Forecasting is the ultimate form of model validation. But even if a …
Forecasting is the ultimate form of model validation. But even if a perfect model is in hand, imperfect forecasts are likely. This course will cover the factors that limit our ability to produce good forecasts, will show how the quality of forecasts can be gauged a priori (predicting our ability to predict!), and will cover the state of the art in operational atmosphere and ocean forecasting systems.
This 15-minute video lesson gives an example involving the preimage of a …
This 15-minute video lesson gives an example involving the preimage of a set under a transformation. It also gives a definition of kernel of a transformation.
In the first half of this module, students identify measurable attributes of …
In the first half of this module, students identify measurable attributes of objects in terms of length, weight, and capacity. Students learn words such as small, big, short, tall, empty, full, heavy, and light so that they will have the vocabulary needed to describe objects (PK.MD.1). The comparison of length, weight, and capacity naturally leads to discussions about quantity and number. In the second half, measurement is connected to quantity as students reason if there are enough, more than, less than, or the same number of objects in a set using matching and counting strategies (PK.CC.5). Comparing concrete sets leads to comparing quantities and abstract numbers. Children will also focus on identifying first and last in quantities up to 5 and 10 in different configurations (PK.CC.6).
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
Module 5 is the culmination of childrens work with number in the …
Module 5 is the culmination of childrens work with number in the Pre-K year. Throughout Modules 1 and 3, they had extensive counting experiences with numbers 010. In Module 4, they examined the relationships between numbers 15 through comparison. In Module 5, children transition from the comparative concept of more (4 apples is more than 1 apple) to the concept of addition (3 apples and 1 more apple make 4 apples). They are ready to begin work with operations, focusing on addition and subtraction stories with numbers 1 to 5. Students will also learn to write numerals 0-5 and explore patterns in this final module.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
Module 1 capitalizes on the energy and excitement young students have as …
Module 1 capitalizes on the energy and excitement young students have as they enter their first day of Pre-K by providing a playful and active yet carefully sequenced structure through which children progress. In this module, we set up a friendly learning environment in which children have sustained interaction with four core ideas, collectively referred to as the number core: rote counting (the number word list), one-to-one correspondence (one object paired with one number word), cardinality (how many in a set), and written numerals. Throughout the module, children have experiences that help them make critical connections between these four understandings.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
In Module 2, in the context of classroom play, children learn to …
In Module 2, in the context of classroom play, children learn to identify, describe, sort, compare, and create two-dimensional (2-D) and three-dimensional (3-D) shapes and objects. Children develop vocabulary to describe the relative position of objects (e.g., top, bottom, up, down, in front of, behind, over, under, and next to), building foundational spatial reasoning abilities. In Module 1, students developed an understanding of numbers to 5. In Module 2, students practice these counting skills in the context of geometry (counting sides, corners, a group of triangles, etc.).
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
Module 3 challenges students to build on their work with numbers through …
Module 3 challenges students to build on their work with numbers through 5 to make sense of and count groups of 0, 6, 7, 8, 9, and 10 objects. Students also continue their work with the number core in the following ways (PK.CC.14): Rote counting (the number word list up to 15); one-to-one correspondence (one object paired with one number word from 0 to 10); cardinality (how many in a set of up to 10 objects); andnumber recognition (matching written numerals 0, 6, 7, 8, 9, and 10 to quantities). Throughout the module, children participate in engaging experiences that help them make critical connections between these four understandings.
**NOTE: The New York State Education Department shut down the EngageNY website in 2022. In order to maintain educators' access, nearly all resources have been uploaded to archive.org and the resource links above have been updated to reflect their new locations.**
Acting as civil engineers hired by the U.S. Department of Transportation to …
Acting as civil engineers hired by the U.S. Department of Transportation to research how to best use piezoelectric materials to detect road damage, student groups are challenged to independently create their own experiment procedures, working with given materials and tools. The general approach is that they set up model roads using rubber mats to simulate asphalt and piezoelectric transducers to simulate the in-ground road sensors. They drop heavy bolts at various locations on the “road,” collecting data and then analyzing the voltage changes across the piezoelectric transducers caused by the vibrations of the bolt hitting the rubber. After making notches in the rubber “road” to simulate cracks and potholes, they collect more data to see if the piezo elements detect the damage. Students write up their research and conclusions as if presenting evidence to USDOT officials about how the voltage changes across the piezo elements can be used to indicate road damage and extrapolated to determine when roads need maintenance service.
The purpose of this task is to help students see that when …
The purpose of this task is to help students see that when you have a context that can be modeled with a ratio and associated unit rate, there is almost always another ratio with its associated unit rate (the only exception is when one of the quantities is zero), and to encourage students to flexibly choose either unit rate depending on the question at hand.
This is a short introduction to the fundamentals of real analysis. Although …
This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.
Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics, …
Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics, including applications from traffic flow, fluids, elasticity, granular flows, etc. The class also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion, and group velocity.
You are probably asking yourself the question, "When and where will I …
You are probably asking yourself the question, "When and where will I use statistics?". If you read any newspaper or watch television, or use the Internet, you will see statistical information. There are statistics about crime, sports, education, politics, and real estate. Typically, when you read a newspaper article or watch a news program on television, you are given sample information. With this information, you may make a decision about the correctness of a statement, claim, or "fact." Statistical methods can help you make the "best educated guess."
By the end of this section, you will be able to: Explain …
By the end of this section, you will be able to:
Explain the meaning of trade balance and its implications for the foreign exchange market Analyze concerns over international trade in goods and services and international flows of capital Identify and evaluate market-oriented economic reforms
By the end of this section, you will be able to: Explain …
By the end of this section, you will be able to:
Explain the nature and causes of unemployment Analyze the natural rate of unemployment and the factors that affect it Identify how undeveloped labor markets can result in the same hardships as unemployment
By the end of this section, you will be able to: Analyze …
By the end of this section, you will be able to:
Analyze the growth policies of low-income countries seeking to improve standards of living Analyze the growth policies of middle-income countries, particularly the East Asian Tigers with their focus on technology and market-oriented incentives Analyze the struggles facing economically-challenged countries wishing to enact growth policies Evaluate the success of sending aid to low-income countries
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