Lesson 4

Interpret Measurement Data on Line Plots

Warm-up: Notice and Wonder: A List and a Line Plot (10 minutes)

Narrative

The purpose of this warm-up is to remind students that measurement data can be shown on a line plot, preparing them to interpret a line plot that includes fractional measurements in a later activity. While students may notice and wonder many things about the given data, the general structure of the line plot and how it shows the measurement data in the table are the important discussion points.

Launch

• Groups of 2
• Display the data and line plot.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

Activity

• 1 minute: partner discussion
• Share and record responses.

Student Facing

What do you notice? What do you wonder?

Lengths in Inches

• 3
• 5
• 4
• 4
• 5
• 6
• 7
• 5
• 3
• 4
• 4
• 5
• 6
• 6
• 4

Student Response

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Activity Synthesis

• “How would we adjust the line plot to include a length that is $$6\frac{1}{2}$$ inches?” (Add half inch marks to the scale. Partition the inches into two equal parts.)

Activity 1: A Set of Seedlings (20 minutes)

Narrative

The purpose of this activity is for students to analyze a line plot that represents lengths that are measured to the nearest half inch. They make observations and write statements about the data represented in the line plot, and then generate questions that could be answered with the line plot. When students recognize how organizing data helps to read the information and to answer questions, they learn that line plots are a powerful tool to present data (MP5).

Launch

• Groups of 2
• Display the list and line plot.
• “The list and the line plot both show the heights of seedlings. A seedling is a young plant. Where have you seen seedlings before?” (At the park. In a garden.)
• “Looking at the list, can we tell the height of the shortest seedling?” (Yes, $$\frac{1}{2}$$ inch). “What about the tallest seedling?” (Yes, 5 inches)
• “Draw a quick sketch of the shortest seedling and the tallest seedling at their actual heights. Use what you know about the length of an inch.”
• 1 minute: independent work time
• “What else can we tell about the seedlings from looking at the list?” (Twenty-two seedlings were measured. There are two seedlings that are 3 inches tall.)
• 1 minute: partner discussion
• Share responses.

Activity

• “Now, take a close look at the line plot. Think about what information we can gather from the line plot and what questions it can help to answer.”
• “Work with your partner to complete these problems.”
• 7–10 minutes: partner work time

Student Facing

heights of seedlings (in inches)

• $$\frac{1}{ 2}$$
• 1
• 1
• $$\frac{1}{ 2}$$
• $$1\frac{1}{ 2}$$
• $$2\frac{1}{ 2}$$
• 4
• $$\frac{1}{ 2}$$
• 3
• $$1\frac{1}{ 2}$$
• 5
• $$1\frac{1}{2}$$
• $$1\frac{1}{2}$$
• $$2\frac{1}{2}$$
• 3
• $$\frac{1}{2}$$
• $$2\frac{1}{2}$$
• $$1\frac{1}{2}$$
• 1
• $$1\frac{1}{2}$$
• 4
• 2

1. Write 3 statements about the measurements represented in the line plot.

2. What questions could be answered more easily with the line plot than the list? Write at least 2 questions.

Student Response

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Activity Synthesis

• Display the list and the line plot.
• “How is the information displayed in the line plot different from that in the list?” (In the line plot, all the measurements that are the same length are together. The measurements go from smallest to largest along the bottom. In the line plot, we don’t keep writing the numbers over and over, we would just use an x for each measurement.)
• “What were some questions that could be more easily answered with the line plot than the list?” (“How many seedlings were 3 inches tall?” because we could just count the x’s at 3 instead of searching through the list. “What’s the shortest seedling?” because we can find the x on the left end of the scale. “Which seedling height was the most common?” because we can see which number has the most x’s.)

Activity 2: All About Twigs (15 minutes)

Narrative

The purpose of this activity is for students to use a line plot to answer questions about a set of length data. The data show measurements to the nearest quarter inch. Students may apply their understanding of fraction equivalence to interpret the data and answer the questions.

Engagement: Provide Access by Recruiting Interest. Leverage choice around perceived challenge. Invite students to select complete 6 out of the 8 line plot questions.
Supports accessibility for: Organization, Attention, Social-emotional skills

Launch

• Groups of 2
• “This line plot has data about the lengths of some twigs. What do you notice? What do you wonder?” (Students may notice: The twigs were measured to the nearest quarter inch. The longest twig is $$7\frac{2}{4}$$ inches. Students may wonder: Where were the twigs found? How many twigs are shown on the line plot?)

Activity

• “Work independently to answer the questions about the data shown in the line plot.”
• 5 minutes: independent work time
• “Work with your partner to finish answering all the questions about the data shown in the line plot.”
• 5–7 minutes: partner work time

Student Facing

1. How many twig lengths are represented in the line plot?
2. How many of the twigs are $$6\frac{1}{2}$$ inches long?
3. How many of the twigs are less than 6 inches long?
4. How many of the twigs are more than 6 inches long?
5. What is the length of the shortest twig?
6. What is the length of the longest twig?
7. What is the most common twig length?
8. Add an “x” to the line plot that would represent a twig with a length between 3 and 4 inches.

What is the length of the twig you added to the line plot?

Student Response

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Activity Synthesis

• “Discuss with your partner how you answered the last two questions.” (Since the inches are partitioned into 4 equal parts, I knew the scale shows quarters of an inch. I used the quarter inch marks to add an x for a twig that is $$3 \frac {1}{4}$$ inches long because that is between 3 and 4 inches.)
• “How did you use fraction equivalence to answer the questions?” (When the question asked how many of the twigs were $$6\frac{1}{2}$$ inches long, I used the mark that was at $$6\frac{2}{4}$$, because the lengths are equivalent. When I added a twig to the line plot, it was at the $$3\frac{2}{4}$$ inch mark, but I wrote $$3\frac{1}{2}$$ because the fractions are equivalent.)

Lesson Synthesis

Lesson Synthesis

“What does each x in a line plot represent?” (A measurement)

“How do we know what measurement an x represents?” (The line plot has a number line with labels and tick marks. Where an x falls on the number line tells us the measurement.)

“What else can the line plot tell us about the data it displays?” (The number of x’s tells us how many measurements are in the data. The x on the far left tells us the smallest measurement. The x on the far right tells us the greatest measurement. We can see which measurements are common based on how many x’s there are at certain locations.)

Cool-down: Interpret and Choose (5 minutes)

Cool-Down

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