Auditorium Problem
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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, Auditorium Problem
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Transcript of Auditorium Problem
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
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
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?
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
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?
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?
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.
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?
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
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?
Use Systems of Equations – Method 5
Use
subs
tituti
on
Use Systems of Equations – Method 5
How many students are seated in the auditorium?
Use Systems of Equations – Method 6
7[ ]-5g-5g
Use substitution
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?
Discussion
• How are the solution methods similar?• How are the solution methods
different?• Identify correspondences between
different solution methods.
What is the Error?
What is the Error?
What is the Error?
