lesson 3: equivalent ratios · lesson 3 equivalent_ratios_math_6_wp_summary.notebook august 23,...

Lesson 3 Equivalent_Ratios_Math_6_WP_Summary.notebook August 23, 2014

Jan 88:18 AM

Lesson 3: Equivalent RatiosIn Lesson 3, we learned how to use ratio tables and tape diagrams to find equivalents ratios. Equivalent ratios are ratios that have the same value. First, we built a tape diagram from the ratio relationship:

Shanni and Mel are using ribbon to decorate a project in their art class. The ratio of the length of Shanni’s ribbon to the length of Mel’s ribbon is 7:3.

Then we created equivalent ratios using tape diagrams.

Next, we used tape diagrams to solve equivalent ratio problems.Mason and Laney ran laps to train for the long‐distance running team. The ratio of the number 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.

b. If Laney ran 930 meters, how far did Mason run? Draw a tape diagram to determine how you found the answer.

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Jan 88:18 AM

Lesson 3: Equivalent RatiosCONTINUED from first page...

Finally, we made the connection between tables and tape diagrams for making equivalent ratios.


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Learning Targets By the end of this lesson, you will be able to answer the following questions:(1) How can tables be used to find equivalent ratios?(2) How can tape diagrams be used to find equivalent 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 115:57 PM

ClassworkExercise 1Write a one‐sentence story problem about a ratio.

Write the ratio in two different forms.


Aug 115:57 PM

Exercise 2Shanni and Mel are using ribbon to decorate a project in their art class. The ratio of the length of Shanni’s ribbon to the length of Mel’s ribbon is 7:3.

Read this description. In a few seconds, I am going to take it away. I want you to describe in as much detail what the problem is about without looking at the problem.


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Describe in as much detail what the problem is about without looking at the problem.


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Let's represent this ratio in a table.


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Draw a tape diagram to represent this ratio:


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What does each unit on the tape diagram represent?Each unit represents one length of ribbon.

What if each unit on the tape diagram represents 1 inch? What are the lengths of the ribbons?Each unit represents one inch of ribbon.

What is the ratio of the lengths of the ribbons?


Aug 115:57 PM

Exercise 2Shanni and Mel are using ribbon to decorate a project in their art class. The ratio of the length of Shanni’s ribbon to the length of Mel’s ribbon is 7:3.What if each unit on the tape diagrams represents 2 meters?

What are the lengths of each of the ribbons?

How did you find that?If each unit is 2 meters, you put 2 meters in each unit and add or multiply to find the total for each person's length of ribbon.What is the ratio of the length of Shanni's ribbon to the length of Mel's ribbon now?


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What if each unit represents 3 inches? What are the lengths of the ribbons?

If each of the units represents 3 inches, what is the ratio of the length of Shanni's ribbon to the length of Mel's ribbon?


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We just explored three different possibilities for the length of the ribbon. Did the number of units in our tape diagram ever change?No, the number of units in our tape diagram always stayed 7: 3. All we did was change the value of each of the units.


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What did these 3 ratios, 7:3, 14:6, 21:9, all have in common?


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7:3, 14:6, 21:9

Mathematicians call these ratios equivalent.


Aug 116:09 PM

Exercise 3Mason and Laney ran laps to train for the long‐distance running team. The ratio of the number 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 ran 4 miles. That means his total is four. Since he has 2 units representing his part of the ratio, we divide 4 by 2 to find the value of each unit. Each unit it 2 miles. This means that each unit in Laney's part of the ratio is equal to 2 miles. We write 2 in each of the units of Laney's part of the ratio and use that to find her total. Since 2 + 2 + 2 = 2 x 3 = 6, Laney ran 6 miles.


Aug 116:09 PM

Exercise 3Mason and Laney ran laps to train for the long‐distance running team. The ratio of the number of laps Mason ran to the number of laps Laney ran was 2 to 3.

b. If Laney ran 930 meters, how far did Mason run? Draw a tape diagram to determine how you found the answer.

Laney ran 930 meters, so we label her part of the tape diagram with 930 meters. Then we divide 930 by 3 since there are three units in Laney's part of the tape diagram. The quotient is 310, which means each unit of the tape diagram is 310 meters. Since all units are the same size, we write 310 in each of Mason's units, and add or multiply to find the total meters Mason runs.


Aug 116:09 PM

Exercise 3Mason and Laney ran laps to train for the long‐distance running team. The ratio of the number of laps Mason ran to the number of laps Laney ran was 2 to 3.

c. What ratios can we say are equivalent to 2:3? The two ratios we found to be equivalent are 4:6 and 620:930.


Aug 116:09 PM

Exercise 4Josie 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.


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b. If Josie missed 20 questions, how many did she get right? Draw a tape diagram to demonstrate how you found the answer.


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c. What ratios can we say are equivalent to 2:9?

d. Come up with another possible ratio of the number Josie got wrong to the number she got right.


Aug 116:09 PM

Exercise 4Josie 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. e. How did you find the numbers?


Aug 116:09 PM


f. Describe how to create equivalent ratios. Equivalent ratios are created by taking the original ratio and multiplying both quantities by a constant (the same) number. You can do this in a tape diagram by putting the same number in all of the unit boxes, or you can do it by creating a table of equivalent ratios.


Jan 88:18 AM

Learning Targets Answer the following questions:(1) How can tables be used to find equivalent ratios?Equivalent ratios are created by taking the original ratio and multiplying both quantities by a constant (the same) number. In a table, you can repeat the pattern of the original ratio by adding the original ratio each time to create new (equivalent) ratios in the table.

(2) How can tape diagrams be used to find equivalent ratios?Draw the tape diagram with the original ratio. You can create equivalent ratios by putting the same number in each of the unit boxes and then adding or multiplying to find the value of the units in each line of the tape diagram.


Aug 115:50 PM

Lesson 3: Equivalent Ratios ‐ Exit TicketFor every two dollars that Pam saves in her account, her brother saves five dollars in his account.

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 using the information from part b above.

d. Create another possible ratio that describes the relationship between Pam’s account and her brother’s account.


Aug 106:42 PM

HomeworkProblem Set Lesson 3

lesson 3: equivalent ratios · lesson 3 equivalent_ratios_math_6_wp_summary.notebook august 23,...

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