This final lesson in the unit culminates with the Go Public phase of the legacy cycle. In the associated activities, students use linear models to depict Hooke's law as well as Ohm's law. To conclude the lesson, students apply they have learned throughout the unit to answer the grand challenge question in a writing assignment.

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.

This short video and interactive assessment activity is designed to teach third graders about creating largest and smallest numbers given digits.

Students are introduced to Pascal's law, Archimedes' principle and Bernoulli's principle. Fundamental definitions, equations, practice problems and engineering applications are supplied. A PowerPoint® presentation, practice problems and grading rubric are provided.

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.

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

This short video and interactive assessment activity is designed to teach third graders an overview of area of squares and rectangles - word problems.

This course is an arithmetic course intended for college students, covering whole numbers, fractions, decimals, percents, ratios and proportions, geometry, measurement, statistics, and integers using an integrated geometry and statistics approach. The course uses the late integers model—integers are only introduced at the end of the course.

This short video and interactive assessment activity is designed to teach third graders about arranging numbers in specific orders.

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.

The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.

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.

Students are introduced to the concept of engineering biological organisms and studying their growth to be able to identify periods of fast and slow growth. They learn that bacteria are found everywhere, including on the surfaces of our hands. Student groups study three different conditions under which bacteria are found and compare the growth of the individual bacteria from each source. In addition to monitoring the quantity of bacteria from differ conditions, they record the growth of bacteria over time, which is an excellent tool to study binary fission and the reproduction of unicellular organisms.

This Nrich problem requires some simple knowledge of fractions and multiples and demands some strategic thinking. It may offer a good opportunity to compare methods between students - there isn't just one route to the solution. Note that there is no need to use algebra in this problem.

This Nrich problem fits in well with counting and skip-counting (counting by twos etc.) and can be solved by physically modeling the biscuits and decorations with whatever objects are convenient. It is a good opportunity for children to choose the way they represent the problem in order to solve it. It may also be appropriate to introduce vocabulary such as "multiple".

" BLOSSOMS stands for Blended Learning Science or Math Studies. It is a project sponsored by MIT LINC (Learning International Networks Consortium) a consortium of educators from around the world who are interested in using distance and e-Learning technologies to help their respective countries increase access to quality education for a larger percentage of the population.BLOSSOMS Online"

Students revisit the mathematics required to find bone mineral density, to which they were introduced in lesson 2 of this unit. They learn the equation to find intensity, Beer's law, and how to use it. Then they complete a sheet of practice problems that use the equation.

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.