For students in grades 3 and also up, the leap indigenous multiplication to department can it is in hard! This post explains what division is, in addition to the different parts of a division problem (quotient, divisor, and dividend) and how to use the traditional algorithm for division. Contained are two lessons to introduce and also develop the concept to your students. Both lessons are designed to exercise fluently separating multi-digit numbers utilizing the traditional algorithm, a standard usual in grades 5–6.

You are watching: The answer to a division problem is

Comparing department and Multiplication

In order to teach division, it generally helps to start with multiplication. The mathematical expression 3 × 5 represents three teams with five items in every group. To uncover the product, student can construct a model of three groups with 5 items in each group as shown below.


*
Ask: Let"s shot another problem now. What go 68 represent in 68 ÷ 4?68 ÷ 4 is asking: if you have actually 68 items and divide castle into groups with 4 items in each group, how countless groups would certainly you have? The 68 represents the total variety of items you begin with.Ask: What go 4 stand for in 68 ÷ 4?The 4 to represent how numerous items are in every group.Ask: What is 68 ÷ 4?Since this is not a basic division fact, it is unlikely that students will have the ability to find a exactly quotient. If students carry out think they understand the quotient, have them share their thinking. Compare strategies, and also share that one common strategy for performing more complex division with multi-digit number is using the standard algorithm.Ask: If we want to create 68 ÷ 4 the same method we created the traditional long division express "54 split by 9," what number would go where 54 is and what number would change 9?68 would go in ar of 54 and also 4 in location of 9.Say: When we are separating numbers too huge for united state to instantly know the price to, that is ideal to perform the trouble in several little parts.Say: When completing the long department expression "68 divided by 4," remember the 68 is 6 tens and also 8 ones.Show 6 tens so that the entire course can see them.
Ask: How plenty of equal teams of 4 tens can you make?You have the right to make 1 team that will contain 4 tens.Say: Since you can make only 1 group, you compose a 1 over the tens place in 68.
*

Say: Since you cannot make additional groups containing 4 tens, you will have to regroup the continuing to be 2 because that 20 ones.Show 2 10s being regrouped together 20 people so the the entire class can see. Next, incorporate the 20 ones with the 8 ones.Ask: If we incorporate the 20 ones through the 8 ones, how plenty of ones will certainly we have?28 ones.Ask: How many groups v 4 people in each team can we make native the 28 ones?We can make 7 groups with 4 persons in each group.
*
Say: Since 7 groups of 4 ones deserve to be made, we create 7 above the ones place in 68.
*
Say: Since there are no ones remaining, ours quotient is 17. If us make 17 teams with 4 items in each group, we should have a complete of 68 items.Have student individually or in pairs do 17 teams with 4 item in each group. Then have them counting the total variety of items to check out if over there are undoubtedly 68.Continue this activity using slightly bigger numbers. Have actually the students use their base-ten block to determine the place value because that the quotient. Remember to always have the students check their job-related using their base-ten blocks.

Lesson 2: emerging the ide of Division

After utilizing manipulatives to present the division algorithm for multi-digit numbers, it"s time to build the concept much more fully. Perform not rush the advancement of this concept. Countless students battle with division of multi-digit numbers, and also it is necessary to enable students lot of of time to grasp it.

Materials: Base-ten blocks that all students deserve to see (for example, v an overhead projector); base-ten blocks that students deserve to use

Preparation: Be sure to administer at the very least one set of base-ten blocks because that each pair of students.

Ask: How can we write 276 split by 6?276 ÷ 6 or the long department expression v 276 inside the long department symbol and also 6 external it will more than likely be the two notations provided by the students. Encourage students who shot different representations, such as the portion 276/6 or a drawn visual model.Ask: Which notation will you use to find the quotient of 276 split by 6?Direct college student to use the long department expression to allow them to usage the division algorithm.Say: Use your base-ten blocks to represent 276.
*
Ask: Let"s begin with the hundreds. Because we are splitting by 6, we should make groups containing 6 hundreds. Deserve to this be excellent if us only have 2 hundreds?No. Once you cannot make teams from the existing place, girlfriend will should regroup and also make groups from the following place.Ask: If us regroup the 2 hundreds because that tens, how many tens would certainly we get? If we incorporate the 7 tens, how many tens would certainly that it is in altogether?2 hundreds is equivalent to 20 tens. If we incorporate the 20 10s with 7 tens, we obtain 27 tens.Ask: Since we space working with 10s now, how countless groups of 6 tens can we do from 27 tens? Be certain to use your basic ten blocks.Notice that there room 4 teams of 6 tens with 3 10s left over.
*
Say: Since we have actually 4 groups of 6 tens, we place a 4 over the tens place in 276.
*
Ask: If one team of 6 tens is 60, what is 4 teams of 6 10s worth?240. Encourage college student to usage their base-ten block to show the value.Say: Remember the we began with 276 and want to divide it through 6. Since we have actually made 4 groups, each through 6 tens, we can take 240 away from 276.Ask: How numerous tens and ones space left over once we take away the 4 groups of 6 tens?3 tens and also 6 ones space left over.Say: We can do this by composing 240 below 276 in our division problem and subtracting.
*
Ask: What is 276240? What is the worth of the base-ten blocks the you have actually left over? What perform you notification about the 2 values?36. This help students see the connection between using the base-ten blocks and the typical algorithm.Ask: Since us cannot do any more groups of 6 10s with the staying base-ten blocks, we deserve to regroup the 3 10s for how countless ones?30 ones. In front of the students, regroup 3 tens as 30 ones.Ask: How plenty of ones do we now have?We have 36 ones.Ask: How plenty of groups of 6 ones have the right to we do from 36 ones?We have the right to make 6 groups.Ask: Where do you think we will certainly write the 6 the represents the 6 groups?The 6 is written above the ones ar in 276.Ask: Are there any ones left over?No.Ask: What is the quotient of 276 ÷ 6?46Continue this task using different numbers. Be sure to usage numbers that carry out not use remainders at first. Come reinforce the connection in between multiplication and division, have students examine their work using multiplication.

Wrap-Up and also Assessment Hints

Students need a an excellent deal of practice when discovering to division multi-digit numbers. Execute not it is in in a rush because that students to placed away your manipulatives when learning this difficult concept. This can be a do the efforts time in numerous students" mathematics development!

As a teacher, do not it is in discouraged by slow-moving progress. Remember, this might be the very first time plenty of of your students have ever encountered the concept. Your task is to take the required time and also effort come encourage student to find out this process. As lot as possible, shot to said different department problems to your students. If they"re interested in basketball, for example, have them divide groups of football player or basketballs. Additionally, connect division to various other topics, such together multiplication, fractions, and also equations, when they show up to reinforce the principle many times.

See more: What Is The Meaning Of The Root Word Port Root Words Word List

Continual assessment once teaching division is necessary and also can take it the kind of warm-up problems, digital practice (for instance with our own digital math practice solution, Waggle), or leave tickets, in addition to an ext formal assessment such as quizzes and also tests. Return to the ide throughout the year to ensure retention and also build mastery.

***

Need more ideas come teach what is a divisor in math? in search of more free lessons and activities for elementary and middle school? Be certain to discover our complimentary Teaching resources hub!