This short video and interactive assessment activity is designed to teach fourth graders about finding and completing the number patterns.
This short video and interactive assessment activity is designed to teach third graders about finding and completing the number patterns.
This short video and interactive assessment activity is designed to teach fourth graders about completion of number patterns.
This short video and interactive assessment activity is designed to teach fourth graders about completing a decimal place value chart up to hundredths.
This short video and interactive assessment activity is designed to teach fourth graders about completing a decimal place value chart to tenths.
This problem is intended to reinforce the geometric interpretation of distance between complex numbers and midpoints as modulus of the difference and average respectively.
This 4-minute video lesson introduces Khan's series on complex numbers.
This single minute video lesson looks at how to add complex numbers.
This 4-minute video lesson give an example of a complex conjugate.
This 5- minute video lesson shows how to divide complex numbers.
This 4-minute video lesson looks at the imaginary roots of negative numbers.
This 6-minute video lesson explains how to multiply complex numbers.
This 2-minute video lesson explains how to subtract complex numbers.
This short video and interactive assessment activity is designed to give fourth graders an overview of forming figures with cutouts.
This short video and interactive assessment activity is designed to teach fourth graders about compound unit multiplication - word problems.
This task is preliminary to F-LE Compounding Interest with a 5% Interest Rate which further develops the relationship between e and compound interest.
This task develops reasoning behind the general formula for balances under continuously compounded interest. While this task itself specifically addresses the standard (F-BF), building functions from a context, a auxiliary purpose is to introduce and motivate the number e, which plays a significant role in the (F-LE) domain of tasks.
All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well.
The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures.
This course covers the analytical, graphical, and numerical methods supporting the analysis and design of integrated biological systems. Topics include modularity and abstraction in biological systems, mathematical encoding of detailed physical problems, numerical methods for solving the dynamics of continuous and discrete chemical systems, statistics and probability in dynamic systems, applied local and global optimization, simple feedback and control analysis, statistics and probability in pattern recognition.
This task asks students to perform computations involving complex numbers using the given information.