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.

Concepts

estimation, geometric, scale factors, similarity, scale, environmental science, large numbers

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Additional Tags

math

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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

Common Core

HSG-MG.A.1 HSG-MG.A.2