## Lesson: Three-Digit Addition and Subtraction With Regrouping Introducing the Concept

Earlier in the year, children learned one- and two-digit addition and subtraction, with and without regrouping. They also worked with place value and money. Review the basic facts and skills they have already learned to prepare them for three-digit addition and subtraction with regrouping. Provide exercises or activities for children to review what they already know. Also provide opportunities for children to share what they know in class discussions.

Materials: base-ten blocks (commercial or hand-made), paper or plastic bags, place-value charts, paper, and pencils

Preparation: Place 9 hundreds, 20 tens, and 20 ones blocks in a bag for each pair of children. If necessary, create a place-value chart for each pair of children.

Prerequisite Skills and Concepts: Children should be familiar with basic addition and subtraction facts and with place-value concepts. Children should also understand how to add and subtract one- and two-digit numbers, with and without regrouping.

• Say: You can easily use basic facts and mental math to add two- and three-digit numbers with zeros in the tens and ones places. Let's practice using mental math to add and subtract three-digit numbers.
Ask one or two volunteers to suggest two numbers, such as 400 and 300.
• Ask: If you want to know how much 300 + 400 equals, what should you do?
Children may say that you should add to find the sum. On the chalkboard, write the addition in vertical form.
• Ask: What do you notice that might make this exercise easy to solve using mental math? Children may answer that if you know that 3 + 4 = 7, it is easy to see that 300 + 400 = 700. You just add using the basic fact and write the two zeros in the sum.
• Say: Now let's try subtraction.
Write600 − 200 in vertical form on the chalkboard. Have the children suggest how to find the difference. If necessary, remind them that if they know the basic fact, they can use mental math to subtract and then write the zeros in the difference. Remind them that they can think 6 − 2 = 4, so 600 − 200 = 400.
• Ask: Who can explain how to use a basic fact and mental math to find 500 − 300?
The volunteer may say that you can think 5 − 3 = 2, so it is easy to see that 500 − 300 = 200. Allow volunteers to demonstrate their use of mental math for other addition and subtraction exercises.

Have children arrange themselves in pairs. Give each pair a bag containing 9 hundreds, 20 tens, and 20 ones blocks; a place-value chart; several sheets of paper; and pencils.

Write the number 146 on the board in large print.

• Say: With your partner, use the base-ten blocks to show the number 146 on the place-value chart. Make sure that the hundreds, tens, and ones blocks are in the correct columns on the chart.
If necessary, demonstrate that the hundreds should be in the left column, the tens in the middle, and the ones in the right column. Children should build the number 146 using 1 hundred, 4 tens, and 6 ones.
• Ask: How did you know how to show the number 146?
Children may respond that they used place value to figure out that in the number 146 there are 1 hundred, 4 tens, and 6 ones.

Write the number 219 on the board in large print under the number 146.

• Say: With your partner, use the base-ten blocks to build the number 219. Line up the blocks for the number 219 underneath the blocks you used to make 146. Make sure that the hundreds, tens, and ones are in the correct columns.
Children should build the number 219 using 2 hundreds, 1 ten, and 9 ones.
• Ask: How did you know how to show the number 219?
Children may respond that they used place value to figure out that there are 2 hundreds, 1 ten, and 9 ones in the number 219.

Write a “plus” sign before the number 219 on the board, and draw a line under the number to create an addition exercise.

• Say: Now we are going to add these two numbers. Use your blocks to help you find the sum. Let's start by adding the ones. Put all of the ones together on your charts.
Have children count the ones.
• Ask: How many ones do you have altogether? (15). Can we write 15 in the ones place? (no)
• Say: Since we have more than 9 ones, we need to regroup 15 ones as 1 ten and 5 ones. Take the time to show that on your place-value chart. If you need to, get extra base-ten blocks from your bag and put away ones you don't need.

Children should put 10 ones back in the bag and take out 1 ten.

• Ask: Now how many ones do you have? (5)
• Say: Look at the addition on the chalkboard. Let's write a 5 in the ones place of the sum.
Write the number 5 in the ones place of the sum.
• Say: We got that number by regrouping the 15 ones as 1 ten and 5 ones. I will write a small “1” above the tens column to remind myself to add in the regrouped 10 ones.
Write a small “1” lightly above the tens place.
• Ask: How many tens are there?
Children may count 5 tens, plus the regrouped ten, to get 6 tens.
• Say: Yes, there are 6 tens. Let's write that number in the tens place of the sum.
Write the number 6 in the tens place of the sum.
• Ask: How many hundreds are there? (2 hundreds + 1 hundred = 3 hundreds.)
• Say: Yes, there are 3 hundreds altogether. Let's write that number in the hundreds place of the sum.
Write the number 3 in the hundreds place of the sum.
• Say: Now we have an answer to the addition exercise. 146 + 219 = 365. In this exercise we had to regroup the ones in order to add.

Repeat the activity, using the numbers 152 and 181. Point out to the children that this time they will need to regroup the tens. Allow them to practice using different three-digit numbers until they feel comfortable using the base-ten blocks to help them add three-digit numbers with regrouping.

• Say: Let's try subtraction this time. Let's start with the number 365. We will subtract the number 219 from 365.
Write365 − 219 in vertical form on the chalkboard.
• Ask: Let's begin again with the ones. Can we take away 9 ones from 5 ones? (no) What is the first thing you need to do? (We need more ones, so regroup 1 ten as ten ones and add them to the 5.)
• Ask: Now you have 15 ones. Take away 9 ones. Write the 1 lightly in front of the 5 to remind yourself that you have 15 ones. What is the difference?
(15 ones − 9 ones = 6 ones.) Write a 6 in the ones place on the chalkboard. Remind children that they have regrouped a ten from the 6 tens in 365. Show them how to cross out the 6 in the tens place and write a 5.

Encourage children to finish subtracting on their own, using their blocks and place-value charts. When children have completed the exercise, have them share their answers and methods. Point out that by adding 146 and 219 to get 365 they can check to be sure that 146 is the difference between 365 and 219.

Repeat the subtraction activity using the numbers 333 and 181. Point out to the children that this time, they will need to regroup the hundreds in order to subtract. Allow children to practice using different three-digit numbers until they feel comfortable using their blocks to subtract three-digit numbers with regrouping.