Understanding the + and = Symbols - First Grade Mathematics

Mathematicians are like detectives who use secret symbols to write down big ideas in a short, clear way. Instead of writing long sentences with words like "put together" or "is the same amount as," mathematicians use two of the most famous symbols in history: the plus sign (+) and the equal sign (=). Learning what these two symbols mean and how they work together turns you into a mathematical writer who can record number sentences with precision. In this chapter, you will master the true meaning of the plus sign and the equal sign.

The Plus Sign (+): The Joining Tool

The plus sign looks like a little cross with one vertical line and one horizontal line meeting in the center.

The Plus Sign (+):
      |
    --+--      Means: "ADD", "JOIN", "PUT TOGETHER"
      |

What the Plus Sign Tells You to Do

Whenever you see a plus sign sitting between two numbers, it is an action instruction that says: "Combine the number on my left with the number on my right!" In the expression 4 + 3, the plus sign tells you to combine 4 and 3 into one total.

Addends: The Numbers Being Added

The numbers that are connected by a plus sign are called addends. In the equation 4 + 3 = 7, the number 4 is an addend, and the number 3 is an addend. Addends are the parts that come together to create the whole.

The Equal Sign (=): The Scale of Balance

The equal sign consists of two horizontal, parallel lines of the exact same length, sitting evenly one above the other.

The Equal Sign (=):
   ==================
   ==================
Means: "IS THE EXACT SAME VALUE AS", "BALANCES WITH"

The Balance Scale Model

The most important secret about the equal sign is that it does NOT mean "here comes the answer." The equal sign means BALANCE. It is like a balance scale with two weighing pans: whatever value sits on the left side of the equal sign must weigh the exact same amount as whatever sits on the right side.

The Balance Scale of 5 + 2 = 7:

           /          /       [ 5 + 2 ]    [   7   ]
     \_______/    \_______/
      Left Pan    Right Pan
     (Value: 7)  (Value: 7)
    -------------------------
    PERFECTLY BALANCED!

Both Sides Must Be True

Because the equal sign represents balance, you can write equations in different directions: 5 + 2 = 7 is true because 5 + 2 equals 7. 7 = 5 + 2 is also completely true! The total of 7 sits on the left pan, and the parts 5 + 2 sit on the right pan. Both pans weigh 7!

Anatomy of an Addition Equation

Let us break down a complete addition equation into all its mathematical parts.

Anatomy of an Equation:
    4    +    5    =    9
   ---       ---       ---
 Addend     Addend     Sum
 (Part)     (Part)   (Whole)

Reading an Equation Aloud

When you see 4 + 5 = 9, read it out loud with confidence: "Four plus five equals nine," or "Four and five put together is the same as nine."

Practice Exercises

Exercise 1: Draw the plus sign (+) and explain in your own words what action it tells you to perform.

Exercise 2: Draw the equal sign (=) and explain why it is compared to a balance scale.

Exercise 3: In the addition equation 6 + 2 = 8, identify which numbers are the addends and which number is the sum.

Exercise 4: Is the equation 9 = 5 + 4 written correctly? Explain why or why not using the balance scale idea.

Solutions and Explanations

Solution to Exercise 1: The plus sign (+) is formed by two crossing straight lines (one vertical and one horizontal). It tells you to join, add, or combine two or more quantities together into one group.

Solution to Exercise 2: The equal sign (=) consists of two parallel horizontal lines. It is compared to a balance scale because it shows that the quantity or value on the left side has the exact same value as the quantity on the right side. Both sides are in perfect balance.

Solution to Exercise 3: In the equation 6 + 2 = 8, the numbers 6 and 2 are the addends (the parts being combined), and the number 8 is the sum (the total whole).

Solution to Exercise 4: Yes, 9 = 5 + 4 is written completely correctly. The left side has a value of 9, and the right side (5 + 4) also has a value of 9. Because both sides have the exact same value, the balance scale is level and the equation is true.