After using manipulatives to introduce the division algorithm for multi-digit numbers, full development of the concept should be carefully taught. It is important to give students plenty of time to master division of multi-digit numbers. Do not rush the development of this concept.
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.
Ask: How can we write 276 divided by 6?
276 6 or will probably be the two notations used by the students.
Ask: Which notation will you use to find the quotient of 276 divided by 6?
Preference should be to enable students to use the division algorithm.
Say: Use your base ten blocks to represent 276.
Ask: Let's begin with the hundreds. Since we are dividing by 6, we need to make groups containing 6 hundreds. Can this be done if we only have 2 hundreds?
No. When you cannot make groups from the current place, you will need to regroup and make groups from the next place.
Ask: If we regroup the 2 hundreds for tens, how many tens would we get? If we include the 7 tens, how many tens would that be altogether?
20 tens is equivalent to 2 hundreds. If we combine the 20 tens with 7 tens, we get 27 tens.
Ask: Since we are working with tens now, how many groups of 6 tens can we make from 27 tens? Be sure to use your base ten blocks.
Notice that there are 4 groups of 6 tens with 3 tens left over.
Say: Since we have 4 groups of 6 tens, we place a 4 over the tens place in 276.
Ask: If one group of 6 tens is 60, what is 4 groups of 6 tens worth?
240. Encourage students to use their base ten blocks if necessary to count the value.
Say: Remember that we began with 276 and want to divide it by 6. Since we have made four groups of 6 tens, we can take 240 away from 276.
Ask: How many tens and ones are left over when we take away the 4 groups of 6 tens?
3 tens and 6 ones are left over.
Say: We can do this by writing 240 below 276 in our division problem and subtracting.
Ask: What is 276 240? What is the value of the base ten blocks that you have left over? What do you notice about the two values?
36. This allows students to see the connection and validation between using the base ten blocks and the algorithm they are learning to use.
Ask: Since we cannot make any more groups of 6 tens with the remaining base ten blocks, we can regroup the 3 tens for how many ones?
30 ones. Be sure to show the students the regrouping of 3 tens for 30 ones.
Ask: How many ones will we now have?
We will have 36 ones.
Ask: How many groups of 6 ones can we make from 36 ones?
We can make 6 groups.
Ask: Where do you think we will write the 6 that represents the 6 groups?
The 6 is written above the ones place in 276.
Ask: Are there any ones left over?
Ask: What is the quotient of 276 6?
Continue this activity using different numbers. Be sure to use numbers that will not use remainders at first. Remember to have the students check their answers using multiplication.
Wrap-Up and Assessment Hints
Students need a great deal of practice when learning to divide multi-digit numbers. Do not be in a rush for students to put away their manipulatives when learning this difficult concept. This can be a trying time in many students' mathematical development. One of the keys to success is the opportunity to spend ample time practicing this skill. As a teacher, do not be discouraged with slow progress. Remember, this is the first time most of the students have ever encountered the concept. Your task is to take the needed time and effort to encourage students to learn this process.
Continual assessment when teaching division is a prudent tool. Be sure to provide continual assessment of division once the topic is introduced. Extra practice and assessment later in the year is an excellent tool to be sure that students have mastered this sometimes difficult topic. When assessing students, try to remember back to when you learned how to divide large numbers. This can sometimes help put this concept in better perspective.