Math Background

Lesson: Adding and Subtracting Equal Amounts
Introducing the Concept

When students work with equations, it is important for them to understand that the left side of the equation should be equivalent to the right side.

Materials: overhead projector or chalkboard on which to write

Preparation: Write the equation 3 = 3 on the board or overhead projector.

  • Ask: What is the value of the expression on the left side of the equation 3 = 3? What is the value on the right side?
    Your students may think this is a silly exercise because the answer seems so obvious. It is important, though, that students understand what you mean when you talk about the parts of an equation.
  • Ask: Is the equation 3 = 3 a true statement?
    Many of your students will think this is a trick question because it seems so obvious.
  • Ask: If I add 5 to the left side of the equation, what will the value be on that side of the equals sign? Will this still be a true statement?
    No. This will produce 8 = 3. The left side will be 8 and the right side will still be 3.
  • Ask: What do I have to do to the right side of the equation to make this equation a true statement again?
    The idea is to have students recognize that to keep the equation true, you must perform the same operation on both sides.
  • Say: If I begin with a true statement such as 3 = 3, I will always get a true statement if I add the same number to both sides of the equation.
    If students don't understand why this is so, show them some examples.
  • Say: On a piece of paper, write 9 = 9. Think of a number and add it to both sides of the equation 9 = 9.
    Have students read their results aloud.
  • Ask: Did you all get true statements? Did you all get the same numbers on both sides of the equation?
    It is important for students to understand that even though other students may have used different numbers and got different sums, everyone's equation was a true statement.
  • Say: On your paper, write 5 = 5. Think of a number less than 5 and subtract it from both sides of the equation 5 = 5.
    Have students read their results aloud.
  • Ask: Did we all get true statements?
    Students need to learn that the idea of balancing equations will work with any of the four operations if they are using the same number and operation for both sides of the equation.
  • Continue with additional problems, using different operations.

Houghton Mifflin Math Grade 4