How high is that wall? Elizabeth Daugherty
Lessons Prior to the Performance Task
The lesson will start with students learning how to determine which side in a right triangle is the opposite, adjacent, and hypotenuse when given a specific acute angle. They will then be shown a Sketchpad demonstration that introduces the idea of sine, cosine, and tangent. The focus will be on the idea that trigonometry is the relationship between the sides and angles in a right triangle and that the trigonometric value of a specific angle stays the same no matter the length of the sides of the triangle. After this demonstration, students will be told that they are going to become experts on one of the trigonometric ratios. The students will be split into three groups. One group will learn about the sine ratio with a teacher, one group will learn about the cosine ratio with the other teacher, and one group will learn about the tangent ratio with a video. Students will complete a worksheet while learning about their ratio. At the end of class, an online trig “mini golf” game will be used to summarize what the students learned in their separate groups for the entire class. Students will have homework on their specific ratio.
There will be a brief class discussion of what was learned last class. Afterwards, the students will be split into new groups in which each group has a sine expert, cosine expert, and tangent expert. They will all be given the same worksheet that will need to be completed in the group. Each expert will be expected to teach the other students about their ratio as it is used. The teachers will walk around and help as necessary. In order to prevent students from simply splitting up the problems and just working on their own ratio, the numbers for the sides will be given to students as they complete the previous problem. Students will have homework on all three trig ratios.
Class will begin with a Kahoot in which students need to determine which trigonometric ratio that should be used to solve for a missing side. They will then have time to practice finding the side lengths of right triangles through a relay activity. Each student will be given a question and when they have the answer correct, they will receive the next question. Students will be reminded that the reason they learned all of these ratios is because we wanted to measure the height of the wall in the New Pit. They will then complete the performance task described in detail below. Homework will be a review of all the trig ratios in preparation for the quiz the next class.
Description of Performance Task
Students will work in pairs to complete a worksheet that guides them through determining the height of the wall in the New Pit. In order to do this, they will need to make accurate measurements of their distance from the wall and their eye level. They will then have to determine the angle of elevation to the top of the wall using an altimeter. They will then need to use their measurements and knowledge of trigonometry to find the height of the wall.
- How high is that wall? worksheet
- Measuring tape
- Calculator with trig functions
Class discussion before activity:
The teacher will tell the students that the goal is to determine the height of the wall in the New Pit. However, we do not have a ladder or a measuring tape that is long enough. The students will then be asked how they can use trigonometry to find the height of the wall. The teacher will lead the students through a discussion in which they come up with the plan of which measurements they will need to make in order to accurately find the height of the wall.
The class will be split into two groups and each student will work with a partner. The class is split in half so that the Pit is not too crowded when the students are making their measurements. Both groups will have tasks to complete in the classroom and in the Pit. In the classroom, the students will need to measure the eye height of the partner that is using the altimeter. In the Pit, students will need to measure their distance from the wall and the angle of elevation to the top of the wall. The measuring tape will be taped to the ground so that the students can easily and accurately determine their distance from the wall. One partner will use the altimeter to spot the top of the wall while the other student reads the angle measurement. Once these measurements are completed, students will return to the classroom and send a new pair of students to the Pit to take their measurements. When the students return to the classroom, they will need to determine which trigonometric ratio they should use to find the measurement of the wall. They will then need to complete the appropriate calculations to find the height. Because everyone’s eye height is different and the distance from the wall may be different, each pair will be working with different values. However, they should all have about the same measurement for the height of the wall. Throughout the activity, the teachers are there to answer questions from the students and to double check measurements if the students desire.
Class Discussion after activity:
Students will share their answers with the class. Some questions that will need to be addressed are:
- Why did you chose to use the trigonometric ratio that you chose?
- Does anyone have the exact same answer? Why might everyone have a slightly different answer? Should it be the same?
- How does the accuracy of your measurements effect your answer?
- Do you need to consider your eye height in the final answer?
- As a class, can you agree on the measurement of the wall?
- Exceeds: 60%
- Approaches: 40%
All students exceeded in the first two “I Can” statements in which they needed to identify the correct trig ratio and correctly find the missing side of the triangle using that ratio. They have had a lot of practice doing this so it was great to see that they were successful in performing their new skill.
Some students struggled with measuring the distance and angle of elevation. My co-teacher and I expect measuring to be troublesome for them, as we have had this issue while measuring lengths throughout the year. We were both positioned by the students while they were measuring to help them obtain accurate results. However, some students chose not to take the measuring of the angle seriously which resulted in inaccurate results. Students that did not exceed in the “I Can” statements regarding measuring did so because of a lack of effort, which can be prevalent in this class.
The last “I Can” statement referred to the students ability to transfer their knowledge to a real world situation. In this case, students needed to think through this problem (which we did through a whole class discussion) and remember to consider the eye height of the person who measured the angle of elevation. Only one of the five groups successfully did this without prompting from the teacher. However, once it was pointed out to students that they did not find the height of the entire wall, all considered the diagram we drew during the class discussion and promptly changed their answer.