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: 30:80
90:240, 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: 30:80
90:240, 120:320, 150: 400, 180, 480
• Scaling down: 30:80
6:16, 9:24, 12:32, 15:40, 18:48, 21:56
Example 1
Write a ratio to describe the relationship shown
in the table.
Hours
2
5
6
10
# of Pizzas Sold
16
40
48
80
Example 1
Write a ratio to describe the relationship shown in the table.
Hours
2
5
6
10
# of Pizzas Sold
16
40
48
80
The ratio used to create the table is 1:8, which means
that there are 8 pizzas being sold every hour.
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
Minutes
3
5
7
9
150
250
350
450
Minutes
2
4
6
8
Words
90
180
270
360
3
6
9
12
120
240
360
480
Words
Jenna
Maria
Minutes
Words
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.
Max
Minutes
Words
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.
Max
Minutes
1
Words
55
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.
Max
Minutes
1
2
Words
55
110
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.
Max
Minutes
1
2
3
Words
55
110
165
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.
Max
Minutes
1
2
3
4
Words
55
110
165
220
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 3:1
Franca 5:1
Milton 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 waterto-juice concentrate ratio, and whose juice
would taste the strongest? Be sure to justify
your answer.
Exercise 2b
6:1
5:2
8:3
12:2
15:6
16:6
18:3
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 waterto-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: 8:3
How 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 --- 40:16
Milton: 8:3 -- 8  5: 3  5 --- 40:15
Now 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: 16/6
Franca’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: 8:3
Put the juices in order from the strongest apple
taste to the weakest apple taste.
Exercise 2(b)
Laredo: 6:1 Franca: 5:2 Milton: 8:3
Put the juices in order from the strongest apple
taste to the weakest apple taste.
Franca, Milton, Laredo
Explain 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: 5:2
Milton: 8:3
Explain how the ratio could help you compare
the juices.
Exercise 2(b)
What ratio was used to create each table?
Laredo: 6:1
Franca: 5:2
Milton: 8:3
Explain how the ratio could help you compare
the juices.
How was this problem different than the grape
questions?
Exercise 2(c)
Max
JC
Water
Sheila
JC
Water
Exercise 2(d)
#1
Strawberries
other
#2
Strawberries
other
Exercise 2(c)
Max
JC
Water
4
15
8
30
3
8
6
16
12
45
Sheila
JC
Water
9
24
12
32
Exercise 2(d)
#1
Strawberries
other
2
7
4
14
6
21
3
9
6
18
9
27
#2
Strawberries
other
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.