Math Background

Lesson: Addition and Subtraction of Fractions
Developing the Concept

Once students have practiced addition and subtraction of fractions with like denominators concretely, they can move to a semi-concrete level by drawing their own pictures representing addition and subtraction of fractions. This will allow for an easier transition to abstract operations on fractions in the near future.

Materials: ruler, an old CD-ROM or other round object to trace, a rectangular object, colored pencils or crayons, and paper, overhead projector, or board for teacher demonstration

Preparation: Students can be placed in groups of 2−4 students. Each group needs an old CD-ROM and colored pencils or crayons. Each student needs paper and a ruler.

  • Ask: What shapes have we used to show fractional parts?
    Most of the cases you previously used in class were probably circles and rectangles.
  • Say: Fold your piece of paper in half, then in half again, and in half one last time. This is a total of three folds. Open up your paper and use your ruler to draw line segments along the creases formed by the folds in the paper.
    Be sure to demonstrate these instructions to the students. The paper should look like the figure below.
rectangle divided into eight rectangles
  • Ask: Into how many equal parts is this rectangular piece of paper divided? What does each part represent when compared to the whole sheet of paper?
    Eight equal parts. Each part represents one eighth of the whole paper.
  • Say: Use colored pencils or crayons to shade in two eighths of the paper.
  • Say: Use a different color to shade three more eighths of the paper.
  • Ask: How much of the rectangle is shaded? How do you know?
    Five eighths are shaded because the smaller rectangles represent one eighth of the whole, and a total of five of the smaller rectangles are shaded.
  • Ask: What were the addends in the addition problem you just solved?
    Two eighths and three eighths.
  • Ask: What is the sum of two eighths and three eighths?
    Five eighths.
  • Say: Let's try another problem. Shade one eighth using one color and six eighths using another color.
  • Ask: What is the sum of one eighth and six eighths? How do you know that this is correct?
    The sum is seven eighths because a total of seven smaller rectangles are shaded on the whole sheet of paper. Therefore, seven eighths of the paper is covered.
  • Continue with additional exercises. Be sure to use other denominators. By folding the paper one more time, sixteenths can be used.
  • Students can also draw circles on their paper using an old CD-ROM or other object to trace.
  • Ask: What can you do to your circle to display fourths on it?
    This will generate a class discussion that will lead to drawing segments on the circle to divide the circle into four equal parts.
  • Try the same type of examples you used with rectangles, this time using fractional parts of circles.

Wrap-Up and Assessment Hints
After students have worked with manipulatives to add and subtract fractions with like denominators and have drawn pictorial representations, assess student understanding by providing them with several addition and subtraction exercises in written format, such as one-fourth + two-fourths = empty square. Allow students to use manipulatives to solve exercises.

Houghton Mifflin Math Grade 3