## Properties of Math Operations as Problem Strategies

#### Aligned To Common Core Standard:

**Grade 1 Operations** - OA.3

What Are the Common Properties of Math Operations The basic properties that are used in math operations are fairly simple. In total, there are four basic properties for real numbers: associative, identity, distributive, and commutative. These properties are only applied to the operations of multiplications and addition. 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. 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 multiplication: Any real number multiplied to 1 is equal to the number itself 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. These worksheets use a variety of common property of operations to solve a wide variety of different types of math problems.

- 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 as Strategies - Turn your inner light bulb on.
- Properties of Operations as Strategies - Rewrite this one by simply moving things around, but keeping them the same.
- Rewrite Expressions Lesson - More work on the associative property.

#### 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 - Which operations fit the sum.
- Match Adding Shapes Worksheet- Find the correct sum in each problem.
- Match Equations to the Numbers Worksheet - This is the most advanced worksheet at this skill that I have.