For students in grades 3 and also up, the leap from multiplication to department can it is in hard! This article explains what division is, in addition to the different parts of a division problem (quotient, divisor, and also dividend) and how to usage the typical algorithm because that division. Had are 2 lessons come introduce and develop the concept to her students. Both lessons space designed to exercise fluently separating multi-digit numbers utilizing the typical algorithm, a standard common in grades 5–6.

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## Comparing division and Multiplication

In order come teach division, it usually helps to start with multiplication. The math expression 3 × 5 represents three groups with five items in each group. To find the product, college student can develop a version of three groups with 5 items in each group as presented below. Ask: Let"s shot another problem now. What go 68 represent in 68 ÷ 4?68 ÷ 4 is asking: if you have 68 items and divide castle into teams with 4 items in every group, how numerous groups would you have? The 68 to represent the total number of items you start with.Ask: What walk 4 represent in 68 ÷ 4?The 4 to represent how numerous items space in each group.Ask: What is 68 ÷ 4?Since this is no a basic department fact, it is unlikely the students will have the ability to find a exactly quotient. If students do think they know the quotient, have actually them share their thinking. Compare strategies, and also share that one usual strategy because that performing more facility division through multi-digit numbers is utilizing the standard algorithm.Ask: If we want to write 68 ÷ 4 the same way we wrote the traditional long division express "54 separated by 9," what number would go wherein 54 is and what number would replace 9?68 would go in location of 54 and also 4 in place of 9.Say: When us are dividing numbers too huge for united state to instantly know the prize to, the is best to do the difficulty in several tiny parts.Say: When perfect 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 class can view them.
Ask: How many equal teams of 4 tens can you make?You can make 1 team that will certainly contain 4 tens.Say: Since you deserve to make just 1 group, you create a 1 end the tens location in 68. Say: Since you cannot make extr groups containing four tens, friend will need to regroup the continuing to be 2 for 20 ones.Show 2 tens being regrouped together 20 people so the the entire class can see. Next, combine the 20 ones through the 8 ones.Ask: If we combine the 20 ones through the 8 ones, how plenty of ones will certainly we have?28 ones.Ask: How plenty of groups with 4 people in each team can us make native the 28 ones?We deserve to make 7 teams with 4 persons in each group. Say: Since 7 teams of 4 ones deserve to be made, we create 7 over the ones place in 68. Say: Since there room no people remaining, our quotient is 17. If us make 17 teams with 4 items in each group, we should have a total of 68 items.Have college student individually or in pairs do 17 groups with 4 item in every group. Then have them counting the total number of items to watch if over there are without doubt 68.Continue this task using slightly bigger numbers. Have actually the students use their base-ten blocks to determine the location value because that the quotient. Psychic to constantly have the students examine their work using your base-ten blocks.

## Lesson 2: developing the concept of Division

After utilizing manipulatives to introduce the department algorithm because that multi-digit numbers, it"s time to build the concept an ext fully. Execute not sirloin the advancement of this concept. Numerous students battle with department of multi-digit numbers, and it is necessary to allow students lot of of time to understand it.

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

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

Ask: How have the right to we create 276 split by 6?276 ÷ 6 or the long division expression through 276 inside the long division symbol and also 6 exterior it will probably be the two notations used by the students. Encourage college student who try different representations, such together the portion 276/6 or a drawn visual model.Ask: Which notation will you use to find the quotient of 276 separated by 6?Direct college student to usage the long division expression to permit them to use the department algorithm.Say: Use your base-ten blocks to stand for 276. Ask: Let"s begin with the hundreds. Because we are splitting by 6, we have to make teams containing 6 hundreds. Can this be done if us only have 2 hundreds?No. As soon as you cannot make teams from the existing place, friend will must regroup and make teams from the following place.Ask: If us regroup the 2 hundreds for tens, how countless tens would we get? If we encompass the 7 tens, how countless tens would certainly that it is in altogether?2 hundreds is indistinguishable to 20 tens. If we combine the 20 tens with 7 tens, we obtain 27 tens.Ask: Since we room working with 10s now, how countless groups that 6 tens deserve to we make from 27 tens? Be certain to usage your base ten blocks.Notice that there are 4 teams of 6 10s with 3 tens left over. Say: Since we have actually 4 teams of 6 tens, we place a 4 end the tens ar in 276. Ask: If one team of 6 10s is 60, what is 4 groups of 6 tens worth?240. Encourage students to usage their base-ten block to highlight the value.Say: Remember that we started with 276 and also want to division it by 6. Due to the fact that we have made four groups, each with 6 tens, we have the right to take 240 away from 276.Ask: How countless tens and ones are left over as soon as we take away the 4 groups of 6 tens?3 tens and also 6 ones are left over.Say: We have the right to do this by creating 240 listed below 276 in our division problem and also subtracting. Ask: What is 276240? What is the worth of the base-ten blocks the you have left over? What do you notification about the 2 values?36. This help students view the connection between using the base-ten blocks and the typical algorithm.Ask: Since we cannot make any an ext groups of 6 tens with the remaining base-ten blocks, we have the right to regroup the 3 tens for how plenty of ones?30 ones. In former of the students, regroup 3 tens as 30 ones.Ask: How plenty of ones execute we now have?We have actually 36 ones.Ask: How plenty of groups the 6 ones can we make from 36 ones?We can make 6 groups.Ask: Where execute you think we will certainly write the 6 the represents the 6 groups?The 6 is written over the ones ar in 276.Ask: Are there any type of ones left over?No.Ask: What is the quotient the 276 ÷ 6?46Continue this task using various numbers. Be sure to usage numbers that execute not use remainders in ~ first. Come reinforce the connection between multiplication and also division, have actually students examine their occupational using multiplication.

### Wrap-Up and Assessment Hints

Students require a great deal of exercise when discovering to divide multi-digit numbers. Perform not be in a rush for students to put away your manipulatives when learning this complicated concept. This deserve to be a do the efforts time in numerous students" math development!

As a teacher, execute not it is in discouraged by slow-moving progress. Remember, this might be the an initial time many of your students have ever before encountered the concept. Your task is to take it the essential time and effort to encourage students to learn this process. As much as possible, try to relate different division problems to your students. If they"re interested in basketball, because that example, have them divide teams of football player or basketballs. Additionally, connect department to other topics, such together multiplication, fractions, and also equations, once they appear to reinforce the ide many times.

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Continual assessment once teaching department is necessary and also can take it the type of warm-up problems, digital exercise (for example with our own digital math exercise solution, Waggle), or departure tickets, in addition to much more formal evaluate such together quizzes and also tests. Go back to the ide throughout the year to ensure retention and also build mastery.

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