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Working with Line Plots

Lesson Plan

Working with Line Plots

Objectives

Students will learn how to create and interpret line plots, specifically those involving fractions. Students will:

  • create line plots representing rational data.
  • interpret and solve problems based on information in line plots that represent rational data.

Essential Questions

In what ways are the mathematical attributes of objects or processes measured, calculated and/or interpreted?
What makes a tool and/or strategy appropriate for a given task?
  • What does it mean to estimate or analyze numerical quantities?
  • What makes a tool and/or strategy appropriate for a given task?
  • How can data be organized and represented to provide insight into the relationship between quantities?
  • How does the type of data influence the choice of display?
  • How can probability and data analysis be used to make predictions?

Vocabulary

  • Line Plot: A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.
  • Pictograph: A way of representing statistical data using symbols to match the frequencies of different kinds of data.
  • Tally Chart: A way of representing statistical data using tallies to match the frequencies of different kinds of data.

Duration

60–90 minutes

Prerequisite Skills

Prerequisite Skills haven't been entered into the lesson plan.

Materials

Related Unit and Lesson Plans

Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

  • How to Make a Line Plot

http://ellerbruch.nmu.edu/classes/cs255w03/cs255students/nsovey/p5/p5.html

  • How to Make a Line Plot

      http://www.ehow.com/how_2121853_make-line-plot.html

  • Components of an Exemplary Line Plot

http://mdk12.org/instruction/curriculum/mathematics/graph_line_plot.html

 

Formative Assessment

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    • Each pair of students should turn in a copy of their line plot that shows a completed line plot, including titles, that represents the data on the bar graph as well as the data represented on the Tally Chart as an exit ticket.
    • The Match the Line Plots exercise may be used for a quick check to see that students understand how to match line plots with data sets.
    • The Line Plot Quick Quiz may be used to evaluate how well students can read, analyze, and interpret information in a line plot in order to answer questions about the data displayed.

Suggested Instructional Supports

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    Scaffolding, Active Engagement, Modeling, Formative Assessment
    W: Students will learn how to create line plots, how to interpret them, and how to use them to answer questions about data. 
    H: Students are presented with a simple bar graph about a topic to which they can relate, and they immediately start analyzing the data and constructing their own line plot from the data.  
    E: Students begin creating their line plot with teacher-guided instruction. They are introduced to values that do not “fit” on their line plot and are allowed to explore how to put that data on their line plot. They are also free in Activity 3 to come up with their own methods to determine the total number of books read.  
    R: Students will refine their understanding of a line plot as it moves from representing only integer values to values containing . They will work with a partner to refine their skills regarding labeling their number line with a consistent scale and constructing an accurate line plot. 
    E: Students evaluate their work by comparing it to other students’ line plots. They also evaluate their work in Activity 3 by comparing their responses with other pairs’ responses and working with other pairs to either help them achieve understanding or determine where any of their own misunderstandings or mistakes occurred. 
    T: The Extension section may be used to tailor the lesson to meet the needs of students. The Routine section provides practice opportunities for concept review throughout the year. The Small Group section offers additional learning or practice options for students who may benefit from more time with the lesson concepts. The Expansion section suggests more challenging activities for students who are ready to move beyond the requirements of the standard. 
    O: The lesson begins with large group instruction and Socratic questioning and slowly puts more responsibility on students for interpreting and understanding the material. The lesson culminates with students teaching and helping one another understand the material.  

Instructional Procedures

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    Activity 1

    “Today we are going to talk about graphs. Our main focus will be on something called a line plot. Some of you may know what that is. We’re going to make a line plot together in a minute. But first I want to show you a bar graph. I’ll need your help figuring out what the bar graph shows.”

    Show the following bar graph to students (either on individual worksheets or projected so all students can see it):

     

    “This bar graph shows the results of a survey.”

    To make sure students understand how to interpret the bar graph, ask (and ask for reasoning to support their answers) questions such as:

    • “What do you think the survey question was?” (How many books did you read last month?)
    • “How many people were surveyed?” (26)
    • “What is the most number of books any of the surveyed people read?” (4)
    • “How many people read 1 book last month?” (6)
    • “How many people read at least 3 books last month?” (6)
    • “What is the most common number of books people read last month?” (2)
    • “What is the total number of books read by all 26 people surveyed last month?” (48)

    “There’s another way we can display this data besides a bar graph. We can display the data on a line plot. The first thing we need to make a line plot is a number line.” Give each student a copy of the Number Line.worksheet (M-5-4-2_Number Line.docx) “Notice that the number line is unlabeled. Let’s give it some labels. On the left-hand side of the number line, start with the smallest possible number of books people in our survey could have read and label the mark underneath the number line.” Make sure students label one of the marks near the left end of the number line with a 0.

    “Now, skip over 3 marks and label the 4th mark with a 1, the next number of books people in our survey could have read. You should now have a 0, then three blank spots, and then a 1.” Explain to students that they should always make sure they’ll have enough room to fit every piece of data they must graph. “For example, if we had surveyed someone who read 30 books last month, we probably shouldn’t skip so many spaces, or we’ll run out of room on our number line before we get to 30. But because we only need to get up to 4 for this line plot (the greatest number of books read by anyone in our survey), we can skip 3 marks between each whole number.”

    “Where should we put the 2 on our number line for the spot where we’ll show how many people read 2 books?” Engage students in a discussion about maintaining a constant scale on the number line, i.e., placing 3 empty marks between the whole numbers. Have students finish labeling their number line, and then have them compare with a classmate to make sure their number lines match. (Remind students that they could have started in slightly different places. The important thing is that the distances between the whole numbers are the same.)

    “Now we’re ready to start putting in our data to show how many people read 0, 1, 2, 3,
    or 4 books last month. We’re going to use the same data we used for the bar graph. How many people read 0 books last month?”
    (3)

    “So, above the spot marked 0 on your number line, put 3 Xs, stacked on top of each other like you’re building a tower.” If necessary, demonstrate how to make the Xs on the board. “That’s it. Each X represents one person; in this case, each X represents one person who didn’t read any books last month.”

    “How many people read 1 book last month, based on the data in the bar graph?” (6) “So how many Xs should we put above the spot marked 1 on the number line?” (6)

    Have students finish making their line plot, checking their work against their neighbor’s. After all students have finished transferring the data from the bar graph to the line plot, ask, “Are we done making our line plot?” If students say they are, ask them, “If you handed this to someone who wasn’t in our class and hadn’t seen the bar graph, would that person know what the data represented?” Guide students toward realizing that they still need to provide a title (which can be the same as the bar graph’s title) and label the number line (which can be the same as the label on the horizontal axis of the bar graph). “Remember, titles and labels are important; without them, nobody will be able to tell what the line plot is about.”

    “That’s it—that’s all there is to making a line plot.” Ask students to recount some of the important things to consider when making a line plot. Considerations should include:

    • accurate counting of the number of Xs
    • labels
    • equal spacing between values on the number line

    Activity 2

    Remove the bar graph if projected; it won’t be referred to for the remainder of the lesson. Only the line plot will be updated to reflect new, additional data.

    “But now we have a problem. I decided to survey some more people. The first person I asked said she read half a book last month; she didn’t quite finish it. What should we do with this information?” If students suggest rounding it up to 1, ask them, “What if we have two people who each read half a book. How many books did they read between the two of them?” (One) “But if we round each of them up to 1, it will look like they read 2 books, which is twice as many. There are definitely cases in which rounding is appropriate, but I don’t think it’s what we want to do in this situation.”

    If students don’t suggest simply plotting the data on their line plot, ask students what the spaces on the number line between 0 and 1 represent, specifically the space that is halfway between 0 and 1. After some discussion, have students label the space halfway between 0 and 1 as .

    “Now, we have a spot on our line plot for people who read  of a book last month, so let’s represent our new person with an X in that spot.”

    “The second person I surveyed read   books. Where should we put him?” Have students discuss with one another and then add that person to the line plot. Also, have students label the places on the number line corresponding to both  and 3  books.

    “The third person I surveyed, though, is causing more problems. She’s read of a book. She just didn’t have time to finish the whole thing. How should we represent her on our line plot?” Guide students through a discussion of fourths and help them determine that  is halfway between  and 1. Have students label the appropriate mark on their line plot and then add an X to their line plot to indicate the new person.

    Have students work in pairs. Give each pair a copy of the Tally Chart worksheet (M-5-4-2_Tally Chart.docx). “This Tally Chart represents ALL the extra people I surveyed. That includes the person who read  a book, the person who read books, and the person who read of a book. Your job is to make sure all the people represented in the tally chart are represented accurately on the line plot. Again, remember that you’ve already taken care of representing three of the people from the tally chart.”

    Students should work in pairs to complete a single copy of their line plot. (Students should write both their names on the line plot to be used for assessment.) Once each pair has updated their line plot, have the class come back together.

    Activity 3

    “Now that each pair has a complete, correct line plot, let’s take a look at our new data. Based on your line plot, how many people were surveyed in total?” (43)

    “How many people read 2 books or more?” (23)

    Ask various other questions about the line plot as a whole, including:

    • “What is one number of books that nobody read?” ()
    • “Which fraction or mixed number of books was the most popular survey response?” ()
    • “How many people read more than 1 book but less than 2 books?” (5)
    • And finish with “How many books were read in total by all 43 people surveyed?” ()

    This question should be followed by a discussion of “strategy,” that is, how to approach the problem. Point out that all the whole-number values were the same as the ones on the bar graph, and the class already determined that those responses represented a total of 48 books. Now, have students focus on the fractional amounts.

    Talk about different strategies, focusing on “pairing up” numbers to make wholes: for instance, pairing up a  and  to make a whole book. Recommend that students find suitable pairs, crossing off or otherwise marking the Xs on their line plot to show they’ve counted that person.

    Point out that values involving  can be paired up with themselves (or other values involving ). Depending on the class, a quick review of adding mixed numbers might be useful. (For this activity, students should be able to add the mixed numbers conceptually, i.e., without making common denominators, etc.)

    Have each pair work together to come up a grand total (including the 48 that were represented on the bar graph.) After each pair has a grand total, collect all the different answers and list them on the board. (Hopefully, there is only one different answer, but there may be more.) Make a tally chart if there are multiple different answers to indicate how many groups provided each answer.

    The correct answer is . Select a group that gave the correct answer and have them explain how they tabulated the fractional amounts from their line plot. (If there are multiple groups with the correct answer and multiple groups with the incorrect answer, have a group with a correct answer work with one or two of the “incorrect” groups to explain their reasoning.)

    Have each pair of students turn in their Number Line worksheet (the completed line plot) to be checked for understanding. You may use this as an exit ticket or check them at another time.

    An alternative check to see if students are understanding how data sets relate to line plots is to use the Match the Line Plots exercise (M-5-4-2_Match the Line Plots.docx). It will only take minute or two for students to draw a line matching each line plot with its data source. There are no labels or titles for students to use as clues; they must match the labels and results in the line plot with the data in the tables and tally charts.

    One final option that may be used if time allows is the Line Plot Quick Quiz (M-5-4-2_Line Plot Quick Quiz and KEY.docx). This brief quiz allows the opportunity to gauge how well students can read, analyze, and interpret data in line plots and answer questions based on the data in the plot.

    Extension:

    Use the following strategies to tailor the lesson to meet the needs of your students throughout the year.

    • Routine: As students learn about other types of data displays, they can convert the data in those displays to line plots (or convert data given in line plots to those displays). Students can also be asked questions about the data (whether in line plots or not) that require them to do computations with rational numbers.

    Also, students can get additional practice when refining their skills for working with mixed numbers; problems can be set up that require students to interpret line plots and work with more “difficult” fractions.

    • Small Group: Students can work in small groups to come up with survey questions that could have fractional responses. Have each group create data and a data display that is not a line plot and also write questions (similar to the questions you asked during this lesson) to create a worksheet for another group. The other group should begin completing the worksheet by creating a line plot to represent the data.
    • Expansion: The ideas in this lesson can be expanded to having students conduct actual surveys and creating line plots and worksheets to represent the results. The lesson can also be expanded to include more “difficult” fractions, requiring students to work with common denominators and practice mixed number computation.

Related Instructional Videos

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Final 05/03/2013
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