Auditorium Problem
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Auditorium problem

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

Use Proportional Reasoning- Method 1

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 is the ratio of girls to boys?

What does x represent?

What does x + 48 represent?

What does 32 represent?


Use proportional reasoning m ethod 1

Use Proportional Reasoning - Method 1

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 2

Use Proportional Reasoning – Method 2

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 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 21

Use Proportional Reasoning – Method 2

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 logical reasoning method 3

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 31

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 4

Use Model Drawings – method 4

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?

Girls

16

16

16

16

16

Each box represents 16

48

Boys

16

16


Use systems of equations method 5

Use Systems of Equations – Method 5

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?

Let g = # of girls

Let b = # of boys

Total # of students = b + g


Use systems of equations method 51

Use Systems of Equations – Method 5

Use substitution


Use systems of equations method 52

Use Systems of Equations – Method 5

How many students are seated in the auditorium?


Use systems of equations method 6

Use Systems of Equations – Method 6

7[ ]

-5g

-5g

Use substitution


Use systems of equations method 61

Use Systems of Equations- Method 6

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?

Let g = # of girls

Let b = # of boys

Total # of students = b + g


Discussion

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 error1

What is the Error?


What is the error2

What is the Error?


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