This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, it will support you in identifying and helping students who have the following difficulties: Solving problems relating to using the measures of the interior angles of polygons; and solving problems relating to using the measures of the exterior angles of polygons.

The main objective of this lesson is to illustrate an important application of mathematics in practical life -- namely in art. Most of the pictures selected for this lesson are visible on the walls of Al-Hambra – Granada (Spain), which is one of the most important landmarks in the Islamic civilization. There are three educational goals for this lesson: (1) establishing the concept of isometries; (2) giving real-life examples of groups; (3) demonstrating the importance of matrices and their applications. As background for this lesson, students just need some familiarity with the concept of a group and a limited knowledge about matrices and the inverse of a non-singular matrix.

Students explore the interface between architecture and engineering. In the associated hands-on activity, students act as both architects and engineers by designing and building a small parking garage.

The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.

In this lesson, the students will discover the relationship between an object's mass and the amount of space it takes up (its volume). The students will also learn about the concepts of displacement and density.

This short video and interactive assessment activity is designed to teach second graders an overview of simple figure patterns.

This short video and interactive assessment activity is designed to teach third graders an overview of simple figure patterns.

In this optics activity, learners discover that when they rotate a special black and white pattern called a Benham's Disk, it produces the illusion of colored rings. Learners experiment with the speed of rotation and direction of rotation to observe varying patterns. Use this activity to explain to learners how our eyes detect color and how different color receptors in the eye respond at different rates.

Students examine an image produced by a cabinet x-ray system to determine if it is a quality bone mineral density image. They write in their journals about what they need to know to be able to make this judgment. Students learn about what bone mineral density is, how a BMD image can be obtained, and how it is related to the x-ray field. Students examine the process used to obtain a BMD image and how this process is related to mathematics, primarily through logarithmic functions. They study the relationship between logarithms and exponents, the properties of logarithms, common and natural logarithms, solving exponential equations and Beer's law.

Experiment with rocket designs and a PVC launcher to discover how high—and how far—you can make your rockets go.

This learning video is designed to develop critical thinking in students by encouraging them to work from basic principles to solve a puzzling mathematics problem that contains uncertainty. Materials for in-class activities include: a yard stick, a meter stick or a straight branch of a tree; a saw or equivalent to cut the stick; and a blackboard or equivalent. In this video lesson, during in-class sessions between video segments, students will learn among other things: 1) how to generate random numbers; 2) how to deal with probability; and 3) how to construct and draw portions of the X-Y plane that satisfy linear inequalities.

When will objects float and when will they sink? Learn how buoyancy works with blocks. Arrows show the applied forces, and you can modify the properties of the blocks and the fluid.

This lesson will give students an idea of what to expect when they head to the computer lab. It begins with a brief discussion introducing them to computer lab manners, then they will progress into using a computer to complete online puzzles.

Students will begin using Evaluation Blocks to explore the concept of math as a language, and more specifically, a programming language. By composing arithmetic expressions with Evaluation Blocks, students will be able to visualize how expressions follow the order of operations.

Using the Design Recipe, students will work through a series of word problems about calculating the height of a rocket after a given number of seconds from launch. The functions they write will be used to animate the rocket launch.

To compute more than just numbers, students will need to learn about two new data types, Strings (any string of alphanumeric characters) and Images. Using these new data types, we'll compose programs that produce and manipulate images.

Contracts provide a way for students to better understand and discuss functions. Through this lesson, students will look at known functions and come up with the contracts that describe those functions.

Students will work their way through a number of new functions, first using each to solve a problem, and then writing a contract which describes it.

In this activity, students will learn to define variables that can be used to reference values and expressions. Once defined, their variables can be used repeatedly throughout a program as substitutes for the original values or expressions.