This Math Talk focuses on computing the distance between two points on the number line. It encourages students to think about distance as the absolute value of a difference of two numbers and rely on what they know about subtraction to mentally solve problems. The strategies and understandings elicited here will be helpful later in this lesson when students learn about the absolute value function.

To calculate the distance, students need to look for and make use of structure (MP7).

The goal of this discussion is to review students’ strategies for subtraction involving negative numbers.

Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:

• “Who can restate ’s reasoning in a different way?”
• “Did anyone have the same strategy but would explain it differently?”
• “Did anyone solve the problem in a different way?”
• “Does anyone want to add on to ’s strategy?”
• “Do you agree or disagree? Why?”
• “What connections to previous problems do you see?”

In this activity students subtract 2 values and recall that the distance between the values on the number line is given by the lesser value subtracted from the greater value. Students critique a statement or response that is intentionally unclear, incorrect, or incomplete and improve it by clarifying meaning, correcting errors, and adding details (MP3).

In this activity, students find 2 numbers that are a given distance from a number. In the associated Algebra 1 lesson students find the positive difference between 2 values by figuring out how far away a guess is from an actual value. Students look for and make use of structure when applying their knowledge of distance to situations in context.