Math Background

Lesson: Adding and Subtracting Equal Amounts
Developing the Concept

When students have begun to grasp the idea that you can keep both sides of an equation equal if you perform the same operation on each side, show them how that balancing process can be used to find a missing number in an equation or solve the equation for a variable.

Materials: overhead projector or chalkboard on which to write

Preparation: Write the equation n − 3 = 8 on the board or overhead projector.

  • Ask: What is the value of the right side of this equation? (8)
    What is on the left side? (n − 3)
    What is the n? (a variable)
    What does it stand for? (an unknown number)
  • Say: I want to find out what value of n makes the equation true.
  • Write n − 3 + 3 = 8 + 3 on the board.
  • Ask: Is this still a true equation?
    If students don't remember that they can add the same number to each side of an equation and keep it true, remind them.
  • Ask: What is the value on the right side of the equation now? (8 + 3, or 11)
  • Ask: If I subtract 3 from 5 and then add 3, what number do I get?
    Have students do the exercise on paper if they don't see the answer quickly.
  • Say: If I subtract a number from another number and then add the same number, I get the number I started with.
  • Ask: What value do I get for the expression on the left side of the equation if I use that rule? (n)
  • Ask: What equation do I have now?
  • Write n = 11 on the board.
  • Ask: How can we check to see if that's the right value for n?
    If no one suggests putting the value back in the original equation, suggest it. Have students do the check independently, and then have a volunteer do the exercise on the board to demonstrate that the equation is true when n = 11.

Wrap-Up and Assessment Hints
Students need practice with balancing equations. Assess student progress by asking them to provide five possible solutions to 3 + 12 = blank. If students can only answer 15, then you know that more work is needed for them to understand the concepts regarding balancing equations. The goal is for students to understand eventually that there are many possibilities, such as 4 + 11, 5 + 10, 6 + 9, 20 − 5, and so on. This will allow you to see if students truly understand the concept of balancing equations. To assess their understanding of variables, provide matching exercises. Have them match equations such as n + 9 = 11 with simplified equations (for example, n = 2). You can also have them write equations using variables to model real-life situations you provide.


Houghton Mifflin Math Grade 4