# Ch 1: Common Core Math Grade 6 - The Number System: Operations & Factoring

### About This Chapter

**Standard:** Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. *For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?* (CCSS.MATH.CONTENT.6.NS.A.1)

**Standard:** Fluently divide multi-digit numbers using the standard algorithm. (CCSS.MATH.CONTENT.6.NS.B.2)

**Standard:** Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. (CCSS.MATH.CONTENT.6.NS.B.3)

**Standard:** Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. *For example, express 36 + 8 as 4 (9 + 2).* (CCSS.MATH.CONTENT.6.NS.B.4)

## About This Chapter

Students who meet these Common Core standards will be able to divide fractions by fractions and find common factors and multiples. The lessons in this collection are designed to help students learn about the following:

- Solving complex fractions
- Steps involved in division
- Adding, subtracting, multiplying and dividing decimals
- Finding the greatest common factor
- Identifying the least common multiple with prime factorization
- Method for finding the least common multiple
- Least common multiple and greatest common factor word problems

You'll be able to tell when your students have mastered these standards when they are able to interpret quotients of fractions and solve word problems that require division of fractions by other fractions. They'll also be able to fluently perform operations on multi-digit numbers and decimals and find the greatest common factor of two whole numbers.

### How to Use These Lessons in Your Classroom

These suggestions will help you to incorporate the collection materials into your curriculum:

#### Have a Factor Race

Watch the lesson 'How to Find the Greatest Common Factor.' Call out a pair of numbers and have students race to be the first one to find the greatest common factor. First one to five wins!

#### Write Word Problems

Have students view the lesson 'Word Problems: Greatest Common Factor & Least Common Multiple.' Divide students into small groups, and ask them to work together to create word problems that involve finding the greatest common factor and the least common multiple. Compile the problems and assign them to students as a class activity or for homework.

#### Assign Quizzes for Homework

Use the printable worksheets that accompany each lesson as a homework handout. Discuss the problems and answers in class the next day, using the lesson videos to explain any topics students are unclear on.

### 1. How to Solve Complex Fractions

Did you know fractions can nest within fractions? In this lesson, we'll learn about complex fractions and look at two different methods for solving them.

### 2. How to Perform Division: Steps & Examples

Watch this video lesson to learn how you can divide. Division is one of the basic operations of math. It is one of the fundamental operations that all higher mathematics depends upon.

### 3. Adding and Subtracting Decimals: Examples & Word Problems

In math, we sometimes have to deal with decimal numbers instead of our nice whole numbers. Watch this video lesson to learn the one thing that you have to take into consideration when adding and subtracting decimals.

### 4. Multiplying and Dividing Decimals: Examples & Word Problems

Watch this video lesson to learn what you need to do to get a correct answer when multiplying and dividing decimals. Learn the easy tricks to figuring out where the decimal point goes.

### 5. How to Find the Greatest Common Factor

If the factors of a number are the different numbers that you can multiply together to get that original number, then the greatest common factor of two numbers is just the biggest one that both have in common. See some examples of what I'm talking about here!

### 6. Using Prime Factorizations to Find the Least Common Multiples

Finding the least common multiple can seem like a lot of work. But we can use prime factorization as a shortcut. Find out how and practice finding least common multiples in this lesson.

### 7. How to Find the Least Common Multiple

The least common multiple of two numbers is the smallest number that can be divided evenly by your two original numbers. See some examples of what I'm talking about here!

### 8. Word Problems: Greatest Common Factor & Least Common Multiple

In this video lesson, you will learn what kinds of word problems you can expect to see that involve the greatest common factor or the least common multiple. Learn what you need to do to understand these problems and then to solve them.

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### Other Chapters

Other chapters within the Common Core Math Grade 6 - The Number System: Standards course