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Background: Previous work found four areas critical to understanding evolution: variation, selection, inheritance, and deep time.

Teachers' understanding of science concepts must be deeper than just factual knowledge. They need to understand how the facts are connected and relate to the natural world. Weather, ocean currents, and tectonic movement are all phenomena listed in the Next Generation Science Standards (NGSS). Although understanding density of fluids within fluids is not directly mentioned in the NGSS, students need to understand fluid density in order to explain these common yet complex phenomena. We extended a familiar science activity of making a density column in order to help teachers understand the expectations of NGSS. Understanding the causes of the phenomena is critical for teachers. We found when students do not understand, they are more likely to substitute concrete or active causal factors, such as weight or force. We issued to our teachers the following challenge: "Make a density column with these 4 mystery liquids." As our students were in the process of determining the correct order to add the liquids, we noticed they confused mass and viscosity with density. In light of the expectations of the NGSS, we need to change the way teachers are prepared. They need time and space to practice connecting the concepts in practice. Therefore, teachers need help to connect the concepts to past experiences as well as time to reflect and revise. Teachers need to develop a mindset as a lifelong learner powered by their reflections and drive to help students understand science.

We report on a case study of the mathematical content of a 10 th grade social studies textbook. We develop our case in three analytical steps. First, we identify, describe, and categorize the full range of mathematics in the book. Put simply, we ask: What mathematical forms (e.g., Cartesian graphs and problems) do we find and what kinds of mathematical work do they require? Second, we characterize and critically evaluate the mathematics content in the textbook, focusing in particular on the kinds of mathematics literacy and student reasoning that the book fosters. Third and finally, we operationalize a measure of the "density" of mathematics in the textbook-that is, an estimate of the presence and pervasiveness of mathematical objects and practices relative to other disciplinary contents and track how such "density" has changed over the past three editions of the same volume. Doing so helps us further contextualize and elaborate the prior analyses, but also surfaces shifts in the patterns of mathematics presence in that textbook series, including the growing encroachment of mathematics exercising and visual/representational presence.

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