Math Background

Lesson: Fractions and Wholes
Introducing the Concept

Begin by giving children opportunities to practice identifying and using fractions. Have children practice coloring given parts of shapes and then identifying what fraction of each shape is colored and not colored. Offer different types of shapes divided into different numbers of parts to give children practice with many different fractions. Encourage them to use fractions in their conversation and class discussion. Have children practice looking at groups of different shapes and identifying, for example, what fraction of the group are circles. Provide enough experiences that children feel comfortable talking about and identifying simple fractions and recognizing how fractions are written.

Materials: set of solid shapes including 3 spheres, 4 cubes, 1 cylinder, 2 cones, and 2 rectangular prisms; two blank color wheels for each child—one divided into fourths, one into sixths; red, blue, yellow, and green crayons for each child

Preparation: Arrange solid shapes in a 3-across-by-4-down arrangement. Do not place all like shapes together. Prepare and cut out blank (uncolored) color wheels as indicated above.

Prerequisite Skills and Concepts: Children should be familiar with the names of solid shapes and with the concept of fractions. Children should also have practiced methods of identifying fractional parts.

  • Hand out the color wheels and 4 crayons to each child. Hold up the wheel divided into fourths.
  • Ask: How many parts does this wheel have? (4)
  • Say: Color one part of the wheel red.
    Give students time to color one section red.
  • Ask: What fraction of the wheel is red? (one-fourth)

    Now have students color 2 parts of the wheel blue and identify the fraction of the wheel that is blue. Then tell them to color the last part of the wheel yellow.

  • Ask: What fraction of the wheel is yellow? (one-fourth)
    Make a chart on the board with the names and the fractions for each color to make sure children understand how to write fractions. Show students that if you add each fractional part, you get the total number of parts. (1 + 2 + 1 = 4)

    Repeat this procedure, using the wheel divided into sixths. Ask students to color 1 part of the wheel blue, 2 parts yellow, 2 parts green, and 1 part red. Make sure children have colored their wheels correctly and that they can name the fractional part for each color.

  • Say: Look at the group of shapes. There are several different types of shapes in the group.

    Make sure all children can see the arrangement of solid shapes.

  • Ask: How many shapes are there in all? Have a volunteer provide the answer. (12)
  • Ask: How many of the shapes are cubes? Have a volunteer provide the answer. (4) What fraction of the shapes are cubes? Have a volunteer provide the answer. (four-twelfths) If no one knows the answer, explain that you express the fraction by naming the number of cubes out of the total number of shapes. Write the total number of shapes below a line on the chalkboard, then write the number of cubes above the line. Explain to students how to say this fraction. (four twelfths)

    Repeat this procedure with the other solid shapes in the arrangement. Have students identify what fractional parts of the arrangement are spheres, cones, cylinders, or rectangular prisms. Challenge students to tell what two shapes make up the same fractional part of the arrangement. (cones and rectangular prisms)


Houghton Mifflin Math Grade 2