1st Grade · 1.OA.D.7

The meaning of the equal sign in 1st grade

The meaning of the equal sign is "the same amount as". Many children think it means "write the answer here". In 1st grade, your child learns that both sides of the equal sign must have the same amount, so $3 + 5 = 4 + 4$ is a true equation.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

1.OA.D.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

What it means, in plain words

An equation is a math sentence with an equal sign, like $6 + 2 = 8$ . The equal sign says that the amount on its left and the amount on its right are the same. Think of a balance scale: if both sides weigh the same, the scale stays level.

Children see many problems shaped like $5 + 4 = ?$ , with the answer on the right. From those, many decide that the equal sign means "now write the answer". That idea fails as soon as an equation looks different, such as $8 = 5 + 3$ or $2 + 6 = 4 + 4$ . Learning the meaning of the equal sign early makes these equations easy to read.

True or false equations build this habit. Your child works out the amount on each side and decides whether the two amounts match. $7 = 7$ is true. $10 - 2 = 6 + 3$ is false, because the left side is 8 and the right side is 9.

Your child should be able to:

Explain that the equal sign means "the same amount as"
Decide whether an equation is true or false by working out each side
Read an equation with the answer on the left, such as $9 = 6 + 3$
Read an equation with a sum on both sides, such as $4 + 5 = 3 + 6$

Example

Is $2 + 7 = 4 + 5$ true or false?

Work out the left side: $2 + 7 = 9$ .
Work out the right side: $4 + 5 = 9$ .
Both sides are 9, so the equation is true.

Example

Is $12 = 14 - 3$ true or false?

The left side is 12.
Work out the right side: $14 - 3 = 11$ .
12 and 11 are not the same amount, so the equation is false.

Where children usually get stuck

For $5 + 3 = ? + 6$ , your child writes 8 in the blank.
The child reads the equal sign as "the answer goes next" and stops reading there. The + 6 on the right side gets ignored. The blank should be 2, because $2 + 6$ is also 8.
What helps. Build each side with blocks: a pile of 5 and 3 on the left, a pile of 6 on the right. Ask how many blocks to add on the right so both sides match.
Your child says $9 = 4 + 5$ is backwards, or that it is wrong.
Every equation the child has seen had the answer on the right. The order of the sides got taken as part of the rule.
What helps. Write $4 + 5 = 9$ and $9 = 4 + 5$ on two sticky notes. Ask whether both say the same thing, and check each side with fingers or coins.
To add three numbers, your child writes a chain like $5 + 1 = 6 + 3 = 9$ .
The equal sign is being used to mean "and then". But $5 + 1$ is 6, not 9, so the chain says something false.
What helps. Write each step on its own line: $5 + 1 = 6$ , then $6 + 3 = 9$ . Check each line by asking whether both sides have the same amount.

Try four practice questions

Real 1st grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Select every equation where both sides equal the same number.
A
$\displaystyle 5 + {}$
$\displaystyle 2 = {}$
$\displaystyle 6 + {}$
$\displaystyle 4$
B
$\displaystyle 2 + {}$
$\displaystyle 6 = {}$
$\displaystyle 5 + {}$
$\displaystyle 3$
C
$\displaystyle 3 + {}$
$\displaystyle 4 = {}$
$\displaystyle 4 + {}$
$\displaystyle 3$
D
$\displaystyle 4 + {}$
$\displaystyle 1 = {}$
$\displaystyle 2 + {}$
$\displaystyle 5$
Show the answer and how to solve it
The two true equations are $3 + 4 = 4 + 3$ and $2 + 6 = 5 + 3$ , because both sides of each equation give the same total ( $7$ and $8$ ). The other two equations have different totals on each side, so they are false.
1. 1An equation is true when both sides equal the same number. Add both sides of each equation to find the totals.
2. 2Compute the totals:
3. 3Compare both sides of each equation. Two equations have matching totals: $3 + 4 = 4 + 3$ (both equal $7$ ) and $2 + 6 = 5 + 3$ (both equal $8$ ). The other two have different totals on each side, so they are false.
4. 4Select the two true equations: $3 + 4 = 4 + 3$ and $2 + 6 = 5 + 3$ . Leave the other two unselected.
Common mistake. A common mistake is thinking the equal sign means 'the answer goes here.' A student might not check both sides — for example, $5 + 2 = 6 + 4$ has a total of $7$ on the left but $10$ on the right. The sides are different, so the equation is false.
The idea underneath. The equal sign means 'is the same as,' not 'the answer goes here.' Both sides of an equation must have the same total — even if the addends look different, what matters is whether the sums match.
2On level
Look at the equation below.
$\displaystyle 9 - 4 = 5$
Is the equation true?
A
True
B
False
Show the answer and how to solve it
The equation is True because $9 - 4 = 5$ , and that matches the displayed answer.
1. 1Look at the equation. We need to find $9 - 4$ to check if the answer $5$ is correct.
2. 2Count back from 9 by 4 to find the answer: 8, 7, 6, 5.
3. 3Both sides have the same value, so the equation is True.
Common mistake. A common mistake is computing $9 - 4$ wrong by 1 and then thinking the equation is false.
The idea underneath. The equal sign means "is the same as." To check if an equation is true, find the value of each side and see if they match.
3On level
Maria looked at the equation $4 + 6 = 9$ and said it is TRUE.
Maria's equation:
$\displaystyle 4 + 6 = 9$
Select the statement that best describes Maria's claim.
A
Maria is wrong: $4 + 6$ equals $10$ , not $9$ .
B
Maria is correct because the equation has an equal sign and a plus sign.
C
Maria is wrong: $4 + 6$ equals $11$ , not $9$ .
D
Maria is correct: $4 + 6$ equals $9$ .
Show the answer and how to solve it
Maria is wrong because $4 + 6$ equals $10$ , not $9$ . The equation is FALSE, but Maria said TRUE.
1. 1Maria said the equation is TRUE. To check, find what $4 + 6$ actually equals.
2. 2Add the numbers:
3. 3The equation says the sum is $9$ , but $4 + 6 = 10$ . The two sides are not equal, so the equation is FALSE.
4. 4Maria said the equation is TRUE, but the equation is actually FALSE. So Maria is wrong: $4 + 6$ equals $10$ , not $9$ .
Common mistake. A common mistake is trusting Maria without checking the math. Always add the numbers yourself: $4 + 6 = 10$ , not $9$ .
The idea underneath. An equation is only TRUE when both sides have the same value. Always compute and compare — don't just trust someone's claim.
4Stretch
Maria looked at the equation below and said it is True.
$\displaystyle 12 - 4 = 5 + 3$
Pick the statement that best describes whether Maria is correct.
A
Maria is right. Both sides have the same numbers.
B
Maria is wrong. The two sides give different totals.
C
Maria is right. Both sides equal 8.
D
Maria is wrong. After the equal sign, we should just write 8.
Show the answer and how to solve it
Maria is right. Both sides of the equation equal 8, so the equation is true.
1. 1Subtract to find the left side.
2. 2Add the right side.
3. 3Both sides equal 8, so the equation is true. Maria said it is True, so Maria is right.
Common mistake. A common mistake is thinking the equation is false because the numbers on each side look different. An equation is true when the totals match, not when the digits look the same.
The idea underneath. The equal sign means "has the same value as." An equation with expressions on both sides is true whenever the totals match, even if the addends look different.