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

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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.

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

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?).

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.

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.

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.

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.

**• 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.

**• 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).

**• 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.

**• 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:

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.

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.

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.

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.

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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