As much as possible, try to relate different division problems to your students. If they're interested in basketball, for example, have them divide groups of players or basketballs. Additionally, connect division to other topics, such as multiplication, fractions, and equations, when they appear to reinforce the concept many times.
Continual assessment when teaching division is necessary and can take the form of warm-up problems, digital practice for example with our own digital math practice solution, Waggle , or exit tickets, in addition to more formal assessment such as quizzes and tests.
Return to the concept throughout the year to ensure retention and build mastery. Need more ideas to teach what is a divisor in math? Looking for more free lessons and activities for elementary and middle school? Be sure to explore our Free Teaching Resources hub! Give a lesson on the significance of National Pearl Harbor Remembrance Day with these Pearl Harbor activities for elementary and middle school students.
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Cart 0. My Account. Tweet Tweet Share. Comparing Division and Multiplication In order to teach division, it usually helps to start with multiplication.
Dividend vs. The Standard Algorithm for Division As students master their basic division facts, the need will arise for students to learn how to divide larger dividends. Lesson 1: Introducing the Concept of Division As with addition, subtraction, and multiplication, students practice strategies and algorithms that allow them to perform operations beyond basic facts. Materials: Base-ten blocks that all students can see for example, with an overhead projector ; base-ten blocks that students can use Preparation: Be sure to provide at least one set of base-ten blocks for each pair of students.
The 54 represents the total number of items you begin with. The 9 represents how many items are in each group. The quotient is 6. It is the quotient, but more importantly, the 6 represents the number of groups you will divide the 54 items into groups to have 9 items in each group. The quotient, or number of groups, is written above the Ask: Let's try another problem now. The 68 represents the total number of items you begin with. The 4 represents how many items are in each group.
Since this is not a basic division fact, it is unlikely that students will be able to find a correct quotient. If students do think they know the quotient, have them share their thinking. Compare strategies, and share that one common strategy for performing more complicated division with multi-digit numbers is using the standard algorithm.
Say: When we are dividing numbers too large for us to immediately know the answer to, it is best to do the problem in several small parts. Say: When completing the long division expression "68 divided by 4," remember that 68 is 6 tens and 8 ones. Show 6 tens so that the entire class can see them. Ask: How many equal groups of 4 tens can you make? You can make 1 group that will contain 4 tens. The divisor should be multiplied by the number you have just written above the dividend.
In our example, this is the first digit of the quotient. Record the product. Put the result of your multiplication in step 1 beneath the dividend. In the example, 6 times 4 is After you've written a 4 in the quotient, write the number 24 beneath the 25, again being careful to keep the numbers aligned. Draw a line. A line should be placed beneath the product of your multiplication, 24 in the example. Part 3. Subtract the product. Subtract the number you just wrote below the dividend from the digits of the dividend directly above it.
Write the result beneath the line you just drew. Do not subtract from the complete dividend, but only those digits you worked with in Parts One and Two. In the example, you should not subtract 24 from Bring down the next digit. Write the next digit of the dividend after the result of your subtraction operation.
In this case, you'll grab the 0 from and place it after the 1, making it 10, which 6 can go into. Repeat the whole process. Divide the new number by your divisor, and write the result above the dividend as the next digit of the quotient. Write that number 1 into the quotient above the dividend.
Then multiply 6 by 1, and subtract the result from You should end up with 4. If your dividend has more than three digits, keep repeating this process until you've worked through all of them.
For example, if we we had started with 2, grams Part 4. Record the remainder. Depending on what you're using this division for, you may want to finish up with a quotient that's a whole number, with a remainder, i. Place your remainder after the quotient with a letter "r" before it.
In the example, the answer would be expressed as "41 r4. In a case such as this, it would not be useful think about things in terms of partial cars or partial people.
If you plan to calculate a decimal, you can skip this step. Add a decimal point. If you are planning to calculate a precise answer rather than one with a remainder, you'll now need to move beyond whole numbers. When you've reached a point at which you are left with a number smaller than your divisor, add a decimal point to both the quotient and the dividend. In the example, since is a whole number, every digit after the decimal will be 0, making it Keep repeating. Now you have more digits that can be brought down all of them zeroes.
Bring down a zero and continue as before, determining how many times the divisor can go into the new number. Add that number 6 to the quotient above the dividend and after the decimal point. Then multiply 6 by 6, and subtract the result from You should end up with 4 again. Stop and round. In some cases, you will find that when you start to solve for the decimal, the answer repeats over and over. Line up students in groups.
Each group gets a card to start, and the first students complete the first set of steps for the problem they have. If they finish the problem, they can call for you to come check their work and trade the correct answer for a card with a new problem. This activity is a fun way for your class to celebrate finishing their unit on division.
Get a few boxes and fill them with a small treat everyone in the class can enjoy. For an added challenge, make it a code: Have every quotient match up to a letter of the alphabet so that students have to correctly decode a key phrase to open the box. Worksheets are a tried-and-true staple of math class. Lucky for you, there are lots of websites that will do the work for you and generate a custom worksheet that will give your students the change to practice how to do long division.
Here are a few of our favourites:. The most important thing to remember when teaching students how to do long division is to not rush through the material. Contents A six-step guide to teaching long division Two bonus ways to teach division 8 activities to make long division engaging for your students.
How to do long division in six steps 1. The first step you should take is a step back. View this post on Instagram. First, show students a problem that has a remainder in the ones:. The steps are more or less the same, except for one new addition: Divide the tens column dividend by the divisor Multiply the divisor by the quotient in the tens place column Subtract the product from the divisor Bring down the dividend in the ones column and repeat.
Or is it? For a refresher, check out this video from Khan Academy:. Have them continue regular division steps for one or two places, bringing down the zeros. How to do long division without doing long division Congratulations! Area models.
Partial quotients. Take the difference and subtract it from the dividend. The answer should be Ask how many times 23 goes into Use this method to reinforce place value and the concept of division as repeated subtraction. Now we move on to our last step, which is to bring down. 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 This is shown in the diagram below.
Once you bring down the next number, you start this entire process over with division! 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. 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. The order is: D ivide , M ultiply , S ubtract , B ring down. The first letters of this saying match up with the first letters of the order of long division: D — M — S — B. Once again, our answer quotient is written above the division bar. Ours is written in red.
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