## Course Standards

## General Course Information and Notes

### General Notes

**Honors and Advanced Level Course Note: **Advanced courses require a greater demand on students through increased academic rigor. Academic rigor is obtained through the application, analysis, evaluation, and creation of complex ideas that are often abstract and multi-faceted. Students are challenged to think and collaborate critically on the content they are learning. Honors level rigor will be achieved by increasing text complexity through text selection, focus on high-level qualitative measures, and complexity of task. Instruction will be structured to give students a deeper understanding of conceptual themes and organization within and across disciplines. Academic rigor is more than simply assigning to students a greater quantity of work.

**English Language Development ELD Standards Special Notes Section:**

Teachers are required to provide listening, speaking, reading and writing instruction that allows English language learners (ELL) to communicate information, ideas and concepts for academic success in the content area of Mathematics. For the given level of English language proficiency and with visual, graphic, or interactive support, students will interact with grade level words, expressions, sentences and discourse to process or produce language necessary for academic success. The ELD standard should specify a relevant content area concept or topic of study chosen by curriculum developers and teachers which maximizes an ELL’s need for communication and social skills. To access an ELL supporting document which delineates performance definitions and descriptors, please click on the following link:

http://www.cpalms.org/uploads/docs/standards/eld/MA.pdf

### General Information

**Course Number:**1211300

**Course Path:**

**Abbreviated Title:**TRIG HON

**Number of Credits:**Half credit (.5)

**Course Length:**Semester (S)

**Course Attributes:**

- Honors

**Course Type:**Core Academic Course

**Course Level:**3

**Course Status:**Course Approved

**Grade Level(s):**9,10,11,12

**Graduation Requirement:**Mathematics

## Educator Certifications

## Student Resources

## Original Student Tutorials

Practice identifying faulty reasoning in this two-part, interactive, English Language Arts tutorial. You'll learn what some experts say about year-round schools, what research has been conducted about their effectiveness, and how arguments can be made for and against year-round education. Then, you'll read a speech in favor of year-round schools and identify faulty reasoning within the argument, specifically the use of hasty generalizations.

Make sure to complete Part One before Part Two! **Click HERE to launch Part One.**

Type: Original Student Tutorial

Learn to identify faulty reasoning in this two-part interactive English Language Arts tutorial. You'll learn what some experts say about year-round schools, what research has been conducted about their effectiveness, and how arguments can be made for and against year-round education. Then, you'll read a speech in favor of year-round schools and identify faulty reasoning within the argument, specifically the use of hasty generalizations.

Make sure to complete both parts of this series! Click HERE to open Part Two.

Type: Original Student Tutorial

Examine President John F. Kennedy's inaugural address in this interactive tutorial. You will examine Kennedy's argument, main claim, smaller claims, reasons, and evidence.

In Part Four, you'll use what you've learned throughout this series to evaluate Kennedy's overall argument.

Make sure to complete the previous parts of this series before beginning Part 4.

Type: Original Student Tutorial

Examine President John F. Kennedy's inaugural address in this interactive tutorial. You will examine Kennedy's argument, main claim, smaller claims, reasons, and evidence. By the end of this four-part series, you should be able to evaluate his overall argument.

In Part Three, you will read more of Kennedy's speech and identify a smaller claim in this section of his speech. You will also evaluate this smaller claim's relevancy to the main claim and evaluate Kennedy's reasons and evidence.

Make sure to complete all four parts of this series!

Type: Original Student Tutorial

Want to learn about Amelia Earhart, one of the most famous female aviators of all time? If so, then this interactive tutorial is for YOU! This tutorial is Part Two of a two-part series. In this series, you will study a speech by Amelia Earhart. You will practice identifying the purpose of her speech and practice identifying her use of rhetorical appeals (ethos, logos, pathos, Kairos). You will also evaluate the effectiveness of Earhart's rhetorical choices based on the purpose of her speech.

Please complete Part One before beginning Part Two. Click HERE to view Part One.

Type: Original Student Tutorial

Want to learn about Amelia Earhart, one of the most famous female aviators of all time? If so, then this interactive tutorial is for YOU! This tutorial is Part One of a two-part series. In this series, you will study a speech by Amelia Earhart. You will practice identifying the purpose of her speech and practice identifying her use of rhetorical appeals (ethos, logos, pathos, Kairos). You will also evaluate the effectiveness of Earhart's rhetorical choices based on the purpose of her speech.

Please complete Part Two after completing this tutorial. Click HERE to view Part Two.

Type: Original Student Tutorial

Learn how to use trigonometric ratios to solve a real-world 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

Learn about the radian measures of an angle, finding an angle measure in radians given the arc length and length of the radius, and converting between degree measures and radian measures in this interactive tutorial.

Type: Original Student Tutorial

## Educational Game

This is an online game where students are asked to navigate a boat using vectors to reach a goal. There are 3 different modes of the game to help students deepen their understanding of the concept. This game is to be used in conjunction with a full lesson on vectors.

Type: Educational Game

## Perspectives Video: Experts

The tide is high! How can we statistically prove there is a relationship between the tides on the Gulf Coast and in a fresh water spring 20 miles from each other?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Let this video on wing design lift you up!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

The director of the National High Magnetic Field Laboratory describes electromagnetic waves.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Don't let the motion of the ocean cause a commotion! Learn how vectors describe ocean movement patterns.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

Math is important to help you get where you want to go in life, especially if you plan to fly there!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

When you watch this video, your knowledge related to flight and physics will really take off!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

## 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.

Type: Problem-Solving Task

This problem solving task asks students to find the area of an equilateral triangle.

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 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: 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

This problem solving task challenges students to use trigonometric functions to model the number of rabbits and foxes as a function of time.

Type: Problem-Solving Task

This problem solving task challenges students to trigonometric functions to model the populations of rabbits and foxes over time, and then graph the functions.

Type: Problem-Solving Task

In this task, students use trigonometric functions to model the movement of a point around a wheel and, through space. Students also interpret features of graphs in terms of the given real-world context.

Type: Problem-Solving Task

This problem is intended to reinforce the geometric interpretation of distance between complex numbers and midpoints as modulus of the difference and average respectively.

Type: Problem-Solving Task

## Tutorials

This tutorial gives an introduction to the unit circle. It also extends the students knowledge of SOH CAH TOA so that they can define trigonometric functions for a broader class of angles.

Type: Tutorial

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

This resource explores the electromagnetic spectrum and waves by allowing the learner to observe the refraction of light as it passes from one medium to another, study the relation between refraction of light and the refractive index of the medium, select from a list of materials with different refractive indicecs, and change the light beam from white to monochromatic and observe the difference.

Type: Tutorial

- Observe how the eye's muscles change the shape of the lens in accordance with the distance to the object being viewed
- Indicate the parts of the eye that are responsible for vision
- View how images are formed in the eye

Type: Tutorial

- Learn how a concave spherical mirror generates an image
- Observe how the size and position of the image changes with the object distance from the mirror
- Learn the difference between a real image and a virtual image
- Learn some applications of concave mirrors

Type: Tutorial

- Learn how a convex mirror forms the image of an object
- Understand why convex mirrors form small virtual images
- Observe the change in size and position of the image with the change in object's distance from the mirror
- Learn some practical applications of convex mirrors

Type: Tutorial

- Observe the change of color of a black body radiator upon changes in temperature
- Understand that at 0 Kelvin or Absolute Zero there is no molecular motion

Type: Tutorial

This resource explains how a solar cell converts light energy into electrical energy. The user will also learn about the different components of the solar cell and observe the relationship between photon intensity and the amount of electrical energy produced.

Type: Tutorial

- Observe that light is composed of oscillating electric and magnetic waves
- Explore the propagation of an electromagnetic wave through its electric and magnetic field vectors
- Observe the difference in propagation of light of different wavelengths

Type: Tutorial

- Explore the relationship between wavelength, frequency, amplitude and energy of an electromagnetic wave
- Compare the characteristics of waves of different wavelengths

Type: Tutorial

- Learn to trace the path of propagating light waves using geometrical optics
- Observe the effect of changing parameters such as focal length, object dimensions and position on image properties
- Learn the equations used in determining the size and locations of images formed by thin lenses

Type: Tutorial

## Video/Audio/Animations

With an often unexpected outcome from a simple experiment, students can discover the factors that cause and influence thermohaline circulation in our oceans. In two 45-minute class periods, students complete activities where they observe the melting of ice cubes in saltwater and freshwater, using basic materials: clear plastic cups, ice cubes, water, salt, food coloring, and thermometers. There are no prerequisites for this lesson but it is helpful if students are familiar with the concepts of density and buoyancy as well as the salinity of seawater. It is also helpful if students understand that dissolving salt in water will lower the freezing point of water. There are additional follow up investigations that help students appreciate and understand the importance of the ocean's influence on Earth's climate.

Type: Video/Audio/Animation

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations.

Type: Video/Audio/Animation

## 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

In this online tool, students input a function to create a graph where the constants, coefficients, and exponents can be adjusted by slider bars. This tool allows students to explore graphs of functions and how adjusting the numbers in the function affect the graph. Using tabs at the top of the page you can also access supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

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

Students investigate shapes that grow and change using an iterative process. Fractals are characterized by self-similarity, smaller sections that resemble the larger figure. From NCTM's Illuminations.

Type: Virtual Manipulative

Section:Grades PreK to 12 Education Courses >Grade Group:Grades 9 to 12 and Adult Education Courses >Subject:Mathematics >SubSubject:Trigonometry >