Math Background

Lesson: Fractions and Wholes
Developing the Concept

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Review the concepts taught in the Introducing the Concept lesson. Explain to children that they will be using models to learn more about fractions.

Materials: copies of shapes as shown on Worksheet 3 (PDF file) for each child; set of 20 marbles, 5 each of red, black, yellow, and blue; four plastic bags of marbles, each with a randomly distributed even number of red, black, yellow, and blue marbles in it; red, blue, yellow, green, purple, and orange crayons for each child

Preparation: Copy Worksheet 3 (PDF file) for each child. Put an even number of marbles into each of 4 bags, distributing the colors at random. It does not matter if each bag has the same total number of marbles in it.

Prerequisite Skills and Concepts: Children should be familiar with identifying fractional parts and writing fractions.

  • Hold up the square divided into fourths from the set of shapes.
  • Say: Let's review for a minute. How many equal parts make up this shape? Have a volunteer give the answer. (4)
  • Ask: What fraction names one of the equal parts? (one-fourth)
    Have children color two-fourths of the square orange. Then have them repeat this procedure with each of the other shapes, coloring them as follows: square divided in halves: one-half red; rectangle divided into sixths: four-sixths green; rectangle divided into thirds: two-thirds blue; circle divided into fifths: one-fifth yellow; circle divided into tenths: two-tenths purple. Check to make sure each child has colored the shapes correctly.

    Have children look at the two squares.

  • Ask: What do you notice about the colored fractions in this pair of shapes? Guide children to see that the colored parts of each shape are equal. After discussion, write two-fourths = one-half on the board.

    Have children look at the two rectangles and then the two circles.

  • Ask: Are the fractions shown in each pair of shapes equal? How can you tell? (The colored parts are the same size, or equal.) Have volunteers come to the board to write the equalities for each pair of shapes. (four-sixths = two-thirds; one-fifth = two-tenths)

    Now have children keep out their circles and set aside the other shapes.

  • Say: We can also use models to tell whether one fraction is less than or greater than another. Look at the circle that has one-fifth shaded yellow. Shade 2 more fifths blue. Now look at the circle that has two-tenths shaded purple. Shade 2 more tenths red.
  • Ask: What fraction of each circle is shaded now?
    Have a volunteer provide the answers. (three-fifths and four-tenths)
  • Ask: Which fraction is greater? (three-fifths) How can you tell?
    (A larger part of that circle is shaded.)
  • Say: You can write this by using “greater than” and “less than” signs. On the board, write three-fifths > four-tenths; and four-tenths < three-fifths. Say each inequality while you are writing it on the board.

    Draw additional pairs of shapes divided into unequal fractions on the board or overhead and have children choose the fraction that is greater than or less than the other. If you wish, encourage children to come to the board and draw their own examples for the class.

  • Ask: How do shape models help you decide which fractions are greater than or less than other fractions? (You can compare the size of the colored or shaded section of each shape.)

    Have children set their circles aside. Take out 6 marbles: 3 red, 2 blue, 1 yellow.

  • Say: Fractions can also name parts of a group. Look at this group of marbles.
  • Ask: What fraction of the group of marbles is blue? (two-sixths) What fraction is yellow? (one-sixth) What color stands for the largest fraction of marbles in this group? (red)

    Repeat this exercise with several different groups and numbers of marbles. Make sure to distribute the colors differently each time.

Wrap-Up and Assessment Hints
Children will need a great deal of practice working with fractions in order to become comfortable identifying and using them. Take time each day to point out classroom objects that can be easily divided into fractions (rulers, clocks, and so on.) Try doing some class surveys in which students determine what fraction of the class possesses a certain attribute (for example, red hair, blue eyes) or kind of pet (dog, cat, hamster, fish, and so on.) Pay attention to how children participate in these activities and make sure that no one is having trouble with particular concepts.


Houghton Mifflin Math Grade 2