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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.
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!
All content in “Arithmetic operations”

Adding and subtracting decimals

Honestly, once you remember one very important rule, the rest of adding and subtracting decimals is a snap. That rule is to be sure and align your decimals first. In this tutorial, you'll get a chance to practice this with us and become fluent adding and subtracting decimals. Common Core Standard: 6.NS.B.3

Multiplying decimals

You've already multiplied decimals in the 5th grade. We'll show you some ways to handle slightly more complicated problems. Now you'll become super good at it with a bit more practice! Common Core Standard: 6.NS.B.3

Dividing whole numbers and decimals

You probably know about division, and even a little about dividing decimals. After this tutorial, you'll be comfortable dividing two digit whole numbers and decimals, whether they are in the divisor or dividend position. Pretty exciting, huh? Let me a hear a "Yes!" Common Core Standards: 6.NS.B.2, 6.NS.B.3

Dividing whole numbers and fractions

Let's explore how we can think about dividing a fraction by a whole number and a whole number by a fraction. Remember that a whole number is a fraction expressed differently. What do you do when you divide fractions? Multiply by the reciprocal! You got itI Now try.

Dividing fractions by fractions

We're now ready to get some solid practice dividing fractions by fractions. However, we're not just going to give you practice problems, we're going to explain why we do them this way and where the answer comes from. So let's get going. Common Core Standard: 6.NS.A.1

Dividing decimals

You have already been exposed to dividing decimals in the 5th grade. In this group of videos we'll tackle those pesky decimals in the hundredths place, both in the divisor and the dividend. We'll make sure that you're a pro at it!

Exponents

In 3rd grade, you learned that there is an easier way to write "5+5+5". You saw that 5+5+5=3x5. But is there an easier way to write repeated multiplication (like "5x5x5")? Absolutely! That's exactly what exponents are for! Common Core Standard: 6.EE.A.1