to the letter grading system

Letter grades provide an easy means to generalize a student's performance. They can be more effective than qualitative evaluations in situations where "right" or "wrong" answers can be easily quantified, such as an algebra exam, but alone may not provide a student with enough feedback in regards to an assessment like a written paper (which is much more subjective).

Although a written analysis of each individual student's work may be a more effective form of feedback, there exists the argument that students and parents are unlikely to read the feedback, and that teachers do not have the time to write such an analysis. There is precedence for this type of evaluation system however, in Saint Ann's School in New York City, an arts-oriented private school that does not have a letter grading system. Instead, teachers write anecdotal reports for each student. This method of evaluation focuses on promoting learning and improvement, rather than the pursuit of a certain letter grade in a course. For better or for worse however, these types of programs constitute a minority in the United States, and though the experience may be better for the student, most institutions still use a fairly standard letter grading system that students will have to adjust to. The time investment that this type of evaluation method requires of teachers/professors is likely not viable on university campuses with hundreds of students per course. As such, although there are other high schools such as Sanborn High School that approach grading in a more qualitative way, it remains to be seen whether such grading methods can be scalable. Until then, more generalized forms of grading like the letter grading system are unlikely to be entirely replaced. However, many educators already try to create an environment that limits the role that grades play in motivating students. One could argue that a combination of these two systems would likely be the most realistic, and effective way to provide a more standardized evaluation of students, while promoting learning.

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NFL Draft 2024 rankings: 10 best offensive tackles available in class

T he 2024 NFL Draft arguably features the deepest group of offensive tackle prospects in recent memory. NFL teams searching for solutions at left and right tackle are overjoyed with the amount of instant contributors available all throughout the draft. Upwards of six-plus tackles are expected to be drafted within the opening 32 selections.

SB Nation polled several of its draft analysts to determine the consensus top-ranked offensive tackles. We identified the top-10 prospects by combining the consensus vote. They are as follows:

10. Patrick Paul, Houston

Paul combines 97th percentile arm length (36 ¼”) with a 96th percentile wingspan (84 ¼”). Paul also possesses 91st percentile height (6-7 ½”) and 87th percentile weight (331). You don’t think a general manager is betting on those traits with a top-75 selection? Paul must become more efficient with his footwork, but his size and athletic profile screams moldable traits.

9. Kingsley Suamataia, BYU

BYU continuously churns out athletic offensive tackles and Suamataia is next in line. Suamataia also possesses the length, size, and power to play both left and right tackle. NFL offensive coordinators will appreciate how Suamataia blends athleticism with an aggressive approach to displace defenders in the run game.

8. Jordan Morgan, Arizona

Morgan isn’t the biggest or longest tackle in the class, but he’s among the most experienced and technically sound. Morgan started 37 career games for the Wildcats and faced a slew of high-end pass rushers this season including UCLA’s Laiatu Latu. Morgan pairs strength with enough foot quickness to thrive on an island at the next level.

7. Graham Barton, Duke

Barton is almost certain to kick inside to guard or center in the NFL. Much like Peter Skoronski last season, Barton primarily played tackle at Duke, but his 29th-percentile arm length (32 ⅞”) appears prohibitive to his chances of playing tackle at the next level despite him totaling 2,134 snaps on the blind side for the Blue Devils across the previous three campaigns. Perhaps Barton’s NFL club gives him an opportunity to prove he can continue playing tackle, but the Brentwood, Tennessee, native has been preparing to make a successful positional switch.

6. Tyler Guyton, Oklahoma

Guyton is another high-upside prospect that possesses raw technical traits. Hand placement and punch timing needs to improve, but Guyton is a 6-foot-7, 322-pound blocker with rare size, measurements, and athleticism. Guyton’s athletic profile was evident at the NFL Combine, where he leaped a 34.5-inch vertical. If Guyton lands with the right offensive line coach that’s capable of coaching him through his inconsistencies, the sky’s the limit.

5. Taliese Fuaga, Oregon St.

Fuaga placed third on one ballot, but as low as nine on another. No offensive tackle prospect had a broader range of votes. There’s been some discussion of Fuaga sliding to guard at the professional ranks, and his 33-inch arms (15th percentile) only enhanced those conversations. On tape, Fuaga is a physical blocker with a nasty demeanor that aims to punish opposing defenders as a high-upside run blocker.

4. Amarius Mims, Georgia

Mims arguably possesses the highest ceiling of any tackle prospect in the 2024 NFL Draft. Mims has never played more than 385 snaps in a single season, and that number was actually 297 in 2023. The sample size is significantly smaller than desired, but Mims is a near 6-foot-8, 340-pound monster with a dreamy wingspan (86 ¾”) and length (36 ⅛”). Mims then leaped a 9-foot-3 broad at the NFL Combine. Mims checks the physical boxes teams covet in a franchise blocker.

3. JC Latham, Alabama

Our clear third-place vote-winner, Latham projects as an instant starter at right tackle. Latham’s decision to skip workouts at the NFL Combine and Pro Day raised some eyebrows over his athletic profile, but the tape paints a clear picture. Latham is a dominant mauler with 82nd-percentile or better measurements in weight (342), wingspan (84 ⅜”), arm length (35 ⅛”), and hand size (11 inches). Latham’s unteachables will endear themselves to NFL general managers.

2. Olumuyiwa Fashanu, Penn State

Only two tackle prospects received first and second-place votes. Fashanu earned one vote at the top of one ballot and the rest of the second-place votes. Fashanu began the 2023 college football campaign in a perceived race with Alt for OT1 bragging rights. Some technical (but fixable) warts popped on Fashanu’s tape this past campaign, but the Nittany Lions standout possesses rare movement skills, proven by his 5.11 40-yard dash and 32-inch vertical at the NFL Combine. Fashanu is a top-15 pick.

1. Joe Alt, Notre Dame

Alt was our near-unanimous top player, with just a single second-place vote on the ledger. It’s understandable why. Alt is the most complete offensive tackle prospect in the 2024 NFL Draft. Alt possesses the strength, physical build, and athleticism required to develop into an annual Pro Bowl and All-Pro selection as an elite blindside protector. Alt is plug-and-play at left tackle. His basement is the No. 7 overall pick, which is owned by the tackle-needy Tennessee Titans.