Nov. 1, 1999
Math Lesson Plan
Grade Level 9th
A. Learning Objectives:
After using spreadsheets and graphs on a computer in this lesson, 9th graders will have increased their ability to write algebraic expressions and will have learned to create graphs that represent variable quantities. They will develop the ability to determine profit situations using basic algebraic equations. During the course of this unit, the students ability will increase in the area of correspondence between the elements of two sets. Also, by applying changes to functions and graphs multiple times, students will see at the end of the unit how real-world problems can be solved with highly practical applications.
B. Instructional Context:
This lesson will be used in a 9th grade math classroom such as Pre-Algebra or Basic Math. The actual work by the students will be completed in a computer lab where there is access to a computer by everyone equitably. The students are required to have working knowledge of spreadsheets. They will also have already had formal instruction on creating a basic graph and what an algebraic equation looks like and how it works.
B2. Materials Needed
•Student notes on gym dimensions that were measured earlier
•Computer lab with spreadsheet program(i.e. Excel, ClarisWorks, etc.)
•Printing capabilities
•Handout with student requirements
•Teacher lesson on using spreadsheets and graphing within a spreadsheet
B3.Description of the Lesson and Procedures:
What the Lesson Involves This lesson begins after a certain amount of work is already done. The students have already done some basic algebra functions and equations and can write them when given enough information. Also, the class has collected information about the gym including total seating area (measured manually in inches, feet, etc.) and know what is charged per person for a basketball game.(i.e. adults, students, children) The students are to then determine what kind of profit can be made by the athletic department at the next home game assuming the gym is full and predicting how many of each type of people can fit into the gym. They will then create three “real-world” possibilities and see how those effect the profit and give their choice of a reasonable possibility that produces the best profit. They will give their reasoning for this choice as well as the equations used to determine their outcomes.
The teacher will then lead a short activity on using a spreadsheet and how to use the graphing utility within the spreadsheet. This will only be a short lesson to give the students some basic information on creating their spreadsheets. It is assumed that students have previously worked with spreadsheets. If no previous knowledge is recognized in the students, then this activity should be expanded to ensure everyone understands how to use a spreadsheet and can effectively manipulate one. Equity between students should be a priority so that students without advanced spreadsheet skills do not get lost in the technicalities of the tool.
Step by Step Breakdown This is the third day of a six day unit working on the real world gym problem. The students are aware of the big picture for this unit and have measured the gym and gathered the necessary information. In yesterday's lesson, the instructor provided the students with a review of spreadsheet basics in the computer lab so any necessary questions or uncertainties could be cleared up. Today the focus of the lesson is on using the spreadsheet to create the 3 scenarios. The teacher will begin the lesson by passing out a sheet which explains the problem and the students' tasks. The teacher will remind the students of the algebra equations they had previously done, and then go over the gym space data they have collected. (If the students are working in groups, they will get in their groups before the teacher goes over the problem.) The teacher will reiterate the students' tasks by going over the problem. (The problem will be outlined on a transparency). The teacher will address any questions the students have about what is expected and about the problem in general. After this the students will go to the computer lab to work on their graphs. They will have 40 minutes of in class time to work on the graphs. In the computer lab, the teacher will circulate and assist students as necessary. The teacher will look and listen for comments from students that focus on manipulating the data, approximating numbers of students, kids, and adults, and relating the data to space. The teacher will look for graphs on the screens, algebraic equations and students work on explaining their results. If the kids are in groups, the teacher will be looking for collaboration between all members and ensure that all members of the group are participating in the choices made for projecting the profit to be made.
Ten to fifteen minutes into their computer time, the teacher will make any more necessary comments on things that they have seen in the students progress so far and address any issues that may have not come up previously. As the period comes to a close, the teacher will decide whether the assignment can be finished on the students’ own time or if they will finish them in class the next day. The instructor will base this on the diligence of the students and the progress made in class. If students have been working hard and have not progressed sufficiently in class, more time should be allotted. If other computer access time is not in the students schedule, more time should also be allowed. If students have not worked hard in class, then the instructor may feel the need to require students to complete this on their own time and set a due date accordingly. (Maybe one extra day without in class work time. For hard-working, one more class period with the project due at the end of the period.)
In the final lesson in this unit, the teacher will connect all of the things that have been discussed and continue the project more into the side of optimizing profit. This will require a compilation of all things done for this unit up-to-date and a students’ ability to connect the problem solving skills usually used in the classroom to a real-world problem such as this one.
What the Teacher Does The teacher has the responsibility to lead a formal hands-on activity on spreadsheet use ensuring equity between students. If further instruction is needed, then the instructor must compensate for this by expanding the activity. The instructor will also introduce the project, give a handout with the necessary criteria being looked for, and answer any questions pertaining to it. As the project is being worked on in class, the instructor will also observe progress and give any necessary feedback to keep students on task.
What the Students Do The students are to prepare a document containing three manipulations of the information previously recorded and produce two algebraic equations that relate the information, three graphs that visually show a relationship between two variables, and their prediction of what the athletic department will make in profit for the sold-out home game. Within this document, the students should include an explanation of their reasoning for choosing this scenario and show any necessary calculations that support this calculation. These predictions should be realistic and easily measurable.
C. Role of Computer:
The computer will be utilized by the students and used as a tool to aid them in creating a spreadsheet to report their findings. In the Thomas & Boyson Taxonomy, this would be classified as utilizing. According to Bloom’s taxonomy, this activity would be classified as Comprehension as they are interpreting, explaining and illustrating information. It would also fit under Application as they take their knowledge of algebraic equations and generalize it to a new, concrete situation. It may fit under Analysis because it breaks down the graph information into its parts to determine the relationships between them. The students will further use the computer’s ability to manipulate data within the spreadsheets to optimize their prediction of what the athletic department will profit based on the measurements of the gym and the variable predictions. They will then use the computer to combine their spreadsheet results with a word processing document with their graphs and the reasoning behind their prediction.
D. Evaluation Tool/Measures
Students will be evaluated on the correctness of their graphs. This includes correctly placing axes, labels, appropriate spacing, and including a legend with a title. The instructor will also be looking for an algebraic expression of the graph as well as manipulations of the graph to show an optimization of profit. Three “real-world” situations will be graded on their reasonableness and how accurate and believable the profits are based on the calculations shown by the student.
Since this lesson is part of a larger unit and an overall bigger project, this hand-in will be graded on a simple “Looks good, proceed” or “Needs Work, See Me” rubric. I will be specifically looking for creation of a graph, appropriate information on the graph, implementation of the graph into a Word Processing document, detailed explanation of their graph and the actual algebraic equations. If these things are looking good, then the students will proceed on into the next phase of the unit. Those who are not satisfactory must redo those things that are lacking before they proceed. This will be what is done on day four of the unit. After everyone is working at a satisfactory level on day four, we will continue to day five and the profit information.
http://www.mcrel.org/standards-benchmarks/standardslib/math.html
Mathematics
Standard: 8
•Understands and applies basic and advanced properties of functions and algebra
Level IV: High School (Grades 9-12)
-Uses expressions, equations, inequalities, and matrices to represent situations that involve variable quantities and translates among these representations
-Understands properties of graphs and the relationship between a graph and its corresponding expression (e.g., maximum and minimum points)
-Understands basic concepts (e.g., roots) and applications (e.g., determining cost, revenue, and profit situations) of polynomial equations
-Understands the concept of a function as the correspondences between the elements of two sets (e.g., in algebra, functions are relationships between variables that represent numbers; in geometry, functions relate sets of points to their images under motions such as flips, slides, and turns; in the "real-world," functions are mathematical representations of many input-output situations)
-Uses a variety of models (e.g., written statement, algebraic formula, table of input-output values, graph) to represent functions, patterns, and relationships
-Understands the effects of parameter changes on functions and their graphs
Mathematics
Standard: 9
•Understands the general nature and uses of mathematics
Level IV: High School (Grades 9-12)
-Understands that in mathematics, as in other sciences, simplicity is one of the highest values; some mathematicians try to identify the smallest set of rules from which many other propositions can be logically derived
-Understands that theories in mathematics are greatly influenced by practical issues; real-world problems sometimes result in new mathematical theories and pure mathematical theories sometimes have highly practical applications
F. Example
Scenario #1
Here is our first scenario for what the home game will look like. We predicted that each adult would require one and a half feet of space while each student or child would require about one foot of spacing. Also, based on the costs below, we devised the equation that calculated our profit. Our first graph illustrates the projected mix of people that will be there. The second graph shows how much each group of people will contribute to the total profit.
Gym Measurements and Projected Specifications
Seating(in ft): 1000 Spacing per adult(ft): 1.5 Space per student/child(ft): 1
Cost per adult: 4 Adults: 411 Adult Profit: $1644
Cost per student: 2 Students: 353 Student Profit: $706
Cost per child: 0 Children: 30 Children Profit:$0
Equation #1
Total Feet=1.5 Adults + 1.0 (Students + Children) 999.5
Equation #2
Profit=Children (0) + Adults (4.00) + Students (2.00) $2350
From here the student will change the specifications for number of people attending the game and see how that will effect profits. After doing this for Scenario #2 and Scenario #3 the students should choose which one they think is the best one or most realistic and explain why. This can be accomplished in a brief paragraph. This example has everything that the instructor should be looking for and is what the student should hand in for this lesson.