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6th grade (U.S.)

By the 6th grade, you're starting to become a sophisticated mathemagician. You'll be able to add, subtract, multiply, and divide any non-negative numbers (including decimals and fractions) that any grumpy ogre throws at you. Mind-blowing ideas like exponents (you saw these briefly in the 5th grade), ratios, percents, negative numbers, and variable expressions will start being in your comfort zone. Most importantly, the algebraic side of mathematics is a whole new kind of fun! And if that is not enough, we are going to continue with our understanding of ideas like the coordinate plane (from 5th grade) and area while beginning to derive meaning from data! (Content was selected for this grade level based on a typical curriculum in the United States.)
Community Questions

Ratios, rates, and percentages

A common application of numbers in real life (what is REAL life anyway, huh?) is through ratios, rates, and percentages. Whether following a recipe, changing the oil in a car, or determining the percentage earned on a test...these are skills you will use over and over. Ratios are simply another way to express fractions. Rates combine units of measurements to help us understand their relationship better. Percentages, like ratios, give us another way to express fractions and decimals. We'll explain each to you and then practice until you've mastered each concept.

Arithmetic operations

The most fundamental branch of math is arithmetic operations. It consists of adding, subtracting, multiplying, and dividing numbers. We're willing to bet that doing these operations on whole numbers is a piece of cake, but now we'll mix those numbers up with decimals and fractions. We'll also introduce the idea exponents as they become much more important moving forward. So sharpen that pencil and relax in your chair, we're going for a ride!

Negative numbers

Negative numbers are a necessary part of our understanding of mathematics and the world. The idea of anything "negative" is often seen as "bad." Negative numbers are not only good, but they're fun! Walk through this tutorial with us and we'll show you how they are defined, interpreted, and applied. Absolute value is a type of negative number that is expressed as a positive. Confused? Don't be. We got your back.

Properties of numbers

This group of tutorials will introduce us to some of the common properties of numbers, including the least common multiple (LCM), greatest common factor (GCF), and the distributive property. All three of these will be extremely useful going forward. I know we ALWAYS say that...but really, it's true!

Variables and expressions

Learning algebra is a little like learning another language. In place of words, algebra often uses symbols in the forms of variables (letters) which are sometimes combined with numbers to form expressions (words/phrases) and combined further to create equations or inequalities (sentences). Ok, that comparison may have a few flaws, but you get the idea. In this group of tutorials, we'll learn about and practice writing, evaluating, and adding expressions; order of operations; substitution; combining like terms; and solving equations and understanding inequalities.

Geometry

Here in 6th grade, we start to really understand the fundamentals of Euclidian Geometry. As we've said before, the world around you is built with geometric shapes. Heck, even YOU are built with geometric shapes! Having an appreciation and understanding of how we study, measure, and create these shapes helps us to improve our lives. In this group of tutorials we'll explore plotting points and interpreting the coordinate plane; and measuring area, volume, and surface area of geometric shapes--including different types of polygons.

Data and statistics

In statistics, we try to make sense of the world by collecting, organizing, analyzing, and presenting large amounts of data. For example, you may survey your friends about what tv show is most popular, but the small sample size will not give you an accurate idea of what ALL 6th graders like to watch. To do this you must survey a cross section of students from all around the country and all backgrounds. The data can then be statistically analyzed to give a more accurate picture of what tv show is most popular. So let's dive into a discussion of statistics, including box and whisker plots, bar charts, pictographs, line graphs, and dot plots.
Geometry
Here in 6th grade, we start to really understand the fundamentals of Euclidian Geometry. As we've said before, the world around you is built with geometric shapes. Heck, even YOU are built with geometric shapes! Having an appreciation and understanding of how we study, measure, and create these shapes helps us to improve our lives. In this group of tutorials we'll explore plotting points and interpreting the coordinate plane; and measuring area, volume, and surface area of geometric shapes--including different types of polygons.
All content in “Geometry”

Coordinate plane

We first explored the coordinate plane in the 5th grade, but that was only dealing with positive coordinates. Now we know all about negative numbers so why not have negative coordinates as well? Let's get cozy with the x and y axis, plotting ordered pairs, quadrants, and reflection points. We got it covered. Sit back, relax, and get ready to groove with us. Common Core Standards: 6.NS.C.6, 6.NS.C.6b, 6.NS.C.6c, 6.NS.C.8

Finding area

Let's now extend our understanding of area from triangles into more interesting shapes like quadrilaterals! We'll examine how to find the area of parallelograms, trapezoids, kites, and oddly shaped quadrilaterals. Finding the area of geometric shapes like these is a really important skill. Imagine buying carpet for your bedroom...or fertilizer for your lawn? You'll need to know the area of these shapes. There are lots of real life applications! Common Core Standard: 6.G.A.1

Volume and surface area

Ever wonder how a painter knows how much paint to buy to cover the exterior of your house? Or how much water you'll need to fill up your aquarium? Let's explore the volume and surface area of 3D shapes, such as rectangular prisms, rectangular triangles, and nets of ployhedra. These are fancy names for common shapes which you encounter all the time. Common Core Standards: 6.G.A.2, 6.G.A.4

Polygons in the coordinate plane

We've learned about polygons and have explored all four quadrants of the coordinate plane. Now, let's combine those skills to draw, measure, and solve problems with parallelograms and quadrilaterals in the coordinate plane. Common Core Standards: CC.6.G.A.3