The division is one of the four basic operations in arithmetic, along with addition, subtraction, and multiplication. It distributes a group (or a number) into equal parts, resulting in an equal distribution. Giving your student’s division worksheet and walking them through the steps is the most effective way of educating them on the topic.
A simple way to explain this to your class could be the following: if you made 6 muffins that you wanted to give to your 3 friends. You would evenly distribute the group of 6 muffins among 3 people, meaning that each person would receive 2 muffins.
Learning division has several benefits for your math students. Firstly, it can help them break down bigger, complex calculations into smaller, manageable steps. Second, as children often become easily overwhelmed in math class, taking the time to break things down into small goals will help keep your kids motivated.
In the same way, it helps make complex word problems more manageable. As a result, your students will be able to solve real-life issues using this method, ultimately improving their problem-solving and critical thinking skills.
Finally, learning division will help them understand other math concepts. As the division is directly connected to the other three arithmetic operations, working on this skill will improve their overall comprehension of maths. As you know, math is often a complex subject for students to master. By giving them the tools to understand the subject conceptually, they’ll be more engaged in the long run.
This is why division worksheets are so crucial. In the end, math is learned through practice. If your students become bored throughout, it’s always a good idea to keep them interested via some fun facts.
Here’s just a couple you can keep in your pocket:
- The division symbol is called an obelus.
- A whole number is divisible by 3 if the sum of its digits is divisible by 3. (432 is divisible because 4 + 3 + 2 = 9)
- The oblique bar was designed by De Morgan in 1945 and has since been used as a division sign.
Parts of Division Formula
For your students to understand how to do long division, they must identify the different parts of the formula. Looking at a simple division formula, we can easily describe each of the parts.
These parts are listed below:
- 12 ÷ 4 = 3, remainder 0
In the example above, 12 is known as the dividend. It is the original whole number (the group) that will be distributed.
- The divisor tells you how to distribute the dividend. So here, 4 is the divisor because 12 will be split into four equal parts.
- The result you get is the quotient, 3. So if you take the dividend, 12, and split it according to the divisor, 4, you will get four groups of 3 (the quotient).
- In cases where a number cannot be split evenly, you would get a remainder. In this case, there is no remainder because it is divided evenly. However, in the case of:
8 ÷ 3 = 2
There is a remainder of two as the dividend couldn’t be distributed evenly by the divisor, and there are two parts of the dividend left over.
As the division is the opposite of multiplication, verifying this and making sure it’s correct is possible. In the first example, it’s possible to transform it into a multiplication problem to double-check. 12 = 4×3 + 0. By multiplying the divisor and the quotient, then adding the remainder, you should get the dividend.
Using the verification formula Dividend = (Divisor x Quotient) + Remainder, the second example can be proved as well. 8 = (3 x 2) + 2.
Types of Division
Now that your students understand what division is, it’s important to explain different types of division to them. This is a crucial step during instruction because it will help your students have a firmer grasp of the concept, ultimately leading them to do better in math.
Following are the types of division:
This type of division is also known as rate division because you divide a quantity by a rate. Thinking about our previous example of 12 ÷ 4 = 3, quotative division would be dividing a number (12) into groups of a specific quantity (4), then you get the number of groups (3).
If you have 20 students in your class. You can ask them to stand up and get into groups of 5 people. This would be quotative division because you tell the dividend (20) to split into groups of a specific quantity (5), with the result of the formula being the number of groups formed (4).
In other words, quotative division is X divided into groups of Y.
This type of division is also known as rate quotient division because the resulting number is the rate. We use this type of division when splitting a large group (the dividend) into a specific number of groups to find out how much is in each group.
In the class example, you could tell the students (20) to stand up and get into two groups. Then, you count how many groups there are (10).
Therefore, a partitive division is dividing X into Y number of groups.
What is Long Division
Long division is an extension of the division just mentioned. However, instead of using a dividend of 2 digits and a divisor of 1 digit, typically the dividend is 3 or more digits and the divisor is at least 2 digits long.
As your students will learn about division very early on, they must continue to learn about different types of division to conceptualize this process with a deeper understanding. This way, they’ll start with small numbers and eventually be able to work with larger numbers, as well.
In the UK, these essential concepts were introduced in the early Key Stages. According to curriculum standards, your students should start simple long division by Year 5, but by Year 6, they should be able to complete long division problems with dividends of up to 4 digits by a divisor of up to two digits.
Additionally, your students should be able to do these calculations as word problems. Not only does this tests their conceptual understanding of this arithmetic operation, but it will also improve their abilities to utilize critical academic concepts in real-life situations.
In long division, a large number is going to be divided by another large number. Although the formula is similar, it has some more steps.
For example, for the equation 210 ÷ 14, the dividend (210) would be written on the right, with the divisor on the left. A vertical bar separates the two numbers, with a horizontal bar going over the dividend. Writing them out correctly would be the first step.
It should look like this:
In step two, you would divide 14 into the first digit of the dividend. Since 14 is bigger than 2, we instead divide 4 into the first two digits (21). As 14 can go into 21 one time, you would write 1 over the 2 in the horizontal bar, like this:
Then, you would multiply the divisor by the number found (1). As 14 x 1 = 14, you would write 14 underneath the first two digits of the dividend. Finally, you would subtract the two numbers (21 – 14), then write the answer (7) below, as shown here
In step three, you must bring down the next digit from the dividend. The last digit in the dividend was 0. Therefore, you bring it down with the answer from the subtraction, 7, to create the number 70.
Now, you divide the divisor into 70, resulting in an equal number of 5. Write 5 on top of the digit 0 in the dividend. Repeat the multiplication procedure from step two, with 14 x 5, then subtract the result from the original number
Here is a visual of this process:
And that’s it! Now you can see that 210 ÷ 14 = 15, with a remainder of 2. This is the process for a number that divides evenly into the dividend. However, you should also teach your students what to do if the number does not divide evenly. For example, in problem 186 ÷ 12, we will need to continue into another step.
If we complete the same procedures from the previous example, then we are left with a remainder of 6 on the last step.
Just like this:
Of course, for some of your math classes, this will be sufficient, however, not always. You should explain to your students that you can go one step further to find the exact number by dividing it into decimal places.
Explain to them that 186 is the same as 186.0 and so, by using the decimal place, they can bring down a 0 from the remaining 6 to produce 60, instead of only 6.
Then, you can continue the steps like previously described, adding more zeros to the right as necessary. Remember to also add a decimal point, to correspond with the dividend.
After that, all the steps are the same. Your end result should be 186 ÷ 12 = 15.5, shown below:
Explain to your students that they can continue this process indefinitely for some numbers. The further you continue with the calculations, the more accurate the number is.
However, it’s not always necessary to have calculations to very long digits.
Some divisions could go on infinitely, so usually, the 2nd or 3rd decimal point is sufficient.
Long Division Worksheets
Long Division Math Activities
Long division worksheets are practice exercises that let your students work out several different long division problems. The most common type is a simple worksheet with 15 – 20 long division problems with space to show their work. They can come in many forms, with some of them being simple and others being more complicated. These are absolutely crucial to give to your students, as they will only improve their long division skills by doing long division.
Of course, long division worksheets aren’t the only way you can teach your students this concept. There are plenty of fun games you can play in your classroom to keep things exciting and engaging with your students. This will also help them see that math can apply to the outside world, an idea many students struggle with.
Spin the spinner long division game
This game is quite simple. First, students can create a simple spinner board using two pieces of paper, with a pencil and a paper clip. Then, on each paper, create a circle with 8 equal parts (like a pizza).
For the first paper, roll two die to create a two-digit number. Next, roll the die 8 times to create 8 different numbers that can be placed on the page. These will be the divisors. If you want your students only to do easier problems, you can have them only roll one dice for each section.
On the second paper, do the same, but roll two times for each section to produce four-digit numbers. These numbers will be the dividends. Now, place a paper clip in the center of each paper and use a pencil to hold it down. Your students can flick the paper clip to make a DIY spinner board. They would spin twice to get the divisor and the dividend, then solve for the quotient.
You can make the game more fun by giving them timers or rewards for doing it quickly (and correctly).
Related: Fraction Worksheets for Practice
Long division differentiated color by number
This is an easy game for your students to do in a relaxing way. You can find coloring sheets online for free. To play, each section of the sheet has a long division problem. The quotient corresponds to a specific color. So, for your students to complete the page and know what colors to use, they must solve all the long division problems. This is an excellent activity for a day when you would like the class to be a bit more relaxed.
Are you looking for division worksheets to use when teaching your students mathematical concepts? Don’t worry; we’ve got you! Download our free are ready-to-use division worksheet templates today and get started. Our templates are easy to use and customize. For your convenience, you can download the format that best fits you.
Grade 4 practice division worksheet
These are worksheets that teachers provide to students with the aim of making learning easier. Students mostly use them for practicing technical mathematical problems without having to consult their calculators. It emphasizes their mental development where they can even divide odd numbers using even divisors.
Division made easy worksheet
These are worksheets that are available online, and students can access them freely for printing. The teachers only recommend them for students in grades 3, 4, and 5. The topics that the division made easy worksheets include mental division, division with remainders, psychological division, division facts, equations, long division, the order of operation, and even factoring.
Math division 0-5 facts worksheet
The worksheet is printed out on one sheet of paper with single digit problems that only test one operation. It is usually given to students to enhance their speed in solving mathematical problems. The questions can either be 100 with a deadline that lasts for 5 minutes. Others have 20 issues for 1 minute and 3 minutes to solve 60 puzzles.
Long division worksheets for grade 4-6
The worksheet comprises of three sections. The first section has single-digit divisors only. The other has problems that require two-digit divisors, and there is also a section that contains divisions that need three-digit divisors. The teachers also have remainder divisions in this category but on distinct pages. However, the problems that fall under this worksheet do not result in remainders. To make work easier, teachers print the PDF formats of the long division worksheets and hand them to their students for practice.
Math class is one of the most challenging subjects to teach, especially since many students find it frustrating and demotivating. That’s why you, as the teacher, should find ways to make math as approachable as possible.
Long division is one of the basic principles that your students need to comprehend. Therefore, the best plan is to explain it progressively. Start with easy topics and slowly introduce more challenging problems. This way, your students don’t become overwhelmed, and you can locate comprehension issues immediately.
Feel free to use this guide to explain long division to your students and include some of the games and long division worksheets in your class.