Algebra Niess Dynamic Speadsheet Function Machine

jennyrueter's picture
Content Area(s):  
Grade Level(s):  
Oregon Common Core State Standards: 
Math 7.1.4
Math 8.1.5
Lesson Plan Details
Duration: 
2 class periods
Objective: 
  • Students will learn...
  • to use and adjust a spreadsheet tool to find the intersection solution of two linear equations.
  • the algebraic relationship between independent and dependent variables as the spreadsheet graph dynamically adjust changes in variables.
  • that spreadsheets are helpful in solving algebraic problems.
Resources: 
  • One computer for each students with Excel spreadsheet software and the Niess Dynamic Function Machine (attached)
  • An InFocus or SMART board to project the Excel spreadsheet for whole class viewing
  • References: Maggie Niess, Professor Emeritus Mathematics Education Science and Mathematics Education, Oregon State University, Corvallis, OR 97331,SED 522 online course

Preparation: 
  • Download the Niess Dynamic Function Machine (attached)
  • Become familiar with the Niess Dynamic Function Machine... adjusting functions, initial and incremental values, and graph titles and axis labels
  • References: Maggie Niess, Professor Emeritus Mathematics Education Science and Mathematics Education, Oregon State University, Corvallis, OR 97331,SED 522 online course

Instruction: 
  • Adjust the Niess Dynamic Function Machine initial and increment values so the "Carnival Bracelet #1" solution does not show.
  • Introduce Niess Dynamic Function Machine spreadsheet with the "Carnival Bracelet" problem:

To go on rides at the fair you must first pay the $7.50 entrance fee and then pay $1.50 for each ride. Some students choose to buy the $25 carnival bracelet which is good for one day’s entrance fee plus unlimited rides.  Use the Dynamic Function Machine to determine for  which numbers of rides is the $7.50 entrance fee plus $1.50 per ride less expensive than the carnival bracelet? For which numbers of rides is the $25 carnival bracelet less expensive than the $7.50 entrance fee plus $1.50 per ride? Is there a number of rides where the cost would be the same either way?

  • Adjust the Niess Dynamic Function Machine initial and increment values to show the intersection
  • Niess "Cell Phone #2" problem:

Juan and Sylvia each have a cell phone.  They were comparing their costs to see who has the better deal. Juan’s company charges 20 cents for making a call and then charges 60 cents for each minute of the call. Sylvia’s company charges 30 cents per minute but charges 80 cents for making the call. All call charges are for 1-minute minimum.  How many minutes can they talk on the phone such that their charges are equal?

  • Demonstrate how to translate the cell phone problem into two algebraic equations, how to enter the equations into the function machine, how to adjust the initial and increment values to show a solution and finally how to rename the graph title and axis labels to match the cell phone variables.  
  • Niess "Satellite/DVD #3" problem:

The Smith family is trying to decide between installing a satellite dish and receiving and movies through the satellite or purchasing a DVD and signing up for DVD rentals per month. The Smiths need to compare the cost of each option over several months in order to make an appropriate decision.

Satellite: One time installation of $29 and $49 per month for the service that allows them to unlimited access to their choice of movies with the stipulation that they must maintain this system for at least one year.

DVD: Purchase a DVD player for $250 and unlimited rental of DVDs for  $30 per month.

Help the Smith family make a decision.  For how months is the Satellite less expensive?  For how many months is the DVD player with rentals less expensive?  Is there a number of months when the cost is the same?

  • Demonstrate how to translate the "Satellite/DVD"problem into two algebraic equations, how to enter the equations into the function machine, how to adjust the initial and increment values to show a solution and finally how to rename the graph title and axis labels to match the cell phone variables.
  • "Airplanes" #4:

A plane initially at 28,000 feet is descending at a rate of 1800 feet per minute, and a second plane initially at 1500 feet is climbing at a rate of 2300 feet per minute.  Determine how many minutes it will take for the planes to be at the same altitude.  Create a chart that tracks their progression per minute until they pass each other. 

  • Students work on their own to solve by translating the airplane problem into two algebraic equations, entering the equations into the function machine, adjusting the initial and incremental values to show a solution and finally renaming the graph title and axis labels. Students rename their spreadsheet with their <own name>airplanes and submit Niess Dynamic Function Machine to the teacher. 
  • Students create their own Niess Dynamic Function Machine problem scenario to share with a partner.  They also submit the new problem to the teacher saved as <own name>new problem.
  • After students share with a partner and edit their problem scenarios and function machines, they then are ready to share with the class.
  • References: Maggie Niess, Professor Emeritus Mathematics Education Science and Mathematics Education, Oregon State University, Corvallis, OR 97331,SED 522 online course

Assessment: 
  • Did the student rename the spreadsheet <own name>airplane and submit <own name>airplane with the problem #4 airplane solution?
  • Do the initial and incremental values accurately show the airplane intersection on the line graph? H4:K4
  • Do the line graph title and axis labels represent the airplane problem variables accurately?
  • Did the student submit <own name>new problem on the Niess Dynamic Function machine?
  • Do the initial and incremental values accurately show the new problem intersection on the line graph? H4:K4
  • Do the line graph title and axis labels represent the new problem variables accurately?
  • Did the student effectively use the Niess Dynamic Function Machine tool to solve the algebraic problems?
  • References: Maggie Niess, Professor Emeritus Mathematics Education Science and Mathematics Education, Oregon State University, Corvallis, OR 97331,SED 522 online course

 

 

 

 

 

 

 

 

 

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    Oregon Educational Technology Standards
    Creativity and Innovation: 
    1A. Apply existing knowledge to forecast possibilities and generate new ideas, products or processes.
    1B. Create original works as a means of personal or group expression.
    1C. Develop or apply models and simulations to explore complex systems, issues and trends.
    Communication and Collaboration: 
    2A. Interact and collaborate with peers, experts, or others employing a variety of digital environments and media.
    Research and Information Fluency: 
    3D. Analyze, evaluate, and summarize information or data and report results.
    Critical Thinking, Problem Solving and Decision Making: 
    4A. Identify and define authentic problems and significant questions for investigation.
    4B. Plan and manage activities to develop a solution or complete a project.
    Digital Citizenship: 
    5B. Model and practice a positive attitude toward using digital technology that supports collaboration, learning, and productivity.
    Career Related Learning Standards
    Personal Management: 
    CR2A. Plan, organize, and complete projects and assigned tasks on time, meeting agreed upon standards of quality.
    Problem Solving: 
    CR2A. Identify problems and locate information that may lead to solutions.
    CR2D. Select and explain a proposed solution and course of action.
    Communication: 
    CR3A. Locate, process, and convey information using traditional and technological tools.
    shona314's picture

    I love this lesson!  I just spent time telling my kids how they use algebra when they are working with spreadsheets on Excel.  My friend, who owns a local business, is always asking me to help to set up spreadsheets for his company.  Such a valuable tool.  I haven't looked through your lesson completely - but definitely plan on using parts of it.  Thanks for the idea.  It can be adapted to Geometry very well when working with surface area and volume.

    amberwarren's picture

    This is a great lesson on systems of equations! I would like to know the process in creating a template for any type of problem like this; ie, is this a specific program that needs to be purchased? I like the visual of it. Can you email me with info on this?

    debradunbar's picture

    Thank you for sharing and especially for the spreadsheet visual!

    Keith Holcombe's picture

    This is a great idea!!!  Where do you get the machine that is needed for this lesson?  I can definitely use this in my classroom.  What a great way for kids to use the technology available to them to also check their work to see if they understand the concepts.  It will also bring real life application of the software programs being used in the work place.