## Preview

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: 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

## 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

## 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

## Preview

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:
--------------------------------------------------------------------------------------------------------------------------
Acute Angle:

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

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

An angle with a measure more than 90 degrees.
--------------------------------------------------------------------------------------------------------------------------

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

## 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!

## Preview

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.

## 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

## 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.

## 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

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

## Preview

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.

## 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

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

## 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.

## 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

## 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.

## 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

## 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

## 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!

## 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

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

## Introduction

Congruent means that the figures are the same in size and shape. If you can turn (rotate), flip (reflect) or slide (translate) the figures and the result is the same figure then  they are congruent figures (shapes).

## Introduction

Right Angles are angles that are always 90 degrees. That means that right angles can also be considered complementary angles, since complementary angles are also 90 degrees exact.

## Introduction

In our previous post we said that supplementary angles always add up to 180 degrees.

Complementary Angles are angles that always add up to 90 degrees.
That means that complementary angles are half of supplementary angles because 90 is half of 180!

## Introduction

Supplementary Angles are angles that always add up to 180 degrees.

### Vertical Angles

Vertical Angles are angles that share the same (common) vertex. Therefore, if two angles are vertical, they are congruent angles.

## Introduction

Perpendicular Lines are lines that meet at right angles, or at the measurement of 90 degrees.

## Introduction

Alternate Exterior Angles are angles that are outside of the parallel lines but on opposite sides of the Transversal Line.

## Introduction

Alternate Interior Angles are angles that are between the two lines (parallel) but on opposite sides of the Transversal Line.

## Introduction

Corresponding Angles are angles that are in the same corner of a Transversal.

A and A are corresponding and B and B are corresponding.

## Introduction

Adjacent Angles are angles that have a same vertex or corner and a same side.

## Introduction

In our previous post, we talked about parallel lines. Well, this post will continue the parallel lines concept except this topic will focus on transversal lines.

Transversals are lines that cut through a pair of lines, mostly parallel.

## Preview

A line, yes that is the topic, A line is just basically a vertical or horizontal, long or short, narrow or bold piece.

This is the one thing that everyone has to know because this is not only used in math but in other things as well.In math a line is described to go on forever and used to make number lines.

## Preview

Points are not anything special thing they are the very thing that you use to end a sentence and these points are also used in math except these points are to point out a specific location.

Points are usually used in grids to describe a location.

Rays are not frequencies in math neither are they the fantasy movie rays the come out of a ray gun although they are a type of line and this line starts with a point then it keeps on going

Both points and rays are connected in a way because there has to be a point in  a ray to start it so a ray has the point also.

## Introduction

What are Parallel Lines? Well, parallel lines are lines that never intersect. So if they don't intersect, they always run alongside each other. Take a look at an example of parallel lines below:

## Chapter 4: Introduction to Functions

1. Using Graphs to Relate Two Quantities
2. Linear Functions and Patterns
3. Nonlinear Functions and Patterns
4. Graphing Function Rules
5. Writing Function Rules
6. Relations and Functions
7. Sequences and Functions
8. Find the Missing Coordinates

## Chapter 6: Systems of Equations and Inequalities

1. Solving Systems by Graphing Method
2. Solving Systems by Substitution Method
3. Solving Systems by Elimination Method
4. Linear Inequalities
5. Solving Systems of Linear Inequalities

## Chapter 7: Exponents and Exponential Functions

1. Zero and Negative Exponents
2. Scientific Notation
3. Multiplying Powers with the Same Base
4. Multiplication Properties of Exponents
5. Division Properties of Exponents
6. Exponential Functions
7. Exponential Growth and Decay

## Chapter 9: Quadratic Functions and Equations

1. Quadratic Graphs and Their Properties
4. Solve Quadratic Equations by Factoring
5. Quadratic Formula and The Discriminant
6. Linear, Quadratic, and Exponential Models
7. Systems of Linear and Quadratic Equations

## Chapter 10: Radical Expressions and Equations

1. Introduction to The Pythagorean Theorem

## Chapter 11: Rational Expressions and Functions

1. Simplifying Rational Expressions
2. Multiplying and Dividing Rational Expressions
3. Dividing Polynomials

## Chapter 4: Introduction to Functions

1. Using Graphs to Relate Two Quantities
2. Linear Functions and Patterns
3. Nonlinear Functions and Patterns
4. Graphing Function Rules
5. Writing Function Rules
6. Relations and Functions
7. Sequences and Functions
8. Find the Missing Coordinates

## Chapter 6: Systems of Equations and Inequalities

1. Solving Systems by Graphing Method
2. Solving Systems by Substitution Method
3. Solving Systems by Elimination Method
4. Linear Inequalities
5. Solving Systems of Linear Inequalities

## Chapter 7: Exponents and Exponential Functions

1. Zero and Negative Exponents
2. Scientific Notation
3. Multiplying Powers with the Same Base
4. Multiplication Properties of Exponents
5. Division Properties of Exponents
6. Exponential Functions
7. Exponential Growth and Decay

## Chapter 9: Quadratic Functions and Equations

1. Quadratic Graphs and Their Properties
4. Solve Quadratic Equations by Factoring
5. Quadratic Formula and The Discriminant
6. Linear, Quadratic, and Exponential Models
7. Systems of Linear and Quadratic Equations

## Chapter 10: Radical Expressions and Equations

1. Introduction to The Pythagorean Theorem

## Chapter 11: Rational Expressions and Functions

1. Simplifying Rational Expressions
2. Multiplying and Dividing Rational Expressions
3. Dividing Polynomials

## Multiplying Exponents

In this lesson, you will learn how to multiply exponents. This is a very easy topic because all you have to do is multiply two exponents together!

For example let's say that you have the two exponents 3 to the power of 8 and 2 to the power of 5.

First, find the values of each exponent!
3 to the power of 8 is the same thing as 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 which equals 6,561
2 to the power of 5 is the same thing as 2 x 2 x 2 x 2 x 2 which equals 32
Now, just simply multiply both values.

6,561 x 32 = 209,952

## Subtracting Exponents

In this lesson, you will learn all about exponents and also how to subtract two different exponents. But what is an exponent?

Exponent: A power that a number is given

For example let's say that we have the two exponents 5 to the power of 4 and 7 to the power of 3.

First, find the value of the two exponents.
5 to the power of 4 is the same thing as 5 x 5 x 5 x 5 which equals 625.
7 to the power of 3 is the same thing as 7 x 7 x 7 which equals 343.

Now just simply subtract the two to find the difference!

625 - 343 = 282

That means the difference of the two exponents is equal to 282.

In this lesson, you will learn all about exponents and also how you can add two different exponents together. But to start off, let's review the definition of exponents.

Exponent: a power that a number is given.

For example let's say that we have the number 6 to the power of 3 and 4 to the power of 2. The first step in adding these is to find out the answer to each of these exponents.

6 to the power of 3 is the same thing as 6 x 6 x 6 which equals 216.
4 to the power of 2 is the same thing as 4 x 4 which equals 16.

Now all you have to do is add the two values together!

216 + 16 equals 232.

That means the sum of 6 to the power of 3 and 4 to the power of 2 is equal to 232.

## Preview

The metric measurements consists of the everyday measurements.There are three units of measurements and they are :

• metric units of length
• metric units of weight
• metric units of capacity

They are all used for different measurements like length is used for calculating distance and weight is used for calculating amount of how much something weighs, and capacity is used to calculate the amount of liquid something fills up.
Now try some of these and make sure to watch the video on YouTube.

Sheet 1 What are Metric Measurements