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.

6-8

DURATION
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# Lesson 1: Converting Fractions

In this lesson, students will understand key features of fractions and how to convert fractions to equivalent decimals and percentages to solve real-world problems.

STANDARDS (CCSS & NCTM)

• Grade 7: Multi-Step Real-Life Problems With Fractions, Decimals, and Whole Numbers (CCSS 7.EE.B.3)
• Grade 6–8: Constructing an Argument, Modeling, Using Appropriate Tools, Attending to Precision (CCSS MP3–6); NCTM Number and Operations

OBJECTIVE
Students will be able to:

• Indicate that fractions, decimals, and percentages are different ways to depict a part-to-whole relationship; and
• Convert fractions to equivalent decimals and percentages to solve real-world problems.

MATERIALS

DIRECTIONS
Time required: 20 minutes, plus additional time for worksheet(s)

1. Remind students that fractions, decimals, and percentages are all ways of expressing parts of a whole. Start a basic review lesson by drawing a square on the board.

2. Draw a line vertically through the center of the square drawing. Ask students what fractions you have drawn. [The answer is 1/2 and 1/2.] Write an equation on the board showing how two halves added together equal a whole. [1/2 + 1/2 = 2/2 or 1]

3. Point out that sometimes it can be easier or more natural to convert fractions into a different format, such as decimals, for certain calculations. Ask students to think of a real-world situation in which this might be the case. Examples might include converting fractions to decimals when discussing money (if a younger sibling says he or she found five pennies on the ground and calls this 5/100 dollars, it would be easier to understand if you converted to 0.05 dollars, which can easily be understood as 5 cents).

4. Ask students how the same part-to-whole relationship in the square on the board could be expressed using decimals. [The square drawing shows 0.5 and 0.5.] Note that 0.5 + 0.5 = 1. Indicate that one way of thinking about fractions is that they are division problems, with the numerator as the dividend, the denominator as the divisor, and the fraction bar as the division symbol. To calculate the decimal equivalent of a fraction, simply divide the numerator by the denominator. So 1/2 is 1 ÷ 2, which equals 0.5.

5. Ask students to show the same relationship using percentages. [The answer is 50% + 50% = 100%.] Tell the class that the word percent means “out of 100.” To calculate a percentage equivalent from a fraction, first find the decimal equivalent and multiply by 100. Show how this can be achieved by moving the decimal point two places to the right. For example, 1/2 = 0.50 = 50%.

6. Draw another line horizontally through the square, cutting it in half again. Ask students to describe one of the 4 equal pieces as a fraction [1/4], as a decimal [0.25], and as a percent [25%]. Then draw two lines diagonally through the center of the square to create 8 equal pieces. Ask students to describe each piece as a fraction [1/8], a decimal [0.125], and a percent [12.5%].

7. Tell students that some fractions are not as easy to convert into decimals and percentages. For example, draw an empty box again and divide it into 3 equal bars. Ask students to describe a piece as a fraction [1/3]. Now ask them to show the piece as a decimal and as a percentage. The answer is 1 ÷ 3 = 0.3 or 33.3%. Explain that a line drawn over the top of a number means the digit repeats infinitely.

8. Remind students that when adding fractions, the fractions must have common denominators. For example, when adding 1/3 and 1/2, convert 1/3 to 2/6 and convert 1/2 to 3/6. [The sum is 5/6.] If necessary, remind students how to convert fractions to an equivalent by multiplying or dividing the numerator and the denominator by the same amount, e.g., 1/3 becomes 2/6 when the numerator and denominator are multiplied by 2.

9. Guided Practice: Group students into pairs and ask them to convert the fractions 1/5 and 1/6 to decimals and percentages. [Answer: 1/5 = 0.2 = 20%. 1/6 = 0.16 = 16.6%]

10. Independent Practice: Distribute Printable Worksheet 1: "Stardom: Just a Fraction Away" (PDF) for classwork or homework.

11. Check for Understanding: Review worksheet answers with the class using the Worksheet Answer Key (PDF).

12. Optional: For additional reinforcement or practice, distribute Printable Bonus Worksheet 1: "Ratio Radio" (PDF).Review worksheet answers with the class using the Worksheet Answer Key (PDF).

REAL-WORLD MATH EXTENSIONS

One or both extensions could be used in conjunction with any of the three lessons in Conversions Rock, as the teacher sees fit.

• 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 percentages. Actuaries also use ratios and proportions in predicting the likelihood of events. For example, by analyzing past experience, an insurance company determines 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 plan ahead and put aside money to pay for 500 accidents (based on the proportion 1/20 = 500/10,000).

• The Series of Unfortunate Events books contain types of events for which 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 might analyze?