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7th grade (U.S.)

7th grade takes much of what you learned in 6th grade to an entirely new level. In particular, you'll now learn to do everything with negative numbers (we're talking everything--adding, subtracting, multiplying, dividing, fractions, decimals... everything!). You'll also take your algebraic skills to new heights by tackling two-step equations. 7th grade is also when you start thinking about probability (which is super important for realizing that casinos and lotteries are really just ways of taking money away from people who don't know probability) and dig deeper into the world of data and statistics. Onward! (Content was selected for this grade level based on a typical curriculum in the United States.)
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Rates, proportional relationships, rates

Throughout your day you probably encounter situations where you need to compare two numbers using the same or different units of measurement. Perhaps you want to know how many math problems you can complete in an hour…or how many scoops of ice cream you get out of a gallon bucket. In this set of tutorials you will learn about rate, a special ratio in which two terms are expressed in different units of measurement, and about proportional relationships, how one variable changes in proportion to another. You will practice solving problems and then construct a few of your own.

Negative Numbers

In this group of tutorials, we'll explore the world of negative numbers. Unlike real life where we perceive anything "negative" as being bad, we'll see that negative numbers are quite useful and central to all mathematical concepts. We'll practice adding, subtracting, multiplying, and dividing negative numbers; learn about absolute value, negative exponents, and exponents with negative bases.

Fractions and decimals

I bet if you were asked to give a number, your answer would be whole number. Don't forget about fractions and decimals--they're numbers too only expressed differently. In this set of tutorials we'll demonstrate adding, subtracting, multiplying, and dividing fractions and decimals, as well as converting fractions to decimals and vice versa. Finally, we'll get into some word problems so you can see how often fractions and decimals play a part in our everyday life.

Variables and expressions

In this section, the rubber really hits the road (algebraically speaking, of course). For example, order of operations is the starting point for solving all equations. Learning to combine like terms is equally important. We'll also look at manipulating and interpreting expressions, understanding two step equations, and linear inequalities. Lots of great stuff in this series of tutorials.

Geometry

Why is geometry important? It's all about shapes -- triangles, circles, pyramids, spheres, diamonds, and more. Geometric shapes are all around you, and the world is built with them. In this series of tutorials and exercises you'll become familiar with Euclidean geometry and terms like segments, scale drawings, parts of a circle, area, volume, angles, and geometric figures.

Statistics and probability

We begin our exploration of statistics and probability with a basic understanding of measures of central tendency, including the mean, mode, and median. We'll then look at the importance of sample populations in statistics, in particular that are representative and random. Next up is a discussion of basic probability and the "chances" of a random event occurring. We'll wrap it up looking at different kinds of probability and how we can estimate those, especially when compound events are involved. So get your coins and start flipping. We're going to have some fun!
Rates, proportional relationships, rates
Throughout your day you probably encounter situations where you need to compare two numbers using the same or different units of measurement. Perhaps you want to know how many math problems you can complete in an hour…or how many scoops of ice cream you get out of a gallon bucket. In this set of tutorials you will learn about rate, a special ratio in which two terms are expressed in different units of measurement, and about proportional relationships, how one variable changes in proportion to another. You will practice solving problems and then construct a few of your own.
All content in “Rates, proportional relationships, rates”

Rates

It can be useful to measure 2 things, but in different units of measurement, and then express that difference as a special ratio. Essentially, this is the definition of rate. We might compare how far a car drives with how long it takes to get to a destination, and then express it as miles per hour. Or perhaps we want to compare the cost of different size bags of jellybeans, which can be expressed as dollars per pound. You get the idea. This tutorial helps you understand these fundamental applications of rate. Common Core Standard: 7.RP.A.1

Proportional relationships

The concept of proportionality is pivotal to our understanding of how things in the universe are contructed. Proportional relationships in mathematics examine relationships between two equal ratios. For example, perhaps you're painting your bedroom and need to know how to mix 2 colors together to create a third color. Understanding the ratio of color 1 to color 2 determines your ability to know how many cans of both colors you need to paint your whole room in color 3. Pay attention because you'll find that these ideas will keep popping up in your life! Common Core Standards: 7.RP.A.2, 7.RP.A.2a, 7.RP.A.2b, 7.RP.A.2c, 7.RP.A.2d

Constructing proportions

Your knowledge of ratios has extended into understanding proportions. (If not, back up and be sure you get it!) Now that we know what a proportional relationship is, let's construct some real problems to solve. In this group of tutorials we'll practice writing and solving proportions, with both known and unknown variables. Common Core Standards: 7.RP.A.2, 7.RP.A.3