Exploring Math

With A

Linear Equations Treasure Hunt

Created by Erica Goad

Graph of two intersecting lines
"Graph" Solving Linear Equations. Retrieved October 29, 2005
from http://www.cs.sunysb.edu/~algorith/files/linear-equations.shtml

 

Understanding Statement: 
    Linear equations show a relationship between two variables, and these equations can be represented with a certain type of graph.

Introduction: 
    Math is used all around us every day!  Whether measuring ingredients for a recipe, or trying to figure out the tip at a restaurant- math is involved.  Math is crucial for architects as they design the structural system of a building.  Geologists depend on mathematical models to perform tasks such as finding oil and studying earthquakes.  So many jobs require the use of math!  Math is so important and relevant in today’s society, making it an exciting field to discover.  A very important part of math is being able to understand, interpret, and visualize data.  This treasure hunt is designed to let you experience these aspects of math through investigating and furthering your understanding of linear equations and their graphs. 

Questions:
    Before you begin, understand that this treasure hunt is designed to help you better understand and review linear equations and the graphs generated by them.  However, you will likely develop questions as we explore this topic.  These questions may or may not be addressed within this hunt- math is a wonderful and vast field of study and there is much to learn about it!  Keep a record of questions you may develop about any aspect of this hunt or the problems that are discussed throughout it.

Let’s begin!

 

  1. Describe briefly the difference between a relation and a function.
     
  1. Summarize what an equation is used for.  What is a variable and how is it used in an equation?  
     
  1. After looking at this site:
    a. Describe how the coordinate plane is set up (mention the
        axes and quadrants).
    b. Describe what the first and second term in an ordered pair represent.
     
  1. What does this table show us?  How many input values do you think there are for an equation like this? 
     
  1. Look here again and describe the process used to generate this graph.  Also read the note at the bottom of the page.  What kind of function (equation) did we use?
     
  1. We can also begin a linear equation graph by looking at the intercepts.  Define in your own words the x and y- intercepts.  At least how many coordinate points do you think are needed (minimum) to find a linear equation graph?
     
  1. An important part of a linear graph is the slope.  Try to describe what this equation for slope means.  (Hint: minus describes difference)
     
  1. Use this site to modify and/or add more details to your definition of slope.
     
  1. View these images of graphs.  Do you see how slope is used to find a line?
     
  1. Look at the example at the bottom of the page.  What do you think the equation y = (3/5) x + 3 will look like? 
     
  1. The equation in the problem above uses slope-intercept form.  How do we know this is a linear equation?
     
  2. What are the questions that you had during this treasure hunt?

                                                  math on chalk board                 
                                                         "Equations" Fresno County Public Library.  Retrieved           
November 1, 2005 from http://www.fresnolibrary.org/teen/hc/math.html

Putting it all together:                                    

Look at these graphs.  Find and describe the slopes (are they positive, negative, steeply slanted or not?)  Write an equation for the graphs (Hint: The y-intercepts are zero).  What makes these graphs and equations linear?  Review any of the sites in the treasure hunt to help you.

Taking an extra step:

Now visit this site to complete both the crossword puzzle and the word search to help further familiarize yourself with the terms we have used in this treasure hunt!
When the page comes up, click on the center picture.  In the window that appears, click the puzzle button and select the puzzle or word search. 

 

 

 

"Algebra" on chalk board

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Background "Fractal Image" Retrieved October 30, 2005 from
http://www.eyellusions.org/darkside/Fraktale.htm