## Basic Operations and Generating Equivalent Expressions

#### Aligned To Common Core Standard:

**Grade 6 Expressions and Equations** - 6.EE.A.3

What Does Simplifying an Expression Mean?
When we are dealing with algebraic expressions, it is possible that you get expressions that very lengthy. Lengthy expressions are difficult to even understand. However, with the help of simplification, you can make the expression most compact; without changing its original value. This includes taking common terms or adding or subtracting similar values in order to get a simplified form. Below we will discuss some steps that can be considered when you want to simplify an expression.
**Similar Terms:** Similar or like terms can have same powers on same variables, even if their coefficients are different. This is the only difference. 3x, 2x, 5x are like terms.
**Combining Similar Terms:** Combining those similar terms is the next step towards getting a simplified expression. (3x)^2+ (5x)^2+ 5x +3 will get a simplified answer of (8x)^2+ 5x + 3.
**Parentheses:** Parentheses are multiplied beforehand in order to get similar terms; which can then be combined.

### Printable Worksheets And Lessons

- Simplifying Expressions
Step-by-step Lesson- Expressions that include exponents and
compounded variables.

- Guided Lesson -
Rewriting expressions and using the distributive property to create
equal expressions.

- Guided Lesson Explanation
- I might have not provided enough steps. I just never really see
have students have trouble with these types of problems.

- Practice Worksheet
- The entire sheet is dedicated to creating equivalent expressions.

- Visual Expressions Five
Pack - I haven't seen questions like these before. So, I made
them.

- Matching Worksheet - Match the expression that are equal. A really nice way to practice.

#### Homework Sheets

You will find that each sheet is progressively easier, 1 being the hardest in the set.

- Homework 1 - Multiply a sum by multiplying each addend separately.
- Homework 2 - Find a common number or variable that you can use. We are looking for an integer that can easily be divided.
- Homework 3 - Simply (a + a + a)/ 4

#### Practice Worksheets

I tried to make this section slightly more difficult than the basic old problems I see everywhere.

- Practice 1 - Choose and apply the distributive property to the expression to produce an equivalent expression: 2(4 + x)
- Practice 2 - Rewrite the expression: (5a + 50b)
- Practice 3 - Choose and apply the distributive property to the expression to produce an equivalent expression: 5(6 + x)

#### Math Skill Quizzes

You should find as nice mix of difficulty here. 2 easy problems, 2 hard problems and the rest somewhere in between.

- Quiz 1 - Simplify the expression. 5(5^2 + 5x)
- Quiz 2 - Rewrite the expression: (8a + 40 b)
- Quiz 3 - Apply the properties of operations to produce an equivalent expression: (e + e + e) / 4