ࡱ>  ]?bjbj 0hh]7+++++????|?>?XWWWWW^^^>>>>>>>$A8D>+^^^^^>++WW>***^+W+W>*^>** :X>W@-p4?t.a;(>?0>?;DDP>D+>*^^^>>*^^^>?^^^^D^^^^^^^^^ : UBD Lesson Plan Template Stage 3 Learning Plan Back Design Template Task: (Describe briefly)  Instructional Process: WHERE are we going? WHY? WHAT? is expected? Goals: To have students begin thinking about the applications of basic trigonometry and Geometry to other mathematics as well as the real world. For the students to understand the Essential Questions of UBD stage 1: What is the importance of math in the world today? How can we apply the information in the unit to the real world? How does the information in the unit enable us to enter higher mathematics? For the students to understand or know how to: Identify special right triangles and use their properties to find information about them. Find sine, cosine, and tangent of right triangles. Understand the properties and aspects of circles and how to use them along with trigonometry to find information about the circle. Use their knowledge of circles to help them compute the measures of spheres. Expectations: In order to gain understanding of the goals students will: Complete homework assignments for each day of classroom instruction. This will give the students practice and experience in using the ideas learned in class. I will give the students an opportunity during the first ten minutes of class to ask questions concerning the homework. Complete a web quest that enables the students to apply the information learned in class to real world situations in a fun and exciting adventure. They will answer questions concerning the web quest and complete a poster project describing one of the steps in the web quest. (Logical/Quantitative & Narrative Windows) Answer the Essential Questions in essay format upon completion of the unit. After completing the unit exam, they will answer the questions and we will discuss their answers in an open-classroom discussion. This will enable the students to see the point of learning the information in the unit (Foundational Window) Relevance and Value: To set up the basis of knowledge necessary for entering higher mathematics: The students will develop a source of information within their minds that is necessary to every future math class the students take. The basic ideas of trigonometry and geometry learned in the unit are essential to all mathematics. Prerequisite Skills: Understand what a triangle is Know that the three angles in a triangle add up to 180 degrees Understand similar triangles and what makes triangles similar. Understand what complementary angles are. Evaluate if students know and understand what defines a shape as a triangle. Also, determine if they understand that the three angles in any triangle add up to 180 degrees. This will be done by means of a Smart board activity. Also, evaluate the students knowledge of similar triangles. This is done by means of a group activity where they review what a similar triangle is. How will we HOOK and HOLD student interest? MM2G1 (Special Right Triangles): The smart board activity to evaluate prerequisite skills will be on the smart board at the beginning of class. Begin by asking the students general questions concerning triangles. Then, ask volunteers to come to the front of the classroom to participate in the activity of deciding if a shape is a triangle or not. The next aspect of the Hook and Hold step is the other part of the evaluation that determines and exercises knowledge about the sum of the three angles of triangles. MM2G2 (Sine, Cosine, and Tangent to Special Right Triangles): (After ten-minute homework review) Have students divide into groups of 3-4 students. Pass out worksheet that has an activity and questions concerning similar triangles. The students will be given 5-7 minutes to complete this, and then we will discuss their answers. I will then start my lecture about the new topic for the day. (Narrative Window) The next portion of the new topic deals with trig ratios of complementary angles. In order to Hook and Hold my students attention, I will have a smart board activity that gives them a visual representation and participation in the activity. (Aesthetic Window) MM2G3 (Properties of Circles): The first portion deals with chords, tangents, and secants. In order to hook and hold my students I will have my acoustic guitar in class that day and begin by telling them we will be learning about chords today. I will play a few chords on my guitar, and then ask them if they know of any other types of chords that exist in the world. I will then use the hole in the guitar and a string that crosses it to describe the mathematical chord. This will then lead into discussion of secants and tangents of circles as an application of triangle symmetry. (Aesthetic Window) The next portion deals with properties of central, inscribed, and related angles. In order to Hook and Hold the students attention, I will allow the students to come up to the smart board and select which images display central and inscribed angles. MM2G4 (Find and Compare Measures of Spheres): In order to Hook and Hold the attention of my students, I will hand out Styrofoam balls and flexible tape measures. I will then give them specific instructions to measure the circumference and give them a formula that will allow them to determine the diameter of the sphere with that information. I will then begin the lesson on how to use previously known/gained information to discover the surface area and volume of a sphere. (Experiential Window) How will we EQUIP students for expected performances? Every day I will explain each new segment of the standards within the Geometry Unit. The students will be strongly encouraged to take detailed notes. If they are absent, I will print a copy of my Smart Board Notebook for that day to give to them (I will write all the lecture notes and example problems on the Smart Board). With every lesson, I will incorporate specific Smart Board activities and visual representations in order to give the students visual representations of the ideas. (Aesthetic Window) I will reserve a computer lab or a mobile lab one day during the unit so the students can complete an activity with Geometers Sketchpad (by KCP Technologies). (Experiential Window) Hand out several sheets that summarize the main topics and ideas within the unit Students will complete the group assignment worksheet for similar triangles. During the lesson concerning the area of a sector of a circle, I will order pizza for the class and we will have a math lab concerning the area of a slice of pizza (Experiential Window) How will we help students RETHINK and REVISE? Each night, the students will be given about 15-30 problems of homework to practice the new topics. We will take the first ten minutes of every class session to answer any questions concerning the previous nights homework assignment. Students will keep a math journal where each night they will summarize what they learned in class that day. Students will grade each others daily quizzes. I will read the answer aloud, and the students will mark right or wrong. If they know the answer, they can explain it to their classmate(s). How will students self-EVALUATE and reflect on their learning? Quizzes of 2-3 questions will be given each day. They will cover the topic(s) that were on the homework. Students will trade quizzes and grade each other. An exam will be given at the end of the unit. It will cover all topics in the unit. When I return the tests to the students, they can come to me before or after school to ask questions concerning the test. The Web Quest National Treasure: The Geometers Key will evaluate the students learning. They will answer questions throughout the Web Quest and turn them in to me. The students must also generate a poster explaining one of the steps within the Web Quest and present to the class. The students will answer the Essential Questions of the unit in paragraph form (after the unit exam). This enables them to realize the enduring understandings of the unit and for me to analyze their learning. (Foundational Window) How will we TAILOR learning to varied needs, interests, styles? Visual Learners: The Smart Board applications will equip their learning style Auditory Learners: They will learn best by listening to the lectures. Attention Deficit Students (ADD/ADHD): By breaking the class in to segments of 1)Homework review 2) Hook and Hold (which has various hands-on/involvement activities) 3) Lecture (which is also broken into different topics and also has various activities and visual aids scattered throughout). One complete day will be spent in the computer lab working on the Web Quest. Part of another day will be spent in the computer lab working with Geometers Sketch Pad. Hearing Impaired Learners: I will give them a copy of my notes for the day prior to class, as well as a copy of the lecture notes and examples I worked on the Smart Board. Basically everything I say in reference to the lesson will be written on the Smart Board. Visual Impaired Learners: They can utilize a tape recorder in class so they can review the lecture as many times as possible. I can also set the smart board to display large text. Slow Learners: Copies of the lecture notes will be given to them. The math journal will help them to recall what they learned and analyze it without actually working math problems. How will we ORGANIZE and sequence the learning? Day 1: MM2G1 & First Part of MM2G2 Day 2: MM2G2 Special Right Triangles & Sine, Cosine, and Tangent Ratios to Similar Right Triangles: Specific: Length of the sides of 30,60,90 triangles Length of the sides of 45,45,90 triangles Relationship of Trigonometry ratios for similar triangles Steps in Lesson: (No homework questions necessary, no homework assigned prior to class) Smart Board activity to hook and hold attention, as well as to recall prerequisite skills. Instruction time: I teach the new topic, while using the Smart Board for visual representations. When finished with Special Right Triangles, use the group activity about similar triangles to transition into trigonometry ratios to similar right triangles Assign homework Sine, Cosine, and Tangent Ratios to Similar Right Triangles Specific: Relationship between trigonometric ratios of complementary angles. Solve application problems using trigonometric ratios. Steps in Lesson: First ten minutes of class, allow for questions concerning homework. 2-3 Question quiz concerning the homework. Students trade quizzes and grade for one another. Smart Board Activity to hook and hold attention, as well as recall the idea of complementary angles. Instruction Time: I teach the new topic, describing how trigonometry ratios and complementary angles are related. (I will also use a smart board application concerning the unit circle). I will then teach the students how to use the information to solve application problems. Assign Homework Day 3: MM2G3 Day 4: MM2G4 (Pizza Lab Day) Properties of Circles Specific: Properties of chords, tangents, and secants as an application of triangle symmetry Properties of central, inscribed, and related angles Steps in Lesson: Ten minutes for homework questions 2-3 Question quiz concerning the homework Hook and Hold: Use my acoustic guitar to show musical chords. Transition discussion to mathematical chords. Instruction time: Utilize the Smart Board to display what a chord, secant, and tangent line are. Then explain the triangles created by each of them and the symmetry of those triangles. Transition to: discussion of central, inscribed, and related angles (They are created by chords, secants, and tangents). Discuss their properties. Assign Homework Properties of Circles Specific: Use properties of circles to solve problems involving length of an arc and the area of a sector Steps in Lesson: Ten minutes for homework questions 2-3 Question quiz concerning the homework Hook and Hold: Use description of a pizza (and picture of one on Smart Board) to describe a slice of pizza as the area of a sector of a circle. (If possible/permitted by the school, I will have pizza waiting on the class) Instruction: Explain the formulas/ processes of finding the arc length and area of a sector of a circle. The students will then measure the pizza and use the formulas to discover the area of their slice. Assign Homework Day 5: MM2G3 Day 6: MM2G4 Properties of Circles Specific: Justify measurements and relationships in circles using geometric and algebraic properties Steps in Lesson: Ten minutes for homework questions 2-3 Question quiz over the homework Hook and Hold: Use a real-life application problem concerning a circular object (possibly the rotunda in the Capitol). Get the students to guess the angle (on the unit circle) that a certain object would be at. Transition from the hook and hold step into the actual Lesson. Show them that it is possible to use geometry and algebraic properties to find the exact location. Assign homework Find and Compare Measures of Spheres Specific: Use and apply Surface Area and Volume of a sphere Determine the effect on surface area and volume by changing the radius or diameter of a sphere Steps in Lesson: Ten minutes for homework questions 2-3 Question quiz concerning the homework Hook and Hold: Distribute Styrofoam balls to the classroom for the activity mentioned in the UBD Hook and hold section Teach the lesson concerning volume and surface area of spheres Go to the computer lab to use Geometers Sketchpad. 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TaWlF@*F@!L)Qother mathematics as well as the x...G...G.**.*;/.*..TXa lF@*F@X L)Qdreal world. /.<./TT a lF@*F@ L)QP - TB  lF@*F@ FL)QFor the students to understand the Essential Questions of UBD stage 1:3...*/../*./...*.....7**...A..*./*.<7<*../.TTC o  lF@*F@C L)QP -Rp @Symbol  Ob   Ob  wd  IGxd'2X5Symbolb%՟bHGE/H j:d yd IGdv% % %  % % % TT  lF@*F@p L)QP&Rp @"Arial Obx dObx wdx Gxd/2X3. *Cx Arialb՟bMGhK/j:dydGdv% % % TT&  lF@*F@p L)QP p% % % TT& r lF@*F@p ,L)QWhat is the importance of math in the world Q-.*..G....*..G.....<..Tps & m lF@*F@s p L)QXtoday?/.0(/TTn & lF@&" WMFC Mح*F@n p L)QP - % % % TT  lF@*F@ L)QP&% % % TT  lF@*F@ L)QP p% % % T  lF@*F@ ?L)QHow can we apply the information in the unit to the real world?</;*..<././(....G.......//././;../TT @ lF@*F@ L)QP - % % % TT L lF@*F@; L)QPr&% % % TT L lF@*F@; L)QP p% % % T L lF@*F@; KL)QHow does the information in the unit enable us to enter higher mathematics?%</;/..*/...G....././/../..*.../../.G...G.**-TT FL lF@*F@; L)QP - ThQ lF@*F@ /L)QFor the students to understand or know how to: 3...*/../*./...*....+..;./;.TT Q lF@*F@ L)QP - % % % TT  lF@*F@ L)QP&% % % TT  lF@*F@ L)QP {p% % % T B  lF@*F@ =L)QIdentify special right triangles and use their properties to ...(*..*..//./.*....*./......*.TC L lF@*F@C L)Qfind information about them.....G..../../.GTTM y lF@*F@M L)QP - % % % TT w lF@*F@f L)QPe&% % % TT w lF@*F@f L)QP p% % % Tx w lF@*F@f 2L)QFind sine, cosine, and tangent of right triangles.3..*..*.+././././.../.../.*TT   w lF@*F@ f L)QP - % % % TTx  lF@*F@ L)QP&% % % TT  lF@*F@ L)QP p% % % T,  lF@*F@ PL)QUnderstand the properties and aspects of circles and how to use them along with <...*/...../...*....*..**.**.*./../;..*...G../.;/ Tx < lF@*F@+ 2L)Qtrigonometry to find information about the circle.../.G.'../..G-././....**.TT & < lF@*F@ + L)QP %- % % % TT=  lF@*F@ L)QP&% % % TTF  lF@*F@ L)QP p% % % T\F lF@*F@ -L)QUse their knowledge of circles to help them c<*../+..<./...**.*././..G*T F h lF@*F@ L)Qompute the measures of spheres.-G.../.G..*..*.*....*TTiF  lF@*F@i L)QP - % % % T  lF@*F@ L)QdExpectations7.3/..33.' % Ld    !??% ( % % % TT  lF@*F@ L)QP:TT  8 lF@*F@  L)QP - T  a lF@*F@P ;L)QIn order to gain understanding of the goals students will: ...../.../..*./....././.**./..*<TT  C a lF@*F@ P L)QP - % % % TTc  lF@*F@ L)QP&% % % TTl  lF@*F@ L)QP p% % % T\l  lF@*F@ XL)QComplete homework assignments for each day of classroom instruction. This will give the <.G.../.G.;.+.**..G..*...*../(.*.**..G&" WMFC -ح.*.*..4.*;.)... T  &lF@*F@>L)Qstudents practice and experience in using the ideas learned in*....*..**.....*./..*...*././/..*/.....TT  &lF@*F@ L)QP T &lF@*F@ L)Q|class. I will give the +.**</*./. Th+lF@*F@uZL)Qstudents an opportunity during the first ten minutes of class to ask questions concerning *....*../..../(......*/.G...*.*.**..*+...*..**..*/... T%lF@*F@ L)Qdthe homework../.G.;.+TX&SlF@*F@&L)QP. TTTlF@*F@TL)QP - % % % TTKlF@*F@:L)QP&% % % TTKlF@*F@:L)QP p% % % TdKlF@*F@:YL)QComplete a web quest that enables the students to apply the information learned in class <.G....<.....*...../.*..*/...*.//.(/...G...../...*.** T0P8 lF@*F@&L)Qto real world situations in a fun and ../;..*....*.......Th9 PlF@*F@9 /L)Qexciting adventure. They will answer questions .**/./.*....4./(;..+;....*..+ TP lF@*F@VL)Qconcerning the web quest and complete a poster project describing one of the steps in *..*.././.;/./..*/..*.G......*.../*..**.../.....*/.*. TeklF@*F@ZL)Qlthe web quest. ..<../..*TTfklF@*F@fZL)QP - % % % TTn5lF@*F@L)QP(% % % T6nlF@*F@6L)QtLogical/Quantitative...*/A/...*.% % % TTn'lF@*F@L)QP TX(nvlF@*F@(L)QP& 8% % % TwnlF@*F@w L)Q`Narrative<..*.% % % TTnlF@*F@L)QP T|nN lF@*F@L)Q\Windows)R...;*TTO n{ lF@*F@O L)QP I- % % % TT0lF@*F@L)QP&% % % TT0lF@*F@L)QP \% % % T 0lF@*F@?L)QAnswer the Essential Questions in essay format upon completion 7.+;...7**...B..+..*..**/(.G.....*-G....T 0lF@*F@ L)Qtof the unit. After o.../.7. T@.5lF@*F@.SL)Qcompleting the unit exam, they will answer the questions and we will discuss their *-G.........*.G./(<..+;......*/.*...<.</**.**.. T.lF@*F@.L)Qpanswers in an open..+;.*/..../.TTlF@*F@L)QP-TlF@*F@EL)Qclassroom discussion. This will enable the students to see the point *.**..G.**.**..4.*<//.../.*./..*/*../../. T8.q OlF@*F@.>'L)Qof learning the information in the unit..........G....././TTr  OlF@*F@r >L)QP - % % % TT.SIlF@*F@.L)Q&" WMFC حP(% % % TJS?lF@*F@J L)QhFoundational 3....//./% % % Tx@SlF@*F@@L)Q\Window)S...;TTSlF@*F@L)QP - % % % TdlF@*F@L)QTRele<..T)lF@*F@L)Qlvance and Valuel/.3...338.3.' % Ld)< !??% ( % % % TX*XlF@*F@*L)QP: TTYlF@*F@YL)QP t- TolF@*F@^KL)QTo set up the basis of knowledge necessary for entering higher mathematics:4.*..../..**.+..<./../.*.**.(..../.....G...G.**TT2olF@*F@^L)QP - % % % TTqlF@*F@L)QP&% % % TTzlF@*F@L)QP c\% % % ThzlF@*F@ZL)QThe students will develop a source of information within their minds that is necessary to 4..*....*</.*././*..*....G...;.../G..*..*..*.*+.(/ TH.4 4lF@*F@.#*L)Qevery future math class the students take..).(...G..*.**//*.../*.+.TT5 a 4lF@*F@5 #L)QP - % % % TT6lF@*F@L)QP&% % % TT?lF@*F@L)QP n\% % % T?_lF@*F@L)QThe basic ideas of trigonomet4....**/..*./../G.T`?4lF@*F@`9L)Qry and geometry learned in the unit are essential to all (./../.G.'..././././...**..//. T.lF@*F@. L)Qdmathematics.G..-G.**TTJlF@*F@L)QP - % % % TYlF@*F@GL)QtPrerequisite Skills7 / .33/.8..' % LdPXP !??% ( % % % TTXlF@*F@GL)QP:TTXlF@*F@GL)QP - % % % TT[lF@*F@L)QP&% % % TTdlF@*F@L)QP p% % % TdPlF@*F@L)QUnderstand what a triangle iso<...*/..<..././.*TTQd}lF@*F@QL)QP - % % % TT$lF@*F@L)QP&% % % TT$lF@*F@L)QP p% % % T $lF@*F@>L)QKnow that the three angles in a triangle add up to 180 degrees7./<.//.././...*.//././....../..../.*TT E $lF@*F@ L)QP - % % % TT&lF@*F@yL)QP&% % % TT/lF@*F@yL)QP p% % % T/ lF@*F@y>L)QUnderstand similar triangles and what makes triangles similar.<...*/..*G...//*...<..G.+.*....+*G.TT /6 lF@*F@ yL)QP - % % % TTlF@*F@L)QPt&% % % TTlF@*F@L)QP p% % % TlF@*F@ L)Q`Understan<...*/.T  lF@*F@ L)Qd what complementary angles are..<..*.G..F...(./..*..TT  lF@*F@ L)QP - TOlF@*F@>`L)Q Evaluate if students know and understand what defines a shape as a triangle. Also, determi& WMFC حne if 7*./..*../.*+..;/../...*/..<...../*.*.../.*../..8+../.G.." % Ld!??%  % Ld(f!??%  % Ld),)!??%  % LdP!??%  % LdQTQ!??%  % LdQTQ!??%  % LdQ(TQf!??%  % Ld),P)!??%  % Ld)Q,T)Q!??%  % Ld)Q,T)Q!??% % % ( 666666666666666666666666666666666666 6 66 6  6 66 6  6 66 6  6 66 6  6 66 6 66666666666666666666  c."System???????????--@Times New Roman--- @Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman- @Times New Roman--@Times New Roman------ 12 WZcUBD Lesson Plan Template e       2 Wc 2 W"c +2 W&cStage 3 Learning Plan      --- 2 Wc  2 eZc @"Arial--- )2 qZcBack Design Template  2 qc   - @ !5tU-  - @ !5t - ,tU@"Arial---@"Arial--- - @ !tZ- ---2 ZUtTask: )---%2 Ut(Describe brieflya@"Arial---2 Ut)  2 Ut --- - @ !Z-  2 ZUt  - @ ! Z-  2 ZUt --- - @ ! 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This will give the   h2 ~>Ustudents practice and experience in using the ideas learned in 2 U .2 Uclass. I will give the 2 ~ZUstudents an opportunity during the first ten minutes of class to ask questions concerning 2 ~ Uthe homework 2 U.  2 U - - - 2 lU- - - 2 pU ---2 ~YUComplete a web quest that enables the students to apply the information learned in class  D2 ~&Uto real world situations in a fun and R2 /Uexciting adventure. They will answer questions 2 ~VUconcerning the web quest and complete a poster project describing one of the steps in #2 ~Uthe web quest.  2 U --- 2 ~U(---)2 ULogical/Quantitative--- 2 U 2 U& ---2  UNarrative--- 2  U 2 UWindows)  2 <U - - - 2 nU- - - 2 sU ---j2 ~?UAnswer the Essential Questions in essay format upon completion   (2 Uof the unit. After 2 SUcompleting the unit exam, they will answer the questions and we will discuss their i&2 %Uanswers in an open 2 %U-s2 %EUclassroom discussion. This will enable the students to see the point F2 0'Uof learning the information in the unit  2 0!U --- 2 ;U(---2 ; UFoundational ---2 ;UWindow))  2 ;U ---2 GZURele"2 GoUvance and Value- @ !cHZ----2 GU:  2 GU |2 SZKUTo set up the basis of knowledge necessary for entering higher mathematics:   2 SU - - - 2 _nU- - - 2 _sU ---2 _~ZUThe students will develop a source of information within their minds that is necessary to  J2 j*Uevery future math class the students take.  2 j9U - - - 2 vnU- - - 2 vsU ---72 v~UThe basic ideas of trigonometsa2 v9Ury and geometry learned in the unit are essential to all 2  Umathematics.  2 U ---(2 ZUPrerequisite Skills- @ !VZ---- 2 U: 2 U - - - 2 lU- - - 2 pU ---72 ~UUnderstand what a triangle iss 2 U - - - 2 lU- - - 2 pU ---h2 ~>UKnow that the three angles in a triangle add up to 180 degrees 2 U - - - 2 lU- - - 2 pU ---h2 ~>UUnderstand similar triangles and what makes triangles similar.    2 U - - - 2 lU- - - 2 pU ---2 ~ UUnderstan;2  Ud what complementary angles are.  2 DU 2 Z`UEvaluate if students know and understand what defines a shape as a triangle. Also, determine if  '- @ !T-- @ !U-- @ !-- @ !#T-- @ !T-- @ !T-- @ !U-- @ !#-- @ !-- @ !---ccbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaa````՜.+,0( hp  Piedmontn CollegedA7 1UBD Lesson Plan Template Stage 3 Learning Plan Title  !"#$%&'()*+,-./0123456789:;<=>?@ABDEFGHIJLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmopqrstuvwxyz{|}~Root Entry F 2w4Data C1TableKJEWordDocument0SummaryInformation(nDocumentSummaryInformation8CompObjy  F'Microsoft Office Word 97-2003 Document MSWordDocWord.Document.89q