For student in grades 3 and up, the leap from multiplication to division can it is in hard! This article explains what department is, in addition to the different parts the a department problem (quotient, divisor, and also dividend) and how to use the conventional algorithm for division. Consisted of are 2 lessons to introduce and develop the concept to your students. Both lessons room designed to exercise fluently separating multi-digit numbers making use of the conventional algorithm
, a standard common in grades 5–6.
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Comparing department and Multiplication
In order to teach division, it generally helps to start with multiplication. The mathematical expression 3 × 5 represents three groups with 5 items in each group. To discover the product, student can build a model of three teams with five items in each group as displayed below.
Ask: Let"s shot another difficulty now. What does 68 represent in 68 ÷
4 is asking: if you have 68 items and divide them into groups with 4 item in every group, how numerous groups would you have? The 68 represents the total variety of items you begin with.Ask: What walk 4 represent in 68 ÷
4?The 4 to represent how many items are in each group.Ask: What is 68 ÷
4?Since this is not a basic division fact, it is unlikely the students will have the ability to find a correct quotient. If students carry out think they understand the quotient, have actually them share their thinking. Compare strategies, and share that one usual strategy for performing more facility division v multi-digit number is utilizing the typical algorithm.Ask: If we want to write 68 ÷
4 the same method we wrote the traditional long department express "54 split by 9," what number would certainly go wherein 54 is and what number would replace 9?68 would certainly go in place of 54 and 4 in place of 9.Say: When us are separating numbers too large for us to automatically know the answer to, that is ideal to perform the problem in several tiny parts.Say: When completing the long department expression "68 separated by 4," remember the 68 is 6 tens and 8 ones.
Show 6 10s so that the entire class can watch them.Ask: How countless equal teams of 4 tens deserve to you make?
You deserve to make 1 group that will contain 4 tens.Say: Since you deserve to make only 1 group, you write a 1 end the tens location in 68.Say: Since you can not make extr groups containing 4 tens, you will should regroup the remaining 2 because that 20 ones.
Show 2 tens being regrouped as 20 ones so the the entire course can see. Next, combine the 20 ones v the 8 ones.Ask: If we integrate the 20 ones through the 8 ones, how numerous ones will certainly we have?
28 ones.Ask: How numerous groups with 4 ones in each group can us make from the 28 ones?
We can make 7 teams with 4 persons in each group.Say: Since 7 groups of 4 ones deserve to be made, we create 7 over the ones place in 68.Say: Since there room no ones remaining, our quotient is 17. If we make 17 teams with 4 item in every group, we should have actually a full of 68 items.
Have student individually or in pairs do 17 groups with 4 items in each group. Then have actually them counting the total number of items to view if there are undoubtedly 68.Continue this task using slightly larger numbers. Have the students use their base-ten block to recognize the ar value because that the quotient. Psychic to constantly have the students examine their job-related using your base-ten blocks.
Lesson 2: arising the concept of Division
After utilizing manipulatives to introduce the division algorithm for multi-digit numbers, it"s time to construct the concept an ext fully. Perform not rush the advancement of this concept. Plenty of students struggle with department of multi-digit numbers, and also it is necessary to allow students lot of of time to grasp it.
Materials: Base-ten blocks that all students deserve to see (for example, with an overhead projector); base-ten blocks the students deserve to use
Preparation: Be sure to carry out at the very least one set of base-ten blocks because that each pair of students.Ask: How can we compose 276 split by 6?
276 ÷ 6 or the long department expression with 276 within the long department symbol and also 6 external it will more than likely be the two notations used by the students. Encourage college student who try different representations, such as the portion 276/6 or a attracted visual model.Ask: Which notation will certainly you use to discover the quotient that 276 separated by 6?
Direct college student to usage the long department expression to permit them to usage the department algorithm.Say: Use her base-ten block to represent 276.Ask: Let"s begin with the hundreds. Because we are dividing by 6, we must make teams containing 6 hundreds. Can this be done if we only have 2 hundreds?
No. As soon as you cannot make groups from the present place, girlfriend will need to regroup and also make teams from the following place.Ask: If us regroup the 2 hundreds because that tens, how plenty of tens would we get? If we encompass the 7 tens, how many tens would certainly that it is in altogether?
2 hundreds is equivalent to 20 tens. If we integrate the 20 10s with 7 tens, we gain 27 tens.Ask: Since we space working with 10s now, how many groups of 6 tens deserve to we make from 27 tens? Be sure to use your base ten blocks.
Notice the there are 4 teams of 6 tens with 3 10s left over.Say: Since we have 4 groups of 6 tens, we ar a 4 over the tens location in 276.Ask: If one group of 6 tens is 60, what is 4 teams of 6 tens worth?
240. Encourage student to use their base-ten blocks to show the value.Say: Remember the we started with 276 and want to division it through 6. Since we have made four groups, each with 6 tens, we deserve to take 240 far from 276.Ask: How countless tens and also ones room left over as soon as we take away the 4 teams of 6 tens?
3 tens and 6 ones are left over.Say: We deserve to do this by creating 240 listed below 276 in our department problem and also subtracting.Ask: What is 276
– 240? What is the value of the base-ten blocks that you have left over? What carry out you notice about the two values?
36. This help students view the connection in between using the base-ten blocks and also the typical algorithm.Ask: Since we cannot do any much more groups that 6 10s with the remaining base-ten blocks, we deserve to regroup the 3 10s for how plenty of ones?
30 ones. In front of the students, regroup 3 tens as 30 ones.Ask: How numerous ones do we currently have?
We have 36 ones.Ask: How countless groups that 6 ones have the right to we make from 36 ones?
We have the right to make 6 groups.Ask: Where execute you think we will certainly write the 6 that represents the 6 groups?
The 6 is written above the ones ar in 276.Ask: Are there any type of ones left over?
No.Ask: What is the quotient of 276 ÷ 6?
46Continue this task using various numbers. Be sure to usage numbers that perform not usage remainders in ~ first. Come reinforce the connection between multiplication and also division, have actually students inspect their work using multiplication.
Wrap-Up and Assessment Hints
Students need a great deal of practice when discovering to divide multi-digit numbers. Do not be in a rush for students to placed away their manipulatives when discovering this complicated concept. This can be a make the efforts time in numerous students" mathematical development!
As a teacher, carry out not it is in discouraged by slow progress. Remember, this might be the an initial time countless of her students have ever before encountered the concept. Your task is to take the essential time and also effort to encourage students to find out this process. As much as possible, shot to called different department problems to your students. If they"re interested in basketball, for example, have them divide teams of players or basketballs. Additionally, connect department to various other topics, such together multiplication, fractions, and equations, once they show up to reinforce the principle many times.
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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 exit tickets, in addition to an ext formal evaluate such as quizzes and tests. Return to the ide throughout the year to ensure retention and build mastery.
Need more ideas come teach what is a divisor in math? trying to find more totally free lessons and tasks for elementary and middle school? Be sure to discover our totally free Teaching sources hub!