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Lesson Planning Assignment – Part 1Trina KelseyEDU-723 – Teaching and Learning in Inclusion SettingsJune 17, 2012University of New EnglandLesson #1Grade Level: Grade 10Student GroupingApprenticeship and Workplace Math – 28 students, mixed ability but age appropriate, on a regular graduation programSeveral students with First Nations ancestry.Content/Skill Area: Trigonometry – Right Triangles and the Tan RatioObjective General Outcome: Develop spatial sense. (Ministry of Education, 2008)Specific Outcome: Demonstrate an understanding of primary trigonometric ratios (sine, cosine, tangent) by: applying the primary trigonometric ratios [and] solving problems (Ministry of Education, 2008)Materials: Scientific Calculators, Appendix A – pictures of triangles in our environment, Appendix B - overhead of a right triangle, Appendix C – Formula sheet, Appendix D - worksheetVocabulary: ratio, angle, measurement, hypotenuse, opposite, adjacent, variable (teaching specialized vocabulary)Teaching Methods/StrategiesAnticipatory Set (10 minutes)Show the students the photos from Appendix A. Ask students what shape they see repeated in the photos. In groups, discuss the question “Where else can a person see triangles?” Record the answers on the board, making a comprehensive list. (understanding relationships) Ask the students “How could you easily measure the height of the triangles in the photos?” Record the answers on the board. “Is there a way to do it without climbing?” (predicting)Lesson (30 minutes)Review the sides of a triangle, which was previously learned in the lesson of Pythagoras Theorem using the picture in Appendix B. Have the students copy three right triangles from the board and label the opposite, hypotenuse and adjacent. Have volunteers come to the board to label the samples and students can check their work. Circulate for understanding of this review concept. (connecting to prior knowledge, scaffolding)Students will need to learn about the tanθ function on their scientific calculators. To practice using this calculator feature, model using the function then record the answers on the overhead. Have all of the students practice with you and round to 3 decimal places. Here are the practice angles:tan 40° ? 0.839 → Hit 40, tan, =tan 55° ? 1.428 → Hit 55, tan, =tan 72° ? 3.078 → Hit 72, tan, =Ensure that everyone is able to correctly input the buttons on the calculator to get a matching answer. Check for understanding and have partners quiz each other using the given practice angles. Go through the answers as a large group. It is crucial to “ensure that the students are able to do the mathematical operations before presenting word problems” (Cohen & Spenciner, 2009). (Ask students to do the math by using a calculator)Explain the meaning of tanθ. It is actually a ratio of two sides of a triangle, tanθ= oppositeadjacent . “Students taught by the ratio method [are] more capable of identifying the correct trigonometry functions,” than students taught with the circle method (Kendal & Stacey, 1997). Show the students that there is an easy way to remember which ratio is used for a question by using the mnemonic SOH CAH TOA. Hand out Appendix C for each student to use as a reference while doing the entire trigonometry unit. (Mnemonics, Using formulas)Draw a triangle on the overhead and assign values (see below). Have the students label the hypotenuse, adjacent and opposite as we have done before. Now that it is labeled, model how to turn it into a tangent ratio question to find the length of a side.914400-381000tanθ=oppositeadjacenttan43°=a11 0.933 = a110.9331 = a1110.258 = aModel each of the lines of the question. First, write out the formula. Second, insert the value of the angle beside tangent and the values of the opposite and adjacent into the ratio. Third, using a calculator find the value of tan 43°. Fourth, turn both sides into fractions by putting the value of tan over 1. Finally, use the cross multiply and divide method (connecting to prior knowledge) to isolate the variable “a”. (Modeling, using formulas, interpreting information, teaching abstract concepts using diagrams, solving a math problem using a calculator)Once the question is done, it is important to look to see that the answer makes sense. Does it fit in with the other numbers? (check that the answer makes sense) Has the unit of measurement (meters, feet and kilometers) been added to the answer? In this case there is no unit of measurement in the questions, so the answer doesn’t need one.Have the students try the following practice question and then check with a partner. Review the answer on the overhead after everyone has tried to work it out. Circulate while they are working on the question to intervene with any problems that arise. (Ask students to draw a picture of the problem, ask students to do the math by using paper and pencil and calculator, prompt students to check mathematics)Now that they can find a side, using the same ratio formula show the students how to find an angle. Have the students label the hypotenuse, adjacent and opposite as we have done before. Now that it is labeled, model how to turn it into a tangent ratio question to find an angle (see below). 45720023495000tanθ=oppositeadjacent tanθ=68 tanθ=0.75 tanθ=37° Model each line of the question. First, write out the formula. Second, insert the value of the sides of the opposite and adjacent into the ratio. Third, using a calculator find the decimal value of 6 over 8. Finally, to turn the decimal into an angle measurement, on the calculator hit the buttons [0.75] [Invert] [tan]. The answer should be rounded to the nearest whole number as it is a degree. Does the answer make sense? (Modeling, using formulas, interpreting information, teaching abstract concepts using diagrams, solving a math problem using a calculator)Check for any final questions before moving forward with individual practice.Activity (30 minutes)The students will need time to practice the concept to see if they have a full understanding of the concept. The activity portion of the lesson allows time for the students to make sense of the information that has been presented. Providing time to complete an activity allows the student to process and internalize the information. It is important to ensure that the activity is promoting new learning at an appropriate level for the students. This means it should match a student's readiness level. Students will practice questions using a worksheet such as Appendix D, or questions from the textbook. Those looking for a challenge with other trigonometry ratios can try a computer program such as Khan Academy (I am a coach and can check their progress online) they complete their work. In order to further differentiate, students will be allowed to work individually, or with a partner. All work must be shown for assessment purposes and to assist with error correction. Lesson #2Grade Level: Grade 10Student GroupingApprenticeship and Workplace Math – 28 students, mixed ability but age appropriate, on a regular graduation program. Several students with First Nations ancestry.Content/Skill Area: Trigonometry – Right Triangles and the Tan RatioObjective General Outcome: Develop spatial sense. (Ministry of Education, 2008)Specific Outcome: Demonstrate an understanding of primary trigonometric ratios (sine, cosine, tangent) by: applying the primary trigonometric ratios [and] solving problems (Ministry of Education, 2008)Materials: scientific calculators, clinometers, trundle wheels, Appendix E -worksheets to record answers (double sided)Vocabulary: clinometer, trundle wheel (teaching specialized vocabulary)Teaching Methods/StrategiesAnticipatory Set (10 minutes)Yesterday students learned about the mathematical calculations of the tangent ratio of trigonometry. Ask the students “How can we use the tangent ratio in everyday life?” “What jobs might use this type of math?” With a partner brainstorm three practical ways that the tangent ratio could be used in the workplace or home. Record the answers on the board and discuss briefly as a class. (Making connections to real life)Ask students to discuss with a partner whether it is possible to measure a distance that is very high, such as a tree or a building? (Show the slide below) If so, how could it be done? What tools might be needed? Make a list. (predicting) (Miller, 2011)Lesson (15 minutes)Today the students are going to have a chance to apply the tangent ratio formula to a real world problem using a method called indirect measurement. They will be using the tangent ratio math formulas that they learned yesterday (connecting to prior knowledge, scaffolding) and applying that knowledge to answer questions in a hands on situation (participating in hands-on experiences, solving real world problems)Tell the students that we are going to be going outside to measure tall objects around our school (trees, flagpole and street lights).The students will work in groups of three to measure four items outside and find the height of each. One person will be measuring along the ground – their job is to measure from the base of the object (tree) using a trundle wheel (connecting to prior knowledge, scaffolding) to measure out a number of meters on the ground. The second person will use a clinometer from that point to measure the angle to the top of the object (tree) and the third person will record the numbers on the worksheet for the group.Trundle WheelClinometerThe students have not used a clinometer before, so explain how it works. Point the clinometer to the top of the tree while squeezing the lever. When the “eye” of the clinometer is lined up with the top of the tree, gently release the lever, so it locks the degree measurement in place. The arrow will be pointing towards the angle (see photo above). The group recorder will put the number of degrees onto the worksheet. Give each of the groups a clinometer and have them practice in the classroom before going outside, by finding the degree angle to the top of the bookshelf, the ceiling etc. (participating in hands-on experiences, using manipulatives/equipment, measuring).45720027114500The final step requires the person using the clinometer to measure their height up to their eye, because that number (meters) will have to be added to the final answer. Show the diagram and explain the rationale. When the group member measures the angle, they are not at ground level; therefore their height must be added to the final answer to ensure accuracy. It is essential that the measurements be taken in the same unit of measurement, so if the tree is being measured in meters, then the group member’s height must also be measured in meters. For example, I would be 1.60 meters tall to my eye. To make this step fairly quick, have measurements pre-done on the whiteboard, so a group can stand in front of the board and swiftly get their measurements taken to the eye. (measuring, participation in hands-on experiences, collecting, organizing, displaying and interpreting information)Activity (45 minutes)Each student will receive a double sided worksheet (Appendix E). The first diagram is shown to get the students started. The rest will have to be drawn by hand depending on the choices the group makes.The first tree will be measured by all groups, with clarification and supportive instruction given as need be. How high do they think the tree is? (Estimation) Remind the students again that they must add the height of the person using the clinometer to their final answer and complete the answer by giving the unit of measurement (meters). Let the students know that they will have time in the classroom to complete the math portion of the equations and that the outside time is for measuring. Model measuring with the trundle wheel from the base of the tree to the person holding the clinometer, then practice measuring with the clinometer (modeling). Have all of the students record their answers on their worksheet. Check for understanding, then let them try on their own. (Prompt students to restate the question)Allow time for the groups to take the measurements of three more objects (school, flag pole, another tree, tennis court fence, goal posts, street lights). If they finish early, they can do more measuring, or help other groups. (Ask students to draw a picture of the problem, Measuring, Solving real world problems, Participating in hands-on experiences, Collecting, organizing, displaying and interpreting information, Teach abstract concepts using drawings and diagrams)Return to the classroom and give time to finish the calculation portion of the assignment. Those who finish early can either assist another student practice with other trigonometry ratios can try/continue with a computer program such as Khan Academy . Students should complete their calculations individually this time. All work must be shown for assessment purposes and to assist with error correction. They should check their work before handing it in. Do the answers make sense? Work must be handed in for assessment. (Using formulas, Solving real world problems, Ask students to do the math by using paper and pencil and a calculator, Prompt students to check mathematics, Require students to review the word problem and to check that the answer makes sense)Final Review: What profession might use this type of math? How could you use trigonometry in your life? Are there any final questions regarding tangent ratio? Next class we will do sine ratio and cosine ratio…Content Relevant to the Whole Instructional UnitAchievement Indicators as per Ministry of Education Guidelines:Identify situations where the trigonometric ratios are used for indirect measurement of angles and lengths. (Ministry of Education, 2008)Solve a contextual problem that involves right triangles, using the primary trigonometric ratios. (Ministry of Education, 2008)Determine if a solution to a problem that involves primary trigonometric ratios is reasonable. (Ministry of Education, 2008)Linking Assessment with InstructionThe students will be assessed on the following criteria at the end of the mini unit:The students have the ability to use a formula to find a solution to a problem as shown on their worksheet. (Lessons 1 & 2)The students have the ability to use trigonometry functions on the calculator as shown during in class work and on their worksheet. (Lessons 1 & 2)The students have an understanding of connection to real life uses and interdisciplinary connections with the tangent ration as shown in the class discussions. (Lessons 1 & 2)The students have the ability to verbalize within a group the components of a trigonometry problem as shown during group discussions. (Lessons 1 & 2)The students have an understanding of the vocabulary of trigonometry and the ability to apply it to questions as shown during class and group discussions. (Lessons 1 & 2)The students have an ability to turn a real life problem into a 2-D drawing with calculations as shown on their worksheet. (Lesson 2)Differentiation Strategies: Multiple Intelligences: - The objective of the trigonometry lesson is based on the “general outcome: develop spatial sense” (Ministry of Education, 2008), however, throughout the lesson the student are encouraged to use multiple intelligences to meet the final goal. Linguistic intelligence is encouraged through the class and group discussions; Logical thinking is a natural part of the performance of mathematical equations; Body-kinesthetic comes into play when the students go outside and measure items in their environment; and Interpersonal contact, cooperation and teamwork are required to complete the measuring portion of the lesson.Pre-assessment: Throughout the unit, prediction and estimation are used to seek out information that is known about a topic.Readiness: The task moved from the simple identification of shapes in photos, to measuring indirect angles using an abstract concept.Interest: The application of information to “real life” is likely to encourage more students, than completing math from a textbook.Learning Profile: The lesson incorporates visual, auditory and kinesthetic methods to meet the natural learning needs of each class member.Process: Different processes give students time to internalize the information that has been presented in the lesson, tapping into the multiple intelligences.Product: The students are able to choose the item they are measuring and then visually present it in a way that meets their needs and shows their understanding. Diversity Strategies: The following excerpt is taken from The Common Curriculum Framework for Grades 10-12 Mathematics: Western and Northern Canadian Protocol. It is part of the curriculum and as such is required to be considered when creating lesson plans for First Nations students. First Nations, Métis and Inuit students often have a whole-world view of the environment; as a result, many of these students live and learn best in a holistic way. This means that students look for connections in learning and learn mathematics best when it is contextualized and not taught as discrete content.First Nations, Métis and Inuit students come from cultures where learning takes place through active participation. Traditionally, little emphasis was placed upon the written word. Oral communication along with practical applications and experiences are important to student learning and understanding. It is also vital that teachers understand and respond to nonverbal cues so that student learning and mathematical understanding are optimized.A variety of teaching and assessment strategies are required to build upon the diverse knowledge, cultures, communication styles, skills, attitudes, experiences and learning styles of students.The strategies used must go beyond the incidental inclusion of topics and objects unique to a culture or region and strive to achieve higher levels of multicultural education (Banks and Banks, 1993). (Ministry of Education, 2008)This has been honoured in this lesson plan sequence, by actively completing math problems in context as a real world problem, rather than just completing work from a book. In addition, during the experiential learning, there is an opportunity to work through learning in an oral, group oriented manner, as emphasized in the First Nations culture. Appendix A (Teacher’s Domain, 2012) (Ilio, 2003) (Puglette, 2009) (Koch, 2011) (Holger Mette, 2012) (Anonymous, 2009)Appendix B(All About Circuits)Appendix CSOH CAH TOA stands for the following operations:sinθ=oppositehypotenusecosθ=adjecenthypotenusetanθ=oppositeadjacentAppendix DFind the following side lengths and angles. Show all work on a separate sheet of paper. (Wessling, 2011)Appendix EDirectionsDraw and label the measurements of the object you are plete the trigonometry equation beside the diagram. Show all work to find the height. Don’t forget the unit of measurement Complete four diagrams and equations. Make sure the answers make sense.Remember: tanθ=oppositeadjacent1. 2.3.4.ReferencesAll About Circuits. (Designer). (n.d.). Right triangle trigonometry. [Web Graphic]. Retrieved from . (Photographer). (2009). Severns’ bridge. [Web Photo]. Retrieved from , L.G., & Spenciner, L.J. (2009). Teaching students with mild and moderate disabilities: Research-based practices. Upper Saddle River, New Jersey: Pearson.Holger Mette. (Photographer). (2012). Retrieved from , K. (Photographer). (2003). Architectural triangles under the harsh sun. [Web Photo]. Retrieved from , M., & Stacey, K. (1997). Teaching trigonometry. Retrieved from , J. (Photographer). (2011). Timeless triangles. [Web Photo]. Retrieved from , L. (Designer). (2011). Retrieved from of Education. (2008). The common curriculum framework for grades 10-12 mathematics: Western and northern Canadian protocol. Retrieved from . (Photographer). (2009). Tower at Ghirardelli square . [Web Photo]. Retrieved from 's Domain. (Photographer). (2012). Retrieved from , M. (2011). Trig ratio triangles here. Retrieved from ................
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