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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. Auditorium Problem

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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?

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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?

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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

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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?

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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?

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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.

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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?

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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? 16 Girls Boys Each box represents 16 16

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Use Systems of Equations – Method 5 Let g = # of girls Let b = # of boys Total # 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?

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Use Systems of Equations – Method 5 Use substitution

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Use Systems of Equations – Method 5 How many students are seated in the auditorium?

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Use Systems of Equations – Method 6 7 [ ] -5g Use substitution

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Use Systems of Equations- Method 6 Let g = # of girls Let b = # of boys Total # 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?

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

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What is the Error?

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