From: Jeanne (for Teacher2Teacher Service)
Date: Feb 07, 2003 at 20:32:15
Subject: Re: Graphing: discrete vs continuous data

>As Mrs. Shidell wrote to Dr. Math
>On 02/04/2003 at 12:13:46 (Eastern Time),
>>[Question]
>>I am using the Connected Math series from Prentice Hall.  The 
module
>>is Variables and Patterns.  Students are learning coordinate
>>graphing.  The teacher's manual doesn't make it clear when to 
connect
>>the points in the line and when not to.  However, the question is
>>repeated throughtout the text, "Is it appropriate to connect the
>>points?"  I'm having a hard time explaining this concept to seventh
>>graders.  Can you help?
>>Thank You,
>>Mrs. Shidell
>>Grade 7 Plainfield Central School
>>
>>[Difficulty]
>>The information in the manual isn't clear or doesn't seem consistent.
>>
>>[Thoughts]
>>In once instance, bicyclists miles are being plotted on a graph with
>>time on the x axis, and miles on the y.  The points are connected.
>>In the next problem, bicyclists are traveling away from a particular
>>city.  Again time is on the x, and miles on the y.  However, in this
>>case, the points are not connected.  The explanation given is that
>>it's the miles away from the city that is being graphed, not the
>>number of miles traveled by the cyclists.  This isn't clear to me.
>

Hello Linda,

The questions are asking the students about the concept of "discrete 
vs continuous" data.

Let's look at some data I've made up for the sake of explanation:

Suppose I have a ball, I drop it from a height of 100 cm and let it bounce 4 
times.  The data I want to collect is height reached after each bounce and I 
want to graph this data.

          Starting ht:        100 cm
          After bounce #1:     80 cm
          After bounce #2:     64 cm
          After bounce #3:     51 cm
          After bounce #4:     41 cm

My x-axis would be the bounce number. My y-axis would be the height in 
centimeters. In this graph, I would NOT connect the dots.  If I draw a line 
segment connecting the (1,80 cm) and the (2,64 cm) dots, the line 
segment implies that there exists data representing bounces between 
the 1st and the 2nd bounce.  Since a "fractional bounce number" 
doesn't exist.  We should not connect the dots.  This is an example of 
DISCRETE data.

Let's change the situation slightly.  The data I want to collect is the 
distance traveled by this ball over time.  To make this example easier, let's 
assume it takes 1 second to travel from the initial drop to the 1st bounce, 
and 1 second to travel between each of the subsequent bounces.  
Here's data.

     time     1 sec.           distance:  100 cm
              2 sec.                      260 cm  (100 + 80 + 80)
              3 sec                       388 cm  (100 + 80 + 80 + 64 + 64)
               etc                          etc.

My x-axis would represent time in seconds and my y-axis would represent the 
distance traveled in cm.  In this graph I WOULD connect the dots. The segment 
connecting the (1,100) and the (2,260) implies that there exists data between 
1 second and 2 seconds.  That is, there is a distance that can be measured 
when the ball travels for any number between 1 and 2 seconds.  This is an 
example of CONTINUOUS data.

When I taught this concept to my students, I'd ask something like "does 
there exist [non-whole number] of _____?"  For example,  "does there 
exist 1 1/2 bicyclists?"  or "can we travel 2 2/3 miles?"  or "is there such 
a thing as 4.2 cars?"  We'd use this kind of question to help us decide 
whether data is discrete or continuous (whether to connect the dots or not).

Hope this helps.
 -Jeanne, for the T2T service


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