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In the early grades of elementary school, students work primarily with whole numbers—the ones we use to count (1, 25, 76, 4…).
However, there comes a moment when students themselves begin to realize that these numbers aren’t enough to describe everything. For example, they might notice that half of 7 is more than 3 but not quite 4.
That’s when we introduce them to other kinds of numbers, such as decimals.
In this article, we’ll explain how we approach decimals in math class, so you can better understand the process and support your child whenever they need help.
Fractions and Decimals
Before diving in, it’s important to understand that in math class, we explore number sets in a way that closely mirrors how they appeared throughout history.
First came the natural numbers, and later—out of necessity—came the rational numbers, which we use for measuring and sharing. In ancient times, people realized that we can’t measure everything using only whole units, and that fair shares don’t always result in whole numbers either.
This naturally leads us to the idea of parts of a whole, which brings us to fractions.
Let’s look at an example:
If we want to share 3 pizzas among 4 friends, each person would get ¾ of a pizza. One way to do this would be to cut each pizza into 4 pieces, and have each friend take one piece from each pizza.
In class, we place a strong emphasis on understanding fractions and discovering their connection to decimals. In fact, every fraction can be represented as a decimal. A decimal is simply another way to express a fraction with a denominator of 10, 100, 1,000, and so on. That’s why they’re called “decimals”—they are built on powers of ten.
Understanding decimals is especially important because children are frequently exposed to them in real life, whether through the metric system or money.
However, it’s important to note that the reverse is not always true: not all decimals can be written as fractions. For instance, some decimals go on forever without repeating. One example is the number pi (π), which students will explore later in measurement and geometry units.
How Do We Introduce Decimals in the Classroom?
In the classroom, we use two main approaches to introduce decimals.
On one hand, we connect decimals to measurement units (such as meters, centimeters, and millimeters, or kilograms and grams), since it’s very common for students to encounter decimals in this context. For example, they might hear phrases like “I’m 1.63 meters tall” or “I weigh 45.6 kilograms.”
On the other hand, we build understanding of decimals through money. Using money helps children see that place value in decimals really matters. One common challenge for students is understanding the value of digits after the decimal point. For instance, it may be confusing at first to realize that 7.2 is greater than 7.18.
By using money, we can clarify this: students can see that 7.2 is the same as 7.20, and that this is clearly more than 7.18. That’s why we start working with two decimal places—it reflects how money works and provides a meaningful, familiar context for understanding.
How Do We Add and Subtract Decimals?
At Innovamat, as we’ve mentioned many times, we strive not to introduce vertical algorithms too early. Instead, across all grades, we focus on alternative strategies that help students reason and truly understand what’s happening with the quantities they’re working with.
When it comes to adding and subtracting decimals, we use two main approaches, both of which students have encountered in earlier grades:
- Using jumps on a number line
For example, to solve 4.60 + 1.75, students can break the second number into parts (1 + 0.70 + 0.05) and make jumps step by step on a number line. This visual and flexible approach helps reinforce place value and mental math.
- Decomposing numbers
Students break down the numbers into smaller, more manageable parts (like tenths and hundredths) and recombine them to find the total or difference.
Once students have internalized these strategies for working with two-digit decimals, it becomes much easier to extend them to decimals with more digits in later grades.
How Do We Multiply and Divide with Decimals?
Just like with addition and subtraction, we begin teaching multiplication and division with whole numbers.
At first, we don’t jump straight into vertical algorithms for multiplication—this is a great opportunity for students to make estimates and reason about quantities.
For example:
3 times 4.80 must be less than 15—this draws on the way we speak when introducing multiplication facts (“3 times” instead of “3 multiplied by”—check out our article on why we use this terminology!).
Since 4.80 is 0.20 less than 5, we can reason that 3 × 4.80 is 0.60 less than 15 (because 3 × 0.20 = 0.60). So the final answer is 14.40.
We introduce division with decimals up to the hundredths place, which makes money an ideal context.
For instance, imagine dividing a decimal amount of money by a whole number. We might propose exchanging a $5 bill and a $2 coin for 7 $1 coins, then asking students to give 2 coins to each person.
At that point, they’ll have $1.20 left to divide among three people. Some may predict that each person gets $0.40. If not, we can make it more visual by exchanging the $1 coin and the $0.20 coin for 12 ten-cent coins, making the division into three equal parts more intuitive.
How to Support Your Child with Decimals at Home
Here are some tips and resources to help you support your child’s learning with decimals at home:
- Reinforce the idea that numbers represent quantities
It’s essential to keep emphasizing that numbers stand for real amounts. One way to do this is by working with measurement units. Measure things around the house and name the quantities together using different units—meters, centimeters, millimeters, kilograms, and grams. - Use mental math through known and derived facts
Look for everyday opportunities to practice mental calculation, using both familiar facts and ones that can be derived from them. This will also help you rely less on the calculator!
For example, if you know that 3.70 + 6 = 9.70, you can easily derive the result of 3.80 + 5.90 by adjusting accordingly.
- Estimate results whenever possible
Encourage your child to make estimates before solving. Estimating helps build awareness of what’s happening during a calculation and makes it easier to spot mistakes.
In the previous example, since you’re adding a number close to 4 and another close to 6, the result should be close to 10.
