Historical+Money

Lisa La Roche
=Historical Money=
 * Introduction & Overview:** The purpose of this lesson is to incorporate the use of technology into an Algebra I classroom. For this lesson I will be using WolframAlpha.com to help teach the concept of graph interpretations. In this lesson, the students are to work in pairs to determine money equivalences across great periods of time. Once WolframAlpha.com has completed the actual money equivalences for certain periods of time, a graph is provided to display the provided data. Once we as a class have discussed how to read and interpret the true meanings of what the graph is telling us, the students will be asked several follow-up questions that can be answered by merely looking at the graph. Their answers to these follow-up questions will help me determine how well my students know how to interpret the data in the graph.


 * Grouping & Classroom set-up:** Students are in pairs and at least one of the students must have access to a computer with a working internet connection. (It is best if both have access to a computer so they both can learn how to use WolframAlpha.com.)


 * Example & Beginning Steps:**
 * 1) Get on a computer and get on the internet. Once on the inter net, type http://www.wolframalpha.com/ in the address bar and type historical money in the menu bar of the site.
 * 2) Once you are at WolframAlpha.com, type historical money in the menu bar of the site.
 * 3) When you are at the correct place in the website, it should look like this.[[image:Historical_Money_Picture_#1.jpg]]

4. For this example, we are going to click on the equal sign for the statement that says, “$100 2001 dollars in 1801.” It is the bottom option in the picture above. 5. This picture is what your screen should now look like.

6. Now that we are at our destination, it is time to examine all the information that WolframAlpha has provided for us to use. From the Input at results boxes at the top of the diagram, we know that $100 in 2001 = $6.96 in 1801. We can verify this by looking at the graph above. The years run along the x-axis while the dollar amounts run along the y-axis. According to the graph, in 2001 we had $100 and in 1801 we had $6.96. Other questions can be asked about this graph as well. For example, I could ask the students to determine what the given amount of $6.96 in 1801 is equal to 1900 and 1950. By just looking at the graph, the students should be able to get a rough estimate of their equivalents.

7. Now that we have completed one example as a class, the students will be asked to complete the following questions: Determine what $15 in 2011 dollars is equal to in 1850. Also use this graph to determine what $15 in 2011 dollars is equal to in 1900 and in 1950. Determine what $600 in 2011 dollars is equal to in 1940. Also use this graph to determine what $600 in 2011 dollars is equal to in 1960, 1980, and in 2000. Determine what $4000 in 2011 dollars is equal to in 1790. Also use this graph to determine what $4000 in 2011 dollars is equal to in 1800, 1850, 1900, 1950, and in 2000.

8. To complete this assignment, each pair will turn in one paper with their answers on it.

Question #1 = 3 points Question #2 = 4 points __Question #3 = 6 points__ Total points = 13 points
 * Grading:**

(Full paper and reflection are below).

Lisa La Roche Math 506 7-26-11 Teaching Mathematics with Web 2.0: Increase Mathematical Rigor and Relevance For this lesson outline, I chose to use Historical Money on //WolframAlpha.com// to help my students learn how to do data interpretations of graphs at a basic to medium level using money. I will incorporate this website into my remedial Algebra 1 class. The type of students that I have in this class ranges from 9th to 12th grade remedial student with different ethnic backgrounds. Some of these students are repeating this class for either the first or second time. Their skill levels are varied as well as their behaviors. Some of these students are in my class because they do have low skill levels, while others are in my class because they have behavior issues. So, it is accurate to say that my students are varied in many ways. The math concepts that I plan to cover in my Algebra 1 class include the following: foundations for algebra, equations, inequalities, functions, linear functions, systems of equations and inequalities, exponents and polynomials, factoring polynomials, quadratic functions and equations, data analysis and probability, exponential and radical functions, rational functions and equations, angle measurements and their basic properties, and various real world word problems. However, since my students are remedial, the actual amount of these concepts that will be covered will depend on their skills and abilities. The way in which I plan to incorporate the use of this website in my classroom comes in the form of an end-of-class activity on a block day. Since my classroom has 30 student computers, my students will be given time on block days (Mondays and Tuesdays) to work on this assignment. For this lesson, I will arrange my students in pairs of two. They will be required to go to the website of http://www.wolframalpha.com/ and type historical money in the menu bar of the site. Once everyone is at the site, we will do the following example as a class to help everyone learn why we are actually trying use this site to help us.
 * 1) When you are at the correct place in the website, it should look like this.[[image:Historical_Money_Picture_#1.jpg]]

2. For this example, we are going to click on the equal sign for the statement that says, “$100 2001 dollars in 1801.” It is the bottom option in the picture above. 3. This picture is what your screen should now look like.

4. Now that we are at our destination, it is time to examine all the information that WolframAlpha has provided for us to use. From the Input at results boxes at the top of the diagram, we know that $100 in 2001 = $6.96 in 1801. We can verify this by looking at the graph above. The years run along the x-axis while the dollar amounts run along the y-axis. According to the graph, in 2001 we had $100 and in 1801 we had $6.96. Other questions can be asked about this graph as well. For example, I could ask the students to determine what the given amount of $6.96 in 1801 is equal to 1900 and 1950. By just looking at the graph, the students should be able to get a rough estimate of their equivalents. 5 Now that we have completed one example as a class, the students will be asked to complete the following questions: 1. Determine what $15 in 2011 dollars is equal to in 1850. Also use this graph to determine what $15 in 2011 dollars is equal to in 1900 and in 1950. 2. Determine what $600 in 2011 dollars is equal to in 1940. Also use this graph to determine what $600 in 2011 dollars is equal to in 1960, 1980, and in 2000. 3. Determine what $4000 in 2011 dollars is equal to in 1790. Also use this graph to determine what $4000 in 2011 dollars is equal to in 1800, 1850, 1900, 1950, and in 2000. 6 To complete this assignment, each pair will turn in one paper with their answers on it. The ways in which I will assess each pair’s performance for this assignment is quite simple. Each initial determination of each question should have an exact answer produced by WolframAlfpha and will be counted as correct or incorrect. The second determinations in each question that requires the students to use the graphs to determine the equivalent amounts must be reasonable because the graph only provides a rough estimate. The actual points that will be awarded for each question are as follows: Question #1 is worth 3 points, Question #2 is worth 4 points, and Question #3 is worth 6 points. Point will be deducted based on the amount of work not completed or turned in. The larger lesson assessment will be done individually and in a paper/pencil format. The students will be given a total of three different graphs similar to the ones shown above and asked to determine dollar equivalents among different years. Each of these questions will be worth 3 points and the answers must be reasonable. In conclusion, I do feel that this internet site will allow the students to connect math with the technology that they are used to using today. Also, this Historical Money lesson will require the students to not only use technology for a math assignment, but also, they will learn that the internet has sites that can help them with their math work. This knowledge will be very helpful for them in their educational future.

Lisa La Roche Math 506 7-26-11

Reflection After reviewing this lesson, I can see many pros and cons with it. One pro that I can see with using WolframAlpha.com is that the students will get to use the internet to learn about interpreting graphs. Another good thing about using WolframAlpha.com is that my students will get to use the internet to learn how to use internet programs to do their math work. In addition, the students will be able to take pride in their math class by knowing that their class is probably the only math class at their school using WolframAlpha.com as a math tool during class. The negative things that I can see happening with using WolframAlpha.com is that the students may think of it as an answer book and not as a learning tool. Another problem with this assignment is that the students may not have a computer at home and may not want to stay after school to work on it in the computer lab. Also, the students who do not do their homework will not be able to complete the assignment and may cause his/her partner to suffer a loss in points. When thinking about the challenges in implementing this technology into my teaching situation, a few things must be considered. The main thing that must be considered is the parents’ views of this system. Some parents may be for it, while others may be against it. Also, the school administrators must agree to allow the use of WolframAlpha.com as well for legal reasons. In addition, the students must be interested enough to follow through with their part in order for this technology usage to be successful. As far as access to computers, the students have access to a computer Monday through Thursday after school in the library until 8 pm in addition to the use of the classroom computers. The final issue regarding the implementation of WolframAlpha.com is that I will have to monitor the students during class to make sure that each pair is on WolframAlpha.com and not browsing the web. In conclusion, I think that WolframAlpha.com could have its benefit, but it also has it pitfalls as well.