Understanding Distance & Coordinates

Distances on Long Street

Opening

Distances on Long Street

Sophie and her friends Karen and Marcus all live on Long Street. This number line shows the locations of their houses. Each unit on the number line represents 1 block. Sophie’s house is located at 0. The house of the friend who lives to the west of Sophie is a negative number.

Karen’s house is at point K and Marcus’s house is at point M.

Karen says, “From my house to your house is 9 blocks.” She wrote the expression this way:

8 − (−1)

Marcus says, “Then from my house to your house, the distance is 9 blocks." He wrote the expression this way:

(−1) − 8

  • Do you agree with Karen’s and Marcus’s statements? Explain why or why not.
  • A distance is always a positive number. If you wanted to describe how to get from Marcus’s house to Karen’s house, what would you say?
  • When subtraction is represented as distance, what would you need to do after you find the distance, in order to find the answer to the subtraction problem?