S3+Mitchell,+Jesse

=Stage 3 Plan Learning Experiences and Instruction=


 * 1. (W)** **Where** (Understanding), **Why** (Real Life), **What** (MLR) and Product
 * 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)
 * 7. (O)** **Organize** (Facet of Understanding - Students will be able to ...)

=Lesson 1= 2.Begin by having students map certain similarities between classmates using the flow sheet on the board. 3.Students will know important formulas: sin, cos, tan, cot, sec, csc. (**Equip**) Students will use a series of flow charts to begin thinking about the different ways in which the important formulas are related. (**Explore**) Students will work in pairs in order to brainstorm ideas. (**Experience**) 4. Students will now pair up with a another set of partners and discuss their charts so far. (**Rethink**) Students can make any changes they would like at based on any information they have gathered from their new partners. Next they will find a different set of partners and repeat. (**Revise**) Students will have the opportunity to present any information they have gathered throughout the activity. (**Rehearse**) The class will then continue a discussion based on what the students had written in their flow charts. By the end of the discussion, students should have revised their flow charts accordingly. (**Refine**) 5. Students will then use the software Inspiration to bring their flow chart to life, and to organize the information in any way that best makes sense to them. (**Evaluate**) Students will also have to complete a blog entry that describes the day's events. The blog is to be posted by the start of next the class period. 6.**Logical**- Students are uncovering logical relationships. 7.Students will be able to show the relationships between the six trigonometric functions. (**Organize**) || = =
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 1.Trigonometry is a branch of Mathematics that deals mainly with right triangles, and the relationships between their sides and angles.(**Where**) This will give students a general introduction the concepts that go into many occupations, such as carpentry, road construction, etc. (**Why**) //Students understand and use basic ideas of trigonometry.// (**What**) Product: Flow Chart using Inspiration.
 * Verbal**- Students are brainstorming ideas.
 * Interpersonal**- Students will be working with partners, then collaborating with other partners.
 * Spatial**- Students will be using Inspiration to visualize the relationships between the functions.
 * Intrapersonal**- Students will be using Inspiration independently in order to create the model that best makes sense to them.
 * Bodily-Kinesthetic**- Students will be up and moving around during the Rethink and Revise stages.

= = =Lesson 2=

9. [|Unit Circle vs Function Graphs] and [|Alternate View Unit Circle Graph] 10.Students will know terminology (unit circle) and relationships (between the 6 trigonometric functions and the unit circle.). (**Equip**) Students will be give a piece of graphing paper, with a circle already drawn for them. They must hold onto this paper throughout the lecture, and fill in each section as necessary. (**Explore**) Students will work alone to gather most of their information, and then can consult with a partner of their choice to compare the validity of their answers. While students are working, music will be played quietly in the background. (**Experience**) 11. Students will compare with a partner their unit circle sketches so far. (**Rethink**) Students can make any changes and ask any questions they would like at this point, and update their sketch accordingly. (**Revise**) Students will take turns explaining their unit circle graphs to their partner. (**Rehearse**) Students will then create a final draft of their sketch to be handed in. (**Refine**) 12. The class discussion will continue as I walk through each step of the unit circle one more time, so that students may take notes on any errors they may have made. (**Evaluate**) 13.**Logical**- Students will be uncovering relationships between unit circle and 6 trig functions. 14. Students will be able to make sense of the unit circle, and its relationship to the trigonometric functions.(**Organize**) || = =
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 8.The unit circle is a fundamental part of Trigonometry. (**Where**) This lesson is essential for students to understand the basis behind the trigonometric functions they learned earlier (as well as to the performance task they will develop later in the unit) (**Why**) //Students understand and use basic ideas of trigonometry.// (**What**) Product: A sketch of the unit circle including all 6 trigonometric functions.
 * Musical**-Background music is playing while students do in class work.
 * Intrapersonal**- Students do most of the work independently during lecture.
 * Interpersonal**- Students compare sketch with one parter of their choice.
 * Bodily-Kinesthetic**- Students are sketching out unit circle, with the freedom to walk around the room for any typr of supply they might need (more graph paper, colored pencils, etc).
 * Verbal**- Will be having class discussion
 * Spatial**- Sketches and Applets will allow visual learners to see exactly where the trigonometric functions derive from.

= = =Lesson 3=

16. Begin by asking leading questions such as "Can any of you name a profession that utilizes trigonometry?", "How can you use trigonometry in your daily life? In nature?" 17. Students will know terminology: reciprocal, opposite, adjacent, unit circle, and relationships: between trigonometric functions, and between the different parts of a triangle. (**Equip**) Students will be given plenty of scratch paper throughout the lesson to map out ideas for problem solving. (**Explore**) Students will be put into groups of 2-3 in order to solve for the missing heights of certain trees in the schoolyard. (**Experience**) 18. Students will meet with their partners to discuss a game plan for problem solving. (**Rethink**) Students are then given the opportunity to ask any questions they have about problem solving with trigonometric functions. (**Revise**) Students will practice presenting their information to the class. (**Rehearse**) Students will then go outside to complete the work and hand in a final copy of their work at the end of class. (**Refine**) Students will also have a questionnaire to fill out at the end of the lesson. The questionnaire will be for informational purposes only, and will not be graded. It will cover questions relating to how the students felt about the group, as well as the activity itself. 19. Students will then have an opportunity to reflect on the activity at hand, with one last chance to ask questions before the period ends. (**Evaluate**) 20.**Logical**- Solving for missing lengths in a right triangle. 21. Students will be able to use trigonometry to solve for missing lengths in right triangles (**Organize**) || = =
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 15. The six trigonometric functions are essential in solving for unknowns within a right triangle. (**Where**) This lesson will give students the abilities to solve real-life problems using trigonometry. (**Why**) //Students understand and use basic ideas of trigonometry.// (**What**) Product: Worksheet showing all steps of how the height of certain trees in the school yard were found.
 * Interpersonal**- Working in groups of 2-3.
 * Verbal**-Discuss/Sketch problem solving ideas in class.
 * Spatial**- Go outside to visualize the trees in context.
 * Naturalist**- Spend part of the class period outside, solving for missing heights of trees.
 * Bodily-Kinesthetic**- Students are up and moving around most of the class period.

=Lesson 4=

23. Leading Questions: "How do you remember the 6 trigonometric functions?" "Is there an easier way?" 24.Students will know Relationships: between trigonometric functions, and between the different parts of a triangle. (**Equip**) Student will use OneNote to take notes throughout the lesson, as well as to map out ideas/tricks to remember the six trigonometric functions. (**Explore**) Students will work in groups of 3 to brainstorm at least 2 ways to remember the 6 trig functions. Music will be playing in the background as students work. (**Experience**) 25. Students will discuss their ideas with their partners. (**Rethink**) Students will then jot down all parts of the thinking process in OneNote, and update their ideas. (**Revise**) Students will read through notes and correct any remaining errors before handing in papers. (**Rehearse**) Students then hand in final copy to teacher, based on all their work in OneNote, as well as a copy of their OneNote notes. (**Refine**) 26. At the end of class students will be given an quiz that will show their ability to apply their knowledge of the six trigonometric functions to new situations. The quiz will not be graded. It is simply to show their progress, and to adjust teaching methods if need be. (**Evaluate**) 27.**Logical**- Brainstorming and applying trigonometric concepts to new situations. 28. Students will be able to recognize which trigonometric functions should be used in certain contexts. (**Organize**) || = =
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 22. Trigonometry is a branch of Mathematics that deals mainly with right triangles, and the relationships between their sides and angles. (**Where**) Trigonometry is an important part of real life, as this lesson and the next will emphasize, so it is important to understand when each function is used, as well as ways to remember the six trigonometric functions. (**Why**) //Students understand and use basic ideas of trigonometry.// (**What**) Product: OneNote organized set of notes showing thinking process.
 * Interpersonal**- Work with partners to brainstorm ideas.
 * Interpersonal**- Take assessment individually to receive individualized feedback.
 * Verbal**- Brainstorming about trigonometry.
 * Spatial**- Using OneNote to organize ideas.
 * Musical**- Background music plays as students work.

= = =Lesson 5=

30. [|That's Mathematics!] Video 31.Students will know all of the skills learned in previous lessons, as well as how to relate them to real life. (**Equip**) Students will be given a worksheet with a few sample professions to get them thinking about different ways each occupation could utilize a knowledge of trigonometry. Will focus on one occupation to explore in depth. [lumber jack] Students may also reenact profession to help them to think of ways to apply trigonometry. (**Explore**) Students will then pick an occupation to research, and write a one page paper including what the occupation is, how it utilizes trigonometry, and what would happen if trigonometry hadn't been invented yet. (**Experience**) 32. Students will work in class, and will continue to ask questions to the teacher as well as their peers. (**Rethink**) Students will revise their work as the class discussion develops. (**Revise**) Students will choose a peer to discuss the worksheet with before handing it in. (**Rehearse**) Students will submit ideas before the end of class, and will be given suggestions on submitted ideas before papers are due. (**Refine**) 33. Students will be given a self-evaluation checklist/rubric to help them focus their thoughts while writing the paper. (**Evaluate**) 34 **All 8**- One example of each will be included on the sample worksheet, allowing students to broaden their focus. 35. Students will be able to relate trigonometry to real-life situations. || = =
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 29. The six trigonometric functions are essential in solving for unknowns within a right triangle. (**Where**) This section continues off of the last lesson, further explaining the real-life importance of trigonometric functions, why they are necessary to know, and their role in real-life professions. (**Why**) //Students understand and use basic ideas of trigonometry.// (**What**) Product: One page paper on a profession that utilizes trigonometry, posted to blog entry, and including at least one link.
 * Logical**- Students must show examples of how each profession utilizes trigonometry.
 * Musial**- Class began with song about real life mathematical applications.
 * Intrapersonal**- Students work on papers individually.
 * Verbal**- Ongoing class discussion about professions.
 * Spatial**- Worksheet includes pictures of each sample profession, as well as how they utilize trigonometry.
 * Naturalist**- Discussion of the importance of Trigonometry to lumber jacks.
 * Bodily-Kinesthetic**- Students have option of reenacting professions.

= = =Lesson 6=

37. [|New Math] Video 38. Students will know all knowledge learned in previous lessons. (**Equip**) Students will be given a worksheet that they will fill out comparing different approaches to problem solving, as well as the pros and cons of each. (**Explore**) Students will work individually to brainstorm, then create groups of 2-3 to compare responses. The class will end with a class discussion. (**Experience**) 39. Students will be given the opportunity to review answers with (a) partner(s). (**Rethink**) Students will be given the opportunity to continually update worksheets until the end of the period (**Revise**) Students will talk with teacher one on one for individual feedback. (**Rehearse**) During class discussion, the teacher will give any additional feedback based on any ideas students wish to talk about. (**Refine**) 40.Students will hand in their worksheets at the end of the class period, and be given a venn diagram for homework, where they research and compare 2 approaches in depth. (**Evaluate**) 41. **Verbal**- Class discussion. 42.Students will be able to compare different approaches to solving problems. ||
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 36. The six trigonometric functions are essential in solving for unknowns within a right triangle. (**Where**) It is important to take several view points into consideration, as some approaches may be more suitable than others. (**Why**) //Students understand and use basic ideas of trigonometry.// (**What**) Product: Worksheet to be handed in at the end of class.
 * Logical**- Brainstorming ways to problem solve.
 * Interpersonal**- Share brainstorming with a partner.
 * Intrapersonal**- Do initial brainstorming individually.
 * Spatial**- Filling out chart of pros and cons, as well as venn diagram.
 * Musical**- Class began with song about different approaches to problem solving.

2004 ASCD and Grant Wiggins and Jay McTighe