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|Topic: Trigonometry – Sine law and cosine law: which to use? |Grade: 10 |Date: February 8th, 2017 |
|Lesson overview |Mathematical instructional goals |
|The goal of this lesson will be for students to be able to decide when to use the sine law or the cosine|Goals for students’ learning of mathematical concepts: |
|law in order to solve a triangle. Students will be able to determine which of the two methods would be | |
|the most effective depending on the problem and the information provided. At this point in time, |-Students will know the sine law formula |
|students will already know how to apply trigonometric ratios, the sine law and the cosine law. Students |-Students will know the cosine law formula |
|also already know when to apply trigonometric ratios. The first part of the lesson will be a small |-Students will know what information provided allows for the use of sine law and cosine law: |
|review session on sine law and cosine law. After the review session, students will engage in a |Sine law is used when we are given either a) 1 side and 2 angles; or b) 2 sides and 1 non-included|
|think-pair-share activity during which they will solve, in groups, a problem involving sine law and |angle |
|cosine law. After solving the problems, the students will participate in a class discussion and, with |Cosine law is used when we are given either a) 3 side; or b) 2 sides and 1 included angle |
|the help of the teacher and their classmates, draw the desired conclusions regarding when to use sine | |
|law and cosine law. |Goals for students’ learning of mathematical processes: |
| | |
| |- Students will be able to determine which method, between sine law and cosine law, is the most |
| |appropriate to use given the information provided. |
| |- Students will be able to apply sine law and cosine law in direct problems involving sides and |
| |angles of a triangle. |
| |- Students will be able to apply sine law and cosine law in word problems involving sides and |
| |angles of a triangle |
|Expectations and Competencies |Is there a Connection for Students? Connections to other Curricular Areas? Connections to |
| |Cross-Curricular Competencies? |
|Competency 2: Uses mathematical reasoning | |
| |The problems that the students will have to solve will be word problems and some of them might |
|Geometry |relate to their lives (calculating distances, calculating angles when playing pool, etc.). |
|G. #2 b) i, ii |Cross-curricular competencies |
|Algebra |Competency 1 : Uses information |
|C. #2 a) , #3, #7, #11 f) |Competency 2 : Solves problems |
| |Competency 5: Adopts effective work methods |
| |Competency 7: Achieves his/her potential |
| |Competency 8: Cooperates with others |
| |Competency 9: Communicates appropriately |
|Equity/ Diversity and Social Justice (Teacher Actions) |Expectations for students’ participation |
| | |
|The think – pair – share component allows the lesson to be equitable and attainable for all students. |Students will be encouraged to participate during the “share” component of the lesson, but |
|The group work will allow students to share their ideas together and get help from their teammates. It |participation will not be mandatory. |
|will also allow students to double-check their work and their answers. The share component of the lesson|The “pair” component of the lesson will nevertheless allow students to actively participate in the|
|will allow students to share their work with the class and to see their work as well as their |activity on a smaller scale. Students who feel anxious speaking in front of the whole class might |
|classmates’ work displayed on the board. Participation from all students would be ideal, but not |feel more comfortable sharing their ideas with their small group. This way, students who feel |
|mandatory. Participation will be voluntary so students who feel anxious about public speaking or about |nervous will still have the opportunity to participate in the activity. |
|sharing their work will not feel pressure. Students will be allowed to use their notes during the | |
|activity. | |
| |Questions to Ask |Accommodations/ Modifications |Materials |
| | |(content/process/product) | |
|Part 1: | |What is the sine law formula? |Students will be able to access |Smartboard |
|Minds On|Students will already have learned trigonometric ratios, sine law and cosine law. At this |What is the cosine law formula?|their class notes during this part | |
|(TIMING)|point in time, students will already know how to apply trigonometric ratios, sine law and |If I’m using the sine law |of the lesson |Calculators |
| |cosine law. Students also already know when to apply trigonometric ratios. |formula, how can I find the | | |
| |The lesson will begin with a review of sine law and cosine law in order to solidify the |measure of a missing side? A |Students will be able to solve a |Class notes |
| |students’ foundation. The teacher will do a review of sine law and cosine law. The teacher |missing angle? |problem on the board on a voluntary| |
| |will project on the smartboard a problem asking for the sine law and will solve it with the |If I’m using the cosine law |basis (no student will be forced to|At least two problems to |
| |help of the students. The teacher will do the same for the cosine law. Volunteer students |formula, how can I find the |come up to the board) |project on the smartboard |
| |will be invited to the board to solve the problems projected. After each solution, the teacher|measure of a missing side? A | |(one for sine law and one for|
| |will make a short summary of the students’ solution and answer any questions the students |missing angle? |Students will have the opportunity |cosine law) |
| |might have. The problems and their solutions will be saved and will be displayed on the smart |What are the hints that I have |to learn from their pairs as the | |
| |board during the second part of the activity as a reference for students. |to look for to know I didn’t |problems will be solved by the | |
| |After the review, students will be reminded that they know when to apply trigonometric ratios |make a mistake along the way? |students and guided by the teacher | |
| |as it involves a right-angle triangle, but that it might not be so obvious for sine and cosine|(e.g. taking the cosine of | | |
| |law. |something greater than 1 would |The teacher will go over the | |
| | |be impossible) |problems to make sure that all of | |
| | | |the important steps are covered and| |
| | | |that nothing is missing | |
| |Questions to Ask |Accommodations/ Modifications |Materials |
| | |(content/process/product) | |
|Part 2: |After the review portion of the lesson, a think-pair-share activity will take place. The | |Students will be working in teams |Worksheets (different problem|
|Action |students will be placed in groups of 3 and each team will receive an activity sheet with a |Why do you think I asked you to|of three, which will allow them to |for each team) |
|(TIMING)|problem calling for the sine law or the cosine law. Each group will have to solve their |specify the number of side, the|get help from their teammates | |
| |problem and, after, fill out the following information: |number of angles, the type of | |Pencils/pens |
| |1. # of sides given |angle and the method you used? |The teacher will be circulating in | |
| |2. # of angles given |Can you predict any kind of |the classroom and will assist any |Class notes |
| |3. Angle included or non-included (if there is only one angle) |pattern? |team that needs help | |
| |4. Method used (sine or cosine). |With the information provided, | |Calculators |
| |Each problem will be different so that students can compare their findings with other groups |would you have been able to use|Students will be allowed to use | |
| |during the class discussion that will follow. |the other method to solve your |their notes in order to solve the | |
| |During the part of the activity, the teacher will walk around the class and answer questions |problem? Why or why not? |problem | |
| |students might have without giving away too much information. Ideally, students should start | | | |
| |discussing in teams any patterns they might notice regarding number of sides, number of angles| |The problems that were solved at | |
| |and the method they chose to use. The teacher will gradually collect the papers and organize | |the beginning of the class will be | |
| |them on the board until the last team is done. | |displayed on the smart board and | |
| | | |the students will be allowed to | |
| | | |refer to them if needed | |
| |Questions to Ask |Accommodations / Differentiation |Materials |
| | |(content/process/product) | |
|Part 3: |The class will then engage in a discussion (“share” component of the activity). The teacher | | | |
|Consolida|will collect the findings of the students and will display on the board the different |How many sides were given to |Not every student will be obligated|Chalkboard or white board to |
|te/Debrie|situations. The teacher will divide the problems in three different sections: |you in this situation? |to share their solution, but |display the problems solved by|
|f |Problems with 1 side and 2 angles |How many angles were given to |participation is encouraged. |the students |
|(TIMING) |Problems with 2 sides and 1 angle |you in this situation? |If a student struggles to explain | |
| |Problems with 3 sides |Was the angle given included or|their reasoning, the teacher will |Magnets/scotch tape to hang |
| |The teacher will initiate the discussion and encourage different students from different |non-included? |help them by asking guiding |the problems on the board |
| |groups to describe their problem and discuss their solution. The teacher will draw the |Why did you choose to use that |questions. Other students will also| |
| |students’ attention to the problems displayed on the board and how they are organized. The |method? |be encouraged to help their peers. |Markers/chalk to write around |
| |teacher will ask questions (see next column) in order to guide the students towards the |Why do you think I arranged the|The worksheets will be displayed on|the sheets displayed on the |
| |desired conclusions. By the end of the discussion, the students should conclude the following:|problems the way I did? |the board as a visual aid. |board. |
| | |Would any of you would’ve |The teacher will write on the | |
| |Use sine law when we have |arranged the problems |board, in large letters, the |Problems solved by the |
| |1 side and 2 angles |differently? |important aspects of each worksheet|students. |
| |2 sides and 1 non-included angle |Would you eliminate a section? |so that the students can see them. | |
| |Use cosine law when we have |Create a new section? What |The teacher will read the aspects | |
| |3 sides |would it be? Why? |on the board so that the students | |
| |2 sides and 1 included angle |What do you notice in the |hear them. | |
| |After these conclusions are drawn by the students, the teacher will project the above list on |problems in the first section? | | |
| |the smart board and summarize the students’ conclusions in order to solidify their |In the other ones? | | |
| |understanding. Students will be ask to add these conclusions to their notes. The worksheets |What can you conclude? | | |
| |will be redistributed to the groups so they can adjust their solution and picked up by the | | | |
| |teacher again for assessment. | | | |
|Assessment Tools (diagnostic/formative/summative) |
|Public record of students’ thinking (problems solved during review + worksheets completed in teams) |
|The teacher will collect the revised worksheet |
|The teacher will collect, at the beginning of the next class, the word problems created by the students |
|The students work will be assessed according to the following criteria |
|Mathematical content (algebraic manipulations, trigonometric manipulations) |
|Choice of method (sine law or cosine law) |
|Justification of method used |
|Next Steps |
|As homework, students will have to individually create 2 short word problems, one using sine law and the other using cosine law. For each problem, they will have to justify the chosen method. The problems|
|will be collected at the beginning of the next class. |
|The next lesson will be on solving for the area of a triangle |
|The last lesson will be a culminating task: students will have to solve a situational problem involving trigonometric ratios, sine law and cosine law. |
|Self Reflection |
|What went well? |What didn’t go so well? |What do I need to change? |
| | | |
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