For student in qualities 3 and also up, the leap native multiplication to division can it is in hard! This short article explains what department is, together with the different parts the a division problem (quotient, divisor, and also dividend) and also how to usage the conventional algorithm because that division. Contained are 2 lessons come introduce and develop the concept to her students. Both lessons room designed to exercise fluently splitting multi-digit numbers making use of the conventional algorithm, a standard usual in grades 5–6.

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Comparing division and Multiplication

In order to teach division, it commonly helps to start with multiplication. The math expression 3 × 5 to represent three teams with 5 items in every group. To discover the product, college student can construct a model of three teams with 5 items in each group as presented below.


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Ask: Let"s try another trouble now. What go 68 stand for in 68 ÷ 4?68 ÷ 4 is asking: if you have actually 68 items and also divide lock into teams with 4 items in each group, how countless groups would you have? The 68 to represent the total number of items you start with.Ask: What go 4 represent in 68 ÷ 4?The 4 represents how numerous items are in every group.Ask: What is 68 ÷ 4?Since this is not a basic division fact, the is unlikely the students will be able to find a exactly quotient. If students do think they recognize the quotient, have actually them share their thinking. Compare strategies, and share that one common strategy for performing more complex division v multi-digit number is utilizing the typical algorithm.Ask: If we desire to create 68 ÷ 4 the same way we wrote the standard long division express "54 divided by 9," what number would go whereby 54 is and also what number would replace 9?68 would go in place of 54 and also 4 in location of 9.Say: When us are splitting numbers too big for us to instantly know the price to, that is best to perform the problem in several little parts.Say: When completing the long department expression "68 separated by 4," remember that 68 is 6 tens and also 8 ones.Show 6 10s so the the entire course 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 create a 1 over the tens ar in 68.
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Say: Since you cannot make additional groups containing four tens, friend will need to regroup the remaining 2 for 20 ones.Show 2 tens being regrouped as 20 ones so the the entire class can see. Next, combine the 20 ones with the 8 ones.Ask: If we combine the 20 ones with the 8 ones, how plenty of ones will certainly we have?28 ones.Ask: How plenty of groups with 4 ones in each team can we make from the 28 ones?We have the right to make 7 teams with 4 ones in every group.
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Say: Since 7 groups of 4 ones have the right to be made, we write 7 over the ones place in 68.
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Say: Since there space no people remaining, ours quotient is 17. If we make 17 teams with 4 items in every group, us should have actually a full of 68 items.Have student individually or in pairs make 17 teams with 4 items in every group. Then have actually them count the total variety of items to see if over there are indeed 68.Continue this task using slightly larger numbers. Have the students use their base-ten block to recognize the place value for the quotient. Remember to always have the students inspect their work-related using your base-ten blocks.

Lesson 2: developing the ide of Division

After making use of manipulatives to present the division algorithm because that multi-digit numbers, it"s time to build the concept much more fully. Execute not sirloin the advance of this concept. Numerous students battle with division of multi-digit numbers, and also it is crucial to allow students plenty of time to master it.

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

Preparation: Be certain to administer at least one collection of base-ten blocks for each pair that students.

Ask: How can we compose 276 separated by 6?276 ÷ 6 or the long department expression v 276 inside the long department symbol and 6 external it will most likely be the 2 notations used by the students. Encourage college student who shot different representations, such together the portion 276/6 or a drawn visual model.Ask: Which notation will you use to find the quotient that 276 split by 6?Direct students to usage the long division expression to permit them to usage the department algorithm.Say: Use her base-ten block to represent 276.
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Ask: Let"s start with the hundreds. Due to the fact that we are separating by 6, we must make teams containing 6 hundreds. Have the right to this be excellent if us only have 2 hundreds?No. When you can not make teams from the current place, girlfriend will need to regroup and make groups from the next place.Ask: If we regroup the 2 hundreds because that tens, how plenty of tens would we get? If we include the 7 tens, how numerous tens would certainly that be altogether?2 hundreds is tantamount to 20 tens. If we integrate the 20 tens with 7 tens, we obtain 27 tens.Ask: Since we room working with 10s now, how countless groups the 6 tens have the right to we make from 27 tens? Be certain to use your base ten blocks.Notice that there are 4 groups of 6 10s with 3 tens left over.
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Say: Since we have actually 4 groups of 6 tens, we ar a 4 end the tens location in 276.
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Ask: If one team of 6 10s is 60, what is 4 teams of 6 tens worth?240. Encourage college student to usage their base-ten blocks to show the value.Say: Remember that we began with 276 and also want to division it by 6. Since we have actually made four groups, each through 6 tens, we can take 240 far from 276.Ask: How many tens and also ones room left over once we take away the 4 teams of 6 tens?3 tens and 6 ones space left over.Say: We deserve to do this by composing 240 listed below 276 in our division problem and subtracting.
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Ask: What is 276240? What is the worth of the base-ten blocks the you have left over? What execute you an alert about the two values?36. This help students see the connection between using the base-ten blocks and the standard algorithm.Ask: Since us cannot make any an ext groups the 6 10s with the staying base-ten blocks, we deserve to regroup the 3 10s for how many ones?30 ones. In former of the students, regroup 3 10s as 30 ones.Ask: How plenty of ones execute we currently have?We have actually 36 ones.Ask: How countless groups that 6 ones deserve to we make from 36 ones?We have the right to make 6 groups.Ask: Where carry out you think we will write the 6 the represents the 6 groups?The 6 is written above the ones place in 276.Ask: Are there any ones left over?No.Ask: What is the quotient of 276 ÷ 6?46Continue this task using various numbers. Be sure to use numbers that carry out not use remainders in ~ first. To reinforce the connection in between multiplication and also division, have students check their job-related using multiplication.

Wrap-Up and also Assessment Hints

Students need a great deal of exercise when discovering to division multi-digit numbers. Carry out not it is in in a rush for students to placed away their manipulatives when learning this challenging concept. This have the right to be a do the efforts time in plenty of students" mathematics development!

As a teacher, carry out not be discouraged by slow-moving progress. Remember, this may be the very first time numerous of your students have ever before encountered the concept. Your job is to take it the necessary time and also effort to encourage student to discover this process. As lot as possible, shot to relate different department problems to her students. If they"re interested in basketball, because that example, have actually them divide groups of players or basketballs. Additionally, connect department to other topics, such together multiplication, fractions, and also equations, when they appear to reinforce the principle many times.

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Continual assessment once teaching division is necessary and can take the kind of warm-up problems, digital exercise (for example with our own digital math practice solution, Waggle), or exit tickets, in enhancement to more formal assessment such together quizzes and tests. Return to the concept throughout the year come ensure retention and also build mastery.

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