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! @ @ * | l @ t @ L * H , @ , p , Lesson 11: Comparing Ratios Using Ratio Tables
Classwork
Example 1
Create four equivalent ratios (2 by scaling up and 2 by scaling down) using the ratio 30 to 80.
Write a ratio to describe the relationship shown in the table.
HoursNumber of Pizzas Sold2165406481080
Exercise 1
The following tables show how many words each person can text in a given amount of time. Compare the rates of texting for each person using the ratio table.
Michaela
Minutes3579Words150250350450
Jenna
Minutes2468Words90180270360
Maria
Minutes36912Words120240360480Complete the table so that it shows Max has a texting rate of 55 words per minute.
Max
Minutes
Words
Exercise 2: Making Juice (Comparing Juice to Water)
The tables below show the comparison of the amount of water to the amount of juice concentrate (JC) in grape juice made by three different people. Whose juice has the greatest water-to-juice concentrate ratio, and whose juice would taste strongest? Be sure to justify your answer.
Laredos JuiceFrancas JuiceMiltons JuiceWaterJCTotalWaterJCTotalWaterJCTotal1241610212821015520153181642021728255302463045156040848401050
Put the juices in order from the juice containing the most water to the juice containing the least water.
___________________ ____________________ _____________________
Explain how you used the values in the table to determine the order.
What ratio was used to create each table?
Laredo ___________________________ Franca ____________________________
Milton ___________________________
Explain how the ratio could help you compare the juices.
The next day, each of the three people made juice again, but this time they were making apple juice. Whose juice has the greatest water-to-juice concentrate ratio, and whose juice would taste the strongest? Be sure to justify your answer.
Laredos JuiceFrancas JuiceMiltons JuiceWaterJCTotalWaterJCTotalWaterJCTotal1221415621166221832120828249333053535144940155542749502070642488
Put the juices in order from the strongest apple taste to the weakest apple taste.
___________________ ____________________ _____________________
Explain how you used the values in the table to determine the order.
What ratio was used to create each table?
Laredo ___________________________ Franca ____________________________
Milton ___________________________
Explain how the ratio could help you compare the juices.
How was this problem different than the grape juice questions?
Max and Sheila are making orange juice. Max has mixed 15 cups of water with 4 cups of juice concentrate. Sheila has made her juice by mixing 8 cups water with 3 cups of juice concentrate. Compare the ratios of juice concentrate to water using ratio tables. State which beverage has a higher juice concentrate-to-water ratio.
Victor is making recipes for smoothies. His first recipe calls for 2 cups of strawberries and 7 cups of other ingredients. His second recipe says that 3 cups of strawberries are combined with 9 cups of other ingredients. Which smoothie recipe has more strawberries compared to other ingredients? Use ratio tables to justify your answer.
Problem Set
Sarah and Eva were swimming. Use the ratio tables below to determine who the faster swimmer is.
Sarah
Time (min)351217Distance (meters)75125300425 Eva
Time (min)271020Distance (meters)52182260520
Explain the method that you used to determine your answer.
A 120 lb. person would weigh about 20 lb. on the moon. A 150 lb. person would weigh 28 lb. on Io, a moon of Jupiter. Use ratio tables to determine which moon would make a person weigh the most.
Lesson Summary
Ratio tables can be used to compare two ratios.
Look for equal amounts in a row or column to compare the second amount associated with it.
3612307142870
You can also extend the values of the tables in order to get comparable amounts. Another method would be to compare the values of the ratios. Write the values of the ratios as fractions and then use your knowledge of fractions to compare the ratios.
When ratios are given in words, students can create a table of equivalent ratios in order to compare the ratios.
12:35 compared to 8:20
Quantity 112243648Quantity 23570105140
1025304516404872
Quantity 1856Quantity 220140
Lesson 11
61
MATHEMATICS CURRICULUM
Lesson #
XX
NYS COMMON CORE MATHEMATICS CURRICULUM
Topic X: Topic Title
Date: TIME \@ "M/d/yy" 8/19/14
PAGE 1
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