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

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## 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:

#### Ratio

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.

## 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.

#### Expressions and Equations

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

1. Students will begin to identify and evaluate expressions that replace letters for numbers (e.g., add x to 8 to get x + 8).
2. They will identify parts of an expression using the terms they have learned from previous grades (e.g., quotient, factor, sum, and so on).
3. They will create and evaluate expressions using whole-number exponents.
4. They will apply the order of operations to equations, especially those without parentheses.
5. They will apply the distributive property to reach equivalent equations. For example, 2 (x + 4) is the same as 2x + 8.
6. 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.

#### Geometry

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

1. 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.
2. The will learn how to find the volume of a right prism.
3. They will draw polygons in the coordinate plane based on given vertices, and they will apply this concept to word problems.
4. 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.

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:

#### 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.

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