Math Background

Lesson: Interpreting Equations
Developing the Concept

As your students master the meaning of equations, introduce the idea of a variable. The idea that a symbol, such as a letter, can be part of an equation or expression may take some getting used to. Provide many examples.

Materials: overhead projector or chalkboard on which to write

Preparation: Write the equation 5 + 7 = 12 on the board or overhead projector.

  • Ask: What is the value of the expression on the left side of the equation 5 + 7 = 12? What is the value of the expression on the right side?
    It is important that students understand that the left side of the equation equals the right side.
  • Draw a balance on the board. Write 5 + 7 on one side and 12 on the other.
  • Ask: Can anyone tell me what equation this picture shows?
    Lead them to see that the balance represents the equation 5 + 7 = 12. Remind them that an equation must balance: both sides must be equal.
  • Next, erase the numbers and write the following equation below the picture: 6 + square = 14.
  • Ask: What number needs to go in the box to make the equation true? How can you tell?
    If students have trouble figuring this out, draw 6 objects on one side of the balance and 14 objects on the other. Ask how many more would be needed to make the scale balance.
  • Next, erase the box and write an x in its place.
  • Say: This letter is called a variable. It stands for an unknown number. It works just like the box. We don't have to use an x. We could use any other letter we want. Many people use x and y for variables.
  • Ask: What value for x would make 17 = 10 + x a true mathematical statement? How do you know?
    Be sure to provide ample examples and exercises for students with the variable or box on the right side of the equation as well as on the left. You do not want students to think that the box will appear on one side only.
  • Continue with examples like the previous two and then with examples in which there are two addends on each side of the equation. Be sure to place the variable in different positions in the equations.

Wrap-Up and Assessment Hints
Students need significant practice with equations. Assess student progress by providing them with problem sets such as

3 + 8 = 4 + n
3 + n = 4 + 7
n + 8 = 4 + 7
3 + 8 = 4 + 7

The goal is for students to understand the concept that the expression on the right side of an equation equals the expression on the left side and that more than one addend can be on each side. This is an important concept and worth taking extra time to develop.


Houghton Mifflin Math Grade 4