UBD Lesson Plan Template – Stage 3 Learning Plan
UBD Lesson Plan Template – Stage 3 Learning Plan
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|Task: (Describe briefly) |
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|Instructional Process: |
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|WHERE are we going? WHY? WHAT? is expected? |
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|Goals: |
|To have student’s 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 student’s |
|knowledge of similar triangles. This is done by means of a group activity where they review what a similar triangle is. |
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|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) |
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|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 Geometer’s |
|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) |
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|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 night’s 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 other’s 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). |
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|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 Geometer’s Key” will evaluate the student’s 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) |
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|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 Geometer’s 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. |
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|How will we ORGANIZE and sequence the learning? |
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|Day 1: MM2G1 & First Part of MM2G2 |
|Day 2: MM2G2 |
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|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 |
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|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. |
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|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 |
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|Day 3: MM2G3 |
|Day 4: MM2G4 (Pizza Lab Day) |
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|Properties of Circles |
|Specific: Properties of chords, tangents, and secants as an application of triangle symmetry |
|Properties of central, inscribed, and related angles |
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|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 |
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|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 |
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|Day 5: MM2G3 |
|Day 6: MM2G4 |
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|Properties of Circles |
|Specific: Justify measurements and relationships in circles using geometric and algebraic properties |
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|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 |
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|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 Geometer’s Sketchpad. |
|Assign homework |
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|Day 7: Web Quest Day |
|Day 8: Unit Exam Day |
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|Steps in Lesson |
|Homework Questions |
|No Quiz Today |
|Go to computer labs to complete the Web Quest |
|Steps in Lesson |
|Students begin examination upon entering the room |
|When they finish the test they will begin working on answering the Essential Questions |
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|Resources/Materials: (List items) |
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|References: |
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Adapted/formatted from Understanding by Design by Grant Wiggins and Jay McTighe
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