Division For Kids: How To Teach 3 Division Methods From Kindergarten To 5th Grade
We’ve worked with primary math experts to create a parent’s guide to division, using arrays, area models and the dreaded standard algorithm (long division).
In here we’ve explained everything you need to know to help your child with these tricky topics!
It doesn’t matter whether you are dividing using an array, area model, or the standard algorithm, for many children and their parents just the mere mention of the ‘D’ word can send shivers down the spine of many young mathematicians, but it doesn’t need to be the case!
Here at Third Space Learning we are on a mission to make math accessible for all, and this includes using arrays, area models, and long division too…
In the past, division was taught without much concrete modeling (using physical items to help represent the math problem), so it’s no wonder that many of us parents find it difficult to this very day.
Nowadays though, with children spending a lot of time at school understanding how division works, rather than just memorizing the method, the fear around division is melting away. Recapping and helping your child to do division at home will make a big difference.
But before you find out everything you need to know about division for kids, we’ve prepared a brief division recap for you!
This blog is part of our series of blogs designed for teachers, schools and parents supporting home learning.
- Division methods in a nutshell
- What does my child need to know about division methods in elementary?
- Division in Primary Grades (K-2): how you can help
- Division for 3rd grade: how you can help
- Division for Upper Elementary (3rd – 5th grade)
- Division methods for kids
- Using arrays in division
- Using area models in division
- Using the standard algorithm to divide up to a four digit number by single digit
- How to help kids divide a three or four digit number by a single digit number
- Division with remainders
- Dividing by a multi-digit divisor
- The standard algorithm (long division) for kids explained
- How to do long division: an easy step by step long division method
- Dividing with decimals
- An example of dividing with decimals
- How do we know when to divide and which method to use?
- Division assessment questions
Division methods in a nutshell
We know how difficult division can be for both you and your child, so let’s start off with some definitions and a recap of what you may have forgotten since school.
What is division in math?
Division is the operation that is the opposite of multiplication and it involves splitting into equal parts or groups.
In elementary school, 3 methods of division are taught, each of which vary in difficulty. They are:
- Area Models
- Standard Algorithm (long division)
What are rectangular arrays?
Rectangular arrays are a visual representation that can be used in both multiplication and division. The array is organized into equal columns and rows. The rows and columns represent the number of groups and the number of objects in each group, or the size of each individual group.
What is the area model?
The area model is a rectangular model that can be used in both multiplication and division. In division, the quotient (answer) and the divisor are used to define the length and width of the rectangular model.
What is the standard algorithm?
The standard algorithm, or long division, is a method that is used when dividing a large number (usually three digits or more) by a single- or multi-digit number.
Your child will be introduced to division using pictures and visual representations, arrays and the area model, and will ultimately use the standard algorithm.
Once the standard algorithm is introduced, your child should start with a smaller number as the dividend and a single digit divisor. Once they feel comfortable with the strategies, they can be used to solve a division problem with a very large dividend by following a series of easy steps.
In this example four goes into nine two times, and it leaves a remainder of one.
This remainder is then passed onto the next number (six) to make it 16. Four goes into 16 four times, so when put together the answer becomes 24.
We have a very detailed article written for teachers on this subject you might enjoy if you want to go into more depth about teaching the long division method.
Terminology you need to know when teaching division
In our blogs we try to avoid too much jargon, but the following three terms really are essential to know for anyone looking at division.
- The dividend is the number you are dividing’.
- The divisor is the number you are dividing by.
- The quotient is the amount each divisor receives i.e. the answer in most cases.
A good way to remember it is dividend ÷ divisor = quotient
Parts of a division problem labeled for kids and parents
By learning the correct vocabulary of all the parts of a division problem, your child will find lots of elements of division much simpler.
What does my child need to know about division methods in elementary?
With division for kids changing from year to year throughout elementary school, there is a lot to cover in the blog, but to help you out we’ve broken it down on a year by year basis.
Division in Primary Grades (K-2): how you can help
In the US, students are not introduced to the term “division” until 3rd grade. This doesn’t mean that you cannot start helping your child build some foundations that would help them when they begin division.
Division is usually referred to as sharing in the lower grades and is introduced using concrete items like counters, blocks, or even items of food such as pasta. This helps children to understand division as sharing between groups.
A simple example of this can be found below.
Some simple word problems for K – 2nd grade
Grab a set of blocks and help your child try to figure out these sample problems.
Make sure that you remember to use words like share, divide, and equal groups throughout so that your child becomes familiar with the concepts. As your child moves up in grade level, you can increase the number of blocks they begin with, with 40 being maximum in 2nd grade.
Start with 4 blocks. Share them into 2 equal groups.
Start with 10 blocks. Share them into 2 equal groups.
Start with 6 blocks. Share them into 3 equal groups.
Division for 3rd grade: how you can help
In 3rd grade, your child will be formally introduced to division. Your child will need to be able to divide within 100 using different strategies. These strategies include arrays, area models, and strip diagrams.
Before jumping into division strategies, a key concept to understand and really get to grips with at this age is commutativity.
If you are struggling to remember exactly what commutativity means, the definition is simple.
In math, the commutative property states that order does not matter.
Multiplication is commutative; you can switch around the numbers and it makes no difference.
2 x 3 = 6
3 x 2 = 6
Division is not commutative. If you switch the order of the numbers, it changes the answer.
4 ÷ 2 = 2
2 ÷ 4 = 0.5
Division and commutativity in 3rd grade
At this age, it’s good to master the 2, 5, and 10 multiplication tables with their corresponding division facts. For example:
2 x 5 = 10
Corresponding division facts:
10 ÷ 5 = 2
10 ÷ 2 = 5
Knowing these facts makes division much easier later on, and they are a great example of why commutativity is important.
If your child is comfortable with the difference between 10 ÷ 5 and 10 ÷ 2 even after seeing that 5 x 2 is the same as 2 x 5, they will be best placed to move comfortably up to higher elementary grade division.
Your child will be focusing on writing down division calculations and solving simple division problems that involve missing numbers.
This missing number problem will help you see why multiplication knowledge makes division much easier:
5 x 4 = 20
__ ÷ 5 = 4
20 ÷ __ = 5
There are two visual methods that are introduced at this age, arrays and area models, and they are broken down below.
Division for Upper Elementary (3rd – 5th grade)
Schools following Common Core
Starting in third grade, students will begin dividing up to 100, using equal groups, arrays and drawings. In 4th grade, your child will be expected to use arrays and/or area models to calculate four-digit dividends and one-digit divisors. Moving into 5th grade, your child will calculate whole number quotients with four-digit dividends and two-digit divisors. It is typical to begin using the standard algorithm, or long division, in 5th grade.
Based on your child’s state and school curriculum, they may be introduced to different strategies in different grade levels. The strategies are explained below.
Division methods for kids
Using arrays in division
Unlike how you and I began our division journey, your child will most likely be introduced to division by using pictures. This is the next step in the progression past using concrete objects, as they did in the primary grades.
In this strategy, students will be provided a graphic that will represent the division equation they are to solve. Because your child can see the graphic, they are able to use it to group the objects, by circling or crossing out, to represent one group. See the graphic below for an example:
Using area models in division
The area model is a rectangular model that uses the length and width to help students visualize division. It is more abstract than arrays, and should be used after your child has a good grasp on simple division concepts.
The rectangular model represents the total area that the shape takes up. When using this model for multiplication, you would multiply the length by the width to find the area. However, when using the area model for division, you are given the total area (dividend), and the width (divisor), and you will need to calculate the length (quotient).
Using the standard algorithm to divide up to a four digit number by single digit
The standard algorithm, or long division, at the beginning involves single digit divisors and 3 or 4 digit dividends.
Sit down with your child and take a look at the diagram below to get to know the names and places for each part of the division problem.
They can look very unfamiliar when you’re used to writing your sums out in a line, so work with your child to ensure they know their divisor from their dividend!
By this stage the process of dividing becomes much more of a struggle if your child doesn’t have their multiplication tables by heart so one of the best things you can do for them is support the learning of these.
How to help kids divide a three or four digit number by a single digit number
Here’s a graphic detailing how to divide a three or four digit number by a single digit number.
Division with remainders
Remainders can be a tricky concept to grasp when children are first introduced to long division, but it is important that your child understands them well as they can drastically change depending on the question that is being asked.
They’ll also need to choose what kind of remainder to use depending on the question, and some common questions will involve real-life situations, like sharing groups between cars or items between boxes.
Dividing by a multi-digit divisor
The key when it comes to the standard algorithm for kids is to go slow and encourage them to present their work neatly so that they can spot mistakes easily and work to rectify them.
Even when knowing this though, long division can still be a daunting prospect for children (and parents alike!), so take a look at our example below to get to grips with how to tackle a long division problem.
The standard algorithm (long division) for kids explained
The example below shows one of the most popular ways to divide. This is most likely the way you were taught in school and are familiar with. All you’ll need to complete the calculation 528 ÷ 24 is a pen, some paper and a child who is willing to practice with this method!
After having a go at a few long division questions (with your help to begin with), your child will soon see that this method can help them figure out how to work out long division problems regardless of the numbers involved
How to do long division: an easy step by step long division method
Don’t worry if it takes a while to truly embed the process. It’s a long chain of things to remember, so it’ll take regular practice to get this method memorized.
Just remember the process: divide, multiply, subtract, bring down; and repeat.
Hard work will pay off in the long run, so it is worth putting the time in with your child now to make sure long division is explained well early on to lessen the number of times you will hear the inevitable:
“Mommmmm…….How do you do long division…?”
Dividing with decimals
The standard algorithm will be used for numbers involving decimals for the first time in upper elementary.
This means that it is a good time to revise place value so that your child understands how decimals work.
Decimals are parts of a whole (similar to fractions), but the important thing to remember when it comes to dividing decimals is that place value columns decrease in value each time you move to the right.
An example of dividing with decimals
How do we know when to divide and which method to use?
Different division questions call for different methods of division to solve them, but here is a quick and easy guide to show which method your child should use and when:
- Arrays are best for smaller numbers and arithmetic.
- Area models are great for dividing larger numbers by one digit numbers.
- Long division is handy for dividing large numbers by numbers with 2 or more digits.
Of course there may be occasions when each of the above methods can be used in slightly different scenarios, but as a general rule this should be enough to help your child make the right decision.
Division assessment questions
When it comes time to take math assessments it is more than likely that your child will have to answer some division based questions.
Problem solving and reasoning can be tricky when it comes to division problems. Often, the problems require more than one operation to be solved which can add an element of complication into an already stressful environment, so encourage your child to look out for words like share or group to help them identify what needs to be done to solve the problem.
It’s easy to spot these questions because they will use the division symbols, either:
or they may involve fractions.
As a rule of thumb, encourage your child to divide mentally where possible.
While written methods are great for bigger numbers, being able to divide mentally will give them an edge. It means that when they are done using the written method, they will be able to see whether or not their answer is roughly correct by estimating.
That should have covered everything you need to know about division for kids. If you’re looking for more ways to help with math homework, then we recommend you also take a look at the following ‘parent and child explainer’ guides too.
- Fractions for Kids: How to Help at Home
- How To Learn Multiplication at Home
- Word Problems Explained with Examples
- Divisibility Rules
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The content in this article was originally written by primary school teacher Sophie Bartlett and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza.