Explore size estimation in one, two and three dimensions! Multiple levels of difficulty allow for progressive skill improvement.
This book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalistic.
Compare distributions using the features of shape, center, spread, and outliers.
Overview of the Intermediate Value Theorem, the Extreme Value Theorem and the Mean Value Theorem.
The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways.
The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example.
Students apply what they know about light polarization and attenuation (learned in the associated lesson) to design, build, test, refine and then advertise their prototypes for more effective sunglasses. Presented as a hypothetical design scenario, students act as engineers who are challenged to create improved sunglasses that reduce glare and lower light intensity while increasing eye protection from UVA and UVB radiation compared to an existing model of sunglasses—and make them as inexpensive as possible. They use a light meter to measure and compare light intensities through the commercial sunglasses and their prototype lenses. They consider the project requirements and constraints in their designs. They brainstorm and evaluate possible design ideas. They keep track of materials costs. They create and present advertisements to the class that promote the sunglasses benefits, using collected data to justify their claims. A grading rubric and reflection handout are provided.
Through this lesson and its series of hands-on mini-activities, students answer the question: How can we investigate and measure the inside of an object or its structure if we cannot take it apart? Unlike the destructive nuclear weapon test (!), nondestructive evaluation (NDE) methods are able to accomplish this. After an introductory slide presentation, small groups rotate through five mini-activity stations: 1) applying Maxwell’s equations, 2) generating currents, 3) creating magnetic fields, 4) solving a system of equations, and 5) understanding why the finite element method (FEM) is important. Through the short experiments, students become familiar with the science and physics being used and make the mathematical connections. They explore components of NDE and see how engineers find unseen flaws and cracks in materials that make aircraft. A pre/post quiz, slide presentation and worksheet are included.
In this task students prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
This problem illustrates how an exponentially increasing quantity eventually surpasses a linearly increasing quantity.
In this task students observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
This problem shows that an exponential function takes larger values than a cubic polynomial function provided the input is sufficiently large.
The purpose of this task is to help students see the "why" behind properties of logs that are familiar but often just memorized (and quickly forgotten or misremembered). The task focuses on the verbal definition of the log, helping students to concentrate on understanding that a logarithm is an exponent, as opposed to completing a more computational approach.
This task and its companion, F-BF Exponentials and Logarithms I, is designed to help students gain facility with properties of exponential and logarithm functions resulting from the fact that they are inverses.
This 8-minute video lesson looks at adding and subtracting rational expressions.
This 4-minute video lesson looks at multiplying and dividing rational expressions.
This 5-minute video lesson looks at multiplying and dividing rational expressions.
This 4-minute video lesson looks at multiplying and dividing rational expressions.
This short video and interactive assessment activity is designed to teach second graders an overview - hundredths.
This short video and interactive assessment activity is designed to teach second graders an overview - tenths.