Estimated division with numbers greater than 1,000

Students learn to estimate quotients with numbers greater than 1,000.

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The students learn to estimate division problems with numbers greater than 1,000.

CCSS.Math.Content.5.NBT.B.6

Students will be able to estimate quotients with numbers greater than 1,000.

You ask a number of students to come up to the board and divide them into two groups. You name a division problem and the group that gives the correct answer first gets a point. Choose rounded numbers.

First you explain what the dividend, the divisor, and the approximately equals sign are. Then you tell the students that with estimated division you always look for a dividend that is divisible by the divisor. With numbers greater than 1,000 you round to the nearest hundred or thousand. For this, sometimes you also need to round the divisor (for example to the nearest tens number). Both are possible; the only difference is in how accurate the estimate is. Discuss this together with the students. Next you show how estimated division works step by step. After that the students practice by choosing the correct estimated quotient. Then the students are going to estimate division problems on their own. Ask how they rounded the numbers to solve the problem. After that, walk the students through the steps of solving a story problem. Have the students solve the next story problems on their own, and ask how they arrived at their answer.

Check whether the students can estimate division problems by asking the following questions:

- When is it useful to estimate a quotient?

- When is it not useful?

The students test their understanding of estimated division with numbers greater than 1,000 through ten exercises. In each of these exercises, the students must choose an estimated quotient to use, and answer a question about the problem. Some of the exercises are story problems.

You discuss with the students once again how it is important to be able to estimate division problems, because then you quickly know approximately how much you can divide a number by. Check whether the students can estimate division problems by having them complete a number of division problems on the interactive whiteboard with thousands numbers. Can they do it within 40 seconds?

When students have difficulty with estimated division with numbers greater than 1,000, then you can first have the students practice with dividing thousands and hundreds numbers. For each estimated division problem, ask the students which estimated quotient they choose.

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