## Meadows and Malls Reflection

When first diving into this unit, we were first taught how to use a 3D coordinate plane, with three variables, x, y, and z. When learning how to use the 3D coordinate plane and learning about what z did as a function and variable, we then dove into three variable equations. With learning how to solve these equations and how to graph a 3D triangle, we were then taught how to solve two equations using the systems of substitution and elimination. When learning how to use these two types of equations, with using this type of algebra we found x and y. As this unit is mostly about matrices, we learned that matrices were lots of numbers put into a system of equation multiplied by an x,y or z variable that will give you the products of all these numbers. We also learned about another function on the calculator that would help us figure out what the variables, x, y, and z were. We would have A with the inverse as the variable multiplied by B which would give us what x,y, and z were as variables. When solving the main problem, we were told to figure out which equation would work best as to what property would be less expensive. By putting these numbers and equations into the calculator, we were able to find the total cost of each property and which one was less expensive. This led to us have our answer.

Evidence:

When looking at how I had solved the unit problem, on the first page you will see that we were given a set of equations. When looking at these equations and figuring out which ones were accurate as to which equation would help us solve the main problem. When looking at the second page, you will see that we are given equations, variables, and a set of numbers. With help from my teacher I had discovered that it would not solve the problem if any of the properties or variables had a negative number. When adding up all of the numbers altogether listed under the type of inverse, I got the amount of money it would cost for what property should be made into a mall or meadow. When finding a negative number, I had figured out that the equation would have no solution that would not give us our answer to our problem.

An assignment that had helped learn how to solve linear equations by using systems of elimination and substitution rather than using matrices would be Solving Systems by Substitution #2. When doing this worksheet I learned how to solve problems with substitution, we learned that you have to use the naked variable in order to start solving the equation this way. By finding the naked variable and making it equal to the other side of the equation, we were able to figure out y and with two equations in one set we would soon find x. As you can see in this worksheet I was able to find both variables and some equations were unsolvable because these equations were just doubled so they would not have a point of interception and were just parallel.

Seeing as this unit was mostly about matrices, one worksheet that I was able to do when learning about Matrix Operations was the Matrix Multiplication assignment. This worksheet had helped me to learn about the rule that a matrix like 1X2 and 2X2 are able to multiply and you will get an answer. Whereas a matrix with a 2X2 matrix and a 1X3 would not be compatible and you will not find an answer. I also learned put information with numbers into a matrix and how to solve the problem using the matrices, and also how to sort the answers and information into a matrix table. This had given me a better understanding on how to multiply matrices.

One POW that I think I did do well on would be POW #5, Letter Code. not only had I scored a 100% on this assignment, but I thought this was very fun and enjoyable. In this POW we had to figure out what letters were what numbers. So what number was A and what number was B. When looking at this problem, you had to come up with a lot of solutions, but also try to be logical. What two same digit number was another two same digit will give a three digit number that has the same number in the hundreds place as it does in the tens place of the equation. SS+EE=SST. So coming up with a lot of logical equations that had then narrowed it down to 99+11=110. When working on this POW you had to pay attention to the numbers and letters being thrown at you and try to come up with a logical solution, but also trying to find multiple solutions on some of the problems. But I had a lot of fun doing this POW and I think that it makes you think logically.

This assignment (the POW) would also be the one that I am proudest of the most because I did really well, understood the concepts that were given, and had a fun time solving this problem. This problem was fun to think about, although occasionally challenging and I was glad that I was able to take the time to figure it out.

One assignment that allowed us to learn with knowing how to solve more than one variable would be the page 184 assignment where we were able to learn how to solve equations with three variables and the characteristics of the coordinate points with the three variables. We would make one point 0, and another point 0, and would figure out which point would be the one to equal the number on the other side. When looking at the other assignments that we did for this type of learning it was found that out that each variable (x,y,z) had to equal the one number on the other side of the equation.

Personal Growth:

My personal growth for this unit was a bit slow going. When first diving into this unit I was very confused on why we were learning, when I realized what was going on with what a 3D triangle looks like with the three variable, that part was a bit easy to understand. Learning how to do substitution was very easy for me and I thought that I did a good job on it. When learning about elimination I was a bit confused and still am. Learning matrices was kinda easy besides getting confused with a bunch of numbers being thrown at us and what specifically needed to be done in order to solve the problem. Although I didn’t understand how to get what the variables were equal to at the very end of the unit, I understand how to get the answers for when needing to find the answers by multiplying and by finding what the variables equal to with the inverse. Though I am still confused by a few things. I guess how connects with geometry would be when using the three variable equation and using matrices you could plug these variables on a coordinate plane and that would let you if theses points intercept or are parallel, just like the two equations in one set, you would know if they were parallel if they were just doubled or even tripled.

Evidence:

When looking at how I had solved the unit problem, on the first page you will see that we were given a set of equations. When looking at these equations and figuring out which ones were accurate as to which equation would help us solve the main problem. When looking at the second page, you will see that we are given equations, variables, and a set of numbers. With help from my teacher I had discovered that it would not solve the problem if any of the properties or variables had a negative number. When adding up all of the numbers altogether listed under the type of inverse, I got the amount of money it would cost for what property should be made into a mall or meadow. When finding a negative number, I had figured out that the equation would have no solution that would not give us our answer to our problem.

An assignment that had helped learn how to solve linear equations by using systems of elimination and substitution rather than using matrices would be Solving Systems by Substitution #2. When doing this worksheet I learned how to solve problems with substitution, we learned that you have to use the naked variable in order to start solving the equation this way. By finding the naked variable and making it equal to the other side of the equation, we were able to figure out y and with two equations in one set we would soon find x. As you can see in this worksheet I was able to find both variables and some equations were unsolvable because these equations were just doubled so they would not have a point of interception and were just parallel.

Seeing as this unit was mostly about matrices, one worksheet that I was able to do when learning about Matrix Operations was the Matrix Multiplication assignment. This worksheet had helped me to learn about the rule that a matrix like 1X2 and 2X2 are able to multiply and you will get an answer. Whereas a matrix with a 2X2 matrix and a 1X3 would not be compatible and you will not find an answer. I also learned put information with numbers into a matrix and how to solve the problem using the matrices, and also how to sort the answers and information into a matrix table. This had given me a better understanding on how to multiply matrices.

One POW that I think I did do well on would be POW #5, Letter Code. not only had I scored a 100% on this assignment, but I thought this was very fun and enjoyable. In this POW we had to figure out what letters were what numbers. So what number was A and what number was B. When looking at this problem, you had to come up with a lot of solutions, but also try to be logical. What two same digit number was another two same digit will give a three digit number that has the same number in the hundreds place as it does in the tens place of the equation. SS+EE=SST. So coming up with a lot of logical equations that had then narrowed it down to 99+11=110. When working on this POW you had to pay attention to the numbers and letters being thrown at you and try to come up with a logical solution, but also trying to find multiple solutions on some of the problems. But I had a lot of fun doing this POW and I think that it makes you think logically.

This assignment (the POW) would also be the one that I am proudest of the most because I did really well, understood the concepts that were given, and had a fun time solving this problem. This problem was fun to think about, although occasionally challenging and I was glad that I was able to take the time to figure it out.

One assignment that allowed us to learn with knowing how to solve more than one variable would be the page 184 assignment where we were able to learn how to solve equations with three variables and the characteristics of the coordinate points with the three variables. We would make one point 0, and another point 0, and would figure out which point would be the one to equal the number on the other side. When looking at the other assignments that we did for this type of learning it was found that out that each variable (x,y,z) had to equal the one number on the other side of the equation.

Personal Growth:

My personal growth for this unit was a bit slow going. When first diving into this unit I was very confused on why we were learning, when I realized what was going on with what a 3D triangle looks like with the three variable, that part was a bit easy to understand. Learning how to do substitution was very easy for me and I thought that I did a good job on it. When learning about elimination I was a bit confused and still am. Learning matrices was kinda easy besides getting confused with a bunch of numbers being thrown at us and what specifically needed to be done in order to solve the problem. Although I didn’t understand how to get what the variables were equal to at the very end of the unit, I understand how to get the answers for when needing to find the answers by multiplying and by finding what the variables equal to with the inverse. Though I am still confused by a few things. I guess how connects with geometry would be when using the three variable equation and using matrices you could plug these variables on a coordinate plane and that would let you if theses points intercept or are parallel, just like the two equations in one set, you would know if they were parallel if they were just doubled or even tripled.