## Division

As with addition, subtraction, and multiplication, students progress by learning algorithms that allow them to perform operations beyond basic facts. After students learn their basic division facts and the concept of division, it is time to introduce algorithms that will allow them to divide larger numbers. It is important to show the students that there is a need to learn how to use algorithms to divide larger numbers.

Materials: overhead base ten blocks, overhead projector, base ten blocks for students.

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.

• Ask: What does 54 represent in 54 9?
54 9 is asking that if you have 54 items and divide the items into groups with 9 items in each group, how many groups would you have? The 54 represents the total number of items you begin with.

• Ask: What does 9 represent in 54 9?
Once again, 54 9 is asking that if you have 54 items and divide the items into groups with 9 items in each group, how many groups would you have? The 9 represents how many items in each group.

• 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 . 54 is the total number of items you begin with and 9 is the number of items you want in each group. The quotient, or number of groups, is written above the 54 like this: .

• Ask: What does 68 represent in 68 4?
68 4 is asking that if you have 68 items and divide the items into groups with 4 items in each group, how many groups would you have? The 68 represents the total number of items you begin with.

• Ask: What does 4 represent in 68 4?
68 4 is asking that if you have 68 items and divide the items into groups with 4 items in each group, how many groups would you have? The 4 represents how many items are in each group.

Since this is not a basic division fact, it is unlikely that students will be able to find a correct answer. This will allow you to show a need for learning an algorithm to divide multi-digit numbers that are not basic division facts.

• Ask: If we want to write 68 4 the same way we wrote , 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 doing , we can think of 68 as 6 tens and 8 ones.

• Place 6 tens on the overhead using base ten blocks.

• Ask: How many equal groups of 4 tens can you make?
You can make 1 group that will contain 4 tens.

• Say: Since you can make only 1 group, you write a 1 over the tens place in 68.

• Say: Since you cannot make additional groups containing four tens, you will need to regroup the remaining 2 for 20 ones.

• Be sure to show the regrouping on the overhead. Next, combine the 20 ones with the 8 ones.

• Ask: If we combine the 20 ones with the 8 ones, how many ones will we have?
28 ones.

• Ask: How many groups with 4 ones in each group can we make from the 28 ones?
We can make 7 groups with 4 ones in each group.

• Say: Since 7 groups of 4 ones can be made, we write 7 above the ones place in 68.

• Say: Since there are no ones remaining, our answer, or quotient, is 17. If we make 17 groups with 4 items in each group, we should have a total of 68 items. You and your partner need to make 17 groups with 4 items in each group. After you have done this, count the total number of items to see if there are indeed 68.

• Continue this activity using slightly larger numbers. Have the students use their base ten blocks to determine the place value for the quotient. Remember to always have the students use their base ten blocks to check the answers.