## Properties of Math Operations

#### Aligned To Common Core Standard:

**Grade 1 Operations** - OA.3

We have discussed all four math operations (addition, subtraction, multiplication, and division) in great detail. An operation is processed when you calculate the value created by using operands and a math operator. Operands are the numbers that we use during any series of operations. Operators as displayed using symbols to indicate how to process a calculation. The common operators are + (addition), - (subtraction), x (multiplication, ÷ (division), = (equal). How we go about processing problems or equations that several instances of these operations can be tricky, but there are some common properties that we can use to our advantage to solve complex problems. There are many other forms of operations that we will learn as we progress further with our math skills. These worksheets use a variety of common property of operations to solve a wide variety of different types of math problems. It is essential that we master the theory and uses of these properties to make our lives easier.

### Properties of Math Operations Worksheets and Lessons

- Commutative Property Step-by-step Lesson-
We work on the commutative property of addition with flowers.

- Associative and Commutative Properties
Guided Lesson - We hit you with a test on that skill from many
directions.

- Properties of Operations Guided
Lesson Explanation - I explain the properties of your basic
operations like adding and subtracting in great detail.

- Which Is The Associative Property?
- We give you four examples and ask you which one shows off the
associative property.

- Matching Problems and Visuals
- Match the diagrams to the problems that they represent.

#### Guided Lessons

I have a strong feeling that kids need visual cues at this age. That is reflected here.

- Associative Property of Addition Step-by-step Lesson - Relate all of that to a broken down word problem.
- Addition of Pictures To Explain Commutative Properties Lesson - Also called the upside down version of addition.
- Light Bulb Properties of Operations - Turn your inner light bulb on. You will rearrange this equation to make it much easier to solve for yourself.
- Properties of Operations as Strategies - Rewrite this one by simply moving things around, but keeping them the same.
- Rewrite Expressions Lesson - See how you can use those parathesis to your advantage. A little bit of shuffling will make this one a cinch.

#### Practice Worksheets

These are a bit more advanced to start working on those upper levels of the curriculum.

- Associative Property Identification - Just make sure that both sides are equal and you are good to go.
- Independent Matching Worksheet - Find all equations that are equal to the number on the left. Circle them.
- Match Adding Shapes Worksheet- Match the shape problems to their numeric sum. Write the letter of the answer that matches the problem. Each row has two choices (a or b).
- Match Equations to the Numbers Worksheet - This is the most advanced worksheet at this skill that I have.

### What Are the Common Properties of Math Operations?

As we move on to more advanced forms of math, we need to have a solid grasp on basic operations that we will use to solve algebra problems. We all know how to perform the basic operations (add, subtract, divide, or multiply), but what happens when you into multiple instances of these operations in an equation. The basic properties that are used in math operations are fairly simple. In total, there are four basic properties for real numbers that apply to the operations of multiplications and addition: associative, identity, distributive, and commutative. These properties are not in-built in division and subtraction operations.

**Commutative Property: (a + b = b + a) or (a x b = b x a)**

The sum or product of two or more real numbers is always the same regardless of the order they are added.

**Associative Property: (a + b) + c = a + (b + c) or (a x b) x c = a x (b x c)**

The sum or product of two or more real numbers will always be the same regardless of how they are grouped in an equation.

While these two properties (commutative and associative) are commonly confused with one another. The commutative property focuses more on individual terms of an equation. The associative focuses on regrouping numbers or moving things as a whole or set.

**Distributive Property (Multiplication over addition): a (b + c) = ab + ac**

Multiplying a factor to a set of real numbers being added together equals to the sum of the factor of products and every addend in the brackets.

As we said previously these properties do not apply to either the division or subtraction operations. That is because the way in which terms are ordered with these operation does matter. Subtraction can be looked as adding negative values to create a sum. Division is the absolute inverse of multiplication, so it does not have its own set of properties, since they are in direct proportion to one another.

**Identity Property: (a + 0 = a) or (a x 1 = a) **

For addition: Any real number added to zero is equal to the number itself. For subtraction: Any real number subtracted by zero is equal to the number itself.

For multiplication: Any real number multiplied to 1 is equal to the number itself. For division: Any real number divided by 1 is equal to the number itself.