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Equivalent Ratios




 
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Lesson Plans and Worksheets for Grade 6

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Common Core For Grade 6

New York State Common Core Math Module 1, Grade 6, Lesson 3

Video solutions to help Grade 6 students learn about equivalent ratios.

Lesson 3 Student Outcomes

• Students develop an intuitive understanding of equivalent ratios by using tape diagrams to explore possible quantities of each part when given the part-to-part ratio.
• Students use tape diagrams to solve problems when the part-to-part ratio is given and the value of one of the quantities is given.
• Students formalize a definition of equivalent ratios: Two ratios, A:B: and C:D , are equivalent ratios if there is a positive number, c, such that C = cA and D = cB.

Lesson 3 Summary

• Two ratios and are equivalent ratios 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.
• This description can be used to determine whether two ratios are equivalent.

Lesson 3

Exercise 1
Write a one-sentence story problem about a ratio.
Write the ratio in two different forms.

Exercise 2
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.
Draw a tape diagram to represent this ratio.

Exercise 3
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.
c. What ratios can we say are equivalent to 2:3?

Exercise 4
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.
b. If Josie missed 20 questions, how many did she get right? Draw a tape diagram to demonstrate how you found the answer. 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.
e. How did you find the numbers?
f. Describe how to create equivalent ratios.



Lesson 3 Word Problem

For every $5 that Mrs. Cramer spends, Mrs. Erno spends $7.
a. Determine a ratio to describe the money that Mrs. Cramer spent to the money that Mrs. Erno spent.
b. If Mrs. Erno spends $84, how much did Mrs. Cramer spend? <



 

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