This Geometry Concept Collection is a rigorous presentation of high school geometry. It is fully correlated with the Common Core State Standards.
The Teacher's Edition covers tips, common errors, enrichment, differentiated instruction and problem solving for teaching CK-12's Basic Geometry Student Edition. The solution and assessment guides are available upon request.
This stand-alone module examines the history, applications, and various proofs of the Pythagorean Theorem. The module also includes student activities and exercise problems. The module assumes the reader has a basic geometry background.
CK-12's Geometry - Second Edition is a clear presentation of the essentials of geometry for the high school student. Topics include: Proofs, Triangles, Quadrilaterals, Similarity, Perimeter & Area, Volume, and Transformations.
In this lesson, students will investigate error. As shown in earlier activities from navigation lessons 1 through 3, without an understanding of how errors can affect your position, you cannot navigate well. Introducing accuracy and precision will develop these concepts further. Also, students will learn how computers can help in navigation. Often, the calculations needed to navigate accurately are time consuming and complex. By using the power of computers to do calculations and repetitive tasks, one can quickly see how changing parameters likes angles and distances and introducing errors will affect their overall result.
In this lesson, students will learn how great navigators of the past stayed on course that is, the historical methods of navigation. The concepts of dead reckoning and celestial navigation are discussed.
In this lesson, students are asked to provide a written description of both an exponential function and its inverse. They are then introduced to the logarithmic function and will practice writing exponential functions as logarithms and logarithms as exponential functions. Students will evaluate logarithmic expressions and will solve logarithmic equations. This lesson results from the ALEX Gap Resource Project.
Graph theory is a visual way to represent relationships between objects. One of the simplest uses of graph theory is a family tree that shows how different people are related. Another application is social networks like Facebook, where a network of "friends" and their "friends" can be represented using graphs. Students learn and apply concepts and methods of graph theory to analyze data for different relationships such as friendships and physical proximity. They are asked about relationships between people and how those relationships can be illustrated. As part of the lesson, students are challenged to find the social graph of their friends. This prepares students for the associated activity during which they simulate and analyze the spread of disease using graph theory by assuming close proximity to an infected individual causes the disease to spread.
Students obtain a basic understanding of microfluidic devices, how they are developed and their uses in the medical field. After conducting the associated activity, they watch a video clip and learn about flow rate and how this relates to the speed at which medicine takes effect in the body. What they learn contributes to their ongoing objective to answer the challenge question presented in lesson 1 of this unit. They conclude by solving flow rate problems provided on a worksheet.
Student teams are challenged to design and build architecturally inspired cardboard furniture, guided by the steps of the engineering design process. They cultivate their industrial engineering and design skills to design furnishings that meet functional, aesthetic and financial requirements. Given constraints that include limited building materials and tools, groups research architectural styles and period furnishings. The teams brainstorm ideas, make small-scale quick prototypes, then make detailed plans and create full-scale prototypes of their best solutions. The full-size prototypes are evaluated by peer critique for aesthetic alignment to the targeted architectural style and tested for functionality. After final refinements, teams present their concepts and display their final prototype furnishings in an exhibition.
This lesson will lead students through a review of the proof of the Law of Sines. This proof will remind them that they can use the right triangle relationship for Sine to find the height of a triangle. They will then apply this knowledge to find the area of a triangle when given two sides and an included angle. Finally, they will be asked to find the area when no values are given. This result should produce the Area Formula for a triangle given two sides and the included angle. This lesson results from the ALEX Resource Gap Project.
This lesson will provide instruction on proving triangles to be congruent using rigid motions. Using the concept of transformations, the students will be able to manipulate the triangle on the coordinate plane. When using the coordinate plane to test congruence, the triangle or other object will slide, rotate, or flip to map onto the other object. Sometimes, the student will use a combination of the transformations. This lesson results from the ALEX Resource Gap Project.
Students learn about the fundamental strength of different shapes, illustrating why structural engineers continue to use the triangle as the structural shape of choice. Examples from everyday life are introduced to show how this shape is consistently used for structural strength. Along with its associated activity, this lesson empowers students to explore the strength of trusses made with different triangular elements to evaluate the various structural properties.
CK-12 Foundation's Trigonometry FlexBook is an introduction to trigonometry for the high school student. It includes chapters on graphs of trigonometric functions, trigonometric identities, inverse trigonometric functions, triangles and vectors, and the polar system.
CK-12 Foundation's Trigonometry FlexBook is an introduction to trigonometry for the high school student. Topics include: Trigonometric Identities & Equations, Circular Functions, and Polar Equations & Complex Numbers.
CK-12 Trigonometry Teacher's Edition provides tips and common errors for teaching CK-12 Trigonometry Student Edition. The solution and assessment guides are available upon request.
This lesson will demonstrate that in order to find the coordinates of the special angles on the unit circle, students will need a knowledge of the first quadrant angles only. Students will use special right triangle relationships for 30degrees - 60degrees -90degrees or 45degrees - 45degrees - 90degrees triangles to find the first quadrant coordinate values. These values will then be reflected across the x- and y-axis to locate the coordinates in the remaining quadrants. Students will also convert the angle measurements from units in degrees to units in radians. They will become familiar with finding angles in the quadrants by using reference angles (π-x, π+x. 2π-x). This lesson results from the ALEX Resource Gap Project.
The purpose of this task is to give students practice writing a constraint equation for a given context. Instruction accompanying this task should introduce the notion of a constraint equation as an equation governing the possible values of the variables in question.