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4th grade (U.S.)

4th grade is the time to start really fine-tuning your arithmetic skills. Not only will you be a multi-digit addition and subtraction rockstar, but you'll extend the multiplication and division that you started in 3rd grade to several digits. You'll also discover that you sometimes have something left over (called a "remainder") when you divide. In 3rd grade you learned what a fraction is. Now you'll start adding, subtracting, multiplying, and comparing them. You'll also see how they relate to decimals. On other fronts, you'll learn how to convert between different units (which is super important when comparing the size and speed of robot unicorns in different countries) and continue your journey thinking about various shapes in two dimensions. Some of the foundational concepts of geometry (like lines, rays and angles) also get introduced. As always, we'll round this out with a healthy dose of applied word problems and explorations of number patterns and properties (including the ideas of factors, multiples and prime numbers). The fun must not stop! (Content was selected for this grade level based on a typical curriculum in the United States.)
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Addition and subtraction

Fourth grade is the time to really fine-tune your addition and subtraction skills to the point that you can add and subtract pretty much any multi-digit, whole number!

Multiplication and division

Let's continue on the multiplication and division adventure that was started in third grade. We'll think about multiplying and dividing with whole numbers and discover that sometimes we have a leftover, or a remainder, when we divide. These tutorials will also help you get comfortable with multiplying multi-digit numbers, long division, and solving word problems. Let's do this people!

Fractions

In 3rd grade, you got a basic conceptual understanding of what a fraction is. Awesome. Now we dig deeper by comparing fractions and starting to perform operations on them. We also see how they relate to decimals. Some of the skills we'll cover here include visualizing equivalent fractions; comparing, adding (with like and unlike denominators), subtracting, and decomposing fractions; adding, subtracting and changing mixed numbers; changing improper fractions; multiplying whole numbers and fractions; and rewriting fractions as decimals.

Measurement and data

When we measure anything, we do it in human-defined 'units'. Different units were defined in different places and for different scales. The two most common are U.S. customary units and metric units. Let's think about how to convert between and among them! We'll also continue thinking about perimeter and area!

Geometry

Finally, we're getting to geometry. We've been waiting for this and hope you have been, too. The foundation of all geometry is the line--so that's a great place to start. From there we'll move into angles, quadrilaterals, and triangles. Our goal is here to get familiar with the basic concepts, skills, and applications of geometry. So jump in and let's go for a ride!

Factors, multiples and patterns

We know that 3x2x5 = 30. So 2, 3, and 5 are factors of 30. 30 is a multiple of each of 3, 2, and 5. If a number only has itself and 1 as factors, then the number is "prime". Don't worry, this is explained in much more depth in the tutorials in this topic. We will also explore some mathematical patterns.

Place value and rounding

We've been exploring place value for several years now, but now we make sure that we **really** get how one place relates to another. We then use this deep understanding for understanding the conventions for rounding.
Fractions
In 3rd grade, you got a basic conceptual understanding of what a fraction is. Awesome. Now we dig deeper by comparing fractions and starting to perform operations on them. We also see how they relate to decimals. Some of the skills we'll cover here include visualizing equivalent fractions; comparing, adding (with like and unlike denominators), subtracting, and decomposing fractions; adding, subtracting and changing mixed numbers; changing improper fractions; multiplying whole numbers and fractions; and rewriting fractions as decimals.
All content in “Fractions”

Equivalent fractions

Do you want 2/3 or 4/6 of this pizza? Doesn't matter because they are both the same fraction. This tutorial will help us explore this idea by really visualizing what equivalent fractions represent. We'll also throw some word problems at you to get you thinking about how to solve real-life equivalent fraction problems. Common Core Standard: 4.NF.A.1

Comparing fractions

In this tutorial, we'll practice understanding fractions and how to best compare them to each other. Two ideas are important here: simplify the fractions and find the common denominator. Common Core Standard 4.NF.A.2

Adding and subtracting fractions with common denominators

You've already got 1/4 cups of sugar in the cupboard. Your grandmother's recipe for disgustingly-sweet-fudge-cake calls for 3/4 cups of sugar. How much sugar do you need to borrow from you robot neighbor? Adding and subtracting fractions is key. In this quick tutorial we'll focus on fractions with like denominators. Common Core Standards 4.NF.B.3, 4.NF.B.3a

Mixed numbers

We can often have fractions whose numerators are not less than the denominators (like 23/4 or 3/2 or even 6/6). These top-heavy friends are called improper fractions. Since they represent a whole or more (in absolute terms), they can also be expressed as a combination of a whole number and a "proper fraction" (one where the numerator is less than the denominator) which is called a "mixed number." They are both awesome ways of representing a number and getting acquainted with both (as this tutorial does) is super useful in life! Common Core Standard: 4.NF.B.3c

Decomposing fractions

In this tutorial, we'll see that a fraction can be broken up (or decomposed) into a bunch of other fractions. You might see the world in a completely different way after this. Common Core Standard: 4.NF.B.3b

Adding fractions with unlike denominators

We've already had some good practice adding fractions with like denominators. We'll now begin to explore adding fractions with unlike denominators. In particular, we'll think about adding fractions with denominators of 10 and 100. Later on, in 5th, grade we'll extend this to adding fractions of any denominator to fractions of any denominator.

Rewriting fractions as decimals

We already know that the same quantity can be represented as a decimal or a fraction. In this tutorial, we'll begin to see how a fraction can be rewritten as a decimal. The trick is to make sure the fraction has been reduced or simplified as much as possible, then to convert the fraction so that you're dealing with tens or hundreds--a much friendlier environment for our decimal friends!