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Over the last decade, reform in science education has placed an emphasis on the science practices as a way to engage students in the process of science and improve scientific literacy. A critical component of developing scientific literacy is learning to apply quantitative reasoning to authentic scientific phenomena and problems. Students need practice moving fluidly (or fluently) between math and science to develop a habit of mind that encourages the application of quantitative reasoning to real-world scenarios. Here we present a student-facing model that challenges students to think across these two fields. The model brings together math and science with a goal to increase scientific literacy by engaging students in quantitative reasoning within the context of scientific questions and phenomena. In the classroom, the model serves to help students visualize the logical and necessary moves they make as they use quantitative reasoning to connect science practices with mathematical thinking. 

Characterizing the population density of species is a central interest in ecology. Eastern North America is the global hotspot for biodiversity of plethodontid salamanders, an inconspicuous component of terrestrial vertebrate communities, and among the most widespread is the eastern red-backed salamander,Plethodon cinereus. Previous work suggests population densities are high with significant geographic variation, but comparisons among locations are challenged by lack of standardization of methods and failure to accommodate imperfect detection. We present results from a large-scale research network that accounts for detection uncertainty using systematic survey protocols and robust statistical models. We analysed mark–recapture data from 18 study areas across much of the species range. Estimated salamander densities ranged from 1950 to 34 300 salamanders ha⁻¹, with a median of 9965 salamanders ha⁻¹. We compared these results to previous estimates forP. cinereusand other abundant terrestrial vertebrates. We demonstrate that overall the biomass ofP. cinereus, a secondary consumer, is of similar or greater magnitude to widespread primary consumers such as white-tailed deer (Odocoileus virginianus) andPeromyscusmice, and two to three orders of magnitude greater than common secondary consumer species. Our results add empirical evidence thatP. cinereus, and amphibians in general, are an outsized component of terrestrial vertebrate communities in temperate ecosystems.