Lesson 2: Decimals
In this lesson, "Rock to the Top with Decimals" students will understand key features about decimals and how to convert them to equivalent fractions and percents.
- Understanding key features about decimals.
- Understanding how to convert decimals to equivalent fractions and percents.
- Printable Worksheet 2: Rock to the Top with Decimals (PDF)
- Printable Bonus Worksheet 2: Driving with Decimals/Mapping with Proportions (PDF)
Time required: 10 minutes, plus additional time for worksheets
- Students need to know that decimals, like fractions and percents, are another way of expressing portions of a whole.
- Tell students that they may be familiar with decimals as they are used with money (100 cents = $1.00, 50 cents = $0.50). When you say a decimal out loud, you express it in terms of tenths, hundredths, or thousandths. The first place after the decimal point represents 10ths, the 2nd place represents 100ths, and the 3rd place represents 1,000ths. For example, you say the decimal 0.2 as two tenths. You say the decimal 0.25 as twenty-five hundredths. You say the decimal 0.125 as one hundred and twenty-five thousandths.
- As soon as you say a decimal aloud, students can see how it converts into a fraction. After converting a decimal to a fraction, show how to simplify it. For example, 0.2 is 2/10, which can be reduced to 1/5. 0.25 is 25/100, which can be simplified to 1/4.
- Remind students that certain fractions do not convert into simple decimals. For example, 1/3 becomes 0.3 to infinity because that is the result you get when dividing 1 by 3.
- To convert a decimal to a percent, students move the decimal point two places to the right. A percent means “out of 100” or “per 100,” so by moving the decimal point two places to the right, you are multiplying the decimal by 100 to arrive at the percent. For example, 0.2 = 20% (0.2 x 100); 0.25 = 25% (0.25 x 100).
- Distribute Printable Worksheet 2: Rock to the Top with Decimals (PDF). Read the first paragraph aloud to your class and have students complete the problems. Have students read their answers aloud. Hearing decimals read aloud reinforces how they convert into fractions. Have someone write down their decimal answers to Question 3, and have them show how the numbers added together equal 1. The student should write on the board:
1.000 or 1
- Be sure to go over all correct answers using the Worksheet Answer Key (PDF).
- Optional: Distribute Printable Bonus Worksheet 2: Driving with Decimals/Mapping with Proportions (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?