Dividing Two-Digit and Three-Digit Numbers
Modeling division is necessary for students to understand the concept behind the division algorithm. Once they understand why each step of the process is performed, they will have greater success in mastering the algorithm.
Materials: base-ten blocks (1 hundred, 12 tens, and 24 ones)
Preparation: Provide at least one set of base-ten blocks for each pair of students.
Prerequisite Skills and Concepts: Students must have a basic understanding of division, and they must know the basic division facts.
- Say: Let's divide 124 by 5. How can I represent 124 by using base-ten blocks?
(Use 1 hundred, 2 tens, and 4 ones.) Display the blocks.
- Say: Dividing 124 by 5 means that 124 must be put into 5 groups with the same number in each group.
- Ask: Can I put 1 hundred block into 5 groups? (no) What must I do in order to divide? (Regroup the 1 hundred as 10 tens.)
Regroup and show students the result. - Say: Since the 1 hundred block cannot be divided without regrouping, no number is placed in the hundreds place in the quotient. The first digit will be in the tens place in the division algorithm.
Write
on the board so that students can see how the algorithm relates to the model. Point to the tens place. - Ask: How many tens blocks do I have now? (12) If 12 tens blocks are divided into 5 groups with the same number in each group, how many tens blocks are in each group? (2) How many tens blocks were used? (10) How many tens blocks are left over? (2)
Demonstrate by putting the tens blocks into 5 equal groups. Place the remaining tens blocks with the ones blocks.Then show how the model relates to the division algorithm.
- Ask: How can the remaining blocks be divided into 5 equal groups? (Regroup the 2 tens as 20 ones.)
Demonstrate the regrouping by using base-ten blocks.
- Ask: How many ones blocks are there altogether? (24) How can 24 be divided into 5 equal groups? (Put 4 ones into each group. Four ones are left over.)
Demonstrate by putting 4 ones blocks into each of the 5 groups. Then show how the model relates to the division algorithm.
- Ask: How many are in each group? (24) How many are left over? (4) What is 124 ÷ 5? (24 R4)
You may wish to model a division problem with a two-digit dividend. Then review with students how modeling with base-ten blocks shows where to place the first digit in the quotient of the division algorithm. Explain how each step in the division algorithm corresponds to the division model.