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Graphing: discrete vs continuous data

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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 Thanks for visiting our on-line community. Visit Teacher2Teacher again at http://mathforum.org/t2t/

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