Lesson 1

The purpose of this warm-up is for students to make sense of a new representation and how it is similar to and different from a ruler. If possible, display an actual ruler next to the number line. This will be useful when students create their own number lines in a later activity. While students may notice and wonder many things about these images, the connections between the features of a number line and a ruler are the important discussion points.

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

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “Today, we are going to think about how the first diagram might be helpful when thinking about numbers.”

The purpose of this activity is for students to learn the features of a number line. Students make sense of and use the features of number lines, such as the sequence of numbers moving from left to right and equal spacing between tick marks to locate and represent whole numbers. In the synthesis, students describe how they filled in the missing numbers on a number line and how they located and represented a specific number.

• Groups of 2
• Display the number line image from the warm up.
• “This diagram is called a number line. What do you notice about this number line?” (It has tick marks like a ruler. The numbers go in order. There is a point at 4. The numbers are equally spaced.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record responses.
• “We noticed some important things about number lines.”
• Summarize the points recorded.
• If it did not come up, make sure the list includes:
  • There is the same amount of space between each tick mark on the number line like a ruler.
  • The numbers on the number line are listed in order from left to right like on a ruler. Each number represents a length from 0.
  • A dot, called a point, on the number line represents a specific number.
• “What number does this point represent? Explain.” (4, because the point is right above the 4. It is 4 length units from 0.)
• 30 seconds: quiet think time
• 30 seconds: partner discussion
• Share responses.

• “Now you are going to do some work with the number line. You have a number line that is missing labels on the tick marks. Label each tick mark with the number it represents. Locate different points on the number line and mark them with a point.”
• 5 minutes: independent work time
• If students finish early, ask them to extend the number line and label different points.

• “Looking at this ruler, what is a measurement that is longer than 6 cm?”
• “How could you show that number on the number line?”

• Display the number line with only 0, 5, and 10 labeled.
• “How did you know which numbers to use to label the tick marks?” (It’s like a ruler, I figured out how many length units each tick mark was from 0. I just counted because I know the numbers need to go in order from left to right.)

The purpose of this activity is for students to learn that numbers are represented on a number line as lengths from 0. Students choose their own length unit to make equally spaced tick marks and label them 0–20. In the synthesis, students compare their number lines and notice that on a given number line the length between successive numbers should be the same. This length represents 1 length unit (the unit interval). Students also notice that, unlike tools that are used to measure standard length units, number lines can use any size of length unit to represent a set of numbers, as long as it's the same between consecutive numbers.

In order to make an accurate number line, students will need to make strategic use of materials in order to measure the units on their number line. This could be a paper clip or a staple or the equally spaced lines on a lined sheet of paper (MP5).

Students will use the number line they create in an upcoming lesson.

• Each student needs a sentence strip or a 24–30 inch rectangular strip of paper.
• Each group of 2 students needs access to assorted objects that can be used as a length unit to construct number lines (base-ten blocks, inch tiles, paper clips, large erasers, small sticky notes).

• Groups of 2
• Give students a long rectangular strip of paper, like a sentence strip, and access to different objects to create a number line.

• “Now you’re going to create your own number line. You can use any of the tools provided to create a number line that represents the numbers from 0 to 20.”
• 10 minutes: independent work time
• Monitor for students who choose different objects as their length unit and create accurate number lines.
• 2 minutes: partner discussion

• “What object did you use to make your number line? Can you show me how you used it?”
• “How can you use your object to check to see that your tick marks are equally spaced?”

• Display 3 student number lines that have different sized unit intervals.
• “What is the same and what is different about these representations?” (They all have equally spaced tick marks. They all show 0 to 20 in order. They all show a point on 3 and 13. The length of the space they used between tick marks is different. They used different objects to create their number lines.)