Level F Lesson 28
Line Graphs and Double Line Graphs
The objective for lesson 28 is, the student will collect data and create line graphs and double line graphs to represent the data.
There are three essential questions that will be guiding our lesson. Number 1, when should a line graph be used? Number 2, how can I determine the intervals for my labels? And number 3, how can I compare two sets of similar information that show change over time?
The SOLVE problem for our lesson is, Ms. Norton’s class kept a record of the high and low temperature for the last five days in their city. They want to compare it with the data last year’s class collected. What is the greatest difference in temperature for one day on the graph?
We’re going to start by underlining the question. What is the greatest difference in temperature for one day on the graph? Then we’re going to complete the statement this problem is asking me to find the greatest difference in temperature for one day.
We’re looking at the line graph that is going to display Henri’s times and the number of minutes that Henri ran each day, in five days. At this point you’ll already have completed the line graph on your fact master curtain. We’re going to transfer that information to the line graph we’re making on your paper. When we look at the information we have, we have a value of 25 ranging all the way up to 45. Let’s look over here and talk about the parts of the line graph. We have a title. Our line graph must have a title, and we’ve called this Henri’s running time. Our line graph also has 2 axis. We’re going to label each of our 2 axis. The X axis or the horizontal axis, we’re going to label with days of the week. And we have day 1, day 2, day 3, day 4, and day 5. Our y axis we’re going to label with the time in minutes. We have 0 minutes, and we need to start and go all the way up so that we can show 45 minutes. So we’re going to need to extend our axis at least to 45. What we can do here is to divide these into groups of 10. So our minutes will be 0, 10, 20, 30, 40, and 50. That way any data that is in our number of minutes column will fall between 0 and 50. We used an interval of 10 to create the time in minutes. The next thing we’re going to do is we’re going to plot the values of Henri’s time on to our line graph. We have day 1, Henri ran for 25 minutes, We going to use the rhombus to plot Henri’s running time. Day 2, Henri ran for 30 minutes, day 3, Henri ran for 35 minutes, day 4, Henri ran for 40 minutes, and on day 5, Henri ran for 45 minutes. I’ve now completed plotting the value of Henri’s running times. The last thing I’m going to do is I’m going to take my ruler or my straight edge, and I’m going to draw a line that will connect those pieces of data. I’ve now created a line graph that displays Henri’s running time. Lets take a look at some questions about Henri’s graph. What do you know about the times from Day 1 to Day 5? We know that the time increased by 5 minutes each day. What is the difference in Henri’s running times on Day 2 and Day 4? Well on day 2 we know he ran 30 minutes and on day 4 he ran 40 minutes so his difference is 10 minutes. How many minutes would you predict Henri would probably run on day 6? If he’s going to continue the same pattern and increase his running time 5 minutes per day we would add 5 minutes to 45 and the prediction would be a time of 50 minutes. For what kind of data do we use a line graph? To show data that is collected over a period of time. We had 5 days passing that we collected Henri’s data.
We’re now going to talk about a Double Line Graph. A double line graph is used to show change over time between more than one set of data and comparing those sets of data. You should have already completed your double line graph on your fact master curtain and we’re going to do the same thing now on this model in your book. We now have the second person added to this which is Marquis and this is a list of his times. If you’ve noticed we’re transferred our data from Henri’s time choosing the rhombus symbol and we have those graphed here. We’re still going to use the same values on our axis, we have 5 days. As far as he Y axis goes we can still use our 0 to 50 because all our data values fall within that range. We have our title now because we’re not only going to have Henri’s running time, we’re also going to include the running time for Marquis. What I’m going to do now is I’m going to plot the number of minutes Marquis ran each day on the line graph. We’ve already done Henri’s times using a rhombus so we want to use a different shape to identify Marquis, so that we won’t confuse the two. Marquis on Day 1 ran 5 minutes; we’re going to use a square. On Day 2, Marquis ran 15 minutes, on Day 3 Marquis ran 25 minutes, On Day 4 Marquis ran 35 minutes and on Day 5, Marquis ran 45 minutes, and we’re going to put the square right over the rhombus because they both had the same value for that day. The next thing we’re going to do is we’re going to take our straight edge again and we’re going to connect those data points for Marquis and now we have a double line graph that not only shows the change over time for each boy, but it also compares the data between the two. We’ve also included a key with the double line graph because we need to identify which boy belongs to which data set on the graph. We now have three questions we’re going to answer about the double line graph. What is the difference in running times on day 3? If we look at day 3 we can see that Marquis at a time of 25, and Henri had a time of 35. To find the difference we simply subtract 35 minus 25 which gives us 10. On each consecutive day, what happened to the difference in running times? What happened is, as the days progressed the difference between the two boys running time lessened. On day 1, there is a difference of 20,. On day 2, there was a difference of 15. On day 3, there was a difference of 10. On day 4, there was a difference of 5 and on the last day they had the same running time. Based on the data, which boy will probably run the greater time on day six? We have the answer of Marquis here, and what we’re going to do is go back up and look at Marquis’ times. His times increased 10 minutes each day which for day 6 would give him a time of 55. Henri’s times only increased 5 for each day, so that would give him a time of 50. So Marquis if he continues to run at the same rate will have a higher number of minutes run on day 6 than Henri.
Let’s go back to the SOLVE problem from he beginning of our lesson. Ms. Norton’s class kept a record of the high and low temperature for the last five days in their city. They want to compare it with the data last year’s class collected. What is the greatest difference in temperature for one day on the graph? At the beginning of the lesson we underlined the question and we completed the statement this problem is asking me to find the greatest difference in temperature for one day.
With the O step, we’re going to start by identifying the facts. I’m going to read the problem and we’re going to put a strike mark after each fact. Ms. Norton’s class kept a record of the high and low temperature for the last five days in their city. That’s a fact. They want to compare it with the data last year’s class collected. That’s a second fact. Now we need to eliminate any unnecessary facts. We do need to know that her class kept a record of the high and low temperatures. That information is included in a chart and a double line graph. We don’t need to know that they need to compare it with last years class, because that does not help us find the greatest difference in temperature for one day. The next step is to list our necessary facts and what we’ve done is list the information that is contained in the chart. The highs are 67, 65, 69, 67, and 71. The lows are 45, 55, 65, 55 and 45.
Let’s move on the L step. We’re going to choose an operation or operations. And since we’re comparing or finding the difference, we know that’s our answer in subtraction. Now we’re going to write in words our plan of action. We’re going to subtract the high and low temperatures for each day and then determine the greatest difference.
In V, we’re making an estimate of about 25. Then we’re going to carry out our plan. What we do carry out our plan is we find the difference between the high and low for each day. Now that we have found the difference of each of the five days, we’re going to go down and look at our results.
Does your answer make sense? Well we were looking for the greatest temperature difference in one day. If we look at those 5 we see that day 5 had the greatest temperature difference. Is our answer reasonable? Well we estimated 25 and our answer is 26, so it is reasonable. Is our answer accurate? We can go back and rework our problem, and we can also confirm it by looking at the information on our double line graph. The answer to our problem is, the greatest difference for one day is 26.
Now we’re going to go back and answer the essential questions from the beginning of our lesson. When should a line graph be used? To show change over time. How can I determine the intervals for my labels? By looking at the numbers, or the spread of the data. How can I compare two sets of similar information that show change over time? By creating a double line graph.