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Lesson 10: Proportion Measuring Height Indirectly

Lesson Component Description of Component For This Lesson
Lesson Opening   (10 minutes)     Introduction of New Material (15 - 20 minutes)   Objective: To use proportionality to find the height of the school flag pole. SWBAT: (1) Create a protractor, straw, string and paper clip surveying tool. (2) Measure the angle of elevation of the flagpole (3) Use proportionality to compute the height of the flag pole   I will use a “Do Now” to review scales. Students will be allowed to use calculators.   If the distance on a map between two cities is 3.25” and the scale is 1” to 50 miles how far apart are the cities?   (3) Mini-lesson I will help students to build their surveying tool (2) Engagement I will mention that the height of Mount Everest was measured with surveying equipment that modern GPS has confirmed is within a few feet of the actual height.
    Student Practice   (35-40 minutes)   (11) Exploration/Application   Use worksheet and rules attached below.   (4) Assessment The assessment will be ongoing as I help students to make their instrument then work in pairs to measure and compute.  
Summary (5 minutes) I will summarize how we determined a height indirectly by using similar triangles.

Estimating the height of the flag pole

 

 

       
 
B
   
 

 


 

Angle of Elevation ( ) = 90o

 

       
   
A
 
C
 

 

 


Steps to follow

 

 

1. Measure and fill in the table

 

 
Angle of Elevation (90o )  
Distance from you to the flag pole  
Distance from the ground to your eyes  

 

E
2. Draw triangle ABC and label it.

 
 


D
F
3. Draw another triangle DEF that is similar to triangle ABC using a protractor and a ruler.

Make sure that the angle D is equal to the angle of elevation and angle F is a right angle

 

4. Measure the lengths of the legs DF and EF with a ruler.

 

5. Write a proportion involving the ratio to and the ratio to .

 

6. Solve the proportion to find the distance . Round the result to one decimal place.

 

7. Calculate the height of the flag pole by adding the distance from the ground to your eyes to the distance .

Rules of the group work.

 

  1. Work in pairs.
  2. While one is observing, his/her partner should measure and record the angle of elevation.
  3. Partners should take turn observing and measuring the angle of elevation.
  4. Partners should work together to set up the proportion and to calculate the height of the flag pole.
  5. A complete report with the drawings and calculations should be submitted by Wednesday, May 14 (for 721 and 723) or Friday, May 16 (for 722).
  6. This group work counts as one of the quiz questions.

 

 

Rubric

 

Followed all the steps, has the drawings and the proportion, and the calculation is correct.  
Followed the steps for the most part, has the drawings, set up the proportion correctly, but the calculation is incorrect.  
Followed the steps for the most part, set up the proportion correctly, but does not have drawings.  
Missed many steps, does not have drawings, or set up the proportion incorrectly.  
Did not attempt to do the assignment.  

 

 


 

 

Graph the triangle:

(-2,-6), (3,-6), (3,6). What is the distance from (-2,-6) to (3,6)?

 

Graph the triangle:

(1,-4), (6,-4), (6,1). What is the distance from (1,-4) to (6,1)?

 


Conclusions

The preparation of this guide has allowed our group to revisit and improve our lessons. The tool that we used the most often has been the exit ticket or slip as described in Fisher, Brozo, Frey & Ivey. We also used variations of concept maps and flow charts. Our rooms are decorated with word walls and vocabulary is a part of every lesson. Future lessons may incorporate additional strategies such as vocabulary cards. While we did not use mnemonics in these particular lessons, “PEMDAS or Please Excuse My Dear Aunt Sally” is used to teach Order of Operations in classrooms across the country.

During the development of this guide, our group has become much more aware of the literacy needs of our students. We will continue to reach out to our students to help them become more proficient in the language of mathematics as well as the language of English.

 


References

 

A Tovani, I Read It, But I Don’t Get It, Stenhouse 2000

Fisher, Brozo, Frey & Ivey, 50 Content Area Strategies for Adolescent Learners, 2006

“Writing Before Writing”, Donald M. Murray, College Composition and Communication, NCTE December 1978

Jurgensen, Brown & Jurgensen, Geometry, McDougal Littell 2000

 

Impact Mathematics Course 2, McGraw Hill 2008

 

Date: 2015-12-24; view: 810

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