S3+McKeown,+Sarah

=Stage 3 - Plan Learning Experiences and Instruction=

// **Note:** // (How are you using technology as a teacher? How are your students using technology?) [|Verbal-Linguistic] [|Logical/Mathematical] [|Visual/Spatial] [|Bodily/Kinesthetic] [|Musical/Rhythmic] [|Intrapersonal] [|Interpersonal] [|Naturalist]
 * 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]), **Experience** ([|Cooperative Learning]), and Resources (Include Web resources)
 * 4. (R)** **Rethink, Revise, Rehearse,** and **Refine** (Feedback, [|Checking for Understanding])
 * 5. (E)** **Evaluate** (Formative Assessment)
 * 6. (T) Tailor** (give an example of each Multiple Inteligences)
 * 7. (O)** **Organize** (Students will be able to ...), Product (Technology) [|Recipes4Success Lesson Library]. Here you will find exciting, standards-based lessons for Tech4Learning products. Each lesson includes step-by-step directions for both teachers and students, as well as links to high-quality examples, templates, and support resources.

=Part 1= 2. I will begin this lesson by asking the class if they have ever done something that seemed logical in the moment but later it turned out to be the wrong thing (share an example: Cleaning a car with Lysol because it was an "all purpose" cleaner only to find the paint on the car peeling a month later)? I will then explain that in this lesson we are going to take the preventative measures to ensure we never do that with the Pythagorean Theorem (a concept that will be discussed in the next lesson) (hook). 3. Students will know the difference between a right triangle and another triangle and will also be able to determine if the information given in a problem is enough to accurately use the Theorem (equip). Students will use a Venn Diagram to illustrate the similarities and differences between right triangles and non-right triangles (explore). Students will "dissect" a triangle as we examine its properties and expose how all the components together define what a right triangle is (experience). 4. To recenter the concept of the day, the class will be presented with thought provoking questions that explore the importance of right triangles in students' lives. Based on the confidence of the answers, I will try explaining the concept in a manner more appropriate for the class's needs (for example, if the class was primarily visual learners, I would spend more time using pictures et cetera) (revise and refine). 5. For a formative assessment, I will have students close their eyes and using their fingers, indicate on a scale of 1 - 5 how confident they feel on individual aspects of right triangles and non-right triangles so far (evaluate). 6. **Verbal Linguistic**: as always, I plan on presenting this lesson using a collection of spoken nouns and verbs to convey my thought process and the correct approach when evaluating triangles. 7. From this lesson, students will be able to evaluate a triangle and determine if it is right or not. Students will demonstrate their understanding through a Blog entry. Anticipated time - one 80-minute lesson (or less). || =Part 2=
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 1. Students will be able to recognize a right triangle (where). Learning this will enable students to use this powerful tool appropriately so that they will be able to construct decent and functional projects in the future (remember the bridge collapsing?) (why). This lesson will also meet the This lesson meets the Maine Learning Results: Mathematics - C. Geometry, Geometric Figures, Grades 9 - Diploma 1. c. Use the Pythagorean Theorem in situations where right triangles are created by adding segments to figures.
 * Mathematical Logical**: as always, I plan on giving a step by step break down of things to look for when determining whether or not a triangle is right or not.
 * Visual Spacial**: as in all geometry classes, I plan on always using visual representations of the shape being discussed and interacting with and utilizing the picture as the lesson develops.
 * Bodily Kinesthetic**: in this lesson, the hands-on constructing of triangles will help the bodily kinesthetic learner to gain first-hand experience with triangles which, hopefully, will solidify the concept of triangle make-up (something that will serve as a basis for all other lessons).
 * Musical Rhythmic**: for my musical learners, I have made up a little rhyme which will hopefully help them to remember the lesson: a leg and a leg together with a right angle, makes the hypotenuse easy to untangle.
 * Intrapersonal:** for the intrapersonal learners, I feel that the time at the beginning of class which we reflect upon the importance of doing things the right way and stressing the importance of right triangles will help to contextualize the concept for them.
 * Interpersonal**: for the interpersonal learners, I feel the activity with a partner will help them to dissect a concept using the people around them to develop and solidify the concept.

9.To hook the students, I will rearrange my classroom to accent the right triangles in the room. This calls attention to all of the underlying shapes we encounter everyday without knowing it which in turn supports the "why" of the lesson. 10.Students will know the anatomy of right triangles (terms such as hypotenuse, leg, right angle, and the Pythagorean Theorem) (equip). To create a memorable learning experience, students will use provided materials such as popsicle sticks and paper clips to build their own right triangles with a partner. We will then measure the legs of the triangles and compute the hypotenuses (experience). Students will use the Ladder graphic organizer to narrate for themselves what information is necessary prior to this lesson (explore). 11. We will pose the question "why is this useful?" and "what if this leg was different?" to take a different approach on the material (rethink). If students' answers seem vague and unsure or if they seem confident and bored, the teacher will either seek an easier method of explanation of the concept or present more challenging examples for the students, respectively (revision and refinement). 12. To self-assess, students will answer problems individually then partner with someone who computed a different answer and compare results. Students must ask "what was different about my method in comparison to my partner's approach?" to gain more perspective on the concept. The teacher will then review the proper method (even if the entire class got all of the practice problems correct) to solidify the concept (evaluation). 13.**Verbal Linguistic**: the majority of my lesson will be presented in a traditional lecture format which relies heavily on verbal communication. 14. Students will be able to Describe the Pythagorean Theorem. They will prove their comprehension by creating a comic life presentation in which the Pythagorean Theorem is applied correctly to a real-life situation. Anticipated time - one 80-minute lesson (or less). || =Part 3=
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 8. Students will understand that the Pythagorean Theorem can only be used under certain conditions and will be able to recognize when it is appropriate to use (where). Learning this will help them to recognize relationships between shapes and equip them with the necessary skills to adequately create structures (examples include fences or failure to perform the Theorem correctly which resulted in the collapsing of a bridge) (why). This lesson meets the Maine Learning Results: Mathematics - C. Geometry, Geometric Figures, Grades 9 - Diploma 3. Students understand and use basic ideas of trigonometry.(what).
 * Logical Mathematical**: in all lessons, I will do a step by step break down of how the concept works, This will allow mathematical students to see the very logical process through which it functions.
 * Visual Spacial**: for my visual learners, I will draw diagrams relevant to the content (in this case, many triangles).
 * Musical Rhythmic**: to help my musical students connect with the content, I have created a song to the tune of "Yankee Doodle" to remember the Pythagorean Theorem (Re-mem-ber the Pythag-orean Theo-rem, a squared plus b squared, adds up to e-equal the hypotenuse that is c squared).
 * Interpersonal**: during the lesson, I have allow for students to spend time developing the concept with partners. This will help my interpersonal students explore the Pythagorean Theorem in a manner which is beneficial to them.
 * Naturalistic**: in order to engage the Naturalistic students in my classroom, I will come to class equipped with examples of right triangles that occur naturally as a means to personalize the lesson and give it meaning for these learners.

16. The hook for this lesson will include looking at tessellations and, as a class, recognizing the relationship between the shapes and images (engage). 17. Students will know the 30/60/90 and 45/45/90 triangles as well as the definitions of "complementary" and "supplementary" (equip). To organize ideas, students will use the "Cluster/Word Web" graphic organizer to establish the main concept and the subcategories of angle/side relationships (explore). To experience first hand the relationship, students will participate in the pencil activity. In this exercise, three sides of a triangle are created by attaching a long piece of string to the end of a pencil and a flat surface such as the student's desk. By tilting the pencil backwards, students can see that the angle between the pencil and the desk increase as the distance between the tip of the pencil and the desk increases as well (as depicted by the string). This demonstrates the relationship between the angles and sides of a triangle (experience). 18. To think about the problem differently, the teacher will pose the questions "what would happen to the triangle if the side depicted by the string was not allowed to increase as the pencil tipped backwards? What if all the sides of triangle were a fixed length? What if all the angles of the triangle were a fixed size?" (rethink). Next, the teacher should check for comprehension. "So what IS the relationship between angles and sides? Is there one at all?" and based on student response, teacher should either seek a different method of explanation (catered to the intelligence of learners who are having difficulty) or seek a more challenging way to express the idea (for example, giving hypothetical examples and having students make their own conclusions about the angle/side relationship) (revise and refine). 19. For this lesson's formative assessment, a short quiz covering the material of the day will be presented. This will give the teacher a concrete idea of how the students are comprehending the material (quiz will include questions about the 45/45/90 and 30/60/90 triangles and a few examples where they must figure out the lengths of either both sides or a side and the hypotenuse) (evaluate). 20. **Verbal Linguistic**: for the verbal students, as always, I will present my lesson using a collection of written and oral verbs and nouns that accurately describe the process and relationship. 21. From this lesson, students will be able to recognize relationships between angles and sides. Students will also learn that for some triangles, the measure of the angles has a set relationship to the lengths of the sides (45/45/90 triangles and 30/60/90 triangles). Students will prove their comprehension of this lesson by taking the quiz at "@http://www.funtrivia.com/playquiz/quiz14712910d9bc0.html" and recording their findings and list three things they could do to change their score if they to take it again. This quiz supplies questions about right triangles and their properties, and taking it will enable students to gauge their own personal comprehension. Students will post their findings and personal suggestions to their blog. This assignment will not be graded critically (it is an "all or nothing" assignment). Anticipated time - one 80-minute lesson. || =Part 4=
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 15. Students will be able to reflect on the relationship between sides and angles (where). This lesson will strengthen the life-long skill of making connections by developing students' ability to recognize subtle patters within a subject, whether that subject is triangles, English, or even Physical Education (why). This lesson pairs with the previous two to create a concrete understanding of the Maine Learning Result: Mathematics - C. Geometry, Geometric Figures, Grades 9 - Diploma 3. a. Identify and find the values of trigonometric ratios for angles in right triangles (what).
 * Mathematical Logical**: for the mathematical students, I will provide the formula through which one can deduce the side lengths for both the 45/45/90 and 30/60/90 triangles.
 * Visual Spacial**: for the visual students, as always in a geometry class, I will include visual representations and labels of the triangles discussed and incorporate those drawings into my explanation.
 * Bodily Kinesthetic**: for the physical students, I have designed the class activity to be one that directly manipulates the relationship between angles and sides which will aid these students in first-hand comprehension.
 * Musical Rhythmic**: for the musical students I will include an example that directly relates to music. Generally, when the dynamics of a piece increase, an ensemble has a tenancy to increase the tempo as well. Similarly, when playing legato, an ensemble tends to slow down the tempo. These are relationships that just happen naturally (even if they usually produce undesired effects) similar to how a side will increase directly with the increase of the angle opposite to it.
 * Intrapersonal**: students will be given approximately two minutes prior to the test to reflect upon the day's lesson and ask questions before the quiz at the end of class (closed note). This will give the intrapersonal students time to consider what they have learned.
 * Naturalistic**: for the naturalistic students, I will also include an example that directly relates to their area of expertise. As animals grow, their skills and abilities refine directly with their age. For example, when a lion cub is born, it does not yet see, let alone can it hunt. As it grows larger, it's abilities increase... very similar to the relationship between an angle and it's opposite side.

23. To start off this lesson and to engage my students in a real life application, I am going to ask the class to close their eyes and think of their favorite slide as a kid. Which of these categories does that slide fall in (the two categories being one that looks like a right triangle and one that is not).? I will then remind the class of how the material we covered prior to this lesson would in fact enable us to find the length of the slide (if we were given enough information), so it would only be fair if we learned how to solve for the length of the other slide as well! 24. Students will know how to analyze given information to determine missing lengths or angles of right triangles and how to solve for those values (equip). To review previous information, students will fill out the "garden gate" graphic organizer (explore). As an active part of class, students will be asked to share with a partner their answer to the day's "hook" question. During this time, students will also be asked to brainstorm other examples of non-right triangles (experience). 25. To take a different perspective on the trigonometric functions, students will be asked to find similarities between them instead of the differences (rethink). With this new found facet to trig functions, what can be concluded? How will they help us find the "length of the slide"? (revise). If students still seem unclear about the concept of trigonometric functions, the pace of the class should be handled accordingly and perhaps a more hands-on or real-example approach would be helpful (refine). 26.The formative assessment that couples with this lesson is a standard, un-graded quiz to review comprehension of concepts (evaluate). 27. **Verbal Linguistic**: for students who are linguistic, as always, I will present my lesson in both written and spoken word. Also, I will introduce the popular acronym Soh Cah Toa for the trigonometric functions. 28. From this lesson, my students will be able to analyze given information to determine missing lengths/angles of triangles and how to solve for those values. Then, using the trigonometric functions, they will be able to describe the given information in such a way that the missing sides or angles can be deciphered. Students will demonstrate their mastery of this concept by performing the following task for homework: Find one right triangle that you encounter every day and, using a ruler, measure the sides of the triangle. Now, use the inverse trig functions to figure out what the unknown angles were. Document your findings either on paper (with your method CLEARLY written) or post to the class wiki (with your method CLEARLY written). Anticipated time - One 80-minute lesson. || =Part 5=
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 22. Students will know how to interpret given information to determine missing lengths/angles of triangles and be able to solve for those values (where). Being able to look at small problems to solve the larger ones is a life long skill that will help students be better problem solvers through out their lives (why). This lesson pairs with the previous two to create a concrete understanding of the Maine Learning Result: Mathematics - C. Geometry, Geometric Figures, Grades 9 - Diploma 3. c. Students will be able to use inverse trigonometric functions to find missing angles in right triangles (what).
 * Mathematical Logical**: for students who gravitate towards math, I will present a step by step analysis of the problem solving method.
 * Visual Spacial**: for students who are visually inclined, I will include pictures with my examples to help relate the shape to the functions that warp the shape.
 * Bodily Kinesthetic**: during the initial "hook" part of the class, bodily kinesthetic students will be urged to get up and act out their own personal slide that they picked.
 * Musical Rhythmic:** for my musical students, I will play the video of the "Trig Rap" found on YouTube.
 * Intrapersonal**: for the intrapersonal students, time will be provided for them to reflect on what they have learned before the quiz is administered.
 * Interpersonal**: during the "hook" of the class, students will be encouraged to work with others as a means of making connections to the material.
 * Naturalistic:** for my naturalistic students, I plan on creating some kind of lose example like the one that follows. In nature, there are specific ratios that animals follow. For example, there can only be one queen be for every hive (a 1 queen : 1 hive ratio). The trig functions are not much different. For example, let's pretend the queen bee is the trig function "tangent". For the one queen bee, she can only use the two sides of the hive closest to her nest. If the workers were the "sine" function, they would only be able to use one of the queens walls (in a triangle that would be the side opposite the adjudicated angle) and the third one that she wasn't using.

30. To hook the class, I have planned an opening activity. Students will be provided with two mirrors per group of 4 students. Placing the mirrors on either side of a student so that they face each other, students will be asked to count how many times they can see their classmate projected into each mirror. The answer, naturally, is infinite. This will lead right into how there are infinitely many triangles within any given polygon. 31. Students will know that properties of right triangles can relate to the properties of other shapes as well (equip). To illustrate what students know about right triangles, they will be asked to refer back to all of their graphic organizers thus far in the unit and underline what they consider to be important (explore). As a class, students will explore other shapes and be asked to draw lines to create triangles (experience). 32. To reorganize the way students think about shapes within shapes, the teacher will ask "what other shapes can we think of that could be found within another shape to make this problem easier?" (rethink). From the list of properties the class listed as important, the class as a whole will group properties together and edit the list (revise). If students seem to be highlighting on the important information and cataloging it correctly, the teacher should continue. If students seem to be leaving out important information or emphasizing too much on one property, the teacher should take time to review past lessons and capitalize on the desired understanding (refine). 33. The formative assessment for this lesson will be an informal observation of the students as they individually find and label triangles (a minimum of four) within a shape (evaluate). 34. **Verbal Linguistic**: as always, class will be presented in a verbal and written presentation. 35. From this lesson, students will apply prior knowledge of triangles to new shapes.. Students will demonstrate their mastery of this lesson by creating a brochure that advertises the "appeals" (properties) of right triangles with your target audience being another shape. Anticipated time - One 80-minute lesson or less. || =Part 6=
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 29. Students understand that properties of right triangles can relate to the properties of other shapes as well (where). This is important in the real world application of math because the real world will not always supply a right triangle to work with. By finding shapes within shapes, problems can be broken down and therefore simplified (why). This lesson meets the Maine Learning Result: Mathematics - C. Geometry, Geometric Figures, Grades 9 - Diploma 1. a. Students can use the properties of triangles to prove theorems about figures and relationships among figures (what).
 * Mathematical Logical**: for my logical thinking students, I will provide a logical analysis as to why we find triangle within shapes.
 * Visual Spacial**: this will be a very rich lesson for my visual spacial students because the entire lesson relies on interpretation of pictures.
 * Bodily Kinesthetic**: for the bodily students, the opening activity should meet their kinesthetic needs and enable them to interact with the material in a manner appropriate to them.
 * Musical Rhythmic**: for my musical students, I will provide an example that they may relate to: When you're improvising, and someone tells you what key the rest of the ensemble is in, you need to know what notes are //in// that key to help you play. You need to know that the first, third and fifth notes of C minor are C, E flat and G in order to make what you're playing fit in. It's all about recognizing the components (or chords) that scales are made up of.... like triangles within squares!
 * Interpersonal**: this lesson will be packed with group activities (or at least, more so than past lessons) that include, the initial group work and almost the entire class time is spent doing triangle evaluation as a class.
 * Naturalistic**: to relate to my naturalistic students, I will compare the shapes within shapes to the rings within the trunk of a tree.

37. Start by asking the class "how many of you have a brother or sister? And does he or she look anything like you? Does he or she play the same sport you do? Does he or she laugh at the same things you laugh at?" etc until all students have answered "yes" and "no" to at least two questions (respectively). Then, to relate it to math, I will explain how brothers and sisters all have their differences, but they also have their similarities, just like the properties and functions of shapes! For example, triangles and octagons have very many different characteristics, but they are both polygons 38. Students will know how to correctly and appropriately apply what we have learned about right triangles to other shapes (equip). Students will be asked to compile all the information they have learned in this unit in a "describing wheel" so that they may capitalize on what is important (graphic organizer). Students will be asked to take out their formative assessments from the previous lesson and be given a new challenge. The will be asked to solve the shapes to find the lengths/angles of the original object using the right triangles they drew (students will be asked to work alone) (experience). 39. To gain a different perspective, the teacher will pose the question "How would we break this down and solve it if we did not have right triangles?" (this will illustrate the importance of the mastery of right triangles) (rethink). Based on the students' graphic organizers, the teacher will have a good idea of where individuals are in the comprehension, application synthesizing process of mastery (revise). To solidify the concept, students will be asked to try some practice problems on the board in class. Other students may assist an individual if he or she gets "stuck" on a problem (rehearse). 40.The formative assessment for this lesson will be during class as students solve for the lengths and angles of shapes (also the "rehearse") (evaluate). 41. **Verbal Linguistic**: for my verbal learners, as always, I plan on providing my lesson in language based way, both written and oral. Musical Rhythmic: since this lesson will be heavy on inverse trig functions, I will relate them to sharps and flats in music (for example, if you have a note that is flat in the key signature and you want to play it natural, you need to neutralize it by adding the opposite symbol to it). 42. From this example, students will be able to relate properties and formulas of triangles to properties and formulas of triangles. Students will demonstrate their understanding through an end of unit project. This project requires students to synthesize all information they have learned in this unit through creating a short iMovie. Anticipated time - One 80-minute lesson or less. ||
 * **Consider the W.H.E.R.E.T.O. elements**. **(L)** ||
 * 36. Students understand that there exist relationships between right triangles and other shapes, not only in their build, but in their function (where). This is important for students to know because it will aid in the simplification and solving of problems in the future (why). This lesson meets the Maine Learning Result: Mathematics - C. Geometry, Geometric Figures, Grades 9 - Diploma 1. a. Students can use the properties of triangles to prove theorems about figures and relationships among figures (what).
 * Mathematical Logical**: for my mathematical learners, as a class we will provide a chart of sequential steps to go through when solving this shape within a shape.
 * Visual Spacial**: for the visual learners, I will provide (and the class will adapt) labeled pictures of the shapes to build a mental image of the subject we are working with.
 * Intrapersonal**: students will be given time to work alone on their "rehearse" problems.
 * Interpersonal**: students will collaborate as a class to solve their formative assessment problems.

2004 ASCD and Grant Wiggins and Jay McTighe