Project Title

Say What?

 

Introduction

Traditionally, in algebra coursework, you are given a problem situation and asked to create an equation or system of equations to solve the problem.  You have no doubt encountered many problems asking, “How many quarters did Bobby have?” or “How much older than Grace is Juan?”  Although solving these types of problems is a core component of becoming proficient at algebra, beginning to think about the linear relationships that are found in the real-world allows you to extend and apply your algebraic knowledge.  In this activity, you will discover that a line on a coordinate plane can have many meanings, depending on the labels associated with the axes.

 

Task

Working together with your group, you will develop your own storyline to represent two linear relationships.  Creativity will be the key in this project, as you get to define your own independent and dependent variables and then describe what the solution to your system would represent within the confines of your storyline.  After developing your own linear relationships and storyline, you will then be put to the test as you try to interpret another group’s graph.  Get ready to start thinking outside the box!

 

Instructions

Solve each problem in the order given.  Save your work along the way, as you will create a display at the conclusion of the project.

 

1                     First problem:

·                     Choose one of the following sets of domain and range values.   You will use the domain and range values to create your graph, equations, and storyline.

 

Domain:

Domain:

Range: 

Range: 

 

 

Domain:

Domain:

Range: 

Range: 

 

 

Domain:

Domain:

Range: 

Range: 

 

2                     Second problem:

·                     Considering the domain and range values that you chose above. Begin discussing what your possible independent and dependent variables might be.  Remember, creativity makes your project stand out!  Some examples include:

 

Independent:  time

Independent:  number of students

Dependent:  distance

Dependent:  number of pizzas

 

 

Independent:  time

Independent:  age

Dependent:  weight

Dependent:  height

 

·                     Once you have decided on your variables, begin thinking about your storyline.  You will write a more detailed storyline later.  For now, simply consider what each line will represent based on your variables.  You will have two lines on your graph.  The first line will represent your first scenario and the second line will represent the second scenario.  Make a data table and sketch a graph of each line.  You will make a more professional looking graph next.

 

3                     Third Problem:

·                     GeoGebra can be used to make the graphs for this project.  GeoGebra is a free program.  The download can be found at: http://www.geogebra.org/cms/en/download

 

To create your graph, choose the Drawing Pad under the Options menu.  You will now be able to enter your minimum and maximum values for each axis, as well as units and labels.  While still in the Drawing Pad, select the grid tab and check grid to show gridlines on your graph. 

 

(Hint: You will need to set a minimum a little less than zero for both your domain and range.  If you do not set the minimum a little less than zero, the axes are not visible on your graph.  You will need to play around with your minimums until you are happy with your axes.) 

 

Once your graph is defined, you will need to plot your points.  In order to plot a point, select the “New Point” button and then click on the grid to drop the point.  Once your points are defined, select the “Line Through Two Points” button.  Click on any two points to create a line.

 

You will now need to save or print two copies of the file.  One will have the labels and units defined.  The other will have the units and labels removed. 

 

(Hint:  To remove the labels and units, go to the Drawing Pad.  The graph with no labels and units will be given to another team.) 

 

4          Fourth problem:

·                     Using the points defined on your graph, find the equation of each line.  Now, solve the system using substitution or elimination.  Show your work neatly, as it will be part of your display.  Compare your solution to the graph to ensure they match.  If not, check your algebra.  

 

(Hint:  To find the equation of a line given two ordered pairs, you first need to find the slope.  Then use either point-slope form or slope-intercept form to find the equation.)

 

5          Fifth problem:

·                     Write a detailed storyline to describe each line and the solution to the system.   Be sure to include a backdrop for your story line.  Keep your story believable, yet creative.  Be sure to describe the story associated with each line and then describe what the solution to the system means within the context of your storyline.

 

Collaboration

Trade unlabeled graphs with another group.  With your new graph, again find the equation of each line.  Use substitution or elimination to find the solution to the system.  Check to ensure that the solution matches with the graph.  Now, create a new detailed storyline.  This detailed storyline will be part of the other team’s project.  Do your best and be creative! 

 

Conclusions

Create a poster display including your labeled graph, algebraic solution to the system, and detailed storyline.  Then, collect the second storyline created by the other team.  Include it on your display, as well.  In order to prepare a more professional looking product, consider using Microsoft Word or a similar word processing program to type your detailed storyline.  Including hand-drawn or computer-generated graphics will also enhance your display.

 

As an alternative to a poster, consider creating a website for your project.  You can save your GeoGebra graph and import it in HTML or as a picture.  An easy, free place to create a website is www.weebly.com.  If you choose to create a website, be sure to include your labeled graph, algebraic solution to the system, detailed storyline, and the other group’s storyline that corresponds to your graph.  Also, consider inserting a page for a poll to determine which storyline is most believable and which is most creative.   

 

Grade

Your project will be given a score of 1 to 4, with 4 being the highest score possible. You will be evaluated based on the following criteria:

 

Score

Content

Presentation

4

Your project appropriately answers each of the problems.  Your graph is professional looking.  The equation of each line is correct and the solution to your system is proven algebraically using substitution or elimination.

 

Your project contains a detailed, believable, and creative storyline that correctly corresponds to each line.  The solution to your system is described within the context of your storyline.

Your poster or website contains information shown in a logical and interesting sequence that is easy to follow.

 

Your poster or website is professional looking with graphics and attractive use of color. 

 

3

Your project appropriately answers each of the problems.  Your graph is neat.  The equation of each line is correct and the solution to your system is proven algebraically using substitution or elimination.

 

Your project contains a believable storyline that correctly corresponds to each line.  The solution to your system is described within the context of your storyline.

Your poster or website contains information presented in a logical sequence that is easy to follow.

 

Your poster or website is neat with graphics and attractive use of color. 

 

2

Your project appropriately answers some of the problems.  Your graph is neat.  The equation of each line is given and the solution to your system is proven algebraically using substitution or elimination.  Minor errors may be noted.

 

Your project contains a storyline that correctly corresponds to each line.  The solution to your system is described, but not in detail.

Your poster or website is hard to follow because the material is presented in a manner that jumps around between unconnected topics.

 

Your poster or website contains low quality graphics and colors that do not add interest to the project.

1

Your project answers some of the problems.  Some parts of the project are missing and/or major errors are noted. 

 

Your project attempts a storyline, but the story does not correctly correspond to the graph. 

Your presentation is difficult to understand because there is no sequence of information.

 

Your poster or website is missing graphics and uses little to no color.

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