What you should learn
To solve percent problems To solve problems involving simple interest NCTM Curriculm Standards 2, 6 - 9
To solve percent problems
To solve problems involving simple interest
NCTM Curriculm Standards 2, 6 - 9
In doing this the teacher wants to make sure that the following words are incorporated into the introductory lesson:
Percent Percentage Base Rate Simple Interest
Percent
Percentage
Base
Rate
Simple Interest
Introduction: Three out of 5 teenage girls wear mascara. What is the rate of teenage girls wearing mascara per 100 girls?
You can solve this problem by using a proportion. The ratio of teenage firls who wear mascara to the total number of teenage firls is 3/5. Write a proportion that sets 3/5 equal to the ratio with a denominator of 100.
Teenage girls wear mascara at a rate of 60 per 100, or 60 percent. A percent is a ratio that compares a number to 100. Percent also means per hundred, or hundredths. Percents can be expressed with a percent symbol (%), as fractions, or as decimals.
Exercise 1: Write 3/4 as a percent
3/4 = n/100 300 = 4n 75 = n Thus, 3/4 is equal to 75/100 or 75%
3/4 = n/100
300 = 4n
75 = n
Thus, 3/4 is equal to 75/100 or 75%
Proportions are often used to solve percent problems. One of the ratios in these proportions is always a comparision of two numbers called the percentage and the base. The other ratio, called the rate, is a fraction with the denominator of 100.
Percent Proportion: percentage/base = rate or percentage/base = r/100
Exercise 2:
a. 30 is what percent of 50? Use the percent proportion. percentage/base = r/100 30/50 = r/100 3000 = 50r 60 = r Thus, 30 is 60% of 50. b. 20 is what percent of 30?
a. 30 is what percent of 50?
Use the percent proportion. percentage/base = r/100 30/50 = r/100 3000 = 50r 60 = r Thus, 30 is 60% of 50.
Use the percent proportion.
percentage/base = r/100
30/50 = r/100
3000 = 50r
60 = r
Thus, 30 is 60% of 50.
b. 20 is what percent of 30?
You can also write equations to solve problems with percents.
Exercise 3:
a. 60% of what number is 54? (60/100) * x = 54 0.6x = 54 x = 90 Thus, 60% of 90 is 54. b. What number is 40% of 37.5?
a. 60% of what number is 54?
(60/100) * x = 54 0.6x = 54 x = 90 Thus, 60% of 90 is 54.
(60/100) * x = 54
0.6x = 54
x = 90
Thus, 60% of 90 is 54.
b. What number is 40% of 37.5?
Percents are also used in simple interest problems. Simple interest is the amount earned for the use of money. The formula I = prt is used to solve problems involving simple interest. In the formula, I represents the interest, p represents the amount of money invested, called the principal, r represents the annual interest rate, and t represents time in years.
Activity: Making Circle Graphs
Materials: compass and protactor You can use a circle graph to compare parts of a whole. Follow the steps to display the data below in a circle graph.
Materials: compass and protactor
You can use a circle graph to compare parts of a whole. Follow the steps to display the data below in a circle graph.
Never
1 - 5
5 or more
Don't Know
220
190
85
5
YOUR TURN a. Find the total number of people surveyed. b. Find the ratio that compares the nubmer of people that responded for each category to the total number of people that responded. c. Since there are 360 degrees in a circle, multiply each ratio by 360 to find the number of degrees for each section of the graph. Round to the nearest degree. d. Use a compass to draw a circle and a radius. e. Use a protractor to draw angles. Start with the least number of degrees. Repear for the remaining sections. Label each section and give the graph a title. f. What is the sum of the percents in your graph?
YOUR TURN
a. Find the total number of people surveyed.
b. Find the ratio that compares the nubmer of people that responded for each category to the total number of people that responded.
c. Since there are 360 degrees in a circle, multiply each ratio by 360 to find the number of degrees for each section of the graph. Round to the nearest degree.
d. Use a compass to draw a circle and a radius.
e. Use a protractor to draw angles. Start with the least number of degrees. Repear for the remaining sections. Label each section and give the graph a title.
f. What is the sum of the percents in your graph?
Exercise 4:
a.Luis Hernandez has some money he has saved over the summer from mowing lawns. He wants to put some of it in a 6-month certificate of deposit (CD) account that would pay 6% annual interest. He doesn't want to put all of his money in the CD because he wants some spending money. He is hoping to earn $45 in interest to buy a new video game. How much money should Luis put in the CD? Explore Let p = the amount of money Luis should deposit. Plan I = prt 45 = p(0.06)(0.5) Solve 45 = 0.03p 1500 = p Examine When p is 1500, I = (1500)(0.06)(0.5) or $45. Luis should deposit $1500. b. Whitney Williamson has $30,000 she would like to invest. She has a choice of two-interest-paying bonds, one offering a 6% annual interest and the other paying 7.5% annual interest. She would liek to earn $2100 in interest in one year. If she earns any more than $2100, she would need to pay a higher rate of income tax. How much money should she invest in each bond?
a.Luis Hernandez has some money he has saved over the summer from mowing lawns. He wants to put some of it in a 6-month certificate of deposit (CD) account that would pay 6% annual interest. He doesn't want to put all of his money in the CD because he wants some spending money. He is hoping to earn $45 in interest to buy a new video game. How much money should Luis put in the CD?
Explore Let p = the amount of money Luis should deposit. Plan I = prt 45 = p(0.06)(0.5) Solve 45 = 0.03p 1500 = p Examine When p is 1500, I = (1500)(0.06)(0.5) or $45. Luis should deposit $1500.
Explore
Let p = the amount of money Luis should deposit.
Plan
I = prt 45 = p(0.06)(0.5)
I = prt
45 = p(0.06)(0.5)
Solve
45 = 0.03p 1500 = p
45 = 0.03p
1500 = p
Examine
When p is 1500, I = (1500)(0.06)(0.5) or $45. Luis should deposit $1500.
b. Whitney Williamson has $30,000 she would like to invest. She has a choice of two-interest-paying bonds, one offering a 6% annual interest and the other paying 7.5% annual interest. She would liek to earn $2100 in interest in one year. If she earns any more than $2100, she would need to pay a higher rate of income tax. How much money should she invest in each bond?
Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.
Homework: The homework to be assigned for tonight would be: 17 - 45 odd, 46, 47 - 53 odd, 55 - 64
Alternative Homework: Enriched: 16 - 44 even, 46 - 64
Extra Practice: Students book page 765 Lesson 4-4
Extra Practice Worksheet: Click Here.
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