Lesson: Adding and Subtracting Decimals
Introducing the Concept
Adding and subtracting decimal numbers follow the same rules as adding and subtracting whole numbers. The trick is to be sure that the place values line up. Because students are used to lining up numbers starting on the right, this is easy for numbers with the same number of decimal places, but errors start to occur when they do not.
Materials: grid paper or notebook paper turned sideways, play coins and bills
Prerequisite Skills and Concepts: Students must be comfortable adding and subtracting whole numbers with and without regrouping.
- Ask: What is the sum of twenty-four and thirty-two?
Encourage students to use mental math to arrive at a sum of fifty-six. After they have found the sum, write the problem on the board:
- Ask: What is the sum of two and four tenths and three and two tenths?
Encourage students to use mental math to arrive at a sum of five and six tenths. After they have found the sum, write the problem on the board, next to the first one:
- Ask: What is alike about these two sums?
Discuss this idea thoroughly. The decimal point is just a device to separate ones from tenths. Students should suggest that they may be able to use the same procedures to add decimal numbers that they use for adding whole numbers. - Ask: What is the sum of two and forty hundredths and three and twenty-five hundredths?
Encourage students to use mental math to arrive at a sum of five and sixty-five hundredths. After they have found the sum, write the problem on the board, next to the other two:
- Ask: What is the sum of two and four tenths and three and twenty-five hundredths?
Students may not be able to answer. If so, help them to see that four tenths has the same value as forty hundredths, so this sum must be the same as the last one. Write it as stated next to the other three:
- Ask: You can see that lining up the addends on the right as we do with whole numbers doesn't always work. Can you think of a rule for lining up the addends that will work for all whole numbers and decimal numbers?
If students think of the rule for lining up addends in whole-number addition as line up the ones, instead of line up from the right, they can use this rule in all cases. Lining up the decimal points works in all cases as well, but the decimal point is implied rather than written in whole-number addition. - Say: An easy way to be sure you always line up digits properly is to use a place-value chart or a piece of notebook paper turned sideways.
Demonstrate the use of both techniques
- Ask: What is the difference of thirty-two and twenty-four?
Encourage students to use mental math to arrive at a difference of eight. After they have found the difference, write the problem on the board:
- Ask: What is the difference of three and two tenths and two and four tenths?
Encourage students to use mental math to arrive at a difference of eight tenths. Then write the problem on the board, next to the first one:
- Ask: What is alike about these two differences?
Discuss this idea thoroughly. The decimal point is just a device to separate ones from tenths. Students should suggest that they may be able to use the same procedures to subtract decimal numbers that they use for subtracting whole numbers. - Ask: What is the difference of three and twenty-five hundredths and two and forty hundredths?
Encourage students to use mental math to arrive at a difference of eighty-five hundredths. After they have found the difference, write the problem on the board, next to the other two:
- Ask: What is the difference of three and twenty-five hundredths and two and four tenths?
This may stump students. Help students to see that four tenths has the same value as forty hundredths, so this difference must be the same as the last one. Write it as stated next to the other three:
Hand out play coins and bills and have students work in pairs to create, write, and solve addition and subtraction problems involving decimal numbers. Ask students to put an asterisk beside each amount that can be written as a decimal in another way (for example, 2.40 and 2.4).