Decimals can be tricky. Therefore, it is important to divide it into steps to teach it. First, the place value of whole numbers, such as tens and hundreds, must be explained. You can describe decimals as "middle" numbers that have their own place values, such as tenths and hundredths. Mention that these are related to fractions and show your students how to convert from one to the other. Once you've taught the basics, introduce some math operations with decimals, like addition and subtraction.
Method 1 of 3: Explain the Basics
Step 1. To get started, review the topic of place value of whole numbers
Write down some whole numbers and explain that each one has a place value. Show your students which corresponds to the ones, tens and hundreds.
For example, you could write the number 382. Tell your students that the number closest to the right, 2, is in the ones place; the next one on your left, number 8, is in the tens place; and the one closest to the left, the 3, occupies the hundreds place
Step 2. Explain that decimals are like "middle" numbers
Mention that not all numbers are integers. For example, you can start by saying that 5 and 6 are whole numbers, but there are many numbers between them. Show your students how to place the decimal point to the right of the ones and mention that all the numbers that come after are between two whole numbers.
Write "5" and explain the following: "If they see another 5 after the comma (write '5, 5') it means that this number is between 5 and 6."
Step 3. Present the place values of the decimals
Explain that, as with whole numbers, there are place values to the right of the decimal point. Show your students that the units are always to the left of the decimal point. Also, teach them that tenths are always immediately to the right of the decimal point, followed by hundredths and thousandths.
Emphasize the end of the words tenths and hundredths to differentiate them from their counterparts in integer values, which are tens and hundreds, respectively
Step 4. Describe the relationship between fractions and decimals
Explain that decimals and fractions are two ways to represent these "middle" numbers. Mention that a fraction can be converted to a decimal and that they will both represent the same number.
It is a good idea to use grids or figures. For example, you can draw a rectangle and draw lines to divide it 10 equal parts. Students can color one of these parts. Then explain that this is how 1/10 of the rectangle is represented. Also, teach them that you can also write this same number as 0, 1
Step 5. Explain how to convert fractions to decimals with divisions
Write down some simple fractions, like ¼, ½, and ¾. Explain that the fraction means that the numerator is divided by the denominator. Show your students that dividing the numerator, which is 1, by the denominator, which is 4, will give you a decimal value, which is 0.25.
Practice using division to convert basic fractions to decimals. Then show how the decimal place value, such as tenths and hundredths, is related to the numerator and denominator of the fraction. For example, 0.25 equals 25/100
Step 6. Practice reading fractions and decimals aloud
Write down several decimal numbers and read them out loud. Teach your students to use the correct place value when reading instead of having them read 1, 5 as "one point five."
- Write 25, 45 and read it aloud as "twenty-five forty-five hundredths." Write 54,035 and read it as "fifty-four and thirty-five thousandths."
- After showing students how to read decimals, write down several examples and ask them to read them aloud. Make corrections if necessary, and don't forget to encourage them with kind words: "That was a good try, but remember that number has a thousandths value. Try again."
Step 7. Explain how to know if one number is greater than another
Describe the difference in place values of whole numbers and decimals. That is, while hundreds are greater than tens, tenths are greater than hundredths. Put two decimal numbers in a column, one above the other, to show how to find the largest number.
For example, you can write the following numbers:
- Explain that to find the largest number, they must start with the tenths place. Since 5 is greater than 3, then it follows that 3,535 is greater than 3,353.
Step 8. Add zeros to help display place values
A beginner may find it difficult to compare numbers like 3, 5 and 3, 350, since 350 seems greater than 5. In this case, you can tell your students to put zeros to the right of the decimal number to fill in place values. Mention that doing this does not alter the value.
It may be easier to understand that 3,500 is greater than 3,350. Adding zeros to decimals is also useful for doing operations like addition and subtraction
Method 2 of 3: Use Visual Aids
Step 1. Fill in a grid to display the decimal values
Grids with 10 to 100 spaces are very useful for showing what a decimal number is and how to compare it to other numbers. You can create your own grid by drawing a rectangle and dividing it into 10 equal parts or by drawing a square and dividing it into 100 squares. You can also download and print a ready grid.
- Explain that the complete rectangle or square is worth 1. Color 6 of the 10 spaces and say the following: "I have colored 6 of 10 spaces. That is equal to 0, 6 or 6/10 (six tenths) of the total of the spaces."
- Color 25 spaces of a square with 100 spaces and say the following: "We have colored 25 out of 100 squares. That is equal to 0, 25 or 25/100 (twenty-five hundredths) of the total of the squares."
- Find which decimal number is greater by coloring the grids. For example, you can color 35 of 100 squares in the first one and then 25 of 100 squares in the second. Explain that 35/100 is greater than 25/100, so 0.35 is greater than 0.25.
Step 2. Draw number lines to compare the values
Number lines are another useful tool for teaching that decimals are found among whole numbers. Create a horizontal line with vertical stripes at each end. Write 5 above the left line and 6 above the right line.
Create another dash in the center of the line and write 5, 5. Explain that this number is right in the middle of 5 and 6. Ask the students where they would place the values 5, 75 and 5, 25, and continue putting more values along the line
Step 3. Use money to explain decimal numbers
Money is an excellent tangible tool for teaching this subject. Explain how the coins represent 0, 01, 0, 05, 0, 10 and 0, 25, depending on the monetary system of your country. Put together several coins in different combinations and use them to demonstrate the addition and subtraction of decimals.
Method 3 of 3: Solve Operations with Decimals
Step 1. Introduce the topic of how to round decimal numbers
Explain that decimals can be rounded by looking at the number to the right of the value to be rounded, and that place value can be tenths, hundredths, and so on. Tell students to check if the number to the right of the rounded value is greater than or equal to 5.
- Write 2, 527 and round it to the nearest hundredth. First, identify the place value of the hundredths in 2,527. Then, show them the number to the right. Since 7 is greater than 5, the number can be rounded to 2.53. Mention that if the case had been 2.522, it would have had to be rounded to 2.52.
- After solving some examples with the students, give them several practice exercises.
Step 2. Place the numbers on top of each other to add and subtract
Do a review of adding and subtracting whole numbers. Tell your students that adding and subtracting decimals is basically the same as with whole numbers. Emphasizes the importance of lining up the decimal point for these operations.
- Remind them that they can put zeros to fill in the blanks. It will be easier to subtract 3,350 from 3,500 if you can see all of the place values clearly.
- Write some examples and help them add or subtract as appropriate. Then have them work out some exercises on their own.
Step 3. Continue with the topic of multiplying decimals
First, check out the multiplication of whole numbers. Explain that the main difference between multiplying whole numbers and decimals is that in the second case, the decimal places must be added to find the answer. The product, which is the result of the multiplication of two numbers, must have as many decimal numbers as the combination of the decimal places of both numbers.
- For example, if you multiply 2, 5 by 5, 5, count the number of decimal values, which is two (each number has one decimal place). The product, which is 13, 75, must have 2 decimal places. If you multiply, 4.55 by 2.25, the product, which is 10, 2375, must have 4 decimal places.
- Work through some examples with your students and then give them some exercises to practice on their own.
Step 4. Move the decimal point to the right to divide the decimals
Review the topic of long division with whole numbers before teaching your students how to divide decimal numbers. Explain that you should move the decimal point of the divisor (the number that divides) to the right and the decimal point of the dividend (the number that is divided) the same number of places to the right.
- If you are dividing 15.75 by 1.5, place 1.5 outside the division symbol and 15.75 inside. Move the decimal point to the right to make the number 15. Since this involves moving the comma one place, you will have to move the comma of the number inside one place to the right as well, which will make it 157, 5.
- Place a decimal point above the division symbol directly above the decimal point of the number inside (which is now 157, 5 and not 15, 75). Do the division of 157, 5 by 15 and it will give you 10, 5. Emphasize the importance of moving and aligning the decimal points.
Step 5. Create or download exercises to practice
Solving exercises for practice is an essential part of learning math. You can create your own exercises or download a ready-made reprint from a website, such as Math.com (https://www.math.com/school/subject1/lessons/S1U1L2GL.html).
- Have your students work through at least 10-15 exercises to learn how to identify place value, rounding, converting to fractions, addition, subtraction, multiplication, and division. Help them with the first two or three problems and then have them solve them on their own.
- Be patient and encourage the students during the exercises. Decimals are a tricky subject, so kindly make corrections and remind them that it is a matter of practice.