6th Grade Math—Semester A
Take the friction out of fractions.
If this course were a self-help book, we'd probably title it something along the lines of Numbers: How to Identify, Reason, and Negotiate with Them in Order to Win Friends and Influence People.
But clearly, we haven't titled our course that because…well, try fitting that onto a paperback. Besides, we already know you have lots of friends and can influence people with your endless charm. And this isn't exactly a self-help book, anyway. It's way better than that. Full of readings, examples, and problem sets, this Common Core-aligned course covers
- venturing bravely into the realm of integers and rational numbers.
- understanding and working with decimals.
- adding, subtracting, multiplying, and a whole lot of dividing with different types of numbers.
- the basics of number theory, primes, and factors.
- performing all sorts of operations with fractions and mixed numbers.
- converting smoothly between ratios, proportions, and percents.
And who knows? Maybe knowing about operations with decimals, fractions, and factors actually will help you win friends and tackle real-world problems with ease. More than you already do, that is.
P.S. 6th Grade Math is a two-semester course. You're looking at Semester A, but you can check out Semester B here.
Unit 1. Rational Numbers, Integers, and Number Lines
We're diving below sea level to find the negative end of the rational number line. Integers, fractions, and repeating decimals will now all be fair game, no matter their sign. It's like diving for buried treasures, where "buried treasures" include all the rational numbers below zero. And they hopefully double as the right answers to your homework, too.
Unit 2. Computation with Decimals
It's in our best interest to know how to work with decimals; we probably see them more often on a daily basis than any other type of number. Radio stations, price tags, and your fastest game of Solitaire (82.3 seconds? Nice!) are all given in decimals. So in this unit, we'll get straight to the point—the decimal point, that is.
Unit 3. Division
We know that you're no newbie to the world of division; you've got a few years of practice under your belt. But here's where we'll put your division chops to the test. From really small numbers to the big kahunas, we'll help you become the master of divisionland in no time. Besides, sharing is caring, and it can be fun. (And since sharing is really just dividing, that means dividing can be fun, too!)
Unit 4. Number Theory
Number theory is fairly concrete compared to Quantum Theory, Relativity Theory, and the Lost Sock Theory (the disappearance of single socks in the washing machine). Maybe it's because we have concrete strategies like prime factorization, factor trees, and Venn diagrams that we can use to approach it. They're all strategies that can be learned and mastered with practice, and we'll get plenty of practice right here.
Unit 5. Addition and Subtraction of Fractions and Mixed Numbers
Fractions and mixed numbers are sneaky little creatures that can be a bit terrifying to deal with, not unlike vampires. But don't you worry. We'll help you understand exactly what they are, how to find equivalent fractions with common denominators, and we'll be adding and subtracting them together by the end. We'll be fine…but you might want to keep a clove of garlic handy, just in case.
Unit 6. Multiplication and Division of Fractions
Here, your exploits with numerators and denominators will continue. You'll learn how to split citrus and eggs with your BFFs. You'll figure out how long (or maybe not so long) it will take you to paint a room just by observing what you've finished in half an hour. Got a great recipe to cook for a dinner date, but it serves two dozen people? Here come fractions to the rescue!
Unit 7. Ratios, Proportions, and Percents
The entire history of science and philosophy could be summed up by the question, "How exactly do all these things relate to each other?" And mathematics isn't immune to this relationship obsession. We've devoted an entire branch to it, and that is what this unit is all about. Ratios, proportions, and percents describe how two things relate to one another, and we don't mean whether or not they get each other's jokes. (Although that is pretty important.)
Sample Lesson - Introduction
Lesson 6: Dividing Decimals by Whole Numbers
Nothing goes together better than division and cute puppies, right? Okay, maybe those two things aren't usually related, but there are some connections. Work with us here.
Right now, Rex is your cute little fellow in a cute little bed. But soon he will outgrow that bed and he'll be your handsome big fellow in a cute little bed. When that happens he'll need a new bed, or else he'll end up kicking you off your bed and sleeping there instead. Did we mention that Rex will grow up to be big?
What's that got to do with division? So far we have been dividing smaller whole numbers into larger whole numbers, as if we were dividing up cookies. What happens if we divide a decimal by a whole number?
The whole number may even be bigger than the decimal, just like Rex will someday be bigger than his bed. (Sorry, that's the best we can do.)
Don't worry; we already have all the tools we need to solve the problem. We're going to basically ignore the decimal point while we divide, and just make sure it ends up in the right place in the answer. We'll show you how.
Don't try ignoring Rex, though. Rex will not be ignored—especially when he gets bigger. Did you know that Rex's name is short for T. Rex?
Sample Lesson - Reading
Reading 3.6: Dividing Decimals by Whole Numbers
Once again we are confronted with a long division problem, and once again the answer to our problem is to use the DMS system. It's time for the DMS-keteer roll call! Division! Multiplication! Subtraction! Addition has to go play by itself in the corner.
This time, the key is to recognize where the decimal point goes in the answer. Let's see what happens when we divide 14 into 0.28. 14 won't fit into 0.28 any more than Rex will fit in his old bed when he grows up.
The division box will look like this:
Here's the trick: put the decimal point in the quotient directly above the decimal point in the dividend. Then ignore those decimal points as you use the DMS method to solve the problem.
14 won't go into zero, and it won't go into 2, but it can go into 28. It goes into 28 twice, in fact. But be careful: when the divisor doesn't fit into the first few numbers of the dividend and we have to borrow another number, we have to put zeros in the quotient above the first numbers to show that the divisor didn't fit into them.
When dividing whole numbers, we don't show leading zeros in the quotient because they don't matter. For example, we don’t say "24 divided into 120 equals 05," we just say 5. But when our answer is on the right hand side of the decimal point it is important to include the zeros.
So in this case, the quotient looks like this: a decimal point goes over the decimal point in the dividend, zeros go over the zero and the two in the dividend, and two goes over the eight in the dividend. Our answer is 0.02:
If you're shouting, "I must learn more about this!" we gotcha covered. Try this link on for size. Wake Rex up while you're at it, and let's see how he likes long division. Please don't lick the screen, Rex.
- When dividing decimals by whole numbers, follow the same DMS method you did with other long division problems. Just put the decimal point in the quotient above the decimal point in the dividend.
- Remember to include a zero in the quotient every time you have to borrow a number in the dividend to fit the divisor into the dividend.
Sample Lesson - Activity
Activity 3.6: Problem Set
- Credit Recovery Enabled
- Course Length: 18 weeks
- Grade Levels: 6
- Course Type: Basic
Just what the heck is a Shmoop Online Course?
Common Core Standards
The following standards are covered in this course:CCSS.ELA-Literacy.CCRA.L.2