The equal sign tells us that two sides have the same amount. It does not mean that the answer always comes after it. When we write 3 + 2 = 5, we are saying that 3 plus 2 is the same amount as 5.
A balance scale is a helpful picture because it stays level when both sides are equal.
Think of the left side and right side of an equation as two pans on a scale. If the left pan has 3 red apples and 2 blue apples, it has 5 apples in all. If the right pan has 5 apples, the scale balances because both sides show the same amount.
This also means 5 = 3 + 2 is true, because the same amounts are still on both sides.
Understanding Early Learners: The Equal Sign Means Same
An equation can have numbers, groups of objects, or actions on either side. For example, four plus one is the same as two plus three. Children can check this by building each side with counters.
Make one group of four counters and one more counter. Then make a group of two counters and another group of three. Count each total.
Both groups contain five counters, even though they are arranged differently. This helps show that equal does not mean the two sides must look alike. It means they represent one matching quantity.
A blank box in an equation is a place for a number that makes the statement true. In the sentence seven is the same as blank plus two, the blank must be five. Students should not guess only from where the blank appears.
They should think about the whole relationship. Counters, fingers, number paths, and drawings can help find the missing amount. A child may start with two and count on until reaching seven.
The number of counts is five. Later, this idea becomes subtraction, because taking two away from seven leaves five.
The equal sign becomes especially important when there are calculations on both sides. Consider six plus two is the same as five plus three. A student needs to work out both sides before deciding whether the statement is true.
Reading from left to right and stopping at the sign can cause confusion. Some children learn to treat the sign like a signal meaning write the answer next. That habit makes later maths harder.
Teachers may write a true statement such as eight is the same as eight, or three plus four is the same as ten minus three. These examples build the habit of checking the complete statement.
Equality is useful outside a maths book. Sharing snacks fairly means each person receives an equal number. Two bags can hold the same number of blocks even when one bag has large blocks and the other has small ones.
A shopkeeper checks that the money given matches the price. When learning, pay attention to counting carefully and keeping track of what each group represents. Do not decide by the size of a picture, because larger objects do not always mean a larger number.
Focus on how many there are. It is fine to use objects at first, then drawings, then numbers. Each step develops the same idea in a new form.
Key Facts
- The equal sign = means is the same amount as.
- 3 + 2 = 5 means 3 plus 2 is the same amount as 5.
- 5 = 3 + 2 is also true because both sides have the same amount.
- A level balance scale shows equality.
- If both sides of an equation match in amount, the equation is true.
- If one side has more or less than the other, the equation is not equal.
Vocabulary
- Equal sign
- The symbol = that means two amounts are the same.
- Equation
- A number sentence that shows two amounts are equal.
- Same amount
- Two groups have the same number of objects or the same value.
- Balance scale
- A tool with two sides that can show whether amounts are the same.
- Add
- To put amounts together to find how many there are in all.
Common Mistakes to Avoid
- Thinking = means the answer comes next. This is wrong because = means both sides have the same amount, no matter which side the answer is on.
- Saying 5 = 3 + 2 is backwards and wrong. This is wrong because 5 and 3 + 2 are the same amount, so the equation is true.
- Only counting one color of apples in 3 red apples + 2 blue apples. This is wrong because all apples count, so there are 5 apples in all.
- Writing 3 + 2 = 4 because there are two numbers being added. This is wrong because you must count the total amount, and 3 plus 2 makes 5.
Practice Questions
- 1 There are 4 stars on the left side of a scale and 4 stars on the right side. Write an equation using = to show the amounts are the same.
- 2 Fill in the missing number: 2 + 3 = __. Then write the same equation with 5 on the left side.
- 3 A scale has 1 apple and 4 apples on the left pan, and 5 apples on the right pan. Explain why the scale is level using the meaning of the equal sign.