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.

Also assesses:
 Assessment Limits :
Items will assess only sine, cosine, and tangent to determine the
length of a side or an angle measure.  Calculator :
Neutral
 Clarification :
Students will use trigonometric ratios and the Pythagorean theorem
to solve right triangles in applied problems.Students will use similarity to explain the definition of trigonometric
ratios for acute angles.Students will explain the relationship between sine and cosine of
complementary angles.Students will use the relationship between sine and cosine of
complementary angles.  Stimulus Attributes :
For GSRT.3.8, items must be set in a realworld context.For GSRT.3.6 and GSRT.3.7, items must be set in a mathematical
context.For GSRT.3.8, items may require the student to apply the basic
modeling cycle.  Response Attributes :
Items may require the student to find equivalent ratios.Items may require the student to use or choose the correct unit of
measure.Multiplechoice options may be written as a trigonometric equation.
Equation Editor items may require the student to use the inverse
trigonometric function to write an expression.
MAFS.912.GSRT.3.6
MAFS.912.GSRT.3.7
 Test Item #: Sample Item 1
 Question:
In the 1990s, engineers restored the building so that angle y changed from 5.5º to 3.99º.
To the nearest hundredth of a meter, how much did the restoration change the height of the Leaning Tower of Pisa?
 Difficulty: N/A
 Type: EE: Equation Editor
Related Courses
Related Access Points
Related Resources
Assessments
Formative Assessments
Lesson Plans
Lesson Study Resource Kit
Original Student Tutorial
Perspectives Video: Expert
Presentation/Slideshow
ProblemSolving Tasks
Teaching Idea
Tutorials
Video/Audio/Animation
Virtual Manipulatives
MFAS Formative Assessments
Students are asked to solve a problem in a real world context requiring the use of the Pythagorean Theorem.
Students are asked to find the difference between two lengths in a real world context requiring right triangle trigonometry.
Students are asked to find an unknown length in a real world context requiring right triangle trigonometry.
Students are asked to find an unknown length in a real world context requiring right triangle trigonometry.
Students are asked to explain the relationship among angles in a diagram involving a right triangle and to find one angle of the right triangle.
Students are asked to solve a problem in a real world context requiring the use of the Pythagorean Theorem.
Students are asked to find the angle of elevation in a real world situation modeled by a right triangle.
Students are asked to solve a problem in a real world context using the Pythagorean Theorem.
Original Student Tutorials Mathematics  Grades 912
Learn how to use trigonometric ratios to solve a realworld application. There are many famous monuments across the world. The measurements of these monuments were often found using trigonometric ratios. Today, there are devices that use laser beams to measure distances and heights, but trigonometric ratios are still widely used.
Student Resources
Original Student Tutorial
Learn how to use trigonometric ratios to solve a realworld application. There are many famous monuments across the world. The measurements of these monuments were often found using trigonometric ratios. Today, there are devices that use laser beams to measure distances and heights, but trigonometric ratios are still widely used.
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 Midcontinent Research for Education and Learning: 1) Analyze characteristics and properties of two and threedimensional 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 realworld 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
ProblemSolving 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.
Type: ProblemSolving Task
This problem solving task asks students to find the area of an equilateral triangle.
Type: ProblemSolving Task
This task engages students in an openended modeling task that uses similarity of right triangles.
Type: ProblemSolving 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: ProblemSolving Task
This 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.
Type: ProblemSolving Task
This modeling task involves several different types of geometric knowledge and problemsolving: 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: ProblemSolving 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: ProblemSolving 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
Virtual Manipulatives
This virtual manipulative will help the students in understanding that the relationships found in right triangles can be used to solve many applied problems in science and engineering. The right triangle solver manipulative displays a triangle with some its sides and angles given. The student is then asked to determine values of the remaining sides and angles by choosing a workable strategy.
Type: Virtual Manipulative
The triangle solver manipulative displays a triangle with some of its sides and angles given. The students are then asked to determine values of the remaining sides and angles. Students are motivated to choose a workable strategy such as using the Pythagorean theorem, the sine, cosine, tangent relationships, the law of sines, or the law of cosines. They are directed through the key steps of the chosen strategy to find the unknown sides and the angles.
Type: Virtual Manipulative
This web address, from the National Library of Virtual Manipulatives, will help teachers and students validate the Pythagorean Theorem both geometrically and algebraically. It can be used interactively with the Smartboard and the Promethean Board to create a better understanding of the topic.
Type: Virtual Manipulative
Parent Resources
ProblemSolving 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.
Type: ProblemSolving Task
This problem solving task asks students to find the area of an equilateral triangle.
Type: ProblemSolving Task
This task engages students in an openended modeling task that uses similarity of right triangles.
Type: ProblemSolving 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: ProblemSolving Task
This 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.
Type: ProblemSolving Task
This modeling task involves several different types of geometric knowledge and problemsolving: 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: ProblemSolving 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: ProblemSolving Task
Virtual Manipulatives
This virtual manipulative will help the students in understanding that the relationships found in right triangles can be used to solve many applied problems in science and engineering. The right triangle solver manipulative displays a triangle with some its sides and angles given. The student is then asked to determine values of the remaining sides and angles by choosing a workable strategy.
Type: Virtual Manipulative
The triangle solver manipulative displays a triangle with some of its sides and angles given. The students are then asked to determine values of the remaining sides and angles. Students are motivated to choose a workable strategy such as using the Pythagorean theorem, the sine, cosine, tangent relationships, the law of sines, or the law of cosines. They are directed through the key steps of the chosen strategy to find the unknown sides and the angles.
Type: Virtual Manipulative
This web address, from the National Library of Virtual Manipulatives, will help teachers and students validate the Pythagorean Theorem both geometrically and algebraically. It can be used interactively with the Smartboard and the Promethean Board to create a better understanding of the topic.
Type: Virtual Manipulative