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If you know the ratio of students to teachers is 3 to 2 and you know there are 12 teachers, is there a way to figure out the number of students?

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In this lesson you will learn to solve for missing values in a ratio problem by setting up a double number line.

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Let’s Review A ratio can have equivalent ratios just like a fraction can have equivalent fractions. 2 : 1 x3 x3 6 : 3

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A Common Mistake The ratio of students to teachers is 5 to 1. There are 15 teachers. 5 1 wrong line! students teachers 15 ?

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Core Lesson Andy has a ratio of books to DVDS of 3 : 2 in his room. If he has 15 books, how many DVDs does he have? How can I use the ratio to help set up and solve?

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Books to DVDs 3 to 2 15 books ? DVDS Books to DVDs 3 to 2 15 books ? DVDS Books 3 2 6 4 9 6 12 8 15 10 Andy has 15 books and 10 DVDs. +3 +2 DVDs +3 +2 +3 +2 +3 +2

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Core Lesson +3 +3 +2 +2 x 5 x 5 multiplicative reasoning additive reasoning Books 3 23 2 6 46 4 9696 12 8 15 10 DVDs

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In this lesson you have learned to solve for missing values in a ratio problem by setting up a double number line.

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Guided Practice Anita collects shells and stones in a ratio of 2 : 1. If she has a total of 8 shells, how many stones does she have?

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Extension Activities 1 15 3 10 5 students teachers 1 3 5 8 12 16 Fill in the missing values of the double number line. Write a paragraph explaining what ratio properties were used to create and fill in the lines.

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Extension Activities Annie bakes cookies and cupcakes in a ratio of 4 to 3 for her gift boxes. Her school needs 35 desserts to sell in a bake sale. How many cupcakes will she bake? How many cookies will she bake? Create an illustration and a table to support your work.

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Quick Quiz George buys oranges and apples at a ratio of 3 :4 for his party. If he has 15 oranges, how many apples does he have? Kelly bakes cupcakes and cookies in a ratio of 5 to 3 for her bakery. If on any given day she bakes 20 cupcakes, how many cookies did she bake that day?

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How can you prove the Pythagorean Theorem by using the diagram below?

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