6th Grade Math Essentials: Key Skills Students Need to Master This Year

Short answer: In 6th grade, students move from arithmetic to proportional reasoning: ratios, unit rates and percentages. They also master fraction division and multi-digit decimals, meet negative numbers and absolute value on the number line, start algebra with exponents, order of operations and one-variable equations, and learn area, volume, the coordinate plane and basic statistics.

When students enter 6th-grade math, they begin transitioning from the basics to advanced concepts and specialized skills. Knowing the new 6th-grade math topics and techniques to expect can help parents and students plan ahead and achieve long-term success.

Starting on the right foot and preparing your student for complex ideas like ratios and proportions is also possible with the help of a qualified tutor. Here’s what you need to know.

Key points

• Proportional reasoning: Ratios and relationships between values are the main new skill of 6th grade.
• Unit rates and percents: 200 miles in 4 hours is 50 miles per hour; percents handle discounts.
• Fractions and decimals: Fraction division and decimal placement are the common sticking points.
• Negative numbers: The number line makes negatives and absolute value visual.
• Algebra begins: Exponents, PEMDAS and one-variable equations lay the groundwork for algebra.
• Geometry and data: Area, volume, the coordinate plane, mean, median and mode.

What does 6th grade math cover?

Why is proportional reasoning the heart of 6th grade math?

Students starting middle school face many new challenges. Many parents ask what 6th-grade math students learn. The new concepts and formulas build upon previous years, but the main new skill is proportional reasoning.

Proportional reasoning uses basic arithmetic to understand ratios and relationships between different values. These skills are helpful in multiple areas, such as understanding ingredient ratios in a cooking recipe or calculating speed in hours.

How do unit rates and percentages solve real-world problems?

Sixth-grade math will help your child get a handle on unit rates and percentages. These ideas allow students to compare values, make decisions, and solve everyday problems.

Unit rates allow you to compare two different quantities and show that relationship in a single unit. For example, if you drive 200 miles in 4 hours, you’ll be left with a unit rate of 50 miles per hour.

Learning how to find percentages can also help with real-world challenges like calculating how much you’ll pay for something with a 20% discount or how long a battery will last.

Having the skills to solve these types of problems will put your child in a position to excel at both math and science-related courses, as well as tackle day-to-day issues with ease.

What fraction and decimal skills do 6th graders need?

In 5th grade, students make the transition from simple fraction and decimal concepts to adding, subtracting, multiplying, and dividing fractions with unlike denominators (see our 5th grade math guide). In 6th grade, students continue to build their confidence and become more comfortable with fractions and multi-digit decimal operations.

One challenge your child will face is fraction division. One tactic that students learn is the “invert and multiply” rule. For this, students take two fractions and flip the second one, and then multiply. It’s easy to memorize this rule, but it can be challenging for a student to understand why it works.

Tutor tip: Don’t stop at the rule. Ask your child to explain why “invert and multiply” works, for example by asking how many halves fit into 3. A student who sees where the rule comes from is far less likely to misapply it later.

Decimal placement also becomes an important skill that many students can confuse when multiplying decimals. In many instances, students understand how to perform the calculations, but can forget to add a decimal or place it in the wrong position, resulting in an incorrect answer.

Tutor tip: Estimate before you multiply decimals. If 2.9 × 4.1 should be about 3 × 4 = 12, an answer of 1.189 or 118.9 is an instant signal that the decimal point is in the wrong place.

How do 6th graders learn negative numbers and the number line?

In 6th grade, your child will encounter a new idea of the number system: negative numbers. Teachers often try to ease the difficulty of negative numbers by plotting them on a number line, with zero in the middle, negative numbers on its left, and positive numbers on its right.

“Next to fractions, the skill students most often fail to master, and the one that causes them the most grief, is negative numbers. I see it all the way up to high school seniors.”

Sean Alexander, founder of Alexander Tutoring

The number line also eases the idea of absolute value. Absolute value is the positive value of a number, whether it’s positive or negative. For example, on the number line, a student will be able to count how many units a value is away from zero, no matter which direction it is in. This helps them understand that the absolute value of both 3 and −3 is 3.

Using visual models like the number line is a great way to help students process challenging new math ideas. Number lines are also simple to map out, which can ease anxiety for struggling students.

“The number line is the why. It explains why things work the way they do.”

Sean Alexander, founder of Alexander Tutoring

How does algebra start with expressions and equations?

Your child’s work in algebra really kicks off in 6th grade. Prior to this year, most math students practiced and used basic arithmetic operations, such as addition, subtraction, multiplication, and division. These straightforward calculations take on abstract twists that lay the foundation for the advanced math that students will learn in high school and college.

Exponents

Another math idea your child will learn is exponents. Exponents are small numbers placed at the top right of a base number. These signify that the person solving it must multiply the base number by itself that many times. For example, 3² means 3 × 3, and 3⁴ means 3 × 3 × 3 × 3.

Order of operations (PEMDAS)

Exponents are an important concept, but they also appear in the order of operations. This is a specific set of rules that students must use to solve complex math equations. Many abbreviate the order of operations as PEMDAS:

1. Parentheses
2. Exponents
3. Multiplication and division
4. Addition and subtraction

Once students understand PEMDAS, they will find that 3 + 2 × 4 = 11 and (3 + 2) × 4 = 20. Learning these basic algebraic expressions in 6th grade is the first step toward mastering algebra.

How do 6th graders solve one-variable equations and inequalities?

One of the most important new concepts is solving one-variable equations. These are math questions involving an unknown number represented by a letter, such as x or n. Students will move beyond straightforward examples like 2 + 3 = ? and learn how to solve for x in equations like 2 + x = 5.

The idea of including letters in math can lead to stress and confusion. One way teachers can help students master this concept is by using a balance scale. For example, to solve for x in 2 + x = 5:

1. Put 5 blocks on one side of the scale.
2. Put 2 blocks on the other side.
3. Count how many blocks it takes to balance the scale perfectly: three, so x is 3.

This balance scale can also help students understand inequalities. It may be easy to determine when both sides are balanced out and equal. However, students also need to learn the signs for greater than (>), less than (<), greater than or equal to (≥), and less than or equal to (≤).

Knowing what these mean and how to use them to compare values will prepare students for more advanced math in the years ahead.

What geometry do 6th graders learn?

Geometry becomes more prominent in 6th-grade math, which can be a big plus for visual and hands-on students. Your child will learn how to measure and analyze the area of triangles and polygons. In addition to area, they’ll also learn what volume is and how to calculate it by multiplying length, width, and height.

Students also use coordinate planes to plot vertices. These have two axes labeled x, which runs horizontally, and y, which runs vertically. The intersection point of these lines is the origin. From here, students can move left or down to plot negative numbers, or right or up to plot positive ones.

What statistics and probability basics are in 6th grade?

Students in 6th grade will also learn how to meaningfully find patterns and analyze data sets to form conclusions. Two of the most common ways teachers help students do this are through histograms and box plots:

• Histograms are visual tools where you stack data to see patterns.
• Box plots are another way to arrange data and show how data points spread out, highlighting outliers and trends.

Students will also learn how to find the mean, median, and mode, which are extremely useful when analyzing data. When you have a data set:

• The mean is the average value.
• The median is the middle value after arranging the numbers in order.
• The mode is the value that appears most often.

These are building blocks for statistical variability and probability courses that your child will likely take down the road.

How can you build a growth mindset for future STEM success?

Parents and students alike will look to grades to evaluate math skills. However, grades on their own don’t tell the whole story. Students may be able to consistently get the correct answer because they’ve memorized formulas. Still, if they don’t have a deep understanding of the core concepts, they may struggle when they encounter new concepts based on past principles.

The ideas your child will learn in 6th grade will form the foundation for the 7th-grade math curriculum and carry into upper-level math classes, such as statistics, algebra, and geometry. These skills also become the basis of Science, Technology, Engineering, and Mathematics (STEM) courses and majors that students take in high school and beyond.

If your child has had trouble in the past, this may bring you some anxiety. Not being able to keep up in class could mean falling behind in math for years. Some parents may chalk it up to the fact that their child isn’t a “math person.” However, it’s essential to realize that a “math person” isn’t born. They develop into one.

Like anything, math is a skill set. Having poor grades or difficulties in math shows a lack of understanding, not a genetic predisposition. As a parent, you can put your child in a position to succeed at 6th-grade math by taking a proactive approach.

One of the best ways to make sure your child is at or above their grade level is to use a tutor or sign up for a summer math intensive program. You may think that tutors are for students who need extra attention so they don’t fail out of a class. However, using a tutor to get ahead may be even more beneficial than using one to catch up.

Using a professional tutoring service like Alexander Tutoring means your child will have access to expert tutors who understand learning styles and can adapt their lessons to match each individual. This gives them a head start, and much of their year in math can be review of concepts they have already mastered.

It’s also important to manage your child’s expectations. Not every new concept will click instantly. Reassure them as they work through frustration. Teaching them to trust the process and to work on math consistently each day will help them form good habits that build confidence.

Whether your child is trying to figure out the 6th-grade basics or jumping ahead to meet the challenges of 8th-grade math standards, encouraging them to make mistakes is also important. This builds confidence and is the fastest way to learn something new.

Where can you find support for the middle school math transition?

Sixth grade is the start of middle school and an important transition point in a child’s math education. They are moving beyond the basics and building a foundation full of new skills and abstract concepts that will keep them on track for success through high school, college, and into their professional careers.

The pressure to keep up with the Common Core math 6th-grade curriculum and succeed in math, along with the new ideas, can cause a great deal of stress. Instead of having your child stressed out during the year when tests and assignments pile up, you can get them a qualified tutor to give them a head start.

At Alexander Tutoring, our tutors can identify your child’s learning style and find the gaps and weaknesses they need to improve. We can help your child learn complex concepts proactively, so they are ready to expand their skill set as upper-level courses introduce new concepts.

Sixth grade is the best time to turn your child’s “bad at math” narrative into a success story for years to come.

Frequently asked questions