Vishnudas bhave auditorium, vashi - ACOUSTICS - AUDITORIUM - MUMBAI
Auditorium Problem
description
Transcript of Auditorium Problem
![Page 1: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/1.jpg)
6.RP - Understand ratio concepts and use ratio reasoning to solve problems.
7.RP - Analyze proportional relationships and use them to solve real-world and mathematical problems.
8.EE - Understand the connections between proportional relationships, lines, and linear equations.
Auditorium Problem
![Page 2: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/2.jpg)
5/7 of the students seated in an auditorium were girls. There are 48 more girls than boys. How many students are
seated in the auditorium?
![Page 3: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/3.jpg)
Use Proportional Reasoning- Method 1
What does 32 represent?
5/7 of the students seated in an auditorium were girls. There are 48 more girls than boys. How many students are seated in the auditorium?
What does x represent?
What does x + 48 represent?
What is the ratio of girls to boys?
![Page 4: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/4.jpg)
5/7 of the students seated in an auditorium were girls. There are 48 more girls than boys. How many students are seated in the auditorium?
Use Proportional Reasoning - Method 1
![Page 5: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/5.jpg)
Use Proportional Reasoning – Method 25/7 of the students seated in an auditorium were girls. There are 48 more girls than boys. How many students are seated in the auditorium?
What is the ratio of
girls to total students?
What does x represent?
Why does 2x+48 represent
the total # of students?
![Page 6: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/6.jpg)
Use Proportional Reasoning – Method 25/7 of the students seated in an auditorium were girls. There are 48 more girls than boys. How many students are seated in the auditorium?
![Page 7: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/7.jpg)
Use logical Reasoning- Method 3
5/7 of the students seated in an auditorium were girls. There are 48 more girls than boys. How many students are seated in the auditorium?
If 5/7 of the students are girls, then 2/7 of the students have to be boys. Therefore the difference between girls and boys is 3/7 of the students and since there are 48 more girls than boys, then 3/7 of the students must be equal to 48.
![Page 8: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/8.jpg)
Use logical Reasoning- Method 3
If 5/7 of the students are girls, then 2/7 of the students have to be boys. Therefore the difference between girls and boys is 3/7 of the students and since there are 48 more girls than boys, then 3/7 of the students must be equal to 48.
What does x represent?
![Page 9: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/9.jpg)
Use Model Drawings – method 45/7 of the students seated in an auditorium were girls. There are 48 more girls than boys. How many students are seated in the auditorium?
16Girls
Boys
48
16 16Each box represents 16
16 16
16 16
![Page 10: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/10.jpg)
Use Systems of Equations – Method 5
Let g = # of girlsLet b = # of boysTotal # of students = b + g
5/7 of the students seated in an auditorium were girls. There are 48 more girls than boys. How many students are seated in the auditorium?
![Page 11: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/11.jpg)
Use Systems of Equations – Method 5
Use
subs
tituti
on
![Page 12: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/12.jpg)
Use Systems of Equations – Method 5
How many students are seated in the auditorium?
![Page 13: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/13.jpg)
Use Systems of Equations – Method 6
7[ ]-5g-5g
Use substitution
![Page 14: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/14.jpg)
Use Systems of Equations- Method 6
Let g = # of girlsLet b = # of boysTotal # of students = b + g
5/7 of the students seated in an auditorium were girls. There are 48 more girls than boys. How many students are seated in the auditorium?
![Page 15: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/15.jpg)
Discussion
• How are the solution methods similar?• How are the solution methods
different?• Identify correspondences between
different solution methods.
![Page 16: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/16.jpg)
What is the Error?
![Page 17: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/17.jpg)
What is the Error?
![Page 18: Auditorium Problem](https://reader036.fdocuments.us/reader036/viewer/2022062301/56816197550346895dd14451/html5/thumbnails/18.jpg)
What is the Error?