## Adding and Multiplying by Equals

When introducing equations, it is important for students to understand the idea that the left side of the equation should be equivalent to the right side. Therefore, important groundwork is developed when displaying an equation and labeling the left and right sides of the equation.

Materials: Overhead projector or front board on which to write.

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

• Ask: What is the value of the left side of the equation 3 = 3? What is the value of 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 I get on that side of the equal 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 believe you when you tell them this, show them some examples.
• Say: On a piece of paper, write 9 = 9. Think of a secret number and add it to both sides of the equation 9 = 9.
Have students read their results out loud.
• Ask: Did we all get true statements? Did we all get the same numbers on both sides of the equation?
It is important for students to understand that even though other students used different numbers and got unique results, everyone's equations produced true statements.
• Say: On your piece of paper, write 5 = 5. Think of a secret number and multiply it by both sides of the equation 5 = 5.
Have students read their results out loud.
• 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 for both sides of the equation.
• Continue with additional problems using different operations.

Interpreting Equations