Lesson 15

The purpose of this Number Talk is to activate students’ previous experiences with subtracting multiples of ten and subtracting by place. In previous lessons, students found the value of differences within 100 using base-ten blocks, tape diagrams, drawings, or equations. The ability look for ways to make use of the base-ten structure of numbers in expressions to find their values helps students build fluency (MP7).

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “How did the first expression help you find the value of the second expression?” (I already knew that \(47 - 20 = 27\), so I just took away 4 more.)
• Consider asking:
  • “Did anyone approach the problem in a different way?”
  • “Does anyone want to add on to _____’s strategy?”

The purpose of this activity is for students to generate measurement data and represent the data in a line plot. Students measure pencils in centimeters, check the accuracy of their measurements, and use a template to represent their data in a line plot. In the synthesis, students revisit the importance of labels on the line plot and also discuss the importance of keeping the Xs the same size and in rows to help make it easier to read the data (MP6).

Pencils are suggested for this activity because the measurements collected are likely to vary. Pencils could be substituted with other classroom items (for example, pipe cleaners, straws, or the sides of books) that might generate interesting measurement data for classroom discussion.

• Collect 10–12 pencils of varying lengths for each group of 4. 

• Groups of 4
• Give each group a set of 10–12 pencils of various lengths.
• Give each student a centimeter ruler.

• “Today, you are going to collect measurement data and create a line plot. Your first job is to measure the length in centimeters of each of the pencils in your group. Two different people should measure each pencil to make sure your measurements are accurate.”
• 10 minutes: small-group work time
• “Now, use the data you collected to create a line plot. Try to make your Xs the same size.”
• 5 minutes: independent work time
• Monitor for students who write a title and labels on their line plot.

• Share the line plot of a student who wrote a title and labels.
• “Do we know what data _____’s line plot is representing? How do we know?”
• Share a line plot that uses same-size Xs arranged in rows.
• “What do you notice about the Xs in _____’s line plot?”
• “Why is it important to keep the Xs the same size and in rows?” (It can make it look like some measurements have more because the tower looks taller.)
• As needed, draw or display an example of a line plot where the Xs are not in rows (for example, draw different-size Xs and/or draw with a different amount of space above and below each X).

The purpose of this activity is for students to represent measurement data in a line plot with a scale that does not start at 0. In the launch, students compare line plots that show the same data, but have line plots that start and end with different numbers. They learn that line plots do not have to start with 0, but that the numbers still represent lengths from 0, just like their work with torn tape measures in previous lessons.

When students represent measurement data in their own line plot, they use a template that does not have enough tick marks for students to start at 0 and represent each length in the data table. This encourages students to consider ways to label their line plot without starting at 0. Students may choose to use the least or greatest lengths to decide how to start or end their number line, but they do not need to. The synthesis discussion will focus on strategies they used to determine how to label, including how they used what they know about a ruler.

This activity uses MLR8 Discussion Supports. Advances: Speaking

• Groups of 2
• Display the image (2 line plots).
• “What is the same about these line plots? What is different?”
• 1 minute: quiet think time
• 2 minutes: partner discussion
• Monitor for a student who notices that the line plot for Group B doesn’t start at 0, but there are the same number of Xs.
• Share responses.
• “When we make a line plot, we can choose the number to start with, based on the data we have. Once we pick a starting number, we need to make sure we don’t skip any numbers, even if there’s no data there.”

• “You are going to create a line plot to represent some data given in a table. Think about how you want to label the marks with numbers. Be sure to include labels, and try to make your Xs the same size.”
• 10 minutes: independent work time

MLR8 Discussion Supports

• “Compare your line plot with your partner.”
• Display and review the following sentence frames to support partner discussion:
  • “_____ and _____ line plots are the same/alike because. . . .”
  • “______ and _____ line plots are different because. . . .” 
• 2 minutes: partner discussion
• Monitor for students who used two different start and end numbers.

If students label their line plot using only the measurements in the table (for example, they only label 10, 12, 13, 14, 16 without labeling the numbers in between), ask students to look at the line plots from the launch. Consider asking:

• “How is a line plot like a ruler?”
• “How did you decide how to label the numbers on your line plot? How could you revise your line plot so that it represents lengths like a ruler?”

• Show two line plots that use different start and end numbers.
• Consider asking each student:
  • “How did you decide which number to start with?”
  • “How did you use what you know about rulers to label your line plot and place each x?”
• “How are these line plots like a torn tape measure?” (They are missing 0 and some other numbers, but they still show numbers in order. There's still the same length between each number.)