           ## Addition and Subtraction with Regrouping

Last year the children worked with addition and subtraction of 2-digit numbers and money amounts, both without regrouping. Review these skills and basic facts to help prepare them for 3-digit addition and subtraction. Encourage children to share their sums and differences. Assure them that they already have the knowledge needed to add and subtract 3-digit numbers.

Materials: place-value blocks (commercial or hand-made), paper or plastic bags

Preparation: Place 6 tens blocks and 8 ones blocks into a bag for each pair of children.

Prerequisite Skills and Concepts: Children should know basic addition and subtraction facts, be able to find sums to 99 without regrouping, and be able to subtract 2-digit numbers without regrouping. It is also important that children recognize and understand the use of place-value, as its role increases to involve 3-digit numbers.

Give each pair of children a bag containing 6 tens and 8 ones, paper, and pencils.

• Say: With your partner, place 4 tens and 5 ones on the desk. Put the tens in a group together on the left side of the ones.
Children should assemble the number 45 on the desk by showing 4 tens and 5 ones.

• Ask: What number is represented on your desk? How do you know?
Children should answer with the number 45 because there are 4 tens and 5 ones. Some children may count by tens, then by ones, to reach 45.

• Say: I am going to write that number on the board.
Write 45 on the board.

• Say: Now take the remaining blocks out of the bag and model another number.

• Ask: What number do the blocks represent?
Children should respond that the number is 23 because there are 2 tens and 3 ones.

• Say: I am going to write that number on the board.
Write 23 under 45 so that the places are aligned.

• Ask: Suppose we need to join these blocks together. How can we do that so that we get one number as an answer?
Children should respond with words that symbolize addition, such as put together, join, combine, mix together, add, or find the total.

• Ask: What symbol can we use to show that we want to join the numbers 45 and 23?
Children should respond with plus sign, addition sign, or a similar answer.
Write a large plus sign before 23 on the board. Draw a line under the problem, ready to add.

• Ask: How should we start to join the blocks?
If necessary, children should be led to start with the ones blocks.
How many ones do we have? (8)
How many tens do we have? (6)
What number represents 6 tens and 8 ones? (68)

• Say: Count the tens blocks on your desk. Then count the ones blocks.

• Ask: What number represents the total? (68)
What is the sum of 45 and 23? (68)
Continue practicing addition using one addend of 45. Have one partner choose the second addend from the available place-value blocks. The other partner demonstrates the addition with the blocks. Then encourage both students to write their problems on paper like you did on the chalkboard. Repeat until children feel comfortable with addition.

• Say: Now we want to use the number 68 to show subtraction.
On the board, write 68. Below that number write a minus sign and the number 12. Then draw a line to show subtraction.

• Say: Look at the problem on the board. You have the number 68 on your desk. Take away 12 from 68. Put the place-value blocks for the number 12 in your bag.
Observe children to be sure they take 1 ten and 2 ones from the desk and place the blocks in their bag.

• Ask: How many ones are left? (6)
How many tens are left? (5)
What is 68 take away 12? (56)

• Say: Notice that 8 ones minus 2 ones is 6 ones. Notice that 6 tens minus 1 ten leaves 5 tens. That means that 68 minus 12 is 56. Use all the place-value blocks to show your partner 68 take away 33.
Continue practicing subtraction from 68 by having one partner choose the number to subtract while the other partner does the actual subtraction with the blocks. Then encourage students to write their problems on paper like you did on the chalkboard. Repeat until children feel comfortable with subtraction.

Addition and Subtraction with Regrouping:

Commutative and Associative Properties:

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