Tree-Planting Problems

The heart of this unit is noticing the gap between the number of trees and the number of spaces. Along a straight line there is one more tree than spaces, while around a circle the two are equal, and this is confirmed through questions phrased with pictures, with total length, with counts and with spacing.

Treating trees and spaces as equal in a straight-line problem means dividing the total length by the number of trees, so the spacing comes out too short. An answer slightly below the correct value is this pattern. Around a circle the opposite happens, with 1 added because the straight-line reasoning is carried straight over.

Reading a relationship between quantities out of how figures are laid out is put to the test here, taking the shape of a special type of word problem. What it relies on is the sense of length and distance built up in Length (km and Tape Measure). This way of reading carries on, in a changed form, into Various Word Problems, the unit that follows.