This 8-minute video lesson takes some problems from CK12.org to provide Z-score practice. [Statistics playlist: Lesson 31 of 85]
This course is a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics.
The lectures are at a beginning graduate level and assume only basic familiarity with Functional Analysis and Probability Theory. Topics covered include: Random variables in Banach spaces: Gaussian random variables, contraction principles, Kahane-Khintchine inequality, Anderson’s inequality. Stochastic integration in Banach spaces I: γ-Radonifying operators, γ-boundedness, Brownian motion, Wiener stochastic integral. Stochastic evolution equations I: Linear stochastic evolution equations: existence and uniqueness, Hölder regularity. Stochastic integral in Banach spaces II: UMD spaces, decoupling inequalities, Itô stochastic integral. Stochastic evolution equations II: Nonlinear stochastic evolution equations: existence and uniqueness, Hölder regularity.
This problem can be solved in more than one way. The choice in solution method may reflect the comfort and mathematical sophistication of the student.
This is a multi-step problem since it requires more than two steps no matter how it is solved. The problem is not scaffolded for the student, but each step is straightforward and should follow from the previous with a careful reading of the problem.
Students learn about civil engineers and work through each step of the engineering design process in two mini-activities that prepare them for a culminating challenge to design and build the tallest straw tower possible, given limited time and resources. First they examine the profiles of the tallest 20 towers in the world. Then in the first mini-activity (one-straw tall tower), student pairs each design a way to keep one straw upright with the least amount of tape and fewest additional straws. In the second mini-activity (no "fishing pole"), the pairs determine the most number of straws possible to construct a vertical straw tower before it bends at 45 degrees—resembling a fishing pole shape. Students learn that the taller a structure, the more tendency it has to topple over. In the culminating challenge (tallest straw tower), student pairs apply what they have learned and follow the steps of the engineering design process to create the tallest possible model tower within time, material and building constraints, mirroring the real-world engineering experience of designing solutions within constraints. Three worksheets are provided, for each of two levels, grades K-2 and grades 3-5. The activity scales up to school-wide, district or regional competition scale.
This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.
Students learn about contact stress and its applications in engineering. They are introduced to the concept of heavy loads, such as buildings, elephants, people and traffic, and learn how those heavy loads apply contact stress. Through the analysis of their own footprints, students determine their contact stress.
In this task students design a plan to conduct a random sample of the students in their school to estimate the proportion of students who think their parents are strict.
This short video and interactive assessment activity is designed to teach fourth graders about multi-step subtraction of weights with compound units (metric units) - word problems.
This short video and interactive assessment activity is designed to teach fourth graders about subtracting compound units in years and months.
This short video and interactive assessment activity is designed to give fourth graders an overview of conversion between units of weight (english units).
This short video and interactive assessment activity is designed to teach fifth graders about subtracting mixed numbers with different denominators.
This short video and interactive assessment activity is designed to teach second graders an overview of subtraction (numbers to 100).
This short video and interactive assessment activity is designed to teach fourth graders about finding the different weight from tables (metric units).
This short video and interactive assessment activity is designed to teach second graders about subtracting 3 numbers - word problems.
This short video and interactive assessment activity is designed to teach fifth graders about subtracting capacities in compound units (english units).
This short video and interactive assessment activity is designed to teach fourth graders about subtracting capacities in compound units (english units).
This short video and interactive assessment activity is designed to teach fifth graders about adding fractions with common denominators.
This short video and interactive assessment activity is designed to teach fifth graders about subtracting fractions with different denominators.