A Quick Guide for Elementary Math Educators
Many new teachers start teaching decimals with only the background knowledge they learned in school, focusing mainly on how the decimal point moves.
But there’s so much more to decimal numbers than just the decimal point!
I was once that teacher. When teaching how to multiply decimals, I thought teaching the “trick” of counting digits behind the decimal point to place the decimal in the product was enough.
Rather than helping my students understand what was happening with the decimals and how they connected to whole numbers, I focused on the answer.
It’s important for elementary math teachers, especially new ones, to deepen their understanding of decimals as they are a major part of the upper elementary curriculum. Teachers should take time to review these specific standards and skills before teaching them to students.
Here are five things you should know before teaching decimals:
Decimals are Numbers Too
Decimal numbers aren’t some strange type of number just because they include a decimal point. They are just as “normal” as any other number.
Decimals have place values extending beyond the decimal point, which separates whole number place values from decimal place values.
Just as fractions can represent any quantity, decimal numbers can do the same. There are decimals with digits only to the right of the decimal point (tenths, hundredths, thousandths, etc.). There are also decimals with digits on both sides of the decimal point.
- 0.34 is a decimal number with digits to the right of the decimal point.
- 429.7 is a decimal number with digits on both sides of the decimal point.
Providing students with opportunities to work with different types of decimal numbers, appropriate for their grade level, will help deepen their understanding and support them in making connections between whole numbers and decimals.
Understanding Decimals as Fractions and Fractions as Decimals
If your students have already explored fractions in Grades 4 and 5, they are on the fast track to understanding decimal numbers. One-tenth written as a fraction (110) has the same value when written as a decimal (0.1).
All fractions can be renamed or written as decimals. These are sometimes called decimal fractions.
For example, when you say four-tenths, students can think of it as the fraction (410), the decimal (0.4), or both.
While all fractions can be written as either a terminating decimal, one that ends (0.92), or a repeating decimal, one that continues to repeat (0.33333), these concepts aren’t typically explored in Grades 4 and 5. At this level, students focus on fractions with denominators of 10, 100, or 1,000.
Some students may reason that fourths (with a denominator of 4) are equal to 0.25 because they understand that 100 divided by 4 is 25. So, 14 of 1 whole is 0.25, or 25 hundredths.
The ability to rename decimals as fractions and fractions as decimals provides students with more opportunities to make sense of problems involving decimal operations.
While the expression 0.70.6 may stump some students, due to there being decimal points in both factors, seeing it written as 710610 may help.
710610=42100, or 0.42.
Continue to Use Math Manipulatives and Visuals with Decimals
Teaching decimals can be challenging because they are often very abstract for students. Using math manipulatives or visual aids can make a big difference! These tools help students better understand the size of decimal values and lay a foundation for decimal operations.
Base ten blocks are especially useful for teaching decimals. When students work with whole numbers, they use base ten blocks to represent thousands, hundreds, tens, and ones. With decimals, they can use the same blocks to represent numbers with decimal values.
For example, a flat that usually represents a hundred can also represent a ten, one, tenth, or any other decimal place value. This helps students see how our base-10 system works, where each place represents groups of 10:
- 1 ten is the same as 10 ones.
- 1 hundred is the same as 10 tens.
- 1 tenth is the same as 10 hundredths.
Using math manipulatives like base ten blocks allows students to see these groupings and make visual connections.
Another helpful visual aid is a hundredths grid. A hundredths grid is a grid composed of 10 intersecting rows and columns. It mimics the flat piece of the base ten blocks and represents one whole. Students can draw grids or shade in premade grids to represent decimal values less than, equal to, or greater than one whole.
Whatever tool you use, give students many opportunities to use them throughout the unit on decimal concepts and operations. Let them explore decimal sizes, represent and compare amounts, solve problems involving the four operations, and so much more!
Decimal Operations: Similar to Whole Number Operations
The four operations can confuse some students when it comes to where to place the decimal point.
During one-on-one tutoring sessions, I’ve seen students mix up tricks used for multiplication with addition or subtraction. Moving the decimal based on how many digits are behind the decimal point isn’t helpful when adding or subtracting decimals.
It’s more important for students to make sense of the problem and estimate or reason about where to place the decimal using what they know about whole number operations.
For example, 345.78 + 98.2 can look intimidating as an addition problem. Using estimation, 345.78 is close to 350, and 98.2 is close to 100.
For multiplication, take 14.3 x 4.9. Estimating, 14.3 is about 14, and 4.9 is about 5. Knowing that 14 x 5 = 70 can help students figure out where to place the decimal point when multiplying the actual numbers.
In both examples, using estimates helps students determine whether the decimal point should be to the right of the hundreds, tens, ones, or tenths place.
Estimation, whole number operations, and place value understanding are key to students ensuring their answers are reasonable when using any of the four operations with decimals.
Money Is Not the Only Real World Example for Decimals
When you mention decimals in elementary school, most students (and adults) immediately think of money. But did you know that money is not the only real-world example that uses decimals? Of course you did!
There are plenty more examples of decimals in the real world that you can use in math problems with students, such as:
- Volume: Liters of soda, gallons of paint, or gasoline/fuel
- Weight: Canned food items, and pet weights
- Temperature: Weather temperatures, body temperatures
- Distance: Miles/kilometers traveled, track and field race distances
- Medicine: Dosages of medication
- Sports: Timing in races (swimming, running), scores in gymnastics
- Nutrition: Calories, grams of fat, carbohydrates, and protein in food
- Cooking/Baking: Measurements of ingredients (cups, tablespoons, ounces)
And there are many more out there!
While using money to pay for candy or snacks in the cafeteria or food at the grocery store may be our default examples, decimals can be found all around us. A quick Google search for inspiration can open our eyes to even more possibilities!
Decimals are an important extension of place value concepts learned in earlier grades. Just like with whole numbers and fractions, many connections can be made with decimal concepts that go beyond where to place the decimal point.
As educators, it’s essential to review (and sometimes relearn) these concepts to prepare our students to be proficient in all areas of elementary mathematics and to build their confidence.