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EQUIVALENT RATIOS |
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Objective: |
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The student will be able to solve real-world problems with equivalent ratios. |
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Standards: |
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7.4 Proportionality. The student applies mathematical process standards to represent and solve problems involving proportional relationships. The student is expected to:
(D) solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems |
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Success Criteria: |
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Understand and use equivalent ratios in mathematical applications of daily life. |
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Definition: |
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Equivalent ratios express the same relationship between numbers.
They have the same value. |
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Mini Lesson: |
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My mom made two equal cakes. The first cake was split into 4 equal parts. The second cake was divided into 8 equal parts. I ate a slice (a quarter) of the first cake, and my brother ate two slices (two eighths) of the second cake.
My brother says he ate more cake because he ate two slices and I ate only one. What do you think?
My brother is wrong. Cutting one cake into four equal slices and eating one slice, is equivalent to cutting one cake into eight equal slices and eating two.
The ratios are equivalent; they have the same value. |
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Equivalent Ratios in Daily Life: |
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The equivalent ratios are often used in real life. Suppose for example, that you have a cooking recipe with the ingredients to make a cake (4 eggs, 3 cups all-purpose flour, 2 cups white sugar, 1 cup butter, 1 tablespoon vanilla extract, 1 tablespoon baking powder). What is the amount of each ingredient that I need to make 5 cakes?
In construction, the basic mixture of mortar can be made using the volume proportions of 1 water : 2 cement : 3 sand. With this recipe I can prepare 4 volumes of concrete. What is the amount of each ingredient that I need to make 20 volumes of concrete?
When managing relationships of people with people such as employees with clients or teachers with students. At our school, there are 48 teachers and 1200 students. How many teachers are required if the number of students will grow to 1500 next year?
When estimating gasoline consumption or costs on a trip, for example, I know that my car used 10 gallons of gas to go from Laredo to San Antonio, which is 150 miles. How many gallons of gas do I need to travel from Laredo to Houston, if the distance is 315 miles? |
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Vocabulary: |
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Ratio: is a comparison between a pair of numbers. We can write the ratio as a fraction, where the top (numerator) is one value, and the bottom (denominator) is the other value.
Equivalent ratios: are ratios that show the same relationship between the two quantities (they have the same numerical value).
Scaling. To multiply or divide numerator and denominator of a ratio by the same number.
Ratio Table. A table with columns filled with pairs of numbers that have the same ratio. |
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Resources: (from MsGarciaMath) |
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Ratios and Rates Vocabulary |
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Means Extremes Property |
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Proportions in Real Life |
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Ratio and Proportion Vocabulary |
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CM 1 Proportions (unit price) |
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ME20 Liquid |
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ME05 Length 1 |
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Example Problems: |
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Determine whether the ratios 5:7 and 60:84 are equivalent |
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What must X be if the ratio 3:5 is equivalent to X:45? |
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On a scale map, 3 inches correspond to a 25-mile distance. How many inches of the map correspond to 300 miles? |
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A recipe calls for 3 cups all-purpose flour for every cup of butter. If your mom wants to make a large batch of this recipe, how many cups of all-purpose flour will be needed if five cups of butter are used? |
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