Learning Long Division: Start with the Basics

01
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Show the Number with Base 10

Step 1: Introducing Long division. D.Russell

Base 10 blocks or strips to ensure that understanding takes place. All too often long division is taught using the standard algorithm and rarely does understanding occur. Therefore, the student needs to have a good understanding of fair shares. A child should be able to show division of the basic facts by showing fair shares. For instance, 12 cookies divided by 4 should be shown using buttons, base 10 or coins. A child needs to know how to represent 3 digit numbers using base 10. This first step shows how the number 73 is shown using base 10 strips.

If you don't have Base 10 Blocks, copy this sheet onto heavy (card stock) and cut out 100 strips, 10 strips and 1's. It is very important for a student to represent their numbers when beginning long division.

Before attempting long division, students should be comfortable with these exercises.

02
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Using Base Ten, Divide the Base Ten into the Quotient

Long division
Beginning Long Division Using Base 10. D.Russell

The quotient is the number of groups to be used. For 73 divided by 3, 73 is the divident and 3 is the quotient. When students understand that division is a sharing problem, long division makes much more sense. In this case, the number 73 is identified with base 10 strips. 3 circles are drawn to indicate the number of groups (quotient). The 73 is then equally divided into the 3 circles. In this case the children will discover that there will be leftovers - a remainder. .

If you don't have Base 10 Blocks, copy this sheet on to heavy (card stock) and cut out 100 strips, 10 strips and 1's. It is very important for a student to represent their numbers when beginning long division.

03
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Finding the Solution With Base 10 Strips

Long Division
Finding the Solution. D.Russell

As the students separate the base 10 strips into the groups. They realize they must trade a 10 strip for 10 - 1's to complete the process. This emphasizes place value very well.

If you don't have Base 10 Blocks, copy this sheet on to heavy (card stock) and cut out 100 strips, 10 strips and 1's. It is very important for a student to represent their numbers when beginning long division.

04
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Next steps: Base 10 Cuts Outs

Long Division
Step 4. D. Russell

Many exercises should be done where the students divided a 2-digit number by a 1 digit number. They should represent the number by base 10, make the groups and find the answer. When they're ready for the paper/pencil method, these exercises should be the next step. Notice that instead of base ten, they can use dots to represent the 1 and a stick to represent the 10. Hence a question like 53 divided into 4, the student would draw 5 sticks and 4 dots. As the student begins putting the ​strips (lines) into the 4 circles, they realize that a stick (line) must be traded for 10 dots. Once the child has mastered several questions like this, you can move on to the traditional division algorithm and they may be ready to move away from the base 10 materials.