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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.
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!
All content in “Properties of numbers”

Least common multiple

Life is good, but it can always get better. Just imagine being able to find the smallest number that is a multiple of two other numbers! It's called the LCM or Least Common Multiple. Other than making your life more fulfilling, lcm will allow you to do incredible things like adding fractions. Common Core Standard: 6.NS.B.4

Greatest common factor

You know how to find factors of a number, but what about factors that are common to two numbers? Even better, imagine the largest factors that are common to two numbers. These are called the greatest common factors (GCF) or sometimes greatest common divisors (GCD). Yay, acronyms! Too exciting! Common Core Standard: 6.NS.B.4

Distributive property

You've already seen the distributive property in action multiple times so there's nothing that new in this tutorial. However, we'll hear a really good explanation and practice rewriting expressions so that we can extend our understanding of it.