This task provides an opportunity to model a concrete situation with mathematics. Once a representative picture of the situation described in the problem is drawn (the teacher may provide guidance here as necessary), the solution of the task requires an understanding of the definition of the sine function. When the task is complete, new insight is shed on the ``Seven Circles I'' problem which initiated this investigation as is noted at the end of the solution.

In the first of two lessons of this curricular unit, students are introduced to the concept of friction as a force that impedes motion when two surfaces are in contact. Student teams use spring scales to drag objects, such as a ceramic coffee cup, along a table top or the floor, measuring the frictional force that exists between the moving object and the surface it slides on. By modifying the bottom surface of the object, students find out what kinds of surfaces generate more or less friction. They also discover that both static and kinetic friction are involved when an object initially at rest is caused to slide across a surface. In the second lesson of the unit, students design and conduct experiments to determine the effects of weight and surface area on friction. They discover that weight affects normal friction (the friction that results from surface roughness), but for very smooth surfaces, the friction due to molecular attraction is affected by contact area.

The purpose of this lesson is to help students understand the relationship between the mass and the weight of an object. Students will study the properties of common materials and why airplanes use specific materials.

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 modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles (G-C.5), using trigonometric ratios to solve right triangles (G-SRT.8), and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found (MP.7).

This is a comprehensive math textbook for Grade 12. It can be downloaded, read on-line on a mobile phone, computer or iPad. Every chapter has links to on-line video lessons and explanations. Summary presentations at the end of each chapter offer an overview of the content covered, with key points highlighted for easy revision. Topics covered are: language of mathematics, logarithms, sequences and series, finance, factorising cubic polynomials, functions and graphs, differential calculus, linear programming, geometry, trigonometry, statistics, combinations and permutations. This book is based upon the original Free High School Science Text series.

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.

The purpose of this task is to engage students in an open-ended modeling task that uses similarity of right triangles, and also requires the use of technology.

This tasks examines how to calculate the area of an equilateral triangle using high school geometry.

Let's explore some science and math around why seatbelts work. Check out the career video from Billie Jo Deal, Transportation Safety Coordinator from the Oregon Department of Transportation, about how she works to keep people safe on the roads. Then, in the Discovery Challenge, we build crash models and calculate restraining forces.

This lesson introduces NGSS standards, and those standards are listed in the lesson.

Videos are part of the Explore Science Club series, an asynchronous online learning program using YouTube videos that connects elementary and middle school students to STEM professionals through hands-on lessons where students explore science and engineering practices related to the highlighted careers. There is an option to use FlipGrid, an online video recording platform for students to share their discoveries

More info: www.go-stem.org

Air pressure is pushing on us all the time although we do not usually notice it. In this activity, students learn about the units of pressure and get a sense of just how much air pressure is pushing on them.

This resource contains sets of videos that cover Mathematics Vision Project's 6.6 and 6.7 tasks. In these tasks students learn about concentric circles and radians.

In this activity, students will learn about Newton's 2nd Law of Motion. They will learn that the force required to move a book is proportional to the weight of the book. Engineers use this relationship to determine how much force they need to move an airplane.

Students observe the relationship between the angle of a catapult (a force measurement) and the flight of a cotton ball. They learn how Newton's second law of motion works by seeing directly that F = ma. When they pull the metal "arm" back further, thus applying a greater force to the cotton ball, it causes the cotton ball to travel faster and farther. Students also learn that objects of greater mass require more force to result in the same distance traveled by a lighter object.

Students construct rockets from balloons propelled along a guide string. They use this model to learn about Newton's three laws of motion, examining the effect of different forces on the motion of the rocket.

This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.

This lesson introduces students to three of the six simple machines used by many engineers. These machines include the inclined plane, the wedge and the screw. In general, engineers use the inclined plane to lift heavy loads, the wedge to cut materials apart, and the screw to convert rotational motion into linear movement. Furthermore, the mechanical advantage describes how easily each machine can do work and is determined by its physical dimensions.

This course covers Complex Number, Polynomials, Composite Functions, Trigonometry, Vectors, Matrices, Series, Conic Sections, and Probability and combinatorics.

Triangle similarity & the trigonometric ratios is the fundamental to trigonometry. This lesson is developed with CCRS G.SRT.5 Geometry: Similarity, Right Triangles.

Students conduct a simple experiment to see how the water level changes in a beaker when a lump of clay sinks in the water and when the same lump of clay is shaped into a bowl that floats in the water. They notice that the floating clay displaces more water than the sinking clay does, perhaps a surprising result. Then they determine the mass of water that is displaced when the clay floats in the water. A comparison of this mass to the mass of the clay itself reveals that they are approximately the same.