6th Grade is the beginning of middle school for many students. This next step in their educational journey is a huge move forward in how and what students learn. For math students, 6th Grade is all about building a foundation for the more complex math waiting for them in high school and college. 6th grade is where students learn skills they can use in the real world, like the basics of statistics and algebra. Let’s get ready for higher education and the workplace with these top 3 math concepts sixth grade kids should know!Negative Numbers

## 1. Negative Numbers

Up until now, students have only worked with positive numbers. In 6th grade, students learn that every number has a negative version and how they function in math equations. In certain parts of the world, students may have heard of negative numbers, especially in winter. One of the most common ways negative numbers are used is with the weather. A thermometer is a real world version of a number line that kids can use to understand negative numbers. With this new information, students broaden their understanding of math. Negative numbers help explain more complex concepts, especially when talking about data.

### Graphing with Negative Numbers

Students have used number lines for marking points on a graph before 6th grade. Now it’s time to show that those lines don’t start at 0, but can go beyond it with negative numbers. With this new knowledge, students can start graphing with four-quadrant graphs. This creates an easier way to show data using the x and y-axis. This skill makes it possible to compare positive and negative values. These graphs are a great way for businesses to understand what is and isn’t working. The use of negative numbers and using it to create and show data isn’t just for 6th grade, it’s also an important way to judge success all companies use.

## 2. Early Algebra

6th grade math introduces students to the concept of algebra and understanding math in a different way. Algebra is about using all the math knowledge they have built throughout their education and applying it to variables (*x, y, z*) instead of numbers. While solving complex algebraic equations starts in 8th grade and early high school, the formation of a basic understanding of using variables starts in 6th grade. One of the first steps in understanding what algebra includes is understanding the difference between mathematical expressions and equations.

### Algebraic Expressions and Equations

What is the difference between a mathematical expression and an equation? A mathematical expression is a math phrase that doesn’t need to be solved. An easy way to know that you’re looking at an expression is the lack of seeing an equal sign (*=*). Examples of expressions are “5+6” or an algebraic expression like “3x + 2x – 12”. Students learn ways to simplify algebraic expressions (making them easier to understand), by adding like terms and using PEMDAS. Learning how to simplify expressions makes them easier to solve when they are in an equation.

## 3. Statistics (Mean, Median, Mode)

Expressions become equations with the addition of an equal sign and an equivalent number or expression. A simple equation is expressed as “5 + 6 = 11”. In early algebra, an equation can also be 2 expressions that use variables instead of numbers. An example of an algebraic expression is “2x + 4x – 6y = 6x – 4y – 6”. These equations can be simplified, and the goal isn’t to solve the equation but to find the numbers that the variables can represent. This early understanding of expressions and equations is introduced in 6th grade to prepare students for more complex math in the future.

In 6th grade, students start learning simple statistics. Using groups of numbers, also known as a data set, students start learning different ways to interpret information. The 3 metrics students learn in 6th grade are “Mean” “Median”, and “Mode”. Let’s create a simple data set of numbers, “*6, 6, 6, 6, 7, 7, 7, 8, 8, 9*“. When creating or using a set of data, the first thing students need to do is put them in numerical order.

The “Mean” of a data set, is the average of the number. We find the “Mean” by adding all the numbers together and dividing by the total data points we have. When we add up our data set we get, 70, we divide that by the total data points we have, which is 10, and we get our “Mean” of 7.

The “Median” of a data set of numbers is the middle number when the numbers are put in numerical order. For our data set of “*6, 6, 6, 6, 7, 7, 7, 8, 8, 9*“. The “Median” is in the middle of the set, because we have an even number of data points, 10, we take the 2 numbers in the middle and find the “Mean” or average of those numbers. In this case, the 2 middle numbers are the same, 7, So “7 + 7 = 14 and we divide by 2 and get our “Median” of 7. If our data set had an odd number of points like “*1, 3, 3, 4, **5″,* the number in the middle is our “Median”. In this case, it’s “3”.

The “Mode” of a data set is the number that comes up the most, in the data set. In our data set, “*6, 6, 6, 6, 7, 7, 7, 8, 8, 9*” the number that comes up the most is “6”. These 3 ways of grouping information are important in helping better understand situations based on data. The more information avaiable about a situation, the better chance people have of making decisions based on data.

## Final Word

6th grade is a whole new world in a student’s math journey. Mathematics becomes less about specific equations and more about understanding how numbers and equations help explain bigger concepts. These concepts prepare students not only for the rest of middle school and high school but future STEM-based careers. This is the beginning of using skills that help make the world go round.

Want to know more about Pre K to 6 grade math concepts? Check out all our math concept blogs.

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