When Do Children Typically Learn Division? A Comprehensive Guide

Of all the math operations, multiplication and division may be the hardest for kids to learn. Tackling these skills is the logical next step after addition and subtraction. But it’s really more of a leap for most kids. Understanding when children typically learn division involves recognizing the foundational skills required, the grade levels at which these concepts are introduced, and strategies to support their learning journey.

Foundational Skills for Division

Before diving into division, children need a solid grasp of earlier math concepts. A child is ready to tackle multiplication and division once they’re proficient in addition and subtraction. Since multiplication is repeated addition, your child should understand addition before moving on to multiplication. For example, a student should know that seven is the same as one plus six, two plus five, or three plus four. Because multiplication and division are inverse operations, you can check your division answer by multiplying the quotient and divisor to get the dividend. The commutative property of addition (the property that allows you to reverse numbers you’re adding together and get the same result, such as 3+4=7 and 4+3=7) will also apply to multiplication. Each new math skill builds upon the last.

Grade-Level Introduction to Division

Kids start to learn division in third grade. Learning to divide starts in third grade. Kids are introduced to the concept by doing repeated subtraction. (Like 20 - 5, then another 5, and another 5, and one more 5. It’s the same as 20 ÷ 4.) Here’s how and when kids learn to divide:

Third Grade: In third grade, kids begin dividing by repeated subtraction. They learn to divide two digits by one-digit numbers with solutions greater than 10.
Fourth Grade: By fourth grade, kids’ division skills will progress significantly. In fourth grade, kids begin learning how to divide four-digit numbers by single-digit numbers. (Like 4,000 ÷ 2.) Your child will also be expected to be able to estimate and use mental math strategies to come up with reasonable answers to problems. They usually start with long division without remainders in 4th grade.
Fifth Grade: By fifth grade, kids start completing more complex division problems. In fifth grade, kids begin dividing four-digit numbers by four-digit numbers. (Like 8,000 ÷ 4,000.) Also, most kids are introduced to decimals in fifth grade. These include dividing three-digit numbers by one-digit numbers as well as two-digit numbers. Most kids know how to use the common procedure for multiplying large numbers by the end of fifth grade. Some need a little more time and practice to fully understand the concept.

Kids are expected to fully understand how to multiply and divide before moving on to middle school. But that doesn’t mean every child will understand it. Some kids need more time and practice.

Understanding the Components of a Division Equation

A division equation is made up of three parts:

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The dividend is the number that’s being divided (the first number in the problem).
The divisor is the number the dividend is being divided by (the second number in the problem.)
The quotient is the number of times the divisor will go into the dividend (the solution).

Strategies for Teaching Division

Teaching multiplication and division should start with concrete methods before progressing to abstract equations. The best way to teach multiplication and division is to progress through multiple strategies from concrete to abstract. Begin by giving children manipulatives to work with. Putting objects into equal groups creates a physical link between multiplication and division. Eventually children need to have enough understanding of the concepts that they can solve an equation, which is more abstract. Elementary children will gain the most understanding by working with manipulatives and real-life problems to start. In the classroom, a teacher will use most of these strategies to account for different students’ learning abilities, but as a homeschool parent, you can pick and choose which work best for your children.

Give children several manipulatives or objects and ask them to divide these into equal groups.
Using the Measurement Model vs. In the partitive (a part of a whole) model of division, a child will partition counters (manipulatives used to count with) evenly into a certain number of groups (the divisor), in a “one for you and one for me” fashion, and then count the final amount in one group to get the answer. In the measurement model, the child will begin making sets of a certain number (the divisor), and the number of sets she has at the end will be the answer.
Division looks like repeated subtraction on a number line. A child should start at the dividend and make each jump backward on the number line the size of the divisor. The number of jumps will be the quotient. This process is also known as chunking.
As with the multiplication array model, small cubes work well for teaching division. For example, give children 12 cubes, and ask them to create rectangles with even rows. They might first try to make rows of five and discover that there are blocks leftover.
The division number model uses the multiplication facts a child has learned to derive answers.

Concrete to Abstract

The best way to teach multiplication and division is to progress through multiple strategies from concrete to abstract. Begin by giving children manipulatives to work with. Putting objects into equal groups creates a physical link between multiplication and division. Eventually children need to have enough understanding of the concepts that they can solve an equation, which is more abstract.

Manipulatives and Real-Life Problems

Elementary children will gain the most understanding by working with manipulatives and real-life problems to start.

Visual Aids and Real-World Examples

Using visual aids is a great way to support your child’s learning. For example, let’s say you have 10 buttons and you want to divide that by 2. There’s nothing better to help kids grasp math concepts than using real-world examples. If you wanted to give 10 pieces of candy to five of your friends, how many pieces would you have to buy? You can include math learning in everyday moments to make it more natural and connected to real-life events.

Games

For example, you might play multiplication Bingo. Digital games can also be beneficial practice.

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Teaching Long Division

Teach long division as a series of steps: divide, multiply, subtract, and drop down the remainder. Start with dividing numbers that have no remainder in any step, such as 84 divided by 2. With no remainders to worry about, the process is simpler. Then use problems with a remainder in the final step, such as 85 divided by 2. Finally, progress to problems with remainders in the tens, such as 96 divided by 4, or in either or both places.

Supporting Mastery of Multiplication and Division

There are several ways to support your child’s mastery of multiplication and division. You can utilize visual aids when you teach, provide real-world examples, and play math games to build skills gradually.

Practice and Repetition

Practice individual skills one at a time until your child feels confident. Practice makes progress. So, when learning a new skill, repetition is key.

Building a Solid Foundation

Build a solid foundation with HOMER by Begin. Rome wasn’t built in a day, so the saying goes. And neither will be your kids’ math skills!

Addressing Struggles with Multiplication and Division

It’s not uncommon for kids to have trouble with math - especially multiplication and division. There are many reasons for that, and many ways to help. Supports like separate instruction or learning in a smaller group can make a big difference over time.

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Potential Challenges

For example, some kids have trouble understanding basic math concepts, known as number sense. Trouble with focus or with memory can impact learning math. So can anxiety.

Strategies for Special Needs Children

Teaching multiplication and division to special needs children is not that different from the strategies outlined above. Many times, these children will need a longer period in the concrete stage of learning before progressing to more abstract methods. Graph paper might be helpful for children to keep numbers organized. It can also be used to draw arrays while learning multiplication and division.

The Importance of Memorization

Only after children grasp the concept of multiplication should a they start to memorize the single digit multiplication facts. Many curriculum will strongly advise or require memorizing the times tables from 0 to 12 or from 1 to 9. If your children struggle with memorization, give them plenty of practice with their math facts. Being familiar with the math facts, at least with 0 through 9, will be crucial for multiple digit multiplication and long division.

Multiplication as a Prerequisite

In second grade, teach multiplication with very concrete strategies. If children do not progress to memorizing the facts, they will still have a solid foundation for third grade. In the third grade, begin again with concrete examples and word problems. Arrays and skip counting are helpful in third grade as well. Children should continue working with multiplication facts. You can also introduce the idea of area with arrays. Continue using concrete manipulatives with different colors to represent different place values. Use lots of pictures and real life problems. As they multiply and divide multi-digit numbers, provide graph paper to keep children organized.

Early Introduction to Math Concepts

Introduce math concepts to younger children with educational shows. Recently, my four-year-old demonstrated her learning from a show when making hot dogs with her grandma. When grandma asked her how many she thought she would eat.

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