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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, lines, and linear equations.

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

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 - 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

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 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

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 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

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 5

Use substitution

Use Systems of Equations – Method 5

How many students are seated in the auditorium?

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

- How are the solution methods similar?
- How are the solution methods different?
- Identify correspondences between different solution methods.

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