In previous lessons, students interpreted and represented numbers on the number line. They understand that numbers are represented as lengths from 0, consecutive numbers on the number line must be spaced equally, numbers can be represented with tick marks, and specific numbers can be identified on the number line using a point.

The purpose of this activity is for students to make sense of representations that show addition and subtraction on the number lines. They reason that an arrow pointing to the right represents addition because numbers to the right represent greater numbers, while an arrow pointing to the left represents subtraction because numbers to the left represent lesser numbers. Students connect the starting location, ending location, and direction of a jump arrow to equations (MP2). They interpret the length between the numbers (or distance traveled by the jump) as the number that was added or subtracted.

• “Can you explain what you see happening on this number line?”
• “How do you know if the arrow shows addition or subtraction?”

• Display the number line for .
• “We have learned that and have the same value. Why doesn’t match this number line?” (The arrow shows addition, but the arrow starts on 4 and moves 10 units to the right.)

The purpose of this activity is for students to match addition and subtraction equations to number line representations. Some equations use the same numbers, requiring students to look for the direction of the arrow to see if the number line is representing addition or subtraction (MP7). There is one equation that does not have a matching number line representation. Students represent this equation on the last number line.

This last number line can be used as a formative assessment of students' understanding of the connection between equations and their representations on a number line. Teachers can use this information to plan for any additional support that may be needed in the following lesson, where students represent different equations on number lines.

In the Synthesis, students consider how addition and subtraction can look alike on the number line, and how they are different.

• Display the image of the number lines for and .
• “What is the same about these number lines? What is different?” (They both have 3, 17, and 20. One has a long jump of 17, but the other has a small jump of 3. The difference between 17 and 20 is 3 and 20 is 17 away from 3.)