Math Background

Lesson: Modeling Division
Introducing the Concept

Begin the lesson by reviewing basic multiplication facts and parts of a group. See Addition and Subtraction Facts to 20 and Geometry and Fractions. Encourage children to share their thinking as they work through the examples in the lesson. This will allow you to connect what children have already learned to what they are learning in this chapter.

Materials: large sheet of construction paper; 5 containers such as dishpans or boxes; at least 20 countable objects such as pencils, books, crayons, cups, and juice cartons, or manipulatives such as counters or blocks

Preparation: Use a red marker to write Left Over in large letters at the top of a sheet of construction paper.

Prerequisite Skills and Concepts: Children should know the addition and subtraction facts to 20.

  • Place 2 containers and 10 pencils or other countable objects on a table.
  • Ask: How many pencils are there in all? (10)
  • Say: Today we are going to make equal groups. We will use the two containers to see how many pencils are in each group.
  • Ask: How many groups are there? How many are in each group?
    Emphasize that there are two groups of 5.

    Have children line up the two groups to reinforce the idea of equal groups. Then place 3 more containers on the table.

  • Say: Now let's try to make equal groups another way.
  • Ask: Can we make 5 equal groups? (yes) How many are in each group? (2) So we have five groups of 2.
  • Say: Sometimes you can find different ways to make equal groups from the same number.

    When children are comfortable with making equal groups, introduce the idea of making equal groups with some objects left over.

  • Say: Sometimes when you try to make equal groups, you can't do it without having some objects left over.

    Place 2 containers and 11 pencils on the table.

  • Ask: How many pencils are there in all? (11)
  • Ask: How many equal groups did you make? (2)
  • Ask: Are there any pencils left over? (yes) How many? (1)

    Repeat with 11 pencils and 5 containers.

  • Ask: How many equal groups can you make? (5)
  • Ask: Are there any pencils left over? (yes) How many? (1)
  • Say: Put the leftover objects on the sheet of paper that is labeled Left Over. Sometimes when you make equal groups, you will have something left over.

    Repeat the activity with other numbers, making equal groups with left over objects.

Houghton Mifflin Math Grade 2