long division

Learning Long Division

Show the Number with Base 10

Base 10 blocks or strips to ensure that understanding takes place. All too often long division is taught using the standard algorithm and rarely does understanding occur. Therefore, the student needs to have a good understanding of fair shares. A child should be able to show division of the basic facts by showing fair shares. For instance, 12 cookies divided by 4 should be shown using buttons, base 10 or coins. A child needs to know how to represent 3 digit numbers using base 10. This first step shows how the number 73 is shown using base 10 strips.

If you don’t have Base 10 Blocks, copy this sheet onto heavy (card stock) and cut out 100 strips, 10 strips and 1’s. It is very important for a student to represent their numbers when beginning long division.

Before attempting long division, students should be comfortable with these exercises.

Using Base Ten, Divide the Base Ten into the Quotient

The quotient is the number of groups to be used. For 73 divided by 3, 73 is the divident and 3 is the quotient. When students understand that division is a sharing problem, long division makes much more sense. In this case, the number 73 is identified with base 10 strips. 3 circles are drawn to indicate the number of groups (quotient). The 73 is then equally divided into the 3 circles. In this case the children will discover that there will be leftovers — a remainder.

If you don’t have Base 10 Blocks, copy this sheet on to heavy (card stock) and cut out 100 strips, 10 strips and 1’s. It is very important for a student to represent their numbers when beginning long division.

Finding the Solution With Base 10 Strips

As the students separate the base 10 strips into the groups. They realize they must trade a 10 strip for 10 — 1’s to complete the process. This emphasizes place value very well.

If you don’t have Base 10 Blocks, copy this sheet on to heavy (card stock) and cut out 100 strips, 10 strips and 1’s. It is very important for a student to represent their numbers when beginning long division.

Next steps: Base 10 Cuts Outs

Many exercises should be done where the students divided a 2-digit number by a 1 digit number. They should represent the number by base 10, make the groups and find the answer. When they’re ready for the paper/pencil method, these exercises should be the next step. Notice that instead of base ten, they can use dots to represent the 1 and a stick to represent the 10. Hence a question like 53 divided into 4, the student would draw 5 sticks and 4 dots. As the student begins putting the ​strips (lines) into the 4 circles, they realize that a stick (line) must be traded for 10 dots. Once the child has mastered several questions like this, you can move on to the traditional division algorithm and they may be ready to move away from the base 10 materials.

Math: Long Division

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Описание для Math: Long Division

The application will teach you how to do a long division. The application is smart: it tries to understand your mistakes and give you appropriate indications.

The long division is a fundamental concept of math. It includes the division of course, but also the multiplication, the subtraction and the multiplication tables, all math operations. Mastering the long division means mastering all these technics of math.

The application proposes two modes: training and learning.

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In learning mode, the application shows you how to do the long division step by step. Each step of the math exercise is explained and detailed. You can choose the numbers, divisor and dividend, or let the application randomly choose the division to do.

In training mode, you do the long division step by step by yourself. The application detects the mistakes, such as forgetting the carry. It gives you indications if you need all along math exercises.

Several levels are possible for math exercises. The easy level proposes simple numbers, for the early learning of division. The following levels proposes more and more difficult exercises. One can choose between integer long division or decimal numbers, with or without intermediate subtraction.

The application computes a score from time and mistakes during the division. This gives you motivation to train and let you see the progression in the long division.

Note: The application uses vocal synthesis (it speaks) to comment the division during math exercises. On some devices, it will propose to you to install upgrades of vocal synthesis if you want to get better diction quality.

Robot Long Division Practice for 4th Grade+

My oldest is incredible at math. Even new concepts rarely require more than a five-minute conversation and he is ready to go off and try it. And when he comes back, surprise, he has them all right. But we have finally found his Achilles heel. Long division. It is one of the few skills that we have had to spend extra time on, and go back and practice regularly. Even though long division can be long and tedious, I have wanted it to be fun for him. So today I have some fun solve and color long division practice pages…because let’s face it. Even our older kiddos like to color.

*Please Note: This post contains affiliate links which support the work of this site. Read our full disclosure here.*

This is a guest post from Rachel of You’ve Got This Math.

Long Division Practice Prep-Work:

Simply print off the pages you want them to work on, and provide colored pencils and pencils.

Solve and Color Long Division Practice Pages:

The worksheets in themselves are very self-explanatory. On the left-hand side are five long division problems. And on the right-hand side are pictures of fun cartoon robots and the answer or quotient.

All our big kids have to do is solve the problem, find the answer, draw a line to the matching answer, and of course, color in the robot!

Also included is a page of answers to all the problems, making this super easy for you!

Learn some strategies for teaching long division, and then grab the long division practice pages below!

Traditional Long Division Steps:

Now most of us know how to do the traditional division algorithm, but sometimes students need special reminders to help them remember all the steps. And there are some great ones.

Basically, what we want them to remember is that they need to divide, multiply, subtract, check or compare that the divisor is larger than the remainder, bring down the next number and of course start all over again.

That is a lot to remember, so these fun mnemonic devices help our children remember the steps:

Does McDonald’s Sell Cheeseburgers Raw?

These next two, leave off the check but are quite catching.

Or you could always do this fun division rap.

Partial Quotients Division:

I always like to provide my students options. Everyone thinks about math differently, and if they are able to do mental math you may be surprised at the different ways they come upon an answer.

So should we only teach one method, when another way may be the key to unlocking a door for them?

As a public school teacher and now a homeschool mom, I would teach two or three methods. Once they had a pretty good grasp on both ways, I let them choose which one works best for them.

My oldest son has chosen to partial difference while my middle child prefers traditional subtraction.

He also prefers lattice multiplication, and partial quotients when dividing. I look forward to which method my middle child chooses.

How to do Partial Quotients

It may sound scary, but it is not.

Let’s look at this problem: 235/5.

We are dividing 235 up into five equal groups. In partials, we begin by looking at the 2 and asking ourselves what it really stands for.

Well, it stands for 200.

Our next step is to ask _____ x 5 = 200?

Now, this is the best part of partial products. As long as they don’t go over, it can be any number.

I can do 10 x 5 = 50 over and over again till I get the right answer:

Or we can do the easy way and say 40 x 5 = 200. Then we put it in the division problem like this:

Now, all we have left is 35. And we ask the question again. ____ x 5 = 35.

Well, we know that 7 x 5 = 35 so we write that under the 40.

Now, all that is left is finding the answer. And we do this by adding up all the factors in the right-hand side. And we see that the answer is 47.

It is that easy.

And if you want some easy partial quotients practice, this cut and paste activity is a great way to get started.

I hope your children have fun coloring while solving long division problems!

And if you want to know more about teaching long division, you might like this post:

Rachel is a homeschool mom to four little ones, ages 2 to 6. She is a former public elementary teacher, and has recently begun blogging at her page You’ve Got This. You can also find her on Facebook and Pinterest.

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Long Division

When starting division, you may be given simple division problems that you can do in your head, using mental math. Those problems would look like this:

You would think to yourself, what number times 9 gives me 27? And your answer would be 3. However, eventually you will encounter bigger division problems that you cannot do using mental math. In these cases, you will have to use long division.

For example, you might have a problem that looks like this:

You would re-write the problem so that it looks like this:

In this case, 5 is the divisor (the number we’re dividing by) and it goes on the outside of the division bar, as shown. 125 is the dividend (the number we’re dividing) and it goes on the inside of the division bar. The quotient (answer) will eventually sit on top of the division bar, when we’re done. Right now, the top of the division bar should be blank because we have not started yet.

Now, we can start our long division. There are four steps of long division; they are: divide, multiply, subtract, and bring down. Each step will be explained and shown in a different color in the step-by-step image.

Our first step of long division is to divide . In this step, we have to ask ourselves how many times the divisor goes into the first number of the dividend; or, in this case, we ask ourselves how many times we can put 5 into 1. You will notice that we cannot put 5 into 1, because 5 is bigger than one; thus, our first division results in 0. We write this number on top of the division bar, above the number we used (in this case, 1). Your problem so far looks like this:

Our next step of long division is to multiply . In this step, we multiply the divisor (5) by the answer we got to our division (in this case, 0). We multiply the two numbers together like this: 5 x 0 = 0. We write this number below the dividend, lining it up with the number we divided.

Our next step of long division is to subtract . In this step, we subtract our product (answer) from multiplication from the original number in the div >

Now we move on to our last step, which is to bring down . In order to bring down, we have to look at the next number in the dividend that we haven’t worked with yet; in this case, it’s 2. In order to bring down, we draw an arrow from the number in the dividend down to where we just ended our subtraction, and we write this number (2) next to the answer from our subtraction (1) to form a new number (12). This is shown in the diagram below.

Once you bring down the next number, you start this entire process over with division! In the image below, you’ll see the next set of steps performed, starting with this division question: how many times can we put 5 into 12? Follow along with the diagrams:

That was a complete step ( division , multiplication , subtraction , and bringing down ) that we just went through! We keep repeating the process until there are no more numbers to bring down. In this problem, we have one more complete step to go through before we get our answer. Here’s how to go through the last step:

Notice that when you went to bring down, there were no other numbers after the 5, so you had nothing to bring down. This means you are done! Your answer is the number that you have written on top of the division bar. For this problem, our answer is 25, and it is written in red on top of our division bar.

Some people like to have a way to remember the steps to long division, so they’ve come up with a saying to help you remember the order. The order is: Divide , Multiply , Subtract , Bring down . The saying is: Does McDonald’s Sell Burgers? The first letters of this saying match up with the first letters of the order of long division: D — M — S — B . If this helps you, feel free to use it to remember; if it confuses you, then don’t use it—just memorize the steps for long division.

Long Division Examples

Let’s go through one more example like this before we move on. Our new example is:

Let’s re-write the problem using the long division bar, and then follow the steps to long division ( divide — multiply — subtract — bring down ). Re-read the steps to the first problem if you’re still having trouble. Here’s the problem worked out:

Once again, our answer (quotient) is written above the division bar. Ours is written in red. Both of these problems had quotients of 25, but this will not always be the case! You could have any number as your quotient for a division problem.

When we have an answer for our division problem, it is easy to go back and check it. In order to check a division problem, you multiply the quotient (answer) by the divisor, and your product (answer to the multiplication problem) should be the same as the dividend.

Here’s the work for checking the last division problem:

We can see that our product, 100, is the same as the dividend, so we know we did our division correctly.

Now, here’s one for you to try to make sure you get the hang of it!

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