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EQUIVALENT RATIO TABLES |
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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 ratio tables in mathematical applications of daily life. |
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Definition: |
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A ratio table is a list of equal value (equivalent) ratios. |
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Mini Lesson: |
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We are 4 brothers and last week we went to SeaWorld San Antonio. We bought 4 tickets for $ 212, and we had a lot of fun visiting all the attractions. Dad asked how much each ticket costs because he wants to take the whole family there, including the grandparents, and in total, we are twelve people.
As I am studying 7th-grade mathematics, he asked me to do the calculations. I told him that we should divide 212 by 4 to know how much a ticket is worth (the unit price) and then multiply that result by 12, to find out how much 12 tickets cost. What do you think?
Also, asked me to make a table showing how much it would cost to bring a different number of people. |
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Equivalent Ratio Tables in Daily Life: |
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Frequently the sellers of a single product (for example tickets for a movie theater) have next to them tables that indicate how much to charge for different quantities of products (Ex. 1 ticket=$4,25, 2 tickets=$8.50, 3 tickets=12.75, etc.).
Chefs also use tables to know the quantities of ingredients in a recipe when handling different amounts of people. For example, if you have the amount of ingredients in the recipe for 4 people and you want to know the amount of ingredients for 10, 20, 50 or 100 people.
In currency exchange houses, conversion tables are used to know for example: What is the amount of pesos for X (different amounts of) dollars. |
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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. The first number is the x-coordinate, and the second number is the y-coordinate.
Graph. The pairs of numbers in the ratio table can be graphed onto a coordinate plane. |
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Resources: (from MsGarciaMath) |
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What is a Proportion |
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Means Extremes Property |
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PP06 Directly Proportional Word Problems |
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PP05 Solving a Proportion Equation |
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PP10 Proportion_I1 |
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PP11 Proportion_I2 |
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PP12 Proportion_I3 |
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Example Problems: |
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Yesterday 12 students from my classroom went to the circus and paid a total of $ 96 for their tickets. I want to go to the circus today with my brothers. How much do we need to take? |
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Using scaling, write in table 4 ratios equivalent to seven eighths. Use cross products to demonstrate that those ratios are equivalent to the original ratio. |
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My dad estimates that he can run the 42 kilometers of a marathon in 360 minutes. He asks me to complete a ratio table using equivalent ratios, to determine how far he must run in each of the indicated times? |
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We are going to go on vacation by car. My dad's car has a performance of 22 miles per gallon of gas. He asks me to make a table in which the distances between cities are in the first column and in the other column the number of gallons of gasoline it is estimated to consume. |
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