Students will be able to graph their data from their charts (lesson 1).
Students will be able to explain the meaning of the slope of their graph.
Students will analyze ways to improve their profits and decrease their costs using their charts and graphs.
 

Introduction—

1.      Divide students into groups of 2.  Instruct them to work together to check their trading charts.  They should look at one person's trading chart first and then at the other's.  They should check for a good description of the transaction, the appropriate amounts in the accounts payable and accounts receivable sections.  Then they should make sure that the accounts payable and accounts receivable are in the appropriate fixed and variable columns.  For example, one transaction I made this week was to buy some flour from Daniel D.  I should write this under the accounts payable because I paid that money to Daniel.  What column does it belong under?  It is not a fixed price so I should write it under the variable column.  Carefully monitor students as they check their charts.

2.      Put the overhead of the graphing paper on the projector.  Point to it and tell students that today we are going to take a “birds-eye view” of our transactions.  We are going to look at the “trends” of our trading using this graph paper.

Lesson Steps—

1.      Using the graph overhead, draw a line going from the lower left hand corner to the upper right.  Then label the x-axis with seconds and the y-axis with miles per hour.  Ask students if they can explain what is happening on your graph.  Help them to see that as time increases, the miles per hour increase as well.  What is this graph an example of?  Acceleration of a car, bicycle, animal, or person.  For example, when you run a race, you accelerate off the starting line.

2.      Next draw another graph looking like a ‘V.’  Label the x-axis time in years and the y-axis number of doctors visits.  Ask students to discuss with a neighbor what this graph means.  Call on several students to ask them to explain their conclusions.  The answer students should reach is that we have the fewest doctors’ visits when we are middle aged and the most when we are very young and very old.  Is this true?  Ask students for their opinions.  It might be true for some people and it might not.

3.      Explain that the lines on the paper are called the “slope” of the graph.  Think of when you go skiing.  You go on a downhill slope.   What would that slope look like on a graph?  (Have students draw pictures in the air so you can check for understanding.)  Draw it on the overhead.  Label it as a decreasing slope.  Point to the first example and ask students to describe this slope.  It is an increasing slope meaning that it goes up.  Point to the students and ask them to label that example.  They should conclude that it is both decreasing and increasing.

4.  Ask one student to contribute the numbers for his/her accounts payable totals from the first two trading periods.  Graph these on the overhead graph and then analyze it as a class.  Does it show an increasing or decreasing slope line?  What does this show about our profits?  For example, if a store owner has an increasing accounts payable slope, that store owner might have decreasing profits if he/she does not charge more for the goods.  Increasing accounts payable for the store owner is not usually a good thing unless he/she is charging more for the goods or selling more goods.

5.   Hand out graphing paper.  Ask students to section their graphs off into four equal boxes.  Using the top-left box, ask students to think of a situation where a graph would give valuable information.  Some possible examples include the number of cavities in relation to the amount of candy eaten, the number of baseball cards released in relation to the value of the cards, the amount of homework given in relation to the amount of time spent on homework, or the amount of recess time to the number of discipline interventions in the classroom.  Then graph this idea by drawing the slope and labeling the graphs parts. 

5.      Hand your graph to a neighbor and ask them to tell you what it is showing.  Are they confused by your graph?  Make it a little clearer for them if you can.

6.      Graph paper is going to help us become better traders.  Show a graphing example of a person who on the first trading day spent $50 and on the second spent $150.  What type of slope does this graph have?  Is that type of slope a good thing?  What might happen on the third trading day?  Ask students to discuss these two questions in partners and report to the class.  The expected conclusion is that this is an increasing slope and it might be a bad thing if the person continues to spend more money and he/she does not have money to spend.

7.      Ask students to graph the total amount they spent on their accounts payable on the first day and then on the second day.  What type of slope do you have?  We want to increase our profits.  Does this slope show that you are increasing your profits?  Discuss with a partner.

8.      Ask students to graph their total amounts from accounts receivable on day’s one and two.  What type of slope do you have?  Is that a good slope?  Instruct students to do the same thing with their profits from day one and day two.     

Closure—

1.      Now that you have examined your graphs carefully, what problems have you noticed?  For example, Bryan noticed his accounts receivable decreased from day 1 to day 2.  This means that he had less money to spend on day 1 than day 2.  He spent more on day 2 so his profits on day two were less than on day 1.  What could he do to change this problem?  Discuss in groups of 4 from the beginning of class and report to the class.

2.      Look at your graphs and figure out two things that you could do to make more money.  Write them down in your math journal.  Remember and use those ideas as you trade on day 3.
 

Basic—Trade for day 3.  Chart all your transactions in accounts payable/accounts receivable.  When you have finished trading for the day, add to your accounts receivable, accounts payable, and profit charts.  What does the slope of your graph look like now?  Did you use the ideas that you wrote down in your math journal?  Write a short paragraph in your journal about your conclusions to these questions.  (Some class time will be given for the beginning trading.)
Extension—Group similar transactions together.  For example, all the money you spend on food and drink should be grouped together.  Analyze the slopes of these graphs.  Do you notice any problems? 
 

Hand in accounts receivable charts and graphs from the first two days so the teacher can briefly check them for understanding.  Also evaluated on participation in class discussions and cooperation/effort during group work.