In the Meadows or Malls unit students were given the task to find the lowest cost for both recreation and development land when making necessary improvements to the land. There were three lands at first the farm, army base,and mining land.Then the city manager split the land use into 2 recreation; and development so it could minimize the cost on necessary improvements. Are task is to find the lowest cost for the city for necessary improvements while also keeping 300 acres for development while keeping the two part compromise of 200 acres to the army base and mining land could go for recreation and army based land used for recreation and the farm used for development together has to total 100 acres.
To solve this task students had to use many different things like using constraints like we did in the cookies unit, matrices, linear equations with three or more variables, as well as planes on a x,y and z graph. These key ideas were used to solve the central problem by taking multiple variables and learning how to solve it in very different ways like substitution, elimination, and etc. By making constraints from the central problem we learned we could put those constraints/linear equations into matrices because that what we learned and through the multiplying matrices and finding the inverse we could find amount of acres for each category and price and see which combination has the lowest price for the city.
All the papers I chose for the portfolio all plays a part in helping solve the essential problem. I chose both of the paper to solving the unit problem because it shows the final answer to the unit and also shows the process I took in order to solve it and shows that we took what we learned and applied it to the final worksheet. I chose solving systems by elimination because it shows how you can a two variable or three variable equation without using matrices and using the process of elimination which will help with the x,y, and z plane plots. The solving systems of equations with matrices is a worksheet that helped us learn the concepts on how to use matrices with three or more variables from a word problem, we learned to take those word problems and solve them in the calculator. Next the solving matrices I learned ways to multiply matrices without a calculator and see if one has a solution or not. Repeating one of the paper the solving systems of equation with matrices is something I was really proud of because I was able to take word problems turn them into linear equations and matrices which was one of the most difficult parts of the unit. Finally the POW I don’t think it helped solve the unit problem but the marching strip pow was challenging and also fun.
The Meadow or Malls unit was fun but at the same time challenging as it should be. I feel like at the end of this unit I am able to solve matrices, linear equations, and etc. easily without frustration. My experience in the cookies unit previous to meadows or malls helped my work in the meadow or malls unit because it helped me understand how to write constraints and to do linear equation with two or more variables. If I didn't have the cookies unit it probably would’ve been a lot harder for me in the meadows or malls unit. Some of the new mathematical topic I learned in this was without a doubt matrices. When Lauren first introduced matrices I had no clue what that was but now ending the unit it is so easy and is something new I learned. I learned how to find the inverse of matrices, take word problems and form either equations or matrices, and how to solve matrices on a graphing calculator. Geometry has addressed many things in this unit it has addressed when we were doing the plane work on the graph. On a 3D x,y,and z plane and seeing what lines intersect and creating planes through some equations. Some strategies we used to solve system of equations was we used elimination and substation. These strategies were the most common and easy to do. Elimination by eliminating variables and substitution by getting a variable alone. I gained a lot of knowledge in this unit and its something that can be very useful in the future.