S3+Hollingsworth+Tracey

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toc

=Stage 3 Plan Learning Experiences and Instruction= = = Logical: Kinesthetic: Visual: Naturalist: Intrapersonal: Interpersonal: Musical:**
 * 1. (W)** **Where** (Students understand that....), **Why** (Real Life), **What** (MLR)
 * 2. (H)** **Hook** (Engage)
 * 3. (E)** **Equip** (Content - Students will know...), **Explore** (Graphic Organizer), and **Experience** (Cooperative Learning)
 * 4. (R)** **Rethink, Revise, Rehearse,** and **Refine** (Timely Feedback)
 * 5. (E)** **Evaluate** (Self- Assessment)
 * 6. (T) Tailor** (Multiple Intelligences 6 to 8 and use each at least twice)
 * Verbal:
 * 7. (O)** **Organize** (Students will be able to ...) and Product:

Lesson 1 - Pythagorean Theorem
= =
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * **1.** **Where:** Students will understand that there are relationships among angles, lengths, and sides of right triangles. **Why:** Understanding the Pythagorean Theorem is the basis for understanding trigonometric ratios in right triangles**. What: MLR -** //Students understand and use basic ideas of trigonometry.//
 * 2. Hook:** Students will watch and listen to a [|Pythagoras Rap] which will set a foundation for proving the Pythagorean Theorem.
 * 3. Equip:** Students will know historical details about Pythagoras, the Pythagorean Theorem, multiple ways to prove the Pythagorean Theorem, and the relationship between the sides, lengths, and angles of a triangle. **Explore:** Students will use a graphic organizer to summarize the Pythagoras rap. They will also use the Pythagorean Theorem graphic organizers. **Experience:** Students will listen to the Pythagoras Rap individually, then put into groups using the "Parts of a Triangle" worksheet given at the beginning of the year. At the beginning of the year, students will fill out their "Parts of a Triangle" worksheet with their classmate's names. During the cooperative learning activity for this lesson, students will be paired with their "Hypotenuse" partners to hypothesize the Pythagorean Theorem proof. When the teams have finished collaborating, there will be a class discussion reviewing what they learned. Students will be able to review their information and edit it. After the class discussion, students will continue to work on individual assignments.
 * 4.** **Rethink:** Consider other proofs of the Pythagorean Theorem. **Revise/Refine:** Feedback will be given on the graphic organizers,proof, and outline. **Rehearse:** Students will use Inspiration software to create an outline for their project and create a flow chart of their proof of the Pythagorean Theorem.
 * 5.** **Evaluate**: There will be a pre/post blogging assignment to reflect.
 * 6. Tailor:**
 * **Verbal:** Students will be involved in pair, team, and class discussions. They will also be orally presenting their proof to the class.
 * **Logical:** Students will derive the proof of the Pythagorean Theorem.
 * **Kinesthetic:** Students will be moving around the classroom getting in/out of group formation.
 * **Visual:** There will be a visual aide to the Pythagorean Theorem proof. The Pythagorean Theorem will be displayed geometrically and algebraically.
 * **Naturalist:** Homework will include finding right triangles outside the classroom.
 * **Intrapersonal:** Students will be involved in group work.
 * **Interpersonal:** Students will work individually during certain parts of the lesson and will be required to reflect on the class activities.
 * **Musical:** The hook for this lesson is a rap about the Pythagorean Theorem.
 * 7. (O)** **Organize** Students will be able to prove the Pythagorean Theorem. **Product:** Create a digital compilation of right triangle pictures, flowchart, and geometric representation of the Pythagorean Theorem proof. ||

Lesson 2 - Special Triangles
= =
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * **8.** **Where:** Students will understand that certain triangles possess specific "special" properties that allow us to find information about a triangle. **Why:** Understanding special right triangles will allow students to perform calculations easier. **What: MLR -** //Students understand and use basic ideas of trigonometry.//
 * 9. Hook:** Students will [|explore] certain triangles to learn why they are considered "special" and how they make calculations easier.
 * 10. Equip:** Students will know how to use their knowledge of "special" right triangles to solve right triangles. **Explore:** Students will use a graphic organizer to organize and visualize the multiple relationships within a triangle and trigonometric ratios. **Experience:** Students will individually [|explore] "special" triangles, then will be put into groups using the "Parts of a Triangle" worksheet given at the beginning of the year. At the beginning of the year, students will fill out their "Parts of a Triangle" worksheet with their classmate's names. During the cooperative learning activity for this lesson, students will be paired with their "Angle" partners to work on "Dragon" assignment. After the class discussion, students will continue to work on individual assignments.
 * 11.** **Rethink:** Students will think about Lesson 1 and its' relationship to this lesson. **Revise/Refine:** **Rehearse:** Students will take a short quiz.
 * 12.** **Evaluate**: There will be a pre/post blogging assignment to reflect.
 * 13. Tailor:**
 * **Verbal:** Students will be involved in pair, team, and class discussions.
 * **Logical:** Students will work through specific steps to solve a problem.
 * **Kinesthetic:** Students will be moving around the classroom getting in/out of group formation.
 * **Visual:** Students will draw and comment on a VoiceThread. They will also have graphic organizers to organize their material and information.
 * **Naturalist: --**
 * **Intrapersonal:** Students will be involved in group work.
 * **Interpersonal:** Students will work individually during certain parts of the lesson and will be required to reflect on the class activities.
 * **Musical:** Students will have the option of using music in their VoiceThread.
 * 14. (O)** **Organize** Students will be able to solve a right triangle based on the "special" properties of 45°-45°-90° and 30°-60°-90° triangles. **Product:** Interactive discussion about "special" right triangles via VoiceThread. ||

Lesson 3 - Sine & Cosine Ratios

 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * **15.** **Where:** Students will understand what trigonometry and trigonometric ratios are. **Why:** When sides and angles of a triangle are known, trigonometric relationships can be used to find unknown parts. **What: MLR -** //Students understand and use basic ideas of trigonometry.//
 * 16. Hook:** Students will learn about trigonometric ratios and the acronym [|"SOHCAHTOA"].
 * 17. Equip:** Students will know who the "father of trigonometry" is and understand the meaning of trigonometry. Students will know how trigonometric functions are used to determine information to solve right triangles. **Explore:** Students will use a graphic organizer to organize and visualize the sine and cosine trigonometric ratios. **Experience:** Students will individually explore sine and cosine using [|virtual manipulatives]. Then they will work on the "Investigate Trigonometry" handout. Although students are working individually, they may quietly collaborate with the person sitting next to them. Once completed, there will be a class discussion to compare and converse about the results. Students will be able to review their information and edit it. After the class discussion, practice problems will be given and students will continue to work on individual assignments.
 * 18.** **Rethink:** Students will reconsider the importance of trigonometric functions and their relationships within right triangles. **Revise/Refine:** Feedback will be given on their investigative handout. **Rehearse:** Students will use their knowledge about "special" triangle properties to determine the sine and cosine ratios of 45°-45°-90° and 30°-60°-90° triangles.
 * 19.** **Evaluate**: There will be a pre/post blogging assignment to reflect.
 * 20. Tailor:**
 * **Verbal:** Students will be involved in team, and class discussions.
 * **Logical:** Students will use a step-by-step process of solving a right triangle.
 * **Kinesthetic:** Students will be moving around the classroom getting in/out of group formation.
 * **Visual:** There will be a visual aide to the trigonometric ratios. The trigonometric ratios will be displayed geometrically and algebraically.
 * **Naturalist:** Students will work on part of the "In the Park" handout which portrays some of the right triangles that are found outdoors.
 * **Intrapersonal:** Students will be involved in group work.
 * **Interpersonal:** Students will work individually during certain parts of the lesson and will be required to reflect on the class activities.
 * **Musical:** Classical music will be played while students are in groups.
 * 21. (O)** **Organize**: Students will be able to relate the sides of a triangle to its' hypotenuse by using trigonometric functions. **Product:** Create a PowerPoint slide defining one of the trigonometric functions by graphically showing how to solve a right triangle using that specific trigonometric function. ||



Lesson 4 - Tangent Ratios
= = = =
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * **22.** **Where:** Students will understand that there are trigonometric functions that can be used to determine information about right triangles. **Why:** When sides and angles of a triangle are known, trigonometric relationships can be used to find unknown parts. **What: MLR -** //Students understand and use basic ideas of trigonometry.//
 * 23. Hook:** Students will see a quick demonstration of how the [|tangent] function is used in the real world.
 * 24. Equip:** Students will know how trigonometric functions are used to determine information to solve right triangles. **Explore:** Students will add to their "Sine and Cosine" graphic organizer to organize and visualize the tangent trigonometric ratio. **Experience:** Students will individually explore tangent using [|virtual manipulatives], then they will finish their "In the Park" handout. Once completed, there will be a class discussion to compare and converse about the results. Students will be able to review their information and edit it. After the class discussion, practice problems will be given and students will continue to work on individual assignments.
 * 25.** **Rethink:** Students will rethink slope (rise/run) and relate it to the tangent ratio. **Revise/Refine:** Feedback will be given on their practice problems. **Rehearse:** Students will write a rule or mnemonic device to remember trigonometric ratios.
 * 26.** **Evaluate**: There will be a pre/post blogging assignment to reflect.
 * 27. Tailor:**
 * **Verbal:** Students will be involved in team, and class discussions.
 * **Logical:** Students will use a step-by-step process of solving a right triangle.
 * **Kinesthetic: --**
 * **Visual:** There will be a visual aide to the trigonometric ratios. The trigonometric ratios will be displayed geometrically and algebraically.
 * **Naturalist:** Students will work on part of the "In the Park" handout which portrays some of the right triangles that are found outdoors.
 * **Intrapersonal:** Students will participate in a class discussion.
 * **Interpersonal:** Students will work individually and will be required to reflect on the class activities.
 * **Musical: --**
 * 28. (O)** **Organize** Students will be able to compare the different trigonometric ratios. **Product:** Interactive discussion about "tangent ratios" of right triangles via VoiceThread. ||

Lesson 5 - Investigate Trigonometric Ratios
 || > > > **35. (O)** **Organize** Students will be able to represent real world problems geometrically. **Product:** Students will take a screen shot of the scaled drawings they created on Geometer's Sketchpad, prepare a slide or slides with the necessary mathematical information and pictures of giant sequoias, make a pdf of the slide, and link it to the class wiki. ||  || = = = =
 * <span style="color: rgb(0, 0, 0);">**Consider the W.H.E.R.E.T.O. elements**. **(L)**
 * <span style="color: rgb(0, 0, 0);">**29.** **Where:** Students will understand that trigonometric functions can be applied to solve real world problems. **Why:** Understanding how trigonometry is used in real world will help students realize the importance of mathematics. **What: MLR -** //Students understand and use basic ideas of trigonometry.//
 * 30. Hook:** Trigonometry [|cartoon].
 * 31. Equip:** Students will know how to build a hypsometer/clinometer, measure the height of objects, and make scaled drawings showing angles and measures. **Explore:** Students will use a graphic organizer to record their measurements and provide a rough sketch of their final product. **Experience:** Students will investigate real world trigonometric ratios in groups using the "Parts of a Triangle" worksheet given at the beginning of the year. At the beginning of the year, students will fill out their "Parts of a Triangle" worksheet with their classmate's names. During the cooperative learning activity for this lesson, students will be paired with their "Adjacent" partners. When the teams have finished collaborating, there will be a class discussion reviewing what they learned. Students will be able to review their information and edit it. After the class discussion, students will continue to work on individual assignments.
 * 32.** **Rethink:** <span style="color: rgb(0, 0, 0);">Students will revisit the Pythagorean Theorem and trigonometric ratios. **Revise/Refine:** Feedback will be given on their practice problems, graphic organizer, and rough draft. **Rehearse:** Students will create a rough sketch of their final product.
 * 33.** **Evaluate**: There will be a pre/post blogging assignment to reflect.
 * 34. Tailor:**
 * <span style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0);">**Verbal:** Students will be reading word problems, participating in group and class discussions, and writing explanations of their mathematical work.
 * <span style="color: rgb(0, 0, 0);">**Logical:** Students will derive a geometrical approach to solving word problems.
 * <span style="color: rgb(0, 0, 0);">**Kinesthetic:** Students will be moving around the classroom getting in/out of group formation.
 * <span style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0);">**Visual:** Students will d raw a geometric representation of trigono metric word problems.
 * <span style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0);">**Naturalist:** Weather permitting, this project will be worked on outside.
 * <span style="color: rgb(0, 0, 0);">**Intrapersonal:** Students will be involved in group work.
 * <span style="color: rgb(0, 0, 0);">**Interpersonal:** Students will work individually during certain parts of the lesson and will be required to reflect on the class activities.
 * <span style="color: rgb(0, 0, 0);">**Musical:** **--**

<span style="color: rgb(0, 0, 0);">Lesson 6 - Life Applications of Triangular Trigonometry
<span style="color: rgb(255, 0, 0);"> <span style="color: rgb(0, 0, 0);">**37. Hook:** Students will [|explore] trigonometry in the real world. <span style="color: rgb(0, 0, 0);">**40.** **Evaluate**: There will be a pre/post blogging assignment to reflect. > > > <span style="color: rgb(255, 0, 0);"><span style="color: rgb(255, 0, 0);">**<span style="color: rgb(0, 0, 0);">42. (O) **<span style="color: rgb(0, 0, 0);"> **Organize** Students will be able to realize where trigonometry is used, other than in a classroom. <span style="color: rgb(0, 0, 0);">**Product:** Students will create a wordle that will be embedded on the class wiki with all of the words they think of when they hear the words "right triangle" and "trigonometry" <span style="color: rgb(0, 0, 0);">. ||
 * <span style="color: rgb(0, 0, 0);">**Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * <span style="color: rgb(255, 0, 0);"><span style="color: rgb(0, 0, 0);">**36.** **Where:** Students will understand why trigonometry is important in real life, not just in the classroom. **Why:** Many students do not understand the importance of mathematics. This lesson will relate what they have learned to their life. **What: MLR -** //<span style="color: rgb(0, 0, 0);">Students understand and use basic ideas of trigonometry .//
 * 38. Equip:** Students will know that right triangles occur in many real life situations which can be used to indirectly measure lengths and distances. Students will know how to determine what trigonometric ratio can be used to solve the word problem and represent it geometrically.<span style="color: rgb(0, 0, 0);"> Explore: Students will use a graphic organizer to organize their steps for solving their practice problems. **Experience:** Students will be put into groups using the "Parts of a Triangle" worksheet given at the beginning of the year. At the beginning of the year, students will fill out their "Parts of a Triangle" worksheet with their classmate's names. During the cooperative learning activity for this lesson, students will be paired with their "Inverse" partners to practice real life word problems. Once completed, there will be a class discussion to compare and converse about the results. Students will be able to review their information and edit it. After the class discussion, sample problems will be given and students will start their WebQuest.
 * 39.** **Rethink:** Students will reconsider the importance of trigonometric functions and their relationships within right triangles. <span style="color: rgb(255, 0, 0);"> <span style="color: rgb(0, 0, 0);">**Revise/Refine:** Feedback will be given on their graphic organizer and practice problems. **Rehearse:** achieve a deeper and richer experience.
 * 41. Tailor:**
 * <span style="color: rgb(0, 0, 0);">**Verbal:** <span style="color: rgb(0, 0, 0);">Students will be reading word problems, participating in group and class discussions, and defend their mathematical work.
 * <span style="color: rgb(0, 0, 0);">**Logical:** Students will analyze a real world situation and deduce a way to solve it using trigonometry. Students will use a step-by-step process of solving a right triangle.
 * <span style="color: rgb(0, 0, 0);">**Kinesthetic:** Students will be moving around the classroom getting in/out of group formation.
 * <span style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0);">**Visual:** Students will solve real world problems by setting up a geometrical representation of the word problem.
 * <span style="color: rgb(0, 0, 0);"><span style="color: rgb(0, 0, 0);">**Naturalist:** Many of the interdisciplinary applications of trigonometry include navigation, meteorology, forestry, farming, etc.
 * <span style="color: rgb(0, 0, 0);">**Intrapersonal:** Students will be involved in group work.
 * <span style="color: rgb(0, 0, 0);">**Interpersonal:** Students will work individually during certain parts of the lesson and will be required to reflect on the class activities.
 * <span style="color: rgb(0, 0, 0);">**Musical:** Classical music will be played while students are in groups.

2004 ASCD and Grant Wiggins and Jay McTighe