Meaning of the Equal Sign (True or False Statements) - First Grade Mathematics

What does the equal sign (=) really mean? If you ask many students, they might say: "It means the answer is coming next!" But in real mathematics, that is a big misconception. The equal sign does not mean "do the math"; it means "IS THE SAME VALUE AS." It is a symbol of balance, like a playground seesaw that is perfectly level. In this chapter, you will become a mathematical judge who inspects equations and declares whether they are TRUE (balanced) or FALSE (unbalanced).

The Balance Scale Test

To decide whether an equation is true or false, calculate the total value of everything on the left side of the equal sign, and calculate the total value of everything on the right side.

Testing the Equation: 5 + 3 = 8

        Left Side: [ 5 + 3 ]        Right Side: [ 8 ]
        Value:          8           Value:        8
                 \_____________________________/
                                |
                        Are they equal?
                                |
                               v
                     YES! 8 = 8 (TRUE!)

The Rule of the Judge:

If Left Side Value == Right Side Value -> The equation is TRUE! If Left Side Value != Right Side Value -> The equation is FALSE!

Non-Traditional Equation Formats

Because the equal sign represents balance, equations can be written in formats that surprise beginners!

Surprising Equation Formats:

Format 1: Total on the Left!
          8 = 5 + 3
          Left Side = 8 | Right Side = 8.
          Both sides equal 8. This is TRUE!

Format 2: Operations on Both Sides!
          4 + 4 = 6 + 2
          Left Side: 4 + 4 = 8
          Right Side: 6 + 2 = 8
          Both sides equal 8. This is TRUE!

Format 3: Identity!
          7 = 7
          Left Side = 7 | Right Side = 7.
          Both sides equal 7. This is TRUE!

Do Not Be Fooled by Operations on Both Sides

Look at 4 + 4 = 6 + 2. Beginners might look at the plus sign after the equal sign and feel confused. But as a math detective, simply evaluate each pan of the scale: Left pan: 4 + 4 = 8. Right pan: 6 + 2 = 8. Since 8 equals 8, the seesaw is perfectly balanced! The statement is completely true.

Spotting False Equations

Now let us look at statements where the seesaw tips over because the sides do not match.

Testing: 7 + 2 = 10
Left Side:  7 + 2 = 9
Right Side: 10
Does 9 equal 10? NO! 9 is less than 10.
The seesaw tips! This equation is FALSE!

Practice Exercises

Exercise 1: Determine whether each equation is TRUE or FALSE: 6 + 4 = 10 9 = 4 + 5 8 + 2 = 7 + 4 5 + 3 = 9

Exercise 2: Look at the equation 3 + 5 = 2 + 6. Calculate the value of the left side and the right side, and determine if the statement is true or false.

Exercise 3: Explain in your own words why the equation 10 = 10 is a true mathematical statement.

Exercise 4: A student says that 7 = 3 + 4 is written backward and is therefore false. Explain to the student why this equation is actually true.

Solutions and Explanations

Solution to Exercise 1: 6 + 4 = 10 is TRUE (Left is 10, Right is 10). 9 = 4 + 5 is TRUE (Left is 9, Right is 9). 8 + 2 = 7 + 4 is FALSE (Left is 10, Right is 11; 10 does not equal 11). 5 + 3 = 9 is FALSE (Left is 8, Right is 9; 8 does not equal 9).

Solution to Exercise 2: Left side: 3 + 5 = 8. Right side: 2 + 6 = 8. Because both sides have the exact same value of 8, the equation is TRUE.

Solution to Exercise 3: 10 = 10 is true because the quantity on the left (10) is identical in value to the quantity on the right (10). Both sides balance each other completely.

Solution to Exercise 4: Explain to the student: "The equal sign means balance, not 'here comes the answer.' Since 3 + 4 has a value of 7, both the left side and the right side equal 7. The equation is in perfect balance and is completely true, even with the total written on the left."