Back To CourseELM: CSU Math Study Guide
16 chapters | 140 lessons
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Amy has a master's degree in secondary education and has taught math at a public charter high school.
Line graphs are cool! They are cool to look at, and they provide so much useful information once you know how to read them. You know when you are looking at a line graph when you see a graph with a line connecting the data points. The line can be straight, or it can be curved, or it can look like a connect-the-dots line. Whatever the case, there is so much information to be gained from these graphs.
Let's look at the line graph below that shows us the number of correct math problems a particular friend of ours gets right in one minute over the course of a week. Our friend, Joe, is taking a timed math test every day for a week. He is given a minute to solve as many basic arithmetic problems as he can. At the end of the minute, his work is graded, and the number of correct answers is noted down. Let's see what information we can gather from the line graph that was produced from his results.
We see that on day 1, the first day, Joe didn't do very well, with only 1 correct math problem. I see this by looking at the bottom x axis first to locate day 1, drawing an imaginary line straight up, and then looking to find where our actual line crosses the imaginary line for day 1. I find the point where they cross, and then I draw another imaginary line across to see where it hits on the y axis. I see that it hits the y axis at 1, so Joe only got 1 correct math problem.
I keep reading the graph to gain more information. I look at day 2. How many math problems did Joe get right that day? I see where my line crosses day 2, and I see that it is where the y axis equals 5, so Joe got 5 correct math problems on day 2. On day 3, Joe got 8 correct answers. Day 4, he got 15. Day 5, it is 22. Day 6, Joe got 34 correct answers. And at the end of the week, on day 7, Joe was able to get 50 correct answers in one minute. Now that we've read our graph, what kind of interpretations can we make about Joe?
Reading a bunch of mathematical information from a graph is kind of meaningless unless we can interpret that data. What do all the numbers we read from the graph tell us about Joe? Looking at the line, we see that it keeps getting higher and higher. That is good for Joe. We can see that as the line gets higher, Joe's number of correct answers also gets higher. That means that Joe is doing really well. He is progressing in his math ability every day. He started out a bit slow, but then he started understanding more quickly. We can see this by the way the line curves slightly upwards.
We can also make an interpretation of what may happen to Joe's mathematical ability if he keeps going. It would make sense for the line to keep following the same pattern of going up, so if Joe kept this up, he'd be able to do more math problems in a minute on day 8 and day 9. Whether this will happen, we can't be sure, but based on the information we have, it seems likely. We just can't say that it will definitely happen.
Now, let's look at how we can read and interpret a line graph from a real-world scenario. We will see how being able to read and interpret the data will help us in our decisions. The particular line graph below shows the cost of a cell phone plan that includes 250 minutes.
This particular cell phone plan includes 250 minutes per month along with unlimited texting. The basic cost of the plan is $40 per month. Now, I read my line graph and see that after 250 minutes, my cost rises with the number of minutes. I went from $40 for 250 minutes to $65 for 300 minutes. That's a lot of money!
I see that the cost gets higher and higher the more minutes I use, all the way to $115 for 400 minutes. Doing a little math, I figure out that for every 50 minutes I go over my 250 minutes, I have to pay $25 more. If I divide $25 by 50, I figure that for each minute over 250 minutes, I am paying $0.50. I don't want to pay that much for a minute of talking if I go over my allotted time for the month.
I stop and think about this for a minute. I have to think about how much I really use this cell phone. Will I use more than 250 minutes per month with the cell phone? 250 minutes per month works out to a little over 4 hours of talk time. Do I talk that much on the phone every month? Or, do I text more? I like the $40 a month cost, but how likely am I to go over the 250 minutes?
Answering these questions will help me decide whether I should take this plan or upgrade to the next higher plan. After some thought, I decide I will take this plan because I don't talk on the phone that much. Because I text more than I talk, this plan will work for me.
What have we learned? We have learned that a line graph is a graph with a line connecting the data points. To read the graph, we look at the x axis to find one part of what we are looking for. We then draw an imaginary line straight up. We look for the actual line to see where it crosses our imaginary line. Then, we draw another imaginary line across from the point where our line crosses our imaginary straight-up line to see where it meets with the y axis.
We now know the information for that point. We can keep repeating the process until we have read all the points we are interested in. After gathering the data and looking at the line, we can make some interpretations about the data. If our line goes higher and higher, we can say that whatever it is keeps growing. If the line keeps going down, then it's shrinking.
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Back To CourseELM: CSU Math Study Guide
16 chapters | 140 lessons