# Top 5 things I learned in grade 9

The top 5 things that I learned in grade 9. Everything I learnt this year was very helpful but these are some of the 5 things I picked to talk about.

The top 5 things I picked to talk about are: Linear equations, polynomials, powers and exponents, exponent laws, distributive property

Linear equations:

What is an equation? it’s an equation is two algebraic expressions connected by an equal sign

Operations: four things you do to an equation add, subtract, multiply and divide

The Golden rule: whatever you do to one side you do to the other side

I learnt in this unit that what you do to one side you must do to the other sides huge! If you don’t remember this you will be falling of the railroad track. You have to remember this rule. Also recognize what you are doing and what you will need to answer the questions.

Polynomials:

Polynomials include:terms, constants, coefficients, degrees, variables, binomials, trinomials, monomials

Terms- terms are a single number which are separated by the negative and positive sign.

Constants- constants are always the $(+2 +1)$ at the end of the question.

Coefficients- coefficients is the number always at the beginning of a question.

Degree- degree is the small number in a question such as $4^7$ a way to remember this would be if you think of a thermometer and where the degrees sign is where the 7 would be in my example.

Variable- variables are the letters in a question such as $(+4x)$.

Binomials- binomials are equations with 2 terms with a plus or minus added to it. Example $(3x+5)$

Trinomial- trinomials are equations with 3 terms an example would be $2x(x+y)^2$

Monomial- monomials are equations with 1 different term this is an example $7y$

The one thing that I will always take away from this unit is that the degree in the questions is just like the degree on a thermometer. One of the most common sense things I learnt in math, the name of the rule makes it that much easier.

Powers:

Powers and exponents have specific rules: the multiplication law, division law. They are both very specific and you have to remember how each rule works.

Multiplication law:

When the bases are the same you add the exponents together, but if the bases are different its a just do it questions and you have to work out the question.

$7^4$\$7^2$=$7^6$

Division law:

When the bases are the same you subtract the exponents, but if the bases are the same its just like the multiplication law its a just do it.

$6^3$\$6^2$=$6^1$

We used many different strategies to get the answer, and to work out the question. There were ways when we divided the numbers separately and individually, an example would be 5.5.5/5.5.5.

Power of a power and zero exponent law:

power of a power is when you have a base and an exponent in brackets and another exponent on the outside of the brackets. $(5^4)^2$

BEDMAS one of the biggest things to remember doing anything in math but in the case follow the rule and you will be just fine. ( brackets, exponents, division, multiplication, addition and subtraction)\

There were a lot of things I learnt in this unit. It was very easy to follow and were a few things I learnt that will always stick in the brain. If you memorize the way you have to operate the questions it will be easier when you have to do it again.

I also learned that BEDMAS is actually really important and if you don’t use it you will most likely get the question wrong so I learnt that you need to always use it.

Exponent laws:

Exponent laws in my opinion are very important i never learnt all of them last year and had no idea how they worked.  After re learning them this year I understood them and realized that if you don’t follow the rules your whole equation will end up being wrong. An example would be 5 to the power of 2 is 25 $5^2=25$

Exponents are lazy when there is no brackets. When there is brackets you multiply the outside the brackets with the degree on the inside.

NEVER ever multiply 5×2=10 you will get it wrong. The 2 is the number of copies of 5 how many times you need to write out 5 and multiply the 5’s.

Multiplying with the same base: $y^2+y^3=y^5$

P.S the rules are in the powers section above.

Distributive property:

This is a really easy thing to remember, always remember your rainbows!

When doing this you have to get rid of the brackets always the first step in BEDMAS get rid of those brackets.

First step: multiply your number on the outside of the brackets to the numbers on the inside of the brackets. EX. $4(3x+2)$. Once you have multiplied the outer number you should have an answer of $12x+6$

This was very helpful for me to look at and go back to when I needed to.

This is based on a short film about sadness and bullying which we turned into a Cozy Classic book, we created this on a Google slides and put it into Flipsnack to create a flip book which we embedded on our blogs.

In the unit we learned about scale factors. There are steps to follow while doing the work.

Step 1- pick your original and image

Scale Factor- the scale factor is always the image divided by the original The scale factor always has 2 numbers in the fraction.

Step 3- You have to identify the corresponding side on the other image (the matching side, you may have to rotate the picture to see it) drawing the shape also helps.

Step 4-  separate the fractions to get 2 different equations then use the butterfly method.

Butterfly method- Bellow is a picture of what it looks like.

Enlargements and reductions

When the dimensions (length, width, height etc…) of an object are changed by multiplying by the scale factor. This can be in 2D or 3D objects

Enlargement- When the number is multiplied by a number bigger than 1

Reduction- When the number is multiplied by a number smaller than 1

Ratios

What does 1:10 mean?

There is an original and an image, the original is 10 and the image is 1. How do i know this well you always divide the image by the original and the number on the right gets brought down under the number on the left. It will make a fraction 1/10

# Sticks and Stones short film

The emotion of this short film is sadness, we chose bullying because it is a big problem that happens in schools and we just wanted to show what happens, what people go through.

# Reduction and Enlargement

How the numbers changed was when you multiply the number will enlarge but when you divide the number will reduct.

Inequalities

What I have learned about inequalities, there are things to remember when doing these which include BFSD( best friends share desert) or the math version (brackets fractions sort divide). I have also learned a trick for remembering which was the arrow goes when you use the signs. You would do these just like the unit before this when you do the equations.

Signs:

When you have < or > it means less than or greater than. The open mouth is the one that is the bigger number, it eats the bigger number. The point of the arrow is pointing to the smaller number. My trick I have with to remember which was the arrow goes depends on which way the mouth is facing. If the Mouth is eating the x or the other letter that means that the arrow goes to the positive side but if the mouths point is pointing toward the x it goes toward the negative side.

When you have </ or >/  it means that the number is greater than or equal to or less than or equal to.

Graph:

When graphing you have to remember that the little circle on the top is different depending on the sign. If you have < or > the circle is open and when you have </ or >/ the circle is closed. Also when you graph remember the trick to help you with which way the arrow goes. Something else when you are graphing is to just make a simple line and place your answer in the middle and then graph from there.

Check:

When checking you have to take the answer you got at replace it with the letter. So where ever you had a letter you would put your answer there. Then you solve the question and if the answer is the same on both sides the you know the answer is correct.

Solve:

When you are solving you have to follow the BFSD rule to help you get through the question. You would get rid of the brackets or distribute then the fractions then you would sort then you divide but if the number with the variable is negative you have to flip to so the negative switches to a positive and the positive switches with a negative. You can also solve questions or find the equation when its in a sentence.

# Solving Linear Equations Summary Blog Post

What is a linear equation?

A linear equation is an equation between two variables that gives a straight line when plotted on a graph.

How equations can they be modeled using algebra tiles

When you model equations using algebra tiles you have to use the tiles as if they are the numbers. you use the amount of tiles which would be a number with the x. for example if i had 4x-5= 3x-6 i would take the algebra tiles that have an (x) and put 4 of them out and then i would take the little squares (the ones) and i would lay out 5 of them on the blank side which is blank for negative. I would to the same with the rest of the equation depending on the number. The coloured side of the tiles is positive and the blank side on the back is negative.

Solving equations visually

When solving equations visually I would use algebra tiles or i would draw them out on a piece of paper. When you draw them you would draw them the exact same as the tiles just on your page. You colour them in pencil would be positive and leave them blank is negative. It is a helpful way to sort out the equation and slowly go through each step. There are many different ways in doing these equations visually. They can be done in fractions or decimals and or regular numbers.

Solving equations algebraically

Solving equations algebraically you have to write out the equation and go through it step by step as if you were using your algebra tiles. Things you have to remember are zero pairs, common denominators, like terms, distribute.

Solutions – how you know you have the right one (how to check your answer)

To check your answer you have to get the variable and make sure the equations match.

These are some equations (with algebra tiles).