This course develops logical, empirically based arguments using statistical techniques and analytic methods. Elementary statistics, probability, and other types of quantitative reasoning useful for description, estimation, comparison, and explanation are covered. Emphasis is on the use and limitations of analytical techniques in planning practice.

A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, transformation theory, equations of motion, and constants of motion. Symmetry in quantum mechanics, representations of symmetry groups. Variational and perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering theory: phase shifts, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic quantum mechanics of one electron. This is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

This course has been designed to help students focus learning on specific areas of improvement. Unlike a typical college course where you would complete lessons in chronological order, this course allows you to focus on specific skills. Modules include: Arithmetic Review, Percents, Geometric Figures, Measurement, and Statistics

This activity builds student knowledge of ratios by using Cuisenaire rods to determine proportion and form equivalent ratios. Students may use the Cuisenaire rod environment embedded in this resource or they may use actual Cuisenaire rods depending on preference/ability/accessibility. This resource includes teacher notes, solution, and suggestions for questioning.

Add different salts to water, then watch them dissolve and achieve a dynamic equilibrium with solid precipitate. Compare the number of ions in solution for highly soluble NaCl to other slightly soluble salts. Relate the charges on ions to the number of ions in the formula of a salt. Calculate Ksp values.

This activity gives students the opportunity to describe motions along paths involving turns of 45 and 90 degrees. Ideas for implementation, extension and support are included along with a printable sheet of the maps.

This card game for two players helps students learn the days of the week and their proper sequence. The basic game asks students to say "snap" when one day card follows a next or previous day. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and variations. Master sheets of the day card deck are provided (doc or pdf).

This problem asks students to visualize a square drawn on a clock face and estimate and calculate its area. The problem can be solved without use of the Pythagorean Theorem. Ideas for implementation, extension and support are included along with printable sheets of clock faces.

An article based on data and evidence that includes charts and information that can be analyzed statistically by students.

In this investigation students work systematically and keep organized records as they explore forming triangles from unit sticks. Learners look for patterns and trends in the number of triangles possible with a given integer perimeter. Ideas for implementation, extension and support are included along with a printable sheet of the problem.

This interactive Flash game gives students practice in telling time on an analog clock while also developing strategic thinking. Students take turns advancing the clock by 1/4, 1/2, or 1 hour. The winner is the player who moves the hands of the clock to exactly midnight. This activity can merely familiarize students with the clock and time intervals, or it can challenge older students to find the strategy that always wins.

This activity provides students with an opportunity to calculate area and perimeter of rectangles in order to determine the pricing system of objects with given costs (in British Pounds). The resource includes the problem, tips on getting started, a teacher resource page, and a printable student page.

In this activity learners explore the connections of digital time displays with numeric and geometric properties. Students look for times that have bilateral or rotational symmetry, or have a certain digital sum, etc. Ideas for implementation, extension and support are included.

This activity generates discussion about the times of day and the passing of time. Students try to place the daily events shown in pictures in chronological order. They are encouraged to use terms such as afternoon, earlier, and the time units. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, and printable sheets.

An article based on data and evidence that includes charts and information that can be analyzed statistically by students.

The author of this one-page article describes the pedagogical benefits of using math games in the classroom. She analyzes the game context in terms of the kinds of learning that takes place, the behaviors that students exhibit, and the social-emotional experience of students. She concludes by recommending strategies for effective introduction and management of games. [While the author's observations were in the context of geometry games, they generalize to most topics.]

This activity introduces the concept of area and offers students a way to measure it informally, by counting objects in a wallpaper pattern. Students are asked to rank irregular cutouts in order from smallest to largest. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, and printable sheets.

This review is on the first segment of the Grade 5 curriculum of "The Inquiry Project: Seeing the World Through the Scientists' Eyes." Water, A Liquid is a series of 5 investigations about water. Students use readily available materials such as water, sand and gravel to deepen their understanding of weight. Having a conceptual understanding of weight is important because students will use it when they begin exploring matter that is too small to be seen. The students are introduced to the study of matter by looking at images of ships sitting in a dry seabed in the Aral Sea. This introductory investigation will hook students because it is posed as a mystery and has a real life connection. Within this series of 5 investigations students will: -practice measurement using standard units -collect and record data -read a letter from an engineer -compare the weight of sand and water -use a digital scale -learn vocabulary -review volume, estimation -engage in discourse -reflect on the weight of small bits of matter -summarize evidence -collaborate -develop strategies -observe -transform (by crushing). The Inquiry Project is a quality curriculum developed pre-NGSS but closely aligned with The Framework of K-12 Science Education. This curriculum "links the three dimensions together" through the qualitative and quantitative measurement of water and sand using standard units and student observations. Each lesson is "designed to link with the previous lesson" as students build toward the capacity to be able to "make observations and measurements to identify materials based on their properties" in the context of the dry sea phenomena.

An article based on data and evidence that includes charts and information that can be analyzed statistically by students.

This one-page article by the NRICH team reports on the history of the measuring of weight/mass. It is an attempt to provide material and ideas for lessons that address the disciplines of history and mathematics. Topics covered include weighing by comparison, the need for standard units, and weighing methods in various cultures. Questions and suggestions are provided for further research by students.