Ratios and Rates as Percentages

The Lesson Activities will help you meet these educational goals:

·  Content Knowledge—You will find a percentage of a quantity as a rate per 100 and solve problems that involve finding the whole, given a part and the percentage.

·  Mathematical Practices—You will make sense of problems and solve them and use mathematics to model real-world situations.

·  STEM—You will apply mathematical and technology tools and knowledge to analyze real-world situations.

·  21st Century Skills—You will assess and validate information and communicate effectively.

Directions

You will evaluate some of these activities yourself, and your teacher may evaluate others. Please save this document before beginning the lesson and keep the document open for reference during the lesson. Type your answers directly in this document for all activities.

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Self-Checked Activities

Read the instructions for the following activities and type in your responses. At the end of the lesson, click the link to open the Student Answer Sheet. Use the answers or sample responses to evaluate your own work.

1.  Calculating Percentages

In the class election, the student who gets the highest number of votes will become the class president and the one who gets the second highest number of votes will become the class vice president. Tabitha and four other students were candidates. Tabitha’s teacher announces the election results as percentages of the total number of votes. Two hundred votes were cast in the election. In this activity, you will relate the percentages of the votes received to the actual numbers.

a.  The table gives the percentage of votes each candidate received. Use the information in the table to understand the results of the election.

Candidate / Percentage of Votes
Tabitha / 30%
Vincent / 12%
Esmeralda / 22%
Nancy / 5%
Tyler / 31%

i.  How many votes did Tabitha receive?

Sample answer:

Tabitha received 30% of 200 votes:

Tabitha received 60 votes.

ii.  What was the highest number of votes received by a single candidate?

Sample answer:

The candidate who got the highest number of votes was the one who got the highest percentage of the total votes cast. Tyler, who got 31% of the votes, got the highest number of votes:

31% of 200 = = 62 votes.

iii.  What was the second highest number of votes?

Sample answer:

Tabitha, with 30% of the total votes, got the second highest number of votes:

30% of 200 = = 60 votes.

iv.  Did Tabitha win the election? If she did not, will she still get one of the posts?

Sample answer:

No, Tabitha did not win the election. But Tabitha got the second highest number of votes, so she will get the post of class vice president.

b.  Tabitha’s brother, Toby, is in a runoff for president in his grade, which means that there is only one other student in the election. To win, Toby has to get more than 50% of the total votes cast.

i.  Toby gets 78 votes, which is 52% of the total votes cast. How many students voted in Toby’s grade?

Sample answer:

52% of the number of students who voted = 78. So:

number of students who voted = 78

number of students who voted = = 150.

150 students voted in Toby’s grade.

ii.  If 75% of the students in Toby’s grade voted, how many students are in Toby’s grade?

Sample answer:

From the previous question, we know that 150 students in Toby’s grade voted. We also know that 75% of the students in Toby’s grade voted. So:

number of students who voted = 75% = 150

75% of total number of students = 150

total number of students = 150

total number of students =

The total number of students in Toby’s grade is 200.

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