Grade 6 Module 1 Lesson 11

Example 1

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

Example 1

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

• Example of Scaling up:30 to 80 is equivalent to 60 to 160

• Example of Scaling down:30 to 80 is equivalent to 3 to 8

Example 1

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

• Scaling up: 30:8090:240, 120:320, 150: 400, 180:480

Example 1

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

• Scaling up: 30:8090:240, 120:320, 150: 400, 180, 480

• Scaling down: 30:806:16, 9:24, 12:32, 15:40, 18:48, 21:56

Example 1

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

Hours # of Pizzas Sold2 165 406 48

10 80

Example 1

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

The ratio used to create the table is 1:8, which means that there are 8 pizzas being

sold every hour.

Hours # of Pizzas Sold2 165 406 48

10 80

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.

MichaelaMinutes 3 5 7 9

Words 150 250 350 450

Minutes 2 4 6 8

Words 90 180 270 360

Jenna

Minutes 3 6 9 12

Words 120 240 360 480

Maria

Exercise 1

• How can we compare the texting rates?

Exercise 1

• How can we compare the texting rates?• Which girl has the fastest texting rate and

which has the slowest?

Exercise 1

• How can we compare the texting rates?• Which girl has the fastest texting rate and

which has the slowest?• If you used ratios to compare, what do the

ratios mean in the context of this problem?

Exercise 1

• How can we compare the texting rates?• Which girl has the fastest texting rate and

which has the slowest?• If you used ratios to compare, what do the

ratios mean in the context of this problem?• How can we use the ratios to help us compare

the texting rates of the three girls?

Exercise 1

• How can we compare the texting rates?• Which girl has the fastest texting rate and which

has the slowest?• If you used ratios to compare, what do the ratios

mean in the context of this problem?• How can we use the ratios to help us compare

the texting rates of the three girls? • Why can’t I just pick the student that has the

largest number of words at the end of the table?

Exercise 1

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

• Complete the table so that it shows Max has a texting rate of 55 words per minute.

MinutesWords

Max

Exercise 1

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

• Complete the table so that it shows Max has a texting rate of 55 words per minute.

Minutes 1Words 55

Max

Exercise 1

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

• Complete the table so that it shows Max has a texting rate of 55 words per minute.

Minutes 1 2Words 55 110

Max

Exercise 1

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

• Complete the table so that it shows Max has a texting rate of 55 words per minute.

Minutes 1 2 3Words 55 110 165

Max

Exercise 1

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

• Complete the table so that it shows Max has a texting rate of 55 words per minute.

Minutes 1 2 3 4Words 55 110 165 220

Max

Exercise 2

• The tables 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.

Exercise 2

Work with your partner to answer question 2a.

Exercise 2

Franca’s juice has the greatest amount of water in comparison to juice concentrate (5:1), followed by Milton (4:1) and then Laredo (3:1). Because Laredo’s juice has the least amount of water in comparison to juice concentrate, his juice would taste the strongest.

Exercise 2

Put the juice in order from the juice containing the most water to the juice containing the least water.

Exercise 2

Put the juice in order from the juice containing the most water to the juice containing the least water.

Franca, Milton, Laredo

Exercise 2

Put the juice in order from the juice containing the most water to the juice containing the least water. Answer: Franca, Milton, Laredo

Explain how you used the values in the table to determine the order.

Exercise 2

Explain how you used the values in the table to determine the order.Laredo makes his juice by combining 3 cups of water for every cup of juice concentrate.Franca makes her juice by combining 5 cups of water for every cup of juice concentrate.Milton makes his juice by combining 4 cups of water for every cup of juice concentrate.

Exercise 2

What ratio was used to create each table?

Exercise 2

What ratio was used to create each table?

Loredo 3:1Franca 5:1Milton 4:1

Explain how the ratio could help you compare the juices.

Exercise 2(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.

Exercise 2b

6:1 12:2 18:35:2 15:68:3 16:6

Exercise 2(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 who juice would taste the strongest? Be sure to justify your answer. Laredo: 6:1 Franca: 5:2 Milton: 8:3(How do we compare these three ratios?)

Exercise 2(b)

Laredo: 6:1 Franca: 5:2 Milton: 8:3(How do we compare these three ratios?)Laredo: 6:1 is equivalent to 12:2 and 18:3. When comparing Laredo to Franca (5:2) and Milton (8:3), you can see that more cups of water was added to Laredo. This tells us that Laredo’s juice has the weakest apple taste.

Exercise 2(b)

Laredo: 6:1 Franca: 5:2 Milton: 8:3How do we compare the other two ratios?(They currently do not have the same number of cups of water or cups of juice.)We would need to either make the cups of water equal or cups of juice equal.

Exercise 2(b)

Laredo: 6:1 Franca: 5:2 Milton: 8:3(How do we compare the other two ratios?)Franca: 5:2 -- 5 × 8: 2 × 8 --- 40:16Milton: 8:3 -- 8 × 5: 3 × 5 --- 40:15Now we can compare and see that Franca’s juice has more juice concentrate compared to water than Milton’s juice.

Exercise 2(b)

Laredo: 6:1 Franca: 5:2 Milton: 8:3(How do we compare the other two ratios?)Franca: 15/6 Milton: 16/6Franca’s juice is the stronger of the two because it has 1 less cup of water per 6 cups of juice in comparison to Milton’s juice.

Exercise 2(b)

Laredo: 6:1 Franca: 5:2 Milton: 8:3Put the juices in order from the strongest apple taste to the weakest apple taste.

Exercise 2(b)

Laredo: 6:1 Franca: 5:2 Milton: 8:3Put the juices in order from the strongest apple taste to the weakest apple taste. Franca, Milton, LaredoExplain how you used the values in the table to determine the order.

Exercise 2(b)

What ratio was used to create each table?Laredo_________ Franca__________Milton_________

Exercise 2(b)

What ratio was used to create each table?Laredo: 6:1 Franca: 5:2Milton: 8:3Explain how the ratio could help you compare the juices.

Exercise 2(b)

What ratio was used to create each table?Laredo: 6:1 Franca: 5:2Milton: 8:3Explain how the ratio could help you compare the juices.How was this problem different than the grape questions?

Exercise 2(c)

JCWater

Max

JCWater

Sheila

Exercise 2(d)

Strawberriesother

#1

Strawberriesother

#2

Exercise 2(c)

JC 4 8 12Water 15 30 45

Max

Sheila

JC 3 6 9 12Water 8 16 24 32

Exercise 2(d)

Strawberries 2 4 6other 7 14 21

#1

Strawberries 3 6 9other 9 18 27

#2

Closing

Today we used ratio tables to compare two ratios that were not equivalent and answered questions about which situation would reach a given level first. Can anyone think of another way to compare two different ratios?

Closing

Today we used ratio tables to compare two ratios that were not equivalent and answered questions about which situation would reach a given level first. Can anyone think of another way to compare two different ratios? The value of a ratio might be useful because then we could determine which ratio had the larger or smaller value.