Lesson 1: Fractions
In this lesson, "Stardom: Just a Fraction Away," students will understand key features about fractions and how to convert them to equivalent decimals and percents.
- Understanding key features about fractions
- Understanding how to convert fractions to equivalent decimals and percents.
Aligns with NCTM Standards (PDF)
- Printable Worksheet 1: Stardom: Just a Fraction Away (PDF)
- Printable Bonus Worksheet 1: Ratio Radio (PDF)
Time required: 10 minutes, plus additional time for worksheets
- Students need to know that fractions, decimals, and percents are all ways of expressing parts of a whole. Start a basic review lesson by drawing a square on the board.
- Draw a line vertically through the center of the square. Ask students what fractions you have drawn. [The answer is a 1/2 and a 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]
- Ask students to show this same equation in decimals. To get the decimal equivalent of a fraction, divide the numerator (the top number of a fraction) by the denominator (the bottom number of a fraction). So 1/2 is 1 ÷ 2 or 0.5. The equation in decimals is 0.5 + 0.5 = 1.0.
- Ask students to show the same equation in percents. A percent means “out of 100.” By moving the decimal point two places to the right, you are multiplying the decimal by 100 to arrive at the percent. So, 0.5 x 100 = 50%. The equation in percents is 50% + 50% = 100%.
- 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%].
- Draw a new empty square on the board. Ask students how to divide a square into 5 equal shapes. [The easiest way is to make 5 equal bars.] Ask how to describe one of the 5 pieces as a fraction, decimal, and percent. [1/5, 0.20, and 20%]
- Tell students that some fractions are not as easy to convert into decimals and percents. For example, draw an empty box again and divide 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 percent. The answer is 1 ÷ 3 = 0.3 to infinity or 33.3% to infinity. A line drawn over the top of a number means the number continues infinitely.
- Tell students that to add fractions, each fraction needs a common denominator. Ask students how to get the sum of 1/3 + 1/2. [Change 1/3 to 2/6 and 1/2 to 3/6. The answer is 5/6.]
- Distribute Printable Worksheet 1: Stardom: Just a Fraction Away (PDF). Tell students they should complete all the questions. Explain that for the bonus question, ratios and proportions can help solve the problem. A ratio is a comparison of two numbers. For example, the ratio of 1 and 4 can be written as 1:4, or as the fraction 1/4. A proportion is two equal ratios, such as 1/4 = 2/8. Go over correct answers as a class using the Worksheet Answer Key (PDF).
- Optional: Distribute Printable Bonus Worksheet 1: Ratio Radio (PDF).
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?