For instance, write down 382. Tell students that the number farthest to the right, or 2, stands for ones, the next number to the left, or 8, is the tens place, and the next to the left, or 3, is hundreds.
Write “5. ” and say, “If you see another 5 after the point (write ‘5. 5’), that means it’s in between 5 and 6. ”
Over-pronounce tenths and hundredths to avoid confusing decimal place values with tens and hundreds.
Coloring grids or shapes is helpful. Draw a rectangle, then add lines to divide it into 10 equal strips. Have them color in a strip, then explain that the strip is 1/10 of the rectangle. Tell them that 0. 1 is another way of saying 1/10, or one-tenth.
Practice using division to convert basic fractions to decimals. Then show how the decimal place values, such as the tenths and hundredths places, relate to the top and bottom numbers of the fraction. For example, 0. 25 means 25/100.
Write down 25. 45 and read it out loud as “twenty-five and forty-five hundredths. ” Write 54. 035 and read it as “fifty-four and thirty-five thousandths. ” After demonstrating how to read decimals, write down several examples and have them read the numbers out loud. If necessary, correct them gently and say, “That’s a great try, but remember this number means thousandths. Give it another shot!”
For instance, write:3. 5353. 353 Explain that they need to look at the tenths place first to find the bigger number. Since 5 is greater than 3, 3. 535 is greater than 3. 353.
They might have an easier time seeing that 3. 500 is greater than 3. 350. Adding zeroes to decimals will also come in handy when it’s time to teach addition and subtraction.
Explain that the entire rectangle or square stands for 1. Color in 6 of a rectangle’s 10 strips, and say, “We’ve colored 6 out of 10 strips. That’s 0. 6 or 6/10 (six-tenths) of the total strips. ” Color in 25 of a square’s 100 boxes. Say, “We’ve colored 25 out of 100 boxes. That’s 0. 25 or 25/100 (twenty-five hundredths) of the total boxes. ” Find out which decimals are bigger by coloring grids. Color 35 out of 100 boxes, then color 25 of 100 boxes in a second grid. Explain how 35/100 is greater than 25/100, so 0. 35 is greater than 0. 25.
Make another dash in the center and label it 5. 5. Explain that this number is right in the middle between 5 and 6. Ask them where to place dashes for 5. 75 and 5. 25, then fill in other decimal values along the number line.
Write 2. 527 and help them round the number to the nearest hundredth. Identify the hundredth place value in 2. 527, then show them the number to its right. Since 7 is greater than 5, they can round the number to 2. 53. Mention that if the number were 2. 522, they’d round it down to 2. 52. Give them several practice problems after walking them through a couple of examples.
Remind them that they can add zeroes to a decimal to fill in empty place values. They’ll have an easier time subtracting 3. 350 from 3. 500 if they can see all of the place values. Write out example problems and help them add and subtract. Then have them work on problems on their own.
If you multiply 2. 5 by 5. 5, count the total decimal places, which is 2 (each has 1 decimal place). The product, or 13. 75, has to have 2 decimal places. If you multiply 4. 55 by 2. 25, the product, or 10. 2375, has to have 4 decimal places. Work with them on a few examples, then have them practice on their own.
If you’re dividing 15. 75 by 1. 5, place 1. 5 on the outside of the long division symbol and 15. 75 inside the symbol. Move the outside number’s decimal point all the way to the right to make 15. Since you moved it 1 place, you’ll then move the inside number’s point 1 place to make 157. 5. Make a decimal point above the long division symbol, and line it up directly over the inside number’s new point (which is now 157. 5, not 15. 75). Use long division to divide 15 into 157. 5, which is 10. 5. Stress how important it is to move and line up the decimal points.
Have students do at least 10 to 15 example problems each for identifying place values, rounding, converting to fractions, adding, subtracting, multiplying, and dividing. Guide them through the first 2 or 3 problems, then have them practice on their own. Have patience and offer lots of encouragement when working on practice problems. Decimals can be tricky, so offer gentle corrections and reassure them that they’ll get the hang of it.
