The purpose of this resource is to help math teachers unpack, understand, and implement the current math content and practice standards. It describes the progressions of learning within each course and provides content supports that include broad ideas about effective instruction as well as practical instructional strategies. Math teachers,…

An essential understanding of the uses and practices of algebra remain out of reach for many students. In this book, award-winning researcher Dr. Nicole Fonger addresses the issue of how to support all learners to experience algebra as meaningful. In a highly visual approach, the book details four research-based lenses with examples from 9th-grade…

We present adaptable activities for models of drug movement in the human body -- pharmacokinetics -- that motivate the learning of ordinary differential equations with an interdisciplinary topic. Specifically, we model aspirin, caffeine, and digoxin. We discuss the pedagogy of guiding students to understand, develop, and analyze models,…

Harvesting models based on ordinary differential equations are commonly used in the fishery industry and wildlife management to model the evolution of a population depleted by harvest mortality. We present a project consisting of a series of scenarios based on fishery harvesting models to teach the application of theoretical concepts learned in a…

We present noncompetitive adsorption as "particles in a box with one sticky wall." We start with a general model that can be modeled as a simple ordinary differential equation (ODE). To verify the ODE students run a computer simulation. The ODE's solution imperfectly fits the simulation's data. This leads to the diffusion partial…

Teaching the concept of pH buffers is considered to be important both in the final high-school years and at the early undergraduate level. Here, we propose the use of pH-log C diagrams to investigate the properties of pH buffers. This graphical approach is extremely simple to employ because it only requires drawing a simple square that can then be…

Most likely a large number of students have heard of the Northern Lights (Aurora Borealis), and know that they are a phenomenon in the sky. Although they may not have seen the Northern Lights, most have probably seen other phenomena in the sky, such as a rainbow, shooting star, or super moon. These experiences provide an opportunity for students…

Mathematical modeling, a key strand in mathematics, engages students in rich, authentic, exciting, and culturally relevant problems and connects abstract mathematics to the surrounding world. In this, article, the authors describe a modeling activity that can be used when teaching linear equations. Modeling problems, in general, are typically high…

The traditional technique for converting repeating decimals to common fractions can be found in nearly every algebra textbook that has been published, as well as in many precalculus texts. However, students generally encounter repeating decimal numerals earlier than high school when they study rational numbers in prealgebra classes. Therefore, how…

How can we teach inquiry? In this paper, I offer practical techniques for teaching inquiry effectively using activities built from routine textbook exercises with minimal advanced preparation, including rephrasing exercises as questions, creating activities that inspire students to make conjectures, and asking for counterexamples to reasonable,…

Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a…

Mr. Perez and Mrs. Peterson co-teach a ninth-grade algebra class. Perez and Peterson's class includes four students with individualized education programs (IEPs). In response to legislation, such as the No Child Left Behind (NCLB) Act (2001) and the Individuals with Disabilities Education Improvement Act (2006), an increasing number of students…

In October 2014, an interesting new app became freely available in the Apple Store®. It is called PhotoMath®: (1) Hold a phone or tablet up to a mathematics problem in a textbook; (2) The app shows the answer to the problem; and (3) Select Steps to see the step-by-step process for getting from the problem to the solution. The app works for simple…

Mathematics is a language that is characterized by words and symbols that have precise definitions. Many opportunities exist for miscommunication in mathematics if the words and symbols are interpreted incorrectly or used in imprecise ways. In fact, it is found that imprecision is a common source of mathematical disagreements and misunderstandings…

Every day, students collect, organize, and analyze data to make decisions. In this data-driven world, people need to assess how much trust they can place in summary statistics. The results of every survey and the safety of every drug that undergoes a clinical trial depend on the correct application of appropriate statistics. Recognizing the…