This short video and interactive assessment activity is designed to give fourth graders an overview of subtraction (numbers to 1,000).

This short video and interactive assessment activity is designed to teach second graders an overview of subtraction (numbers to 1,000).

Long Description:
A study of derivatives of algebraic and trigonometric functions, applications to tangents and normals, curve sketching and Maximum-Minimum word problems, curvilinear motion, related rates , Newtons method for solving equations, differentiation methods for simple algebraic functions with applications for electronics, determinants, trigonometric identities.

Word Count: 175834

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

In this video, we use direction fields (drawn as quiver plots) to illustrate the numerical integration of differential equations. We include a heuristic example of how one might try to adapt step size by comparing different orders of approximation.

In the first video, we present a biological circuit topology from Ma, Trusina, El-Samad, Lim, and Tang, "Defining network topologies that can achieve biochemical adaptation," Cell, 138: 760-773 (2009). This topology supports adaptation, which is not the absence of change in response to stimulation/stress, but, instead, the ability to produce delayed compensation for those changes. In the second video, we summarize the method of almost linear stability analysis used to solve for the dynamics of this example system.

To describe how oscillations are supported in systems of differential equations, we present a classic "Romeo and Juliet" picture of two-dimensional oscillations, and we analyze how trajectories change as nullclines are arranged at different angles in the phase plane. In addition to models based on traditional systems of differential equations, dynamical systems with time delays and dynamical systems with stochastic fluctuation (i.e. stochastic resonance) can also support oscillations.

This article includes a menu of post-reading activities for use with any nonfiction text. Students spend $50 on their choice of activities.

In the five parts of this video, we define the derivative and then build a cribsheet of rules for expressing the slopes of simple functions and combinations of functions. These include the power rule, the chain rule, the product and quotient rules, and the rules for differentiating sinusoidal functions.

The first video segment presents a canonical mathematical example from quantitative biology, in which mRNA is transcribed from a gene sequence, and protein is translated from mRNA. The second segment uses eigenvector-eigenvalue analysis to sketch the trajectories of the system in a phase portrait. Finally, the third segment generalizes the linear stability analysis used to study this example.

Spreadsheets Across the Curriculum module. Students analyze a given data set to understand the "Digital Divide" by means of percentages and the Subtotal tool in Excel.

The CyberSquad tracks Digital position in time and then studies graphs to figure out what Hacker is scheming in this video from Cyberchase.

This task helps students understand the relationship between digit placement and the value of a number.

This task gives students the opportunity to verify that a dilation takes a line that does not pass through the center to a line parallel to the original line, and to verify that a dilation of a line segment (whether it passes through the center or not) is longer or shorter by the scale factor.

This task requires students to think of dimes and pennies as fractions of dollars.

This task does not actually require that the student solve the system but that they recognize the pairs of linear equations in two variables that would be used to solve the system. This is an important step in the process of solving systems.

The purpose of this task is to illustrate through an absurd example the fact that in real life quantities are reported to a certain level of accuracy, and it does not make sense to treat them as having greater accuracy.

Spreadsheets Across the Curriculum module. Students use spreadsheets to help find the difference in percentages of salaries between dirty and clean jobs.

This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols.

Students discover the mathematical constant phi, the golden ratio, through hands-on activities. They measure dimensions of "natural objects"—a star, a nautilus shell and human hand bones—and calculate ratios of the measured values, which are close to phi. Then students learn a basic definition of a mathematical sequence, specifically the Fibonacci sequence. By taking ratios of successive terms of the sequence, they find numbers close to phi. They solve a squares puzzle that creates an approximate Fibonacci spiral. Finally, the instructor demonstrates the rule of the Fibonacci sequence via a LEGO® MINDSTORMS® NXT robot equipped with a pen. The robot (already created as part of the companion activity, The Fibonacci Sequence & Robots) draws a Fibonacci spiral that is similar to the nautilus shape.

Discrete mathematics is applied in many areas including the physical, engineering, and increasingly, the social sciences. This online textbook, written by mathematics and information technology professors, is aimed at students of information technology, computer science, and applied mathematics. The focus is on applying discrete math techniques from the two broad component areas of discrete math, namely combinatorics or enumerative techniques, and graph theory.