Pattering: Variables, expressions, equations, coefficients, etc.

For pattering, you'll be using a lot of variables. What are variables? Variables are letters that represents a number.
Eg.1 If you had an equation like this: 5+7 You would replace the number(s) with a letter. Instead of 5+7, you could have x+7. x=5 or you could also have 5+y. In this case, y=7. You could also have x+y, meaning your x equals 5 and your y equals 7. You could choose whatever letters you want to represent a number, it does not always have to be an x or a y.
Variables could be used to represent whatever topic or idea the x and y axis has.
For patterning, you'll also be using expressions. What are expressions? An expression is a number sentence without an equal sign.
Eg.1 Instead of having 3+9=12, you'll only need to add, 3+9.
Another important word you need to remember are equations. What are equations? Equations are used to help show a number sentence. A number sentence is basically a math question that uses any type of math devices, such as multiplication, addition, subtraction, or division. These devices are used to help calculate or get the answer of a math question(number sentence). You would also have to add an equal sign =. An equation is the same thing as an expression but you have to add an equal sign with the answer of the math equation.
Eg.1 7+8=15 would be an equation because it uses a math symbol that is needed to complete a math equation. It has the addition sign + an it also has the equal sign =.
For expressions, a multiplication sentence(without the equal sign) is shown a different way.
Eg.1 Instead of 4x3, you could either show it as 4(3) or 3(4), it doesn't really matter what order you put it in. You could also put it as a coefficient.
If you are working with variables, you will need to use something called a  "coefficient". A coefficient is having a number go in front of a variable, this is used especially when you are multiplying, expressions, or equations.
Eg.1 6x3 is your expression. Let's say the 3 will be an x for our variable. We would have 6xx. This will get confusing because you don''t know if you're using a variable "x" or if you're using the multiplication sign. The rule to expressions or equations are to never show the multiplication sign unless you are using an x as a variable. It'll get confusing. This is when you use your coefficients. Instead of 6xx, you will only need to put 6x. (x=3) This shows that you are multiplying "x" 6 times. In this case, "x" is 3. You are multiplying 6 three times. Or you could do it the other way, 3x(x=6).
NOTE: Mrs. Boughton prefers you to put coefficients instead of putting it in brackets.
If we use graphs in class, make sure you label the graph chart. You need to label the x and y axis. The x axis is labelled going left and right(horizontally) and the y axis is labelled up and down(vertically). The x axis is usually labelled as the "Term #" for patterning. The y axis is usually labelled as whatever amount of shapes, toothpicks, or whatever type you are using for patterning.
There will be times when some of the worksheets will ask you for the value of the nth figure using words, numbers, and symbols. It just means to describe what you are doing.
Eg.1 There are three steps to completely answer the nth figure.
The equation using variables. 6x7=42. You'll need to have a variable for each number. In order to do that, you need to write down what number you want to change and write the number you want to replace the number with. If I wanted 6 to be a, I have to put "Let 6 be a." and if I wanted 7 to be h, I have to put "Let 7 be h" to let people know that this letter is the number you want it to be. You would also need to write down what is happening in your expression or equation. 6x7(Let 6 be n). 7n= 42 would be the equation you would need. You have to describe the equation. For example, "I am multiplying 7 by n(which is 6) and it all equals to 42.
To wrap up this up, make sure you figure out whatever pattern you need to answer.