Why Teaching Line Plots is Harder Than it Looks

Much of the "data and graphing" instruction comes quite easily to students. A bar graph or pictograph is really quite intuitive to read- the difficulty in instruction comes in when students are asked to solve comparison word problems based on the data in the charts. And we KNOW that comparison word problems are notoriously difficult for students to solve as word problem types go.

Why then are line plots... which are really just a combination of a bar graph and a pictograph... so difficult for students to read and answer questions about? If we really drill down, creating a line plot and answering questions about a line plot in 4th and 5th grade requires so many components. Understanding which of these components are strengths and areas of need for your students can help you to narrow in on the reason they might be having difficulty. To build and interpret a line plot, students need:

  1. An understanding of the conventions of putting the chart together.
  2. A thorough understanding of what each part of the line plot represents for interpretation.
  3. Last of all, but certainly not least of all, an extensive understanding of fractions on a number line.

In creating a line plot students first need to create a number line. When looking at the data set, helpful questions to ask students would include:

  • What is the smallest fraction in the data set? How can this help us decide where to start the number line?
  • What is the largest fraction in the data set? How can this data point help us to decide where to end the number line? 
  • Where would 1/2, 1/4 and 1/8 be place on the number line. Where do the 1/4 and 1/2 marks overlap? Where do the 1/8 marks overlap with the other fractions. If 2/4 and 1/2 are at the same point, what does that tell us about these fractions? 
So what can you do to help? Give students a hands on opportunity to build a line plot. Give them a set of pencils or clip art pictures all measured to different lengths. Have students place these items out on a life-sized line plot so that they can see where it would make sense to start a number line, end a number line and how the number line could be best labeled. 

 The conventions of creating a line plot aren't all that different from creating a bar graph, pictograph, or any other type of graphing representation. Students need to be sure to include a title, a number line, a label for the number line, they need to mark out a scale on the number line, and finally to represent their data points.

So what can you do to help? It may be helpful to students to link the conventions of a line plot to the conventions of other types of graphs that they already know about. We know that research tells us that whenever we can make links and connections information will stick more easily. Could students look at a bar graph of similar information and find each of these components on both the bar graph and the line plot? 

  • Where on the graphs do we learn what the graph is all about? 
  • Where on the graphs do we find out, for example, the height of the smallest plant?
  • Where on the graphs do we find out if they are measuring, for example, in inches or centimeters? 
  • Where on the graphs can we find out how many plants, for example, are 3 1/2 inches tall? 

A number of difficulties are presented when students are asked to interpret the information on a line plot.

  • If students are creating a number line about the height of a variety of plants- do they really recognize that each "X" on the line plot stands for it's own plant? If they don't, they are going to have a very difficult time in answering a question that asks, for example, "What is the total height of all of the plants measured?" You will know if students aren't understanding the meaning of the "X" if students add up all of the fractions listed on the scale rather than adding up the total of all data points. 
  • Students may need to add fractions with different denominators. If a set of data has pieces measured to the nearest 1/4 inch there is a good chance some pieces of data will be listed as 1/2. The same situation may occur if data points are measured to the nearest 1/8th. Students may have more difficulty performing operations on fractions with different denominators. 
  • Students may have difficulty understanding that each piece of data has multiple labels. For example, consider the story Mike road his bike every day for a week. On each day he wrote down the number of miles he traveled. In his journal his list said: 2 1/4, 3, 5 1/2, 3 1/4, 3 1/4, 5, 2. In this example story, each of these pieces of data really has 2 labels. The first piece of data, 2 1/4, really represents that on day 1, Mike traveled 2 1/4 miles. Each of the pieces of data is a separate day and each of those days has been measured in miles. 
So what can you do to help? I stand by my suggestions in the first two paragraphs. If students are not making these connections when they are looking at a line plot on paper you can either take the line plot off of the paper and bring it into real, hands on life so students can understand the significance and meaning of each "x" on the line plot. You can also relate the line plot to other graphs and representations you use in the classroom to help students to build connections! 

If you are looking for further line plot resources, I have two resources that might be helpful. First is a hands-on line plots exploration. Students work to measure the plants of a fictional kindergarten classroom and help them to best organize their information. Next is a set of differentiated worksheets for students to use in the classroom and for homework. An "easy" "medium" and "hard level" have been created for classwork and homework in both the areas of reading and creating line plots. Plus, I have included task cards perfect for math centers or small group instruction. 

Research Based Strategies 

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Have a Gritty Day!

There has been quite a bit of research about the importance of grit in allowing students to learn and be successful both in school and beyond. I love research, it fuels the choices that I make in the classroom, but I'll be honest, if I can't figure out how a piece of research looks in my teaching, I have a hard time.

The grit research, to me, was difficult because while I could understand the connection between grit and success I didn't think it was enough to be sure I was careful with the language that I was using so that I was using language that promoted a growth mindset and diminishing language that would reinforce a fixed mindset.

I had a principal once that told us that we needed to think of our profession as being equal to the medical profession. That we were diagnosticians and practitioners and that we needed to keep up with current research. If we weren't implementing best practice that would be considered equal to a doctor committing malpractice. It sounds harsh but you really can't argue with the logic!

And so I kept thinking about grit and how I could be more explicit- beyond being purposeful in my choice of language. I needed my students to know what they were working towards! I have figured out how to make this connection more explicit and wanted to be sure to share this strategy with all of you.

I have taught my students that, sometimes, at the end of a math lesson they will feel very confident. This means that they have met the learning target, they might have gotten many questions correct on their exit ticket, they might even be thinking something like "this is easy!". If they are feeling that way they can say that they are having a confident day in math. Other days we might be working on something that feels really tricky! They may feel confused or they might feel like they are thinking really hard but it's still not making a lot of sense. They might start to feel frustrated because even though they are trying, they keep getting answers wrong. They might even see other students having a confident day and they might be wondering why it's not easy for them. I tell my students that if they are feeling like they are having a day that is very tricky they have two choices. They can either get mad/sad/frustrated or they can get gritty. Gritty means that you hunker down and say "I can figure this out!" "I can work at this!" "I will be able to do it!!".

When we are "getting gritty" we even go so far as to make a little fist and make a "tough" face and say "I can get this!!" I practice this with my kids outside of the context of math at the beginning of a lesson. I remind them by saying "We're going to work on some pretty important stuff today! You might get it right away and have a confident day, but if it's feeling tough remember, you can always get gritty and we'll figure it out together. Show me what you will say when you're feeling gritty" and they respond by all saying, emphatically, "I can get this!"

During a lesson when a student is struggling I can then easily put their mind at ease by acknowledging that the work is difficult and that I know they can get gritty and figure it out.

You see, my students know that those two choices they have when work gets hard lead to very different results. If they get mad/sad/frustrated they will still be mad/sad/frustrated at the end of the lesson. If they get gritty, they have a chance of moving over and becoming confident.

Not every math day ends in success for all students. And that's okay. And I want my students to know this is okay too! At the end of a lesson we will often reflect and ask "Who had a confident day? Who had to get gritty today?" and I am able to praise them for sticking to it and working even when the work got tough. I remind them of opportunities they will have in the future to continue practicing this work.

I am including a reflection to use in your classroom either after a math lesson or at any other time during the day when you are noticing that there are some students who could use some reassurance. If students were able to "get gritty" they had a successful learning day and their efforts should be celebrated!

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