# How Many Leaves on a Tree?

##### This How Many Leaves on a Tree? lesson plan also includes:

This is great go-to activity for those spring or fall days when the weather beckons your geometry class outside. Learners start with a small tree, devising strategies to accurately estimate the leaf count. They must then tackle the challenges of scaling a similarity to estimate the leaf count on a much larger tree. The open-ended nature of the problem and variety of attack methods really challenges all learners, from remedial to advanced.

CCSS: Designed

##### Instructional Ideas

• Mentioned extension has students perform for themselves the estimation and scaling activity modeled in the lesson
• Combining with geometric modeling software would allow for a deeper investigation into the similarity and scaling factor concepts broached in the lesson
##### Classroom Considerations

• Discussed in the teacher's notes, but worth highlighting: this activity has far more creative latitude in student interpretation than a worksheet or skills practice problem. Learner discomfort with the lack of explicit step-by-step instructions or a single obtainable correct answer may require some preparation ahead of the lesson
• Areas without maple trees might need to adapt to some other local (and more familiar) vegetation
##### Pros

• Naturally differentiable in approach methods and complexity of analysis
• Open-ended question reinforces skills in explaining math reasoning and thought process
• Excellent mix of low and high thought-level processes, ranging from arithmetic to estimating appropriate scale factors
##### Cons

• Class task is not separated from teacher notes on a handout or worksheet