lesson 6: comparing ratios using ratio tables · pdf filelesson 6...

Lesson 6 Comparing_Ratios_Using_Ratio_Tables_Math_67_WP_Summary.notebook September 07, 2014

Jan 88:18 AM

Lesson 6: Comparing Ratios Using Ratio Tables

In this lesson, we learned to compare different ratios using ratio tables. For example, if you can simplify the ratios in each of the table so there is the same value in one column for each table, then you can compare those ratios.


Jan 88:18 AM

Lesson 6: Comparing Ratios Using Ratio TablesIf you cannot simplify to find a value where one of the numbers in the ratio is 1 in all tables, you can compare the values by creating equivalents ratios that each have the same value in the same column.


Jan 88:18 AM

Lesson 6: Comparing Ratios Using Ratio Tables

If there is the same number in the same column in both ratio tables, you can use that number to compare the two ratios and answer the question. If this is not present, you can create additional equivalent ratios in the table or tables to compare the two ratio tables.


Jan 88:18 AM

Learning Targets By the end of this lesson, you will be able to answer the following questions:(1) How can ratio tables be used to compare two ratios?


Jan 88:18 AM

Learning Targets Why do you need to know this?Ratios can be used to solve all types of real world problems. We use ratios to decide what items have the best price when we shop, which cars get the best gas mileage, and many other real world problems.


Aug 1710:16 AM

ClassworkExample 1Create four equivalent ratios (2 by scaling up and 2 by scaling down) using the ratio 30 to 80.

Let's compare our answers.

Scaling up means to multiply or add to get equivalent ratios.

Scaling down means to divide to get equivalent ratios.


Aug 1710:16 AM

ClassworkExample 1Write a ratio to describe the relationship shown in the table.

Let's compare our answers.


Aug 1710:49 AM

Exercise 1The 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.

How can we compare the testing rates? Michaela texts faster than Maria because she can text more words per 3 minutes (150 words is more than 120 words). Jenna texts faster than Maria because she can text 270 word in 6 minutes and Maria can only text 240 words in 6 minutes. Michaela is faster than Jenna because she would type 300 words in 6 minutes and Jenna would only type 270 words in the same time. Even though there is not a time that is common to all three tables, is it still possible to use the tables to determine which girl has the fastest texting rate and which is the slowests? You can compare the rates if the minutes are the same, which works for comparing Michaela to Maria and Maria to Jenna. You have to write an equivalent ratio to compare Jenna to Michaela.


Aug 1710:49 AM


If you used ratios to compare, what do the ratios mean in the context of this problem? You can write the value or each ratio by simplifying them to find out how many words each girl texts in 1 minutes. In this problem it works because they can all be simplified to 1 minute and you keep whole numbers in both the minutes and the words.


Aug 1710:49 AM


How can we use the ratios to help us compare the testing rates of the three girls? Once you find the words each girl texts in 1 minute, you can see who types more words in the same amount of time.


Aug 1710:49 AM


Why can't I just pick the student that has the largest number of words at the end of the table? Since the times aren't the same, you cannot just pick the girl with the most words. The largest number of words can be seen in Maria's table, but the number of minutes is also the largest and cannot be compared just on sight to the other girls' times and minutes.


Aug 1710:49 AM

Exercise 1If there were a fourth person, Max, who can text 55 words per minute, how could we create a table to show his texting speed?

Start with the first column (1 minute and 55 words). Then repeat the pattern by adding 1 minute and 55 words until the table is full.

You can also think of it as multiplying. Each time, we multiply the number of minutes by 55 to get the number of words.


Aug 1710:56 AM

Exercise 2: Making Juice ﴾Comparing Juice to Water﴿a. 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.

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. Find common numbers in the same column of the tables and compare them to each other.

What ratio was used to create each table?

Laredo _______________ Franca ___________________ Milton______________________Explain how the ratio could help you compare the juices. Franca has the most water per 1 cup of juice concentrate.


Aug 1710:57 AM

b. 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.

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. Since Milton and Franca both have 6 in the JC column, you can compare them and can see that Franca has less water for the same amount of JC (6). Then you can figure out how many cups of water Laredo has when he has 6 cups of JC, which is 36. You can use this to see that his juice is the most watered down.What ratio was used to create each table?Laredo__________________ Franca __________________ Milton _________________Explain how the ratio could help you compare the juices. In this problem you have to figure out what one ratio is where each person has either the same amount of juice or the same amount of water. How was this problem different than the grape juice questions? This problem was different because you could not simplify the ratios and find our how much juice each person put in when they put in 1 cup of water.


Aug 1710:59 AM

c. 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.

WATER JC WATER JC

MAX SHEILA

Sheila has a higher juice concentratetowater ratio because she only has 32 cups of water with 12 cups of juice concentrate, but Max has 45 cups of water for the same amount (12) cups of juice concentrate.


Aug 1710:51 AM

d. 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.

1st RECIPE 2nd RECIPEStrawberries Other Ingredients Strawberries Other Ingredients

The 2nd recipe has more strawberries compared to other ingredients because when there are 6 cups of strawberries, there are only 18 cups of other ingredients compared to the other recipe that has 21 cups of other ingredients when there are 6 cups of strawberries.


Jan 88:18 AM

Learning Targets Answer this question:(1) How can ratio tables be used to compare two ratios? If there is the same number in the same column in both ratio tables, you can use that number to compare the two ratios and answer the question. If this is not present, you can create additional equivalent ratios in the table or tables to compare the two ratio tables.


Aug 106:42 PM

HomeworkProblem Set Lesson 6

lesson 6: comparing ratios using ratio tables · pdf filelesson 6...

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