Define an Angle

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An angle or angles are types of measurements we use when two lines connect like this:

An angle also has degrees which defies the angles measurements. To make the angle to go all the way around it will be 360 degrees, half way around will be 180 degrees and a quarter way around will be 90 degrees. Angles also have names, The 90 degree angle is called the right angle and the angles less than 90 degrees are called acute angles. The angle which is 180 degrees and higher are called obtuse angles. Angles are used in many situations and jobs. One of the most important job that uses angles is construction worker s because they have to get all the measurements correct to make their design successful. Angles are also in shapes like for example the square has four right angles, and of course there multiple types of triangles and they all have different amounts of different angles but they all have three angles.

Solving Equations with Variables on Both Sides

Solving Equations with Variables on both Sides: Example

Let’s say that we have the following equation:

4x – 5 + 3 = 2x + 1

First we have to combine like terms. So, we will combine constants with constants and variables with variables.

Step 1:

4x – 5 + 3 = 2x + 1

4x – 2x = - 5 + 3 – 1

The reason I changed the signs when moving the variables and constants is because if I bring a positive to the other side it becomes negative and if I bring a negative to the other side it becomes a positive.

Next we have to simplify.

Step 2:

4x – 5 + 3 = 2x + 1

4x – 2x = - 5 + 3 - 1

2x = + 3 – 6

2x = - 3

Note: In order to simplify all I did was subtract the variables to get 2x and add

-5 + 3 -1 to get -3

Step 3:

4x – 5 + 3 = 2x + 1

4x – 2x = - 5 + 3 - 1

2x = + 3 – 6

2x = - 3

Now we have a one-step equation. So, we’ll have to divide 2x by 2 and -3 by 2.

4x – 5 + 3 = 2x + 1

4x – 2x = - 5 + 3 - 1

2x = + 3 – 6

2x/2 = - 3/2

x = - 3/2 or –1 1/2

How To Measure Angles

Introduction

In this lesson, we will learn how to find measurements of angles without having to use protractors or any other tool. You see, you can always find the measurement of an angle as long as you know the following terms:

Key Terms:

• Alternate Interior Angles
• Alternate Exterior Angles
• Corresponding Angles
• Vertical Angles
• Supplementary Angles
• Complementary Angles

Note: You can learn in detail about these in the 7th Grade Unit

 Measurement of Angles 

The above is an example of a Transversal. We already know that one of the angles is 110 degrees. In order to find the other angle measurements, we need to keep in mind that the angles will always add up to 180 degrees. Therefore, is we want to know the measurement of the angle directly opposite of the 110 degree angle, all we have to do is subtract 180 and 110 to get 70 degrees. That means the measurement of the opposite angle is 70 degrees!

Now taht we know the measurement of two angles directly opposite of each other, it will be really easy to find the other measurements!

The angle directly underneath the 110 degree angle is the next measurement. To find this we know that the total is 180 so if we subtract we get 70. Then comes the angle underneath the 70 degree angle. Once again, it is going to total an exact 180 degrees. So, if we subtract 180 and 70 we get 110. Notice that there is a pattern. There are only 2 different measurements.

So as you can see it isn't really hard to find the measurements of the angles as long as you know just one of the measurements!

Introduction of Circle

To find the details about Circle please watch below video. The video explain following terminology and examples.

• What is Circle
• What is Radius in Circle
• What is Diameter in Circle
• What is Pi 
• What is Circumference and How to Find Circumference of Circle 

Introduction to Triangles

Types of Triangles

Though we've been introduced to the concept of 'triangles' since kindergarten, what we may not know is that there are so many different types of triangles. That's what we will be learning in this lesson!

Remember that there are 6 types of triangles:

• Equilateral Triangle
• Isosceles Triangle
• Scalene Triangle
• Right Triangle
• Obtuse Triangle
• Acute Triangle

Examples

EQUILATERAL TRIANGLE

ISOSCELES TRIANGLE

SCALENE TRIANGLE

 

RIGHT TRIANGLE

 

 

 

 

 

 

OBTUSE TRIANGLE

 

 

 

 

ACUTE TRIANGLE

 

 

 

 

 

 

Types of Angles

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Angles are a the measure of how how something is positioned. However there are different types of angles.Here are the different types of angles:

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Acute Angle:

 An angle with a measurements less than 90 degrees.
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Right Angle:

 An angle with a measure of exactly 90 degrees.
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Obtuse Angle:

An angle with a measure more than 90 degrees.

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All three of these angles are the angles you will be taught about in 6th Grade.

Exponents in Algebra

Introduction

In this lesson, we will learn how we can use exponents in algebraic expressions. Remember that expressions can only be simplified, not solved. Also keep in mind that when you are combining like terms in expressions, you can only put together what is exactly the same.

Exponents in Expressions

Let's say that we have the following expression:

13x + n^2 - 7x + n^2

Step 1:

Combine like terms
Put together any terms that are alike; exponents with exponents and variables with variable

Note: Exponents must be of same value to be put together while combining like terms

So we have + 13x and - 7x.
Then we have +n^2 and + n^2     ( ^ means to the power of )

Let's look at it like this:

We have 13x ( + 13x) and we owe 7x(- 7x) to a friend. How many 'x' do we have left?

We have to subtract 13 - 7 to get 6
That means we have 6x left. This 6x is positive because we still have this amount.

Step 2:

Rewrite expression and continue to combine like terms

Now we have the following expression:

6x + n^2 + n^2

We have to combine the exponents n^2 and n^2 which equals 2n^2

Step 3:

Rewrite simplified expression

Original Expression: 13x + n^2 - 7x + n^2
Simplified Expression: 6x + 2n^2

I hope you guys understood this topic. I understand it might have been difficult at first attempt, but keep practicing and you will become an expert in expressions before you know it!

Properties of Triangles

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A triangle is a plane shape which always has three sides, and here is the funny thing, there are three types of triangles.Here are the three types of triangles and their definitions:

Equilateral Triangle:

A triangle with the three sides having the same measurement and also the triangle has all three same angles.(HINT* A good way to remember a equal-lateral triangle is the equal in the word equal-lateral because all the sides of a equal-lateral triangle are equal!)

Isosceles Triangle:

An isosceles triangle is a triangle which has two sides that are the same and only one side is different and also a isosceles triangle has only two same angles.(HINT*A good way to remember a isosceles triangle is by the two letter s in the word isosceles because a isosceles triangle has two same sides!)

Scalene Triangle:

A scalene triangle is a triangle with all sides different.The angles of a scalene triangle do not match also.(HINT* A good way to remember a scalene triangle is to always check that it is not isosceles and equal-lateral because then it is surely a scalene triangle because a scalene triangle has no same sides!)

Another thing about triangles is that all the angles in a triangle add up to 180 degrees.Also another way to identify a triangle is to look for no parallel lines.

Simplifying Algebraic Expressions

Introduction

In this lesson, we will learn how to simplify an algebraic expression. Before we start though, let's review the key term:

Key Term

• Expression uses variables, numbers, and operations to express values in Algebra

Simplifying Algebraic Expressions

Let's say that we have the following expression:

15 ( 2n + 3 ) - 10

In order to simplify this expression, we can use the Distributive Property.

Step 1:
Distribute 15 to 2n and 3.

15 x 2n = 30n
15 x 3 = 45

That means we now have
 30n + 45 -10

Step 2:
Combine Like Terms
Remember that Like Terms are terms that are alike and you can put together
Also remember that you can only combine variables with variables and constants with constants.

Variable: a letter used to replace a value in algebra
Constants: Numbers without a variable in algebra

So, our like terms are +45 and -10.

Think of it like this:
I have 45 dollars (+45) and I owe 10 dollars to a friend (-10). How many dollars do I have left?

To find the difference, we'll simply subtract!

45 - 10 = 35

That means we have 35 dollars left or +35!

Step 3:
Rewrite simplified expression!

15 ( 2n + 3 ) - 10

30n +45 - 10

30n +35

Properties of Points and Lines

Preview

You are probably already know about a point and a line but i am going to teach you what points and lines stand for in math.So lets first talk about points first, so we know that a point is a small mark and this is how a point looks like:

A point in math describes a specific location on a grid.

Now lets talk about lines and we already know that a line is long narrow piece and it looks like this:

A line in math is used to calculate measurement and is also used in number lines.A line has a start and a end but it has no points.

Solving 2 Step Algebraic Equations

Introduction

In our previous lesson, we covered solving 1 step algebraic equations. Well, in this lesson, we will be covering the same concept except we will be dealing with 2 step equations. Let's take a look at an example!

Solving 2 Step Equations

Let's say that we have the following equation:

2y + 3 = 15

In order to solve any 2 step equation, you will always do addition/subtraction first. Then you will do multiplication/division.

So, first we will subtract 3 since we have +3 is our equation:
2y + 3 = 15
      - 3 = - 3
2y = 12

Now, we will divide by 2 because we have 2 times y in our equation:
2y + 3 = 15
      - 3 = - 3
      2y = 12
       2  =  2
        y =  6

Checking your Answer!

To make sure that your answer is correct, you can always replace the variable with the answer then solve to get the answer!

2y + 3 = 15
y = 6
2 x 6 + 3 = 15
12 + 3 = 15
15 = 15

What is Plane

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In this topic you will learn what a plane is and how it applies in your daily life.First of a all this how a plane looks like:

A plane is like a flat base or a surface.A plane can be used to make the base of something and also there are things such as your house floor which are a good example of a plane.

Solving 1 Step Algebraic Equations

Introduction

In this lesson, we will learn how to solve 1 Step Algebraic Equations. In our previous lesson, we learned the difference between an expression and an equation. Let's review the term Equation before we get started:

Key Term

• EQUATION shows that TWO Expressions are equal using an '=' sign

Solving Equations

Let's say that we have the following equation:

4x = 16

In order to solve this 1 step equation, we need to apply the same 'reverse operation' on both sides.

4x is the same thing as 4 multiplied by x. The reverse of multiplication is division, so if we divide 4 by 4, we are left with 1 or 1x. Remember that 1x can also be written as x because it is the same thing as a single x, right?!

Now, since we divided by 4 on the left side of the equation, we must do the exact same thing to the right side of the equation. 16 divided by 4 is equal to 4.

That means that 4x = 16
                            x = 4

Check your Answer!

In order to make sure that our answer is correct, we can always replace the variable with the answer and try it out!

4x = 16
x = 4
4 x 4 = 16

Equations and Expressions

Introduction

In this lesson, we will learn the difference between Equations ans Expressions. Before we begin with examples for each, let's go over the definitions of these terms:

Key Terms

• Expression uses variables, numbers, and operations to express a value in algebra
• Equation shows that two Expressions are equal using the "=" sign

Equations vs. Expressions

Equations and Expressions-both are used algebra.
The difference between Equations and Expressions is that Equations show equalities and inequalities while  Expressions do NOT have a value for the variables. Therefore, Expressions can NOT be solved, only simplified.

 

 

Variables and Coefficients

Introduction

In this lesson, we will learn about variables and coefficients in algebraic equations.

Key Terms:

• Equations show that two things are the same or equal using the equal sign "="
• Variables are lower case letters used in algebraic equations to replace an unknown number
• Coefficients are used in equations to multiply variables

Parts of Equations

Solving Algebraic Equations

Let's take a look at the above equation.

3n + 9

In order to solve the equation, we need to find what the variable "n" is. Let's say that n is equal to 17.

So, that means we have to multiply 3 x 17 is 51. Now just add 51 + 9 = 60.

The answer to the algebraic equation 3n + 9 is equal to 60.

Division of Integers

Introduction

In this lesson, we will learn how to divide integers. Remember the following key points for division of integers:

Key Points:

• Integers are distributed in 2 categories: positives and negatives
• Integers are whole numbers
• Zero is neither a positive or negative number
• If the signs are the same the quotient will be positive
• If the signs are different the quotient will be negative 

 Figure 1 Division of Integers Number Line

Division of Integers

Let's say that we have the following problem:

(-100) / (-25)
From the above key points, we know that if the signs are the same the quotient will be a positive number.
In this case we have two negative numbers so we will have a positive result.

Since the sign has been determined, we can now do simple division:

100/25 is 4 because 4 x 25 = 100

That means the quotient is +4.

(-100) / (-25) = +4

Multiplication of Integers

Introduction

In this lesson, we will review the multiplication of integers. In order to multiply integers you must know the following key points:

Key Points:

• Integers are distributed in 2 categories: positives and negatives
• Integers are whole numbers
• Zero is neither a positive or negative number
• If the signs are the same the product will be positive
• If the signs are different the product will be negative 

 Figure 1 Multiplication of Integers Number Line

Multiplication of Integers

Let's say that we have the following problem:

4 x -8

From the above key points, we know that if the signs are different, then the product will be negative.
In this case we have positive 4 (+4) and negative 8 (-8). Since the signs are different we know that the product will be negative. Now just simply multiply 4 x 8 and we get a product of 32. Remember to add the negative sign to get your final product of -32.

4 x -8 = -32

Subtraction of Integers

Introduction

In our previous post we reviewed the addition of integers. Well, subtraction of integers is pretty much the same concept because you are still handing integers except this lesson will deal with subtraction.

Key Points:

• Integers are distributed in 2 categories: positives and negatives
• Integers are whole numbers
• Zero is neither a positive or negative number

 Figure 1 Subtraction of Integers Number Line

Subtraction of Integers

Let's say that we have the following problem:

-7 - 9

The above problem is telling us that we have -7 and we have go back 9 spaces like this:

So as you can see the point of doing -7-9 is to go back -9 spaces or 9 spaces back from the number -7 and so the answer is going to be -17.

I highly recommend to practice this and do so with number lines and later on you will get how to do it and you will easily know how to without the number line!

Addition of Integers

Introduction

In this lesson, we will review how to add integers. Remember that integers are numbers that are distributed into 2 categories: positives and negatives. Integers don't include of any fractions so they are whole numbers. Also, the number 0 (zero) is neither a positive or a negative number.

Figure 1 Addition of Integers Number Line

Addition of Integers

Let's say that we have to add the following numbers:

4 + -9

The number 4 does not have a sign in front of it. If a number doesn't have a sign, it means it is a positive number.

Now we have positive 4 and negative 9.

Let's look at it like this:

We have 4 dollars (+4) and we owe 9 dollars (-9) to a friend. In order to add this we first look at the sign of the larger number.

We know that 9 is greater than 4 so our answer should equal a negative number since 9 has the negative sign in front of it.

Also, since 9 is the greater number, we will use it's operation. 9 is a negative and we know that negative means subtraction. So, if we subtract 9-4 we get 5. 

Remember that our answer must be a negative. So we have -5.

That means that if we have $4 an owe owe $9 to a friend, we still owe them $5.

4 + -9 = -5