Algebra 1
This here is one of my classes at ECHS. Algebra is a good class and learning in this class is pretty fun with our teacher Ms.O'Leary. She's a good teacher and well having her for two years really helped me understand algebra even more, this is a good class and probably so far one of my best math classes I've had so far.
System of Equations Project
This project also done in math had to do with graphing, graphing system of equations. This project was for the purpose of learning new ways in which to predict what could happen in the future, and also to compare to separate things or individuals. For this project we had to of course get some data to start the plotting of the points. First of all we had to make a graphing chart then label the x-axis with the years starting with the year 1996 and going all the way to 2010, well that’s what I labeled mine from. Then we had to go onto the internet and find two sets of tables, like the data of two football players like what I did and then graph the players overall score for every year that has gone by. So then when we finished just plotting the points we had to find a line of best fits in which had to run all the way through the middle of every plotted point and draw in our line of best fit. We couldn’t just lay down a line and just leave that as the line of best fit but we had to see that it made sense how the line belonged there. So then when the line of best fit was drawn in we continued on to the next step, there were supposed to be red dots for one set of data and blue dots for the other so there were two lines of best fit. For my project individually, one of the data sets was for the football player Ronde Barber and the other set for football player Brian Dawkins. So then all the points were plotted for Ronde and Brian so then came in the mathematical part, we had to do the math to see which year the two football player would meet up and have the same exact points. Then comes in the estimating with using the y=mx+b method, we use that for both sets of data and guess the future points and then try to see in which year both players had the same points. I had learned how to do this with past projects but we had two sets of data so there was more math to it and the math had to be exact or everything would go wrong, in my case I made a small peccadillo. Even when that happened It all turned out to be successful, then when all the math was done we had to put everything together, we had to make a colorful title page, which sort of showed what the project was about, then two data set, the plotted graph and some questions asking us what we did step by step when solving the equations that came from our data tables. Then when it was colorful and nice, we stapled and turned it in.
Standards:
5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.
6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality \(e.g., they sketch the region defined by 2x + 6y < 4).
Standards:
5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.
6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality \(e.g., they sketch the region defined by 2x + 6y < 4).
Data And Equations Project
This Project was made for the purpose us the students learn how to graph point on a graph and use the data of tables that we could find and make the equations to then solve and come up with a future prediction of the number, say endangered species, but before anything else we had to just choose an environmental issue take the information, in my case I got the number of endangered species for every year. We used the year as the x-axis of the graph and the environmental issue on the y-axis. This is what my graph showed and what I did, I show the number of the endangered species from the year 1986 to 2004. Then it showed my prediction of how many endangered mammals there will be in the year 2015. Then we had to say if the correlation of our line from graphing the points was either positive or negative, In my graph the correlation that it had was a positive correlation because the numbers in this graph were positive and it had nothing to do with loosing but instead of having an increasing number of endangered species. The number was increasing so the correlation was an increasing slope that keeps on going. Then we had to put in a line of best fit in between the plotted points and had to say or show if the line was an increasing line going up a decreasing line going down. The line of best fit in my graph was increasing from the points that I plotted. First I got two points closest to my line of best fit and chose them. They were (2002,74) and (2004,78), so then I did y2-y1 and x2-x1method, so I got m=2. Then I used a different equation Y=mx+b. I used this for my future prediction. So then the second step in this was plugging in my numbers, y=2x 3930.Then I used my future prediction year which was 2012 and plugged it in for x. Then the final results of this was 100 endangered mammals in 2015. This kind of shows that in the future the number of endangered mammals will rise but some will get to the point where they will be extinct.
Standards:
7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.
9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
Standards:
7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.
9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
Quadratics and Art Project
For this project what was asked for us the students to work out problems and graph parabolas were they went on a graph then make the whole thing into a piece of art using the different lines and parabolas. We started out in this project first by getting the 3 equations that we were going to need to solve the equations and graph our parabolas. Our teacher handed each student 3 different problems because not everyone could have the same work. As soon as each student got their problems we each started to solve them step by step. Help was given to those who needed it; then we had to take all our equations home and finish solving them if not finished and had to then graph the parabolas from each given equation. Then the work was taken back and had to get checked off to see if everything was right or the project would just go wrong. Once checked and told everything was right we started to do a simple design of what ideas we had to make this project real artwork. We all drew something and took back the plans and designs to get checked off and if everything was okay, we started the final product. Then we drew everything in made everything neat. We had to have all our work done because that was important to show we actually did everything to solve these equations. So in the art we had to label were each line and parabola was placed and made them stand out either by highlighting them or just making the lines thicker. Then everything was labeled and ready to go and that was needed was color to be added. The final product to this project was a well made graph artwork and then all the work stapled the the back of the 26x42 graphed project.
My project turned out to be a space ship in space blasting meteors, i never knew i would come up with that idea. I loved this project and it was a simple task that was asked for us students to do. My project came out colorful and nice and got a very good grade on it. What i learned from accomplishing and doing this project was how to solve quadratic formulas and how to graph them. I also learned that art can be made of everything even math because of this project, who new doing this project was fun.
Standards:
21.0 Students graph quadratic functions and know that their roots are the x-intercepts
22.0 Students use the quadratic formula or factoring techniques or both to determine
whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.
20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.
My project turned out to be a space ship in space blasting meteors, i never knew i would come up with that idea. I loved this project and it was a simple task that was asked for us students to do. My project came out colorful and nice and got a very good grade on it. What i learned from accomplishing and doing this project was how to solve quadratic formulas and how to graph them. I also learned that art can be made of everything even math because of this project, who new doing this project was fun.
Standards:
21.0 Students graph quadratic functions and know that their roots are the x-intercepts
22.0 Students use the quadratic formula or factoring techniques or both to determine
whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.
20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.
5 Steps to Solve Quadratic Equations Project
This project all involved teamwork. For this project what was asked for us to do was get into groups and make a brochure showing 5 steps of solving different quadratic equations. The five different steps to solve quadratic equations are factoring, completing the square, graphing, quadratic formula and square rooting. We start this project just by simply getting into a group of 3 people. Then we were given 5 equations and each equation told us what method we had to use. Everyone in the group had to have a fair share of work, i got to do quadratic formula, and the brochure while my partners did all their work. Everyone had to do the work. Then we went into the computer lab and we went to go start on our brochures. Our teacher how to use Microsoft Publisher because that was the program on the computer needed to make our brochures. We were taught the basics on how to do what we needed but we went in further into the program and discovered more tools and other things that helped us to better out brochure. We started and we used something called Microsoft Equation 3.0 to make the equations we needed then we described the steps to take when solving the problem. Every equation was written out in ax2+bx+c=0 format, but some methods don't work so you have to use others. Then each section in the brochure had a different style methods to solving the quadratic equation. We wrote out all the directions and the steps and how the equation had to look in a certain step in the problem to make it easier. So when we were done writing everything out we decorated the brochure and added some color to it so it wouldn't be dull. The final product for this project was a well made brochure made by the whole group, colorful and everything on the brochure makes sense, and clearly shows everything step by step.
I learned in this group project was how to solve quadratic equations in all of the five steps, factoring, completing the square, quadratic formula, graphing, and square rooting. This may have been review from what we learned in the past but it helped me to better understand quadratic equations. I learned that working in a group helps better when it comes to doing a project because then not all the onus is on you. This was a good group project and i would mind having to do another because this is a project you can finish in a day if you really concentrate.
Standards:
14.0 Students solve a quadratic equation by factoring or completing the square
20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations
19.0 Students know the quadratic formula and are familiar with its proof by completing the square
18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion
I learned in this group project was how to solve quadratic equations in all of the five steps, factoring, completing the square, quadratic formula, graphing, and square rooting. This may have been review from what we learned in the past but it helped me to better understand quadratic equations. I learned that working in a group helps better when it comes to doing a project because then not all the onus is on you. This was a good group project and i would mind having to do another because this is a project you can finish in a day if you really concentrate.
Standards:
14.0 Students solve a quadratic equation by factoring or completing the square
20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations
19.0 Students know the quadratic formula and are familiar with its proof by completing the square
18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion
