The purpose of this activity is for students to learn the features of a number line, such as the sequence of numbers moving from left to right and equal spacing between tick marks. Students make sense of and use these features 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.

• “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.

To make an accurate number line, students will need to make strategic use of materials in order to measure and mark the unit intervals. 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.

• “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.)
• The number lines students created in this activity will be used again in a later lesson of this section.