A Program of The Actuarial Foundation. Aligned with Common Core State and NCTM Standards.
What is an actuary? An actuary is an expert in statistics who works with businesses, governments, and organizations to help them plan for the future. Actuarial science is the discipline that applies math and statistical methods to assess risk. Background photo: © Inga Nielsen/iStockphoto.
About This Lesson Plan

SUBJECT
Math

GRADE
6-8

DURATION
1 Class Period

COLLECTION
Lessons: Conversions Rock
Conversions Rock

Lesson 3: Percents

In this lesson, "Show Me the Money with Percents," students will understand key features about percents and how to convert them to equivalent decimals and fractions.

OBJECTIVE

  • Understanding key features about percents
  • Understanding how to convert percents to equivalent decimals and fractions.

Aligns with NCTM Standards (PDF)

MATERIALS

DIRECTIONS
Time required: 10 minutes, plus additional time for worksheets

  1. Students need to know that percents, like fractions and decimals, are another way of expressing portions of a whole.

  2. Remind students that percent literally means “out of 100.” So 20%, for example, is 20 out of 100 or 20/100 or 1/5. To convert a percent to a fraction, put the percent over 100 and simplify the fraction.

  3. Tell students that to convert a percent to a decimal, move the decimal point two places to the left. Since percents are in the hundredths, you need to divide the percent by 100, which is the equivalent of moving the decimal point in the percent two places to the left. For example, 20% = 20 ÷ 100 = 0.2.

  4. Percents are often used to express part of the whole. For example, 35% of 400 people surveyed said they like rock music. How many people like rock music? In a simple math formula, the equation would be calculated as 0.35 x 400 = 140. To understand in terms of a proportion, the set up is 35/100 =  x/400. Students know that 35 out of every 100 like rock music. Since 400 is 4 times greater than 100, the number that like rock is 4 x 35 or 140.

  5. Students can also use proportions to calculate percents. For example, if 450 students out of 1,000 own a portable MP3 player, what percent of students own MP3 players? To get a percent, the goal is to arrive at a ratio with 100 as the denominator. Set up a proportion equation where 450/1000 = x/100. x = 45 or 45%.

  6. Distribute Printable Worksheet 3: Show Me the Money with Percents (PDF). Read the first paragraph aloud to your class and have students complete the problems. Explain to students that percents are used here to understand a budget, and a budget is a useful tool for students to use in tracking their own income and expenses. Tell students that using proportions and ratios can help solve many of the questions. Have students read their answers aloud and go over the correct answers using the Worksheet Answer Key (PDF).

  7. Once you’ve reviewed this activity in class, you may want to distribute Printable Bonus Worksheet 3: Time and Money: It’s a Matter of Math (PDF), which shows how percents can be used in problems regarding time and money. The bonus activity also explains the concept of greater than 100%.

REAL-WORLD MATH EXTENSIONS
  • Ask students if they can think of professions that involve math. Discuss with students what an actuary is. Actuaries use statistics in their job to calculate risks for many different industries, and they look at data in terms of fractions, decimals, and percents. If you ever take an exam to become an actuary, you’ll see that the test is full of fractions, decimals, and percents. Actuaries also use ratios and proportions in predicting likelihood of events. For example, by analyzing past experience, an insurance company believes that 1 in every 20 drivers will have an accident in a given year. If they insure 10,000 drivers this year, the insurance company can put aside money to pay for 500 accidents. The proportion is 1/20 = 500/10,000.

  • The Series of Unfortunate Events books contain types of events actuaries may estimate the likelihood of occurring. For example, they may find that 1/3 of all skiers have accidents. Or that 40% of all skydivers injure their feet. Or 0.20 of all residents in a Kansas town have experienced tornado damage. Can you think of other events actuaries may analyze?
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