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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.)
Community Questions

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 a 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!
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.
All content in “Negative Numbers”

Adding and subtracting negative numbers

You should understand that negative numbers represent how far we are "below zero". Now you are ready to add and subtract them! In this tutorial, we will explain, give examples, and give practice adding and subtracting negative numbers. This is a super-important concept for the rest of your mathematical career so, no pressure, learn it as well as you can! Common Core Standards: 7.NS.A.1, 7.NS.A.1b, 7.NS.A.1c, 7.NS.A.1d

Multiplying and dividing negative numbers

Hopefully you agree that negative numbers aren't so "negative" after all. They're actually very useful and kind fun to play around with! In this section we want to give you a better conceptual understanding of why the products of negative numbers are defined as they are. We also want build on our knowledge and examine multiplying and dividing negative and positive numbers. Common Core Standards: 7.NS.A.2a, 7.NS.A.2b

Absolute value

Absolute value is absolutely straightforward--it is simply the "distance from zero." If you have a positive number, it is its own absolute value. If you have a negative number, just make it positive to get the absolute value. Along with using number line segments, we'll look at constructing and interpreting absolute value within the context of word problems. As you develop mathematically, this idea will eventually extend to more dimensions so it's super important that you understand this core concept now. Common Core Standards: 7.NS.A.1a, 7.NS.A.1b

Exponents with negative bases

If you think about it, exponents is simply repeated multiplication. Knowing that, we can apply what we already know about multiplying negative numbers. Exponents with negative and zero bases are treated differently, as well as power of zero exponents. Order of operations will help us make sense of those circumstances.