Decimal Lesson Plans for Parents and Teachers

Tips for Teaching Decimals to Children

Commonalities of Fractions and Decimals

Children should have a good grasp of fractions before they begin decimals. Then, you can point out that fractions and decimals are different ways of saying the same thing. A number of books are available which may help to bridge these two concepts, including:

• Piece = Part = Portion by Scott Gifford
• Fractured Fairy Tales: Fractions & Decimals by Dan Greenberg
• Parting Is Such Sweet Sorrow: Fractions and Decimals (Adventures in Mathopolis) by Linda Powley

Understanding Decimals

You can expand the familiar place chart to include the decimal and the numbers following it. For example:

State that the numbers before the decimal include zero and larger; numbers after the decimal are smaller than one, just like a fraction. Some children understand the chart better if they think of the decimal point as the 'units column' for numbers smaller than one; this makes the chart more symmetrical for those students.

Practice reading numbers ranging from ones and tenths to hundreds and hundredths. Point out that 1/10 is read 'one tenth,' and 0.1 is also read as 'one tenth.' Explain that 0.10 is still read 'one tenth' and that no matter how many zeroes they add, it'll always be read as 'one tenth.' However, even if one of those zeros to another number, like 0.11, it makes the decimal number (fraction) smaller.

In a number with more than one digit, whether before or after the decimal, each digit is ten times bigger than it would be in the place on its right and 1/10 of what it would be in the place on its left. A good way to illustrate this is with money. Using play money, hold up a $100 bill and ask how many $10 bills you'd need to make $100. Keep moving one place to the right, asking the same kinds of questions. When you come to the decimal, explain that you're changing from bills to coins. Then, reverse directions and move from right to left.

Changing Decimals to Fractions

When children can read decimals correctly, they can then write them like fractions. The steps are read, write and reduce. For instance, 0.50 can be written as 50/100, which can be reduced to 1/2.

Adding and Subtracting Decimals

When adding and subtracting decimals, the only new concept you need to teach them is to line up the decimals. Remind them that the decimal points in all the numbers must be lined up and model a few examples, like 0.00001 + 0.0002 = 0.00021 and 0.01 + 0.02 = 0.03.

Multiplying Decimals

Once you've taught children to line up the decimals for addition and subtraction, you need to teach them to not line up the decimals for multiplication, just as you don't have to line up the tens and hundreds in a multiplication problem. However, always emphasize neatness and lining up numbers in each column to avoid problems of placing numbers in the wrong places for the addition step.

To figure out where to put the decimal place in the answer, count up the number of decimal places in the multiplicand and multiplier. For instance, in the problem, 2.1 x 3.24, the product would have three decimal places because there is one in the first number and two in the second number. Similarly, in the problem 3.256 x 8.01, the product would have five decimal places.

Dividing Decimals

When dividing using decimals, the only new concepts are where to put the decimal and that there is never a remainder. Teach them to move the decimal point in the divisor to the right end of the number, counting how many digits they move it. Have them figure whether they've multiplied that number by 10, 100, 1000, etc.

Just like working with fractions, they must now multiply the dividend by the same amount. Have them move the decimal point in the dividend, and also put one right above it in the quotient. They'll then divide as usual. However, they won't stop with a remainder. Instead, add a zero to the end of the dividend and bring it down to continue dividing. This will be a good place to teach them to round decimals.

For instance, in the problem 3.4 ÷ 2.1, first turn the divisor (2.1) into a whole number by moving the decimal point to the right, so it's now 21. Do the same for the dividend, so the problem is now 34 ÷ 21.

Changing Fractions to Decimals

Now that the children can divide decimals, they can change fractions to decimals. Simply divide the numerator by the denominator. For instance, the fraction 9/10 can be turned into a decimal by dividing nine by ten (9 ÷ 10), which equals 0.9.