Throughout the year, students have working with interpreting line pots for various purposes. They have gained familiarity with the purpose of line plots as well has how to interpret data presented this way.
The standard 5.MD.2 is however, more rigorous than reading and interpreting line pots. Students must now work with data sets that include fractions. This lesson is designed to bring together the skills students have developed throughout the year including:
• operations with fractions
• fractions on a numberline
To initially get students thinking I write "Line Plot" on the board and ask students to share what they know about line plots.
• Have you heard "Line Plot" before? When? Where?
• What is a line plot?
• What is it used for?
I encourage students to share their thinking first with a peer, then with the class. I write the students' ideas on the board and adjust them as more students share their prior knowledge. Through prompting (if necessary) I will make sure the word "data" is included in the definition.
Next, I present a line plot showing the distance toy gilders flew. On this line plot, the whole numbers are labeled, but the fractional distances in between are not. The majority of the data does not include whole numbered distances. I choose this line plot as a warm-up because I want the students to have the chance to try to make sense of it on their own - without me telling them that this line plot includes fractional amounts. More critically, I want the students to connect the line plot to fractional number lines that we worked with so frequently throughout the fractions unit.
When I present students with this line plot, I do not ask any specific questions at first. I keep it simple by showing the line plot. This line plot is essentially a picture. Even though there are only four words on the whole picture, it tells us so much. Some people even say a picture is worth a thousand words. I'm not sure if we can find a thousand words that this picture is communicating, but lets give it a try.
I write "statements" on the board and ask students to share some of the things they learned from reading the graph. As the students share, I list them on the board. I am sure to praise all students' contributions to the discussion, but call extra attention to the statements that are comparative (ex: The farthest distance was 4 and 1/4 feet longer than the shortest distance because 36 and 3/4 - 32 and 1/2 = 4 and 1/4).
Note: I decided to change the word "statements" to "1000 words (?)" because statements implies that hard facts are needed. Throughout the process of prompting students to share their interpretations of the line plot, I found my self repeating that "a picture is worth a 1000 words". With this expectations, students are more likely to open up their discussions and make more statements and comparisons. "1000 words" also allows students to ask questions based on the line plot, not only make statements. One student asks, "I wonder why there is such a big space after the 32 and 1/2 feet before the next gilder distance." Asking questions and interpreting data are a critical part of working with line plots.
Open-ended tasks provide opportunities for increased dialogue between students.
For this portion of the lesson, students will create their own line plot that includes fractions. I have taken components for this part of the lesson from the Fractions on a Line Plot lesson provided by Illustrative Math Project. This website is a helpful resource for unpacking the CCSS.
Students are provided with a set of fraction cards that include 1/2, 1/4, 1/8. I give the students time to look over the data set, then encourage them to make a number line (line plot) that would be appropriate for this set of data. At this point the year, students should be able to recognize that the number line should be divided into eighths. I support those who need it, but encourage as much independence as possible.
Next, students divide the cards evenly between the two partners. They place them face down on the desk. Each partner chooses one of cards and turns it over. The team then adds their fractions together. The sum of the two fractions is then recorded on the number line (there should be 12 data points in the end)
Students publish their line plots by adding a title and label, then post them on the board for a Math Museum.
While looking at all of the examples. Students are presented with the following discussion questions. I use the think-pair-share model for each of these questions because they are dense and all students should have an opportunity to think about them and make sense of them before 1 or 2 call out the answer.
• Choose a line plot. Which values came up the most? Which values did not come up at all?
• Which of the eights did not come up on any of the graphs? Why? (0, 1/8, and 7/8 will never come up because none of the card combinations can make these sums).
• If we were to add another card to make it possible to get 7/8, what should it be? (3/4, 5/8, or 3/8)
The purpose of organizing data in a line plot is for interpretation. The most essential part of this lesson is to make meaningful statements about the data that has been generated.
Choose 1 of the example line plots to "think-a-loud" as a model interpretation. Point out gaps, outliers (if any), clusters, etc).
Then allow students to work together to create 5 statements about a line plot of their choice.