Math Background

Lesson: Adding and Subtracting Fractions With Like Denominators
Introducing the Concept

Adding and subtracting fractions with like denominators is just like adding and subtracting whole numbers with the same units. When you add 6 minutes to 5 minutes, the sum is 11 minutes. When you add 6 eighths to 5 eighths, the sum is 11 eighths. Monitor students' understanding of this process—if they don't keep the idea of denominator-as-units in mind, they may continue to ignore the denominator when adding and subtracting fractions with unlike denominators. The sum of 6 hours plus 5 minutes is NOT 11 hours or 11 minutes just as the sum of 6 tenths plus 5 eighths is NOT 11 tenths or 11 eighths.

Materials: board or overhead projector

Preparation: none

Prerequisite Skills and Concepts: Students should be able to add and subtract whole numbers. They should also understand the functions of the parts of a fraction and be able to write fractions in simplest form.

  • Ask: May I have five volunteers to be five fifths of a whole group?
    Explain to the students that these five are now one group. Each of the five is one fifth of the group. For simplicity, the students are referred to as A, B, C, D, and E, but you should call them by name.
    stick figures
  • Ask: Student A is what part of the group?
    Have A stand slightly apart from the others. Encourage students to speak in unison, saying the denominator a bit louder than the numerator: one fifth.
    stick figures
  • Ask: B and C are what part of the group?
    While A is still slightly apart from the others, ask B and C to move to a different spot. Students should name B and C two fifths.
    stick figures
  • Say: Say a number sentence that tells what part of the group I have if I ask A to join B and C. One fifth plus two fifths equals three fifths.
    stick figures

    Write the number sentence one-fifth + two-fifths = three-fifths on the board or overhead projector.

    Try several more examples with five fifths, and then ask those students to be seated and call for six volunteers.

  • Ask: How many students are in the whole group? (6) A is what part of the group?
    Follow the routine established with the fifths. (one sixth)
  • Ask: B and C are what part of the group?
    (two sixths)
  • Say: Say a number sentence that tells what part of the group I have if I ask A to join B and C.
    One sixth plus two sixths equals three sixths.

    Write the number sentence one-sixth + two-sixths = three-sixths on the board or overhead projector.

  • Ask: What do you notice about the way the sixths are grouped?
    Students should notice that half of the sixths are in one group and half are in the other.
  • Ask: If one-sixth + two-sixths = three-sixths, how can one-sixth + two-sixths also equal one-half? (three-sixths and one-half are equivalent fractions.)
    Discuss equivalent fractions.
  • Ask: If I didn't know that three-sixths = one-half, how could I check three-sixths to decide whether it was in simplest form?
    Encourage students to conclude that they can look for common factors. 3 and 6 both have 3 as a factor, so you can write three-sixths as
    three divided by three over six divided by three equals one-half
  • Say: Say a number sentence that tells what part of the group I have if I start with the three-sixths made by A, B, and C and ask B to return to the other group of sixths.
    Have students say “three sixths minus one sixth equals two sixths”; then write the number sentence on the board or overhead.
  • Ask: How do you know that two-sixths is not in simplest form?
    (I can divide by the common factor 2.)

    Ask the sixths to stand in a row again. Then ask for six more volunteers to make another group of six.

  • Ask: I have twelve sixths here. If 6 sixths form a whole group, how many groups are there? (2)
    Students should recognize that you have two groups. Write twelve-sixths = 2on the board and discuss how the common factor, 6, helps you find the simplest form of the fraction. This should lead to a discussion about how a whole number can be written as a fraction: twelve-sixths = two over one = 2. Talk about this very important rule: When you divide any number by one, you get the number itself.
  • Say: Say a number sentence that tells what part of a group I have if I ask G to join A, B, C, D, E, and F.
    six-sixths + one-sixth = seven-sixths or 1 + one-sixth = 1one-sixth
  • Say: I've got 1one-sixth groups here. Say the number sentence that tells what part of a group I have if I ask C and D to move away from the group.
    1one-sixthtwo-sixths = ? If students get stuck in this form, suggest that they put the 1one-sixth into a different form. The improper fraction seven-sixths is very useful in this situation. seven-sixthstwo-sixths = five-sixths.

    Continue in this way using groups composed of different numbers of students.

Houghton Mifflin Math Grade 4