Transcript NYS Core Curriculum lesson 3 Equivalent Ratios

NYS Core Curriculum lesson 3
Equivalent Ratios
Write a one-sentence story problem about ratios.
The ratio of sunny days to cloudy days in
Montgomery is 3:1.
Write the ratio in two different forms.
3:1 3 to 1
When prompted by your teacher, share your
sentences and ratios with your table partner.
You will have 2 minutes.
Lesson 3 Exercise 2
We can use a tape diagram to represent the ratio of the lengths of
ribbon. Let us create one together.
How many units should we draw for Shanni’s portion of the ratio?
How many units should we draw for Mel’s portion of the ratio?
Let’s represent this ratio in a table.
Shanni’s Ribbon
Mel’s Ribbon
7
3
14
6
21
9
Lesson 3 Exercise 2 Continued
• Shanni and Mel are using ribbon to decorate a project in their art class.
The ratio of the length of Shanni’s ribbon to Mel’s ribbon is 7:3.
• Draw a tape diagram to represent this ratio:
• Shanni (7)
• Mel (3)
• What does each unit on the tape diagram represent? (Students discuss….)
• (some unit that is a length)
• What if each unit on the tape diagram represents 1 inch?
Shanni’s 7 inches and Mel’s 3 inches?
• What is the ratio of the lengths of the ribbons? 7:3
• What if each unit on the tape diagram represents 2 meters? What are the
lengths of the ribbons? Shanni= 14 meters; Mel = 6 meters
• How did you determine that amount?
• What is the length of Shanni’s and Mel’s ribbons now? (Go back to prior
slide with equiv. chart)
Lesson 3 continued
• We just explored 3 different possibilities for
the length of the ribbon; did the number of
units in our tape ever diagram ever change?
No
• What did these 3 ratios, 7:3, 14:6, and 21:9,
all have in common?
• Mathematicians call these ratios equivalent.
What ratios can we say are equivalent to 7:3?
Lesson 3 continued
• Shanni and Mel are using ribbon to decorate a project in their art class.
The ratio of the length of Shanni’s ribbon to Mel’s ribbon is 7:3.
• Draw a tape diagram to represent this ratio.
•
•
•
•
•
•
Shanni
Mel
Shanni
Mel
Shanni
Mel
2
2
2
2
2
2
2
2
2
3
3
3
3
2
3
3
3
3
3
3
7 inches
3 inches
7:3
14 meters
6 meters 14:6
21 inches
9 inches 21:9
Exercise 3 Lesson 3
•
Mason and Laney ran laps to train for the long distance running team. The ratio of laps
Mason ran to the number of laps Laney ran was 2 to 3.
•
•
A. If Mason ran 4 miles, how far did Laney run? Draw a tape diagram to demonstrate
how you found the answer.
Mason (2) 2 2
•
Laney(3)
•
B. If Laney ran 930 meters, how far did Mason run? Draw a tape diagram to determine
how you found the answer.
•
•
Mason (2)
620 meters
310
310
•
•
Laney (3)
930 meters
310
310
•
C. What ratios can we say are equivalent to 2:3? 4:6 , 620:930
2 2 2
310
Exercise 4 Lesson 3
• Josie took a long multiple-choice, end of year vocabulary test. The ratio of
the number of problems Josie got incorrect to the number of problems
she got correct is 2:9.
• A. If Josie missed 8 questions, how many did she get right? Draw a tape
diagram to demonstrate how you found the answer.
• Wrong 4
4
• Right
4
4
4
4
4
4
4
4
4
• B. If Josie missed 20, how many did she get right? Draw a tape diagram
how you found the answer.
• Wrong
10
10
• Right
10
10
10
10
10
10
10
10
10
10
Exercise 4 continued
• C. Based on the tape diagram on the previous slide, what ratios can we
say are equivalent to 2:9?
• 8:36 and 20 :90
• D. Come up with another possible ratio of the number Josie got wrong
to the number she got right.
• Wrong
5 x2 = 10
5
• Right
•
•
•
•
5
?X9=
How do you find these missing numbers?
Multiply 2x5 and 9x5
Describe how to create equivalent ratios.
Multiply both numbers of the ratio by the same number, be sure to use
the same number on the top and the bottom!
Closing of lesson 3
• Two ratios A:B and C:D are equivalent if there
is a positive number ,c, such that C= cA and
D=cB.
• Ratios are equivalent if there is a positive
number that can be multiplied by both
quantities in one ratio to equal the
corresponding quantities in the second ratio.
• Now please complete your exit ticket for
Lesson 3: Equivalent Ratios sheet #29
Exit Ticket Lesson 3
For every two dollars that Pam saves in her account, her brother
saves five dollars.
• A. Determine a ratio to describe the money in Pam’s account
to the money in her brother’s account.
• B. If Pam has 40 dollars in her account, how much money
does her brother have in his account? Use a tape diagram to
support your answer.
• C. Record the equivalent ratio.
• D. Create another possible ratio that describes the
relationship between Pam’s account and her brother’s
account.
Solutions to Exit ticket lesson 3
For every two dollars that Pam saves in her account, her brother saves five
dollars.
•
A. Determine a ratio to describe the money in Pam’s account to the money
in her brother’s account. 2:5
•
B. If Pam has 40 dollars in her account, how much money does her brother
have in his account? Use a tape diagram to support your answer.
• Pam
• Bro
20
20
20
20
2 x 20 = 40
20
20
20
5 x 20 = 100
Solutions to exit ticket lesson 3
• C. Record the equivalent ratio.
• 40:100
• D. Create another possible ratio that
describes the relationship between Pam’s
account and her brother’s account.
• Answers will vary: 4:10, 8:20, etc….