What I have learned about Grade 9 Similarities

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

 

Steps to getting your answer in an equation.

Step 1- pick your original and image

Step 2- make your ratios

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

 

 

 

 

 

what I have learned about grade 9 inequalities

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).

          

 

Linear Relations

In this unit we learned about linear relations. There are many things you have to do such as, graphing, patters, charts and rules.

Patterns: 

Patterns, they can increase or decrease.This pattern is increasing it is going up by 2 so the patter adds 2 dots every time.

Charts: 

Charts, once you have your pattern or if you get the pattern on its own you have to find the formula (the rule) for how the numbers change. In this chart the rule is 2x+1 which means you multiply 1×2 to get 2 and then add 1 to get 3 which is shown in my pattern.

Graphs:

Graphs, to get the dots and lines on you graph you need to have the number first to get the right spot on the graph. You take the (x) number and the (Y) number and put them together like so in my picture. Which then will let you put them on the graph properly.