Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Related Standards
Related Access Points
Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorial
Perspectives Video: Expert
Presentation/Slideshow
Problem-Solving Tasks
Teaching Idea
Tutorials
Video/Audio/Animation
Virtual Manipulative
Student Resources
Original Student Tutorial
Learn how to use trigonometric ratios to find the heights of famous monuments and solve a real-world application in this interactive tutorial.
Type: Original Student Tutorial
Presentation/Slideshow
This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications. It is geared toward high school Geometry students that have completed a year of Algebra and addresses the following national standards of the National Council of Teachers of Mathematics and the Mid-continent Research for Education and Learning: 1) Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; 2) Use visualization, spatial reasoning, and geometric modeling to solve problems; 3) Understand and apply basic and advanced properties of the concepts of geometry; and 4) Use the Pythagorean theorem and its converse and properties of special right triangles to solve mathematical and real-world problems. The video portion is about thirty minutes, and with breaks could be completed in 50 minutes. (You may consider completing over two classes, particularly if you want to allow more time for activities or do some of the enrichment material). These activities could be done individually, in pairs, or groups. I think 2 or 3 students is optimal. The materials required for the activities include scissors, tape, string and markers.
Type: Presentation/Slideshow
Problem-Solving Tasks
Using a chart of diameters of different denominations of coins, students are asked to figure out how many coins fit around a central coin. (For this task, United States coins are used, but the task can be adapted for coins from other countries.)
Type: Problem-Solving Task
This problem solving task asks students to find the area of an equilateral triangle. Various solutions are presented that include the Pythagoren theorem and trigonometric functions.
Type: Problem-Solving Task
This task engages students in an open-ended modeling task that uses similarity of right triangles.
Type: Problem-Solving Task
This is a foundational geometry task designed to provide a route for students to develop some fundamental geometric properties that may seem rather obvious at first glance. In this case, the fundamental property in question is that the shortest path from a point to a line meets the line at a right angle which is crucial for many further developments in the subject.
Type: Problem-Solving Task
This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?
Type: Problem-Solving Task
This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles, using trigonometric ratios to solve right triangles, and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found.
Type: Problem-Solving Task
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.
Type: Problem-Solving Task
Tutorials
This tutorial will show students how to use trigonometry to solve for missing information in right triangles. This video shows worked examples using trigonometric ratios to solve for missing information and evaluate other trigonometric ratios.
Type: Tutorial
This tutorial gives an introduction to trigonometry. This resource discusses the three basic trigonometry functions, sine, cosine, and tangent.
Type: Tutorial
This video discusses how to figure out the horizontal displacement for a projectile launched at an angle.
Type: Tutorial
Parent Resources
Problem-Solving Tasks
Using a chart of diameters of different denominations of coins, students are asked to figure out how many coins fit around a central coin. (For this task, United States coins are used, but the task can be adapted for coins from other countries.)
Type: Problem-Solving Task
This problem solving task asks students to find the area of an equilateral triangle. Various solutions are presented that include the Pythagoren theorem and trigonometric functions.
Type: Problem-Solving Task
This task engages students in an open-ended modeling task that uses similarity of right triangles.
Type: Problem-Solving Task
This is a foundational geometry task designed to provide a route for students to develop some fundamental geometric properties that may seem rather obvious at first glance. In this case, the fundamental property in question is that the shortest path from a point to a line meets the line at a right angle which is crucial for many further developments in the subject.
Type: Problem-Solving Task
This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?
Type: Problem-Solving Task
This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles, using trigonometric ratios to solve right triangles, and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found.
Type: Problem-Solving Task
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.
Type: Problem-Solving Task