In this problem set, learners will analyze an image of Washington, DC, taken from orbit. They will determine scale and take measurements of several features in the image. A link to more images taken from the International Space Station and the answer key are provided. This is part of Earth Math: A Brief Mathematical Guide to Earth Science and Climate Change.

As science extension activities, this book of problems introduces students to mapping the shape of the Milky Way galaxy, and how to identify the various kinds of galaxies in our universe. Students also learn about the shapes and sizes of other galaxies in our universe as they learn how to classify them. The math problems cover basic scientific notation skills and how they apply to working with astronomically large numbers. It also provides exercises in plotting points on a Cartesian plane to map the various features of our Milky Way.

This is an activity about the solar activity cycle. Learners will construct a graph to identify a pattern of the number of observed sunspots and the number of coronal mass ejections emitted by the Sun over a fifteen year time span. A graphing calculator is recommended, but not required, for this activity. This is the second activity in the Solar Storms and You: Exploring the Wind from the Sun educator guide.

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.

In this activity, students use base-two slide rules, log tapes, and calculators to practice raising exponents in base notation and pulling down exponents in log notation. Students will develop an understanding that antilog notation expresses the exact same idea as raising a base to a power.åÊThis activity is activity C2 in the "Far Out Math" educator's guide. Lessons in the guide include activities in which students measure, compare quantities as orders of magnitude, become familiar with scientific notation, and develop an understanding of exponents and logarithms using examples from NASA's GLAST mission. These are skills needed to understand the very large and very small quantities characteristic of astronomical observations. Note: In 2008, GLAST was renamed Fermi, for the physicist Enrico Fermi.

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 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.

This short video and interactive assessment activity is designed to teach third graders an overview - hundredths.

This short video and interactive assessment activity is designed to teach second graders about expressing multiplication sentences.

This short video and interactive assessment activity is designed to teach third graders an overview - tenths.

This short video and interactive assessment activity is designed to teach third graders about completing the number patterns based on the multiplication table.

This short video and interactive assessment activity is designed to teach third graders about relating multiplication and division with illustrations.

This is an instructional task meant to generate a conversation around the meaning of negative integer exponents. While it may be unfamiliar to some students, it is good for them to learn the convention that negative time is simply any time before t=0.

The goal of this task is to develop an understanding of why rational exponents are defined as they are (N-RN.1), however it also raises important issues about distinguishing between linear and exponential behavior (F-LE.1c) and it requires students to create an equation to model a context (A-CED.2

An interactive applet and associated web page that demonstrate the exterior angles that are formed where a transversal crosses two lines. The applet shows the two possible pairs of exterior angles in turn when in animation mode. By dragging the three lines, it can be seen that the angles are supplementary only when the lines are parallel. When not in animated mode, there is a button that alternates the two pairs of angles. The text on the page discusses the properties of the angle pairs both in the parallel and non-parallel cases. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.