Math Background

Lesson: Modeling Division
Developing the Concept

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Once children are comfortable with making equal groups, introduce the terms divide, division sentence, and remainder. If manipulatives are available, the use of counters or other countable objects, such as paper clips or crayons, will be helpful. Encourage children to share their thinking as they work through the examples.

Materials: countable objects such as paper clips or counters; overhead projector; 10 index cards per child

Preparation: Prepare the following worksheet (PDF file) for each child.

Prerequisite Skills and Concepts: Children should know the basic subtraction facts and know how to make equal groups.

  • Say: Today we will learn how to divide. Dividing is not really new to you. It is just a new word for "repeated subtraction."

    Place 12 counters on the overhead.

  • Ask: How many counters are there? (12)

    Place the counters in 6 groups of 2 each.

  • Say: Now the 12 counters are in groups of 2.
  • Ask: How many times can you subtract 2 from 12? (6) How many groups of two make 12? (6)

    Write the following on the board.

  1 2     1 0     8     6     4     2
−   2   −   2   − 2   − 2   − 2   − 2
blank blank blank blank blank blank
1 0 8 6 4 2 0
  • Say: We can subtract each group of 2 counters from 12 counters until there are no counters left and find how many groups there are.

    Write the division sentence on the board:12 ÷ 2 = 6. There are 6 groups.

  • Say: It is much easier to write what we just did in a division sentence.

    Point to the division sign.

  • Ask: What does this sign tell us to do? (divide)

    Have a volunteer write the division sentence for each fact as children write the corresponding division sentence on their index cards.

    Repeat these steps with other even numbers to 20, subtracting groups of 2 and finding how many groups there are in each number. Have a volunteer write each division sentence on the board while the other children write it on their index cards.

    When children show they have a good understanding of repeated subtraction and making groups of 2, spend another lesson having them subtract groups of 5. Begin by using repeated subtraction and then writing the division sentence.

    Introduce equal groups with remainders. Lay 13 counters on the overhead. Follow the steps for repeated subtraction and making equal groups of 2.

  • Ask: What was different this time when we made equal groups?
    (Possible answers: There was one counter left over; one counter didn't have a partner; I couldn't match the counter to another one to make an equal group.)
  • Say: Good! There was 1 counter left over that we couldn't put in a group. We call the leftover counter the remainder.

    Write the division sentence on the board, pointing out the word remainder.

  • Say: Sometimes we will have a remainder when we divide, but not always. When there is a remainder, you must write that remainder. The remainder will not always be 1.

    Distribute the worksheets to children. Place the 13 counters on the overhead and make groups of 5. Point out that the remainder is 3. Repeat with other numbers, making groups of 2 and groups of 5 with and without remainders. Have a volunteer write each division sentence on the board as the other children write the division sentences on their worksheets. Remind children to write a zero in the blank if there is no remainder.

Wrap-Up and Assessment Hints
Children need practice using repeated subtraction and making equal groups. If children are having difficulty doing this, ask them to explain their thinking as they work through an example. Encourage the use of flash cards. Children should have a clear understanding of the meaning of division and its relationship to repeated subtraction.

Houghton Mifflin Math Grade 2