## Equality

#### Aligned To Common Core Standard:

**Grade 1 Operations** - OA.7

**Tips for Working with Equals Signs**

It is important to understand and learn your way around with equals sign, especially when we are working with equations. So, what does equals sign mean? It means "Balance," "Same value as," and "The same amount as."
The use of equal is often found in equations such as:
3 + 2 = 5

1 + 6 = 7

Or

8 + 2 = 2 + 8

We can see that in an equation, we are not saying that the numbers on two sides of the equals sign are equal to each. What the equals sign is saying is that the value on the left-hand side of the '=' sign is equal to the value on the right-hand side. For example:
18 = 81
This is not a correct equation despite both sides having 1 and 8, but the value is different on both sides of the equals sign. Let's do another example.
10 = 1 + 0
This is also an incorrect equation because 1 + 0 can never be equal to 10. This shows that the equals sign is used when the two value on the right side is equal to the total value on the left side of the equation.
These worksheets help student to learn to the concept of being equaland get comfortable with the equals symbol itself.

### Equality Worksheets For You

- Which Equal is Equal Step-by-step Lesson-
Compare two equations and circle the one that is correct.

- Skill Challenge Guided Lesson
- Covers 3 skills: Sign Identification, Long Operations, Basic Operations.

- Operations Guided Lesson Explanation
- We look at the use of all the different operations and how to
work through it.

- Is It Correct? Why Not?
- Basic operations that all include the equals sign. Which are not
right?

- Match What Is Equal - Which two equations are equal? The include sums and differences. The focus is on matching operations to find equality.
- Find the Right One Guided Lesson 1 - What makes 14?
- Guided Lesson 2 - A little less work here, but it is just as important.
- Proper Use of Sums and Differences Lesson 1 - Circle them if they are right. Fix them if they are wrong.
- Add and Subtract Equations with Equal Signs Lesson 2 - What sign is missing here?
- True or False Pyramid Lesson 3 - This is quite a long one for this level.
- Independent Practice Worksheet- You are basically grading someone's homework here. That's what I tell the kids.
- Mark the Right Worksheet- Let's grade another batch of homework.
- Matching Worksheet- This is very advanced but it is worth seeing how they do with it.
- Picture the Missing Sign Worksheet - I really like these types of questions for kids at this level.

#### Guided Lessons

These are a bit more advanced than the work above.

#### Practice Worksheets

These are a lot more creative than most standards based sheets.

### Real Numbers Properties of Mathematical Equality

When a mathematical statement possesses a sense of equivalence between two or more values, we call this a state of equality. We can use this mathematical state to our advantage to help us find balance and solve equations for missing values. This is underlying property that often allows us to manipulate an equation for our own needs. Here is a quick look at how some of these properties allow us to rearrange and ultimately have our way with equations.

**Reflexive** - This just tells that a number is equal to itself. Such as b = b. This is helpful because it allows us to quickly reduce equations that have exceptionally large values.

**Symmetric** - This tells us that the order in which math statements are stated do not matter. If b = c, c = b would also be true. We can use the nature of this to help us rearrange an equation in a fashion that makes it easier to work with.

**Transitive** - This just takes the symmetric property and scales it up a bit. This tells us that if two numbers are equal to the same value, then they are equal to each other as well. For example, if b = c and c = d, then b = d also. This is often helpful to combine or compact values quickly when simplifying equations for ourselves.

**Multiplication Property** - When we are simplifying and reducing equations, this is super helpful. This tells us that we remove things that appear on opposite sides of the equals symbol. For example, if ac = bc can be easily reduced to a = b. This also tells us that as long as we perform the same math operation to both sides of the equal symbol, we can.

**Distributive** - Yes, this is where the parathesis comes into play in equations. The distributive property provides us the standard that says if we put something (single number or full-on math statement) in parathesis and put a number outside. The number outside should be multiplied by everything separated by an operations symbol within that parenthesis. For example, ab + ac can be rewritten as a(b + c).

There are several more properties that we did not detail here. We focused on those properties that we constantly find ourselves using and it also gives you a great deal of insight into how we theoretically rationalize solving math equations.