Teaching Dividend, Divisor, and Quotient in Division


Lesson 1: Introducing the Concept of Division

As with addition, subtraction, and multiplication, students practice strategies and algorithms that allow them to perform operations beyond basic facts. After students learn their basic division facts and the concept of division, show them the standard algorithm that they are likely to encounter outside of school.

By Grade 6, most students should be fluent in dividing multi-digit numbers using the standard algorithm. But no matter the grade, remind students that there are many ways to think about division, just like there are many ways to think about multiplication, and this algorithm is one tool to help solve math problems.

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

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Preparation: Be sure to provide at least one set of base-ten blocks for each pair of students.

Prerequisite Skills and Concepts: Students should know their basic division facts and have used or seen the use of base ten blocks. Introduce students to the vocabulary dividend, divisor, and quotient prior to the lesson.

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  • Ask: What does 54 represent in 54 ÷ 9?54 ÷ 9 is asking: if you have 54 items and divide them into groups with 9 items in each group, how many groups would you have? The 54 is the number of items that you have at your disposal.
  • Ask: What does 9 represent in 54 ÷ 9?The 9 represents how many items are in each group.
  • Ask: What is 54 ÷ 9?The quotient is 6.
  • Ask: What does 6 represent for 54 ÷ 9?It is the quotient, but more importantly, the 6 represents the number of groups you will divide the 54 items into groups to have 9 items in each group.
  • Say: Another way to write 54 ÷ 9 is by drawing the long division symbol, placing 54 “inside” it, and 9 to the left. 54 is the total number of items you begin with, and 9 is the number of items in each group. The quotient, or number of groups, is written above the 54:
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  • Ask: Let’s try another problem now. What does 68 represent in 68 ÷ 4?68 ÷ 4 is asking: if you have 68 items and divide them into groups with 4 items in each group, how many groups would you have? The total number of items that you have at the beginning is 68.
  • Ask: What does 4 represent in 68 ÷ 4?The 4 represents how many items are in each group.
  • Ask: What is 68 ÷ 4?Since this is not a basic division fact, it is unlikely that students will be able to find a correct quotient. Students who think they know the answer to this question can share their thoughts with others. Compare strategies, and share that one common strategy for performing more complicated division with multi-digit numbers is using the standard algorithm.
  • Ask: If we want to write 68 ÷ 4 the same way we wrote the standard long division express “54 divided by 9,” what number would go where 54 is and what number would replace 9?68 would go in place of 54 and 4 in place of 9.
  • Say: When we are dividing numbers too large for us to immediately know the answer to, it is best to do the problem in several small parts.
  • Say: When completing the long division expression “68 divided by 4,” remember that 68 is 6 tens and 8 ones.
  • The entire class will be able to see 6 tens.

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