It might appear that there are few opportunities within these activities to introduce mathematics. However, there are a number of instances where mathematical thinking can be useful and a natural extension of youth’s interest and questions. Challenging youth to develop ways of doing measurements, making estimations, and making graphs are all ways of including mathematics as part of the program.

The following are possible mathematical extensions of some of the activities. You will need to provide a rationale for the youth to carry them out. You can either have them devise their own techniques or provide a structure so that youth have a way of carrying out the measurements in a productive manner.

## Estimating

Trees expend a great deal of energy making seeds and flowers. Estimating the total number of seeds, flowers, or leaves produced by a tree can give youth a sense of the investment in this process. The changing population of daphnia in a container can be estimated using different methods.

## Graphing

When seeds germinate and grow into plants, youth can take direct measurements to create a graph. They should measure the growth of the plant using pieces of paper (cut into strips) or string. For each measurement, they would label the paper/string with the date. Then for their next measurement, they would use a new piece of paper/string. When these pieces of paper or string are placed next to each other in order of date, youth can create a picture (or bar graph) of the growth of the plant.

Of course, youth can take measurements of their seedlings using a ruler and create a paper-and-pencil graph as well.

## Ratios

Youth can also practice using ratios; for instance, they can measure a tree’s girth (its perimeter) and estimate its height, and then create a ratio of girth to height. Or they can find the diameter of a tree by measuring its girth/perimeter and doing some calculations.