**5 important things I learned this year**

This year in Ms. Burton’s block B math 9 class we learned many different things in the following units: Rationals, exponents, linear relations, polynomials, equations and inequalities, similarities, finances, and data analysis. We learned so many things that I will use in my following years of high school and take them with me in my future. There were five things in this unit that really surprised me, that I also found interesting and useful. Those five things were learning to check/ verify a solution, using similar triangles to measure things indirectly, isolating x, finances, and tug of war.

**How to verify (check) a solution (answer) is correct:**

I think being able to check your solution is very important. When you think about it, getting the correct answer is the most important thing. If you can go back and check if your solution is right, then you will know you were right which makes things such as test taking easier. In my opinion the two most important things in math is being able to show how you got the answer and knowing that the answer you got is correct. To check if your answer is right you can just replace x with your answer, if the equation is equal on both sides then you have gotten the correct answer. If it’s not equal on both sides that means you have done something wrong and you should look back over your work to make sure all the moves you did were legal. Here is how to solve the equation (click to download) : medium (7) Here is how to check if that solution is correct (click to download): medium (6)

**Use similar triangles to measure things indirectly (using shadows or a mirror):**

Being able to measure anything with out a huge ruler is cool. In this unit we went outside and found the measurement of the wall and all we used was a mirror, and ourselves. Using shadows or a mirror you can measure objects. So, to start if you have 2 objects and you look at their shadows at the same time and you know the size of one of them than you can figure out the size of the other one.

Ex: if you are 5ft tall and your shadow measures 16ft and you have a wall with a shadow of 48ft than all you must do is find the scale factor for the shadow to the original. With that scale factor, you times it with the 48ft from the wall and you will find the actual height of the wall.

**Isolating x:**

Whenever I am solving for x I use this technique. To solve for x I isolate the variable so it is by itself. I use the golden rule, what you do to one side you must do to the other to get x on just one side of the equation. Like this (click to download): medium (8)

This is a very important rule because it does not just apply to equations but also solving inequalities. I found this technique very useful since I used it a lot this year and it worked for whenever you need to solve x. I will also be able to carry this technique with me the next few years when solving hard equations and inequalities.

**Finances:**

I think that Finances is one of the most important things we learned. In this unit I learned how to understand the importance of saving money, banking and careers. This is very important for all younger people to learn about because saving starts as early as when you were a child. We learned that the earlier you start saving the better, because you will have more money saved up for your future. We talked about some of life’s expenses and we all really realized how much you need to save. Even things as simple as buying a car is very expensive because there are added costs like gas and insurance. Most of the things you learn in math you will need in your future but finances is one of those things you are guaranteed to need. If you are not prepared about finances as a teen, or young adult, you may make poor spending choices not realizing that it could affect your future.

**Tug of war:**

With this technique all long adding and subtracting equations will be so much easier! When you see a lot of positives and negatives all together it make look like a lot but once you sort them and use the tug of war technique it is a lot easier. How to do tug of war (click to download): medium (9) I choose tug of war as one of my five things because I found it useful in many units and I found it a very cool way to solve a long addition and subtraction equations. When I see long equations I automatically panic and using the tug of war method made my life a lot easier.