Task# Distances Between Houses

Illustrative MathematicsVaries

The purpose of this task is for students to solve a problem involving distances between objects whose positions are defined relative to a specified location and to see how this kind of situation can be represented with signed numbers. A full solution requires systematic listing of pairs of houses, a valid list of differences-either subtracting the smaller number from the larger, or taking absolute value of difference in any order - as well as computations which could be done by counting on the number line or subtracting fractions. Note as well the 'twist' with the houses not in 'alphabetical' order on the number line requires students to make sense of the problem attend to precision. This problem framework could be used with integer values or later for tasks involving the Pythagorean Theorem in the plane.