1st Grade · 1.OA.B.4

Related facts in 1st grade

Related facts are an addition fact and a subtraction fact that use the same three numbers, like $5 + 7 = 12$ and $12 - 7 = 5$ . In 1st grade, your child learns to think addition to subtract. To find $12 - 7$ , your child asks what number goes with 7 to make 12.

What the standard says

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

1.OA.B.4 Understand subtraction as an unknown-addend problem.

What it means, in plain words

Any subtraction can be read as an addition with a missing part. $12 - 7$ asks the same question as $7 + ? = 12$ : 7 and what number make 12? The missing part is called the unknown addend. An addend is a number being added.

A fact family is a set of related facts built from the same three numbers. The numbers 5, 7 and 12 make four facts: $5 + 7 = 12$ , $7 + 5 = 12$ , $12 - 7 = 5$ and $12 - 5 = 7$ . The biggest number is the whole. It is the total in each addition and the starting number in each subtraction. The two smaller numbers are the parts.

Related facts in 1st grade matter because most children find adding easier than taking away. Counting back 7 from 12 is slow and easy to get wrong. A child who knows $7 + 5 = 12$ can answer $12 - 7$ at once, with no counting.

Your child should be able to:

Turn a subtraction into an addition with a missing number, such as $12 - 7$ into $7 + ? = 12$
Use a known addition fact to answer a subtraction
Write the four facts in a fact family from three numbers
Point to the whole and the two parts in a fact

Example

What is $14 - 8$ ? Use an addition fact to find it.

Turn the subtraction into an addition: $8 + ? = 14$ .
Ask what number goes with 8 to make 14. $8 + 6 = 14$ .
So $14 - 8 = 6$ . The answer is 6.

Example

Write the four related facts for the numbers 6, 9 and 15.

15 is the biggest number, so it is the whole. 6 and 9 are the parts.
The two addition facts are $6 + 9 = 15$ and $9 + 6 = 15$ .
The two subtraction facts start with the whole: $15 - 9 = 6$ and $15 - 6 = 9$ .
The fact family is these two additions and these two subtractions.

Where children usually get stuck

For $12 - 5$ , your child writes the addition $12 + 5 = ?$ and answers 17.
The child sees two numbers and turns them into an addition without asking which one is the whole. In $12 - 5$ , 12 is already the whole, so it belongs after the equal sign: $5 + ? = 12$ .
What helps. Put 12 coins on the table and cover 5 with your hand. Ask how many are still showing. Then say the addition together: 5 and 7 make 12.
Your child counts back on fingers for every subtraction, even when the matching addition fact is known by heart.
The child has not yet noticed that addition and subtraction facts come in pairs. Each subtraction feels like a brand new problem.
What helps. Say an addition fact your child knows, such as $6 + 4 = 10$ , then ask $10 - 4$ right away. A few pairs like this in the car or at dinner build the link.
In a fact family for 3, 5 and 8, your child writes $5 - 8 = 3$ .
The child copies the order of the addition fact and puts a small number first. In 1st grade, a subtraction always starts with the whole, the biggest number.
What helps. Draw a number bond: one circle on top for the whole and two circles below for the parts. Write 8 on top. When your child writes a subtraction, start with a finger on the top circle.

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
Look at the subtraction below. Which addition sentence has the same numbers, with a blank for the missing number?
$\displaystyle 9 - 4 = 5$
A
$\displaystyle 4 + {}$
$\displaystyle 9 = {}$
$\displaystyle \underline{\phantom{00}}$
B
$\displaystyle 9 + {}$
$\displaystyle 4 = {}$
$\displaystyle \underline{\phantom{00}}$
C
$\displaystyle 9 + {}$
$\displaystyle \underline{\phantom{00}} = {}$
$\displaystyle 4$
D
$\displaystyle 4 + {}$
$\displaystyle \underline{\phantom{00}} = {}$
$\displaystyle 9$
Show the answer and how to solve it
The related addition sentence is $4 + \underline{\phantom{00}} = 9$ . The number being taken away ( $4$ ) becomes one of the numbers in the addition, the total ( $9$ ) stays as the total, and the blank stands for the missing number — which is also the answer to the subtraction.
1. 1Look at $9 - 4 = 5$ . The number $9$ is the total. We are taking $4$ away from $9$ .
2. 2The related addition asks: ' $4$ plus what number equals $9$ ?' The numbers from the subtraction ( $9$ as the total, $4$ as one of the numbers in the addition) match the addition sentence above.
3. 3The blank stands for the missing number. The answer is $4 + \underline{\phantom{00}} = 9$ .
Common mistake. A common mistake is switching which number is the total, like writing $9 + \underline{\phantom{00}} = 4$ . In $9 - 4 = 5$ , $9$ is the total. The total stays as the total in the related addition.
The idea underneath. For $9 - 4 = 5$ , you can ask ' $4$ plus what equals $9$ ?' That is why $9 - 4 = 5$ matches $4 + \underline{\phantom{00}} = 9$ .
2On level
Pat said $4 + 7 = 11$ . Max said $4 + 3 = 7$ . Whose addition correctly explains $11 - 4 = 7$ ?
A
Both Pat and Max.
B
Neither Pat nor Max.
C
Only Pat.
D
Only Max.
Show the answer and how to solve it
Only Pat is right. Pat's fact $4 + 7 = 11$ uses the same three numbers ( $11$ , $4$ , $7$ ) as the subtraction $11 - 4 = 7$ , with $11$ as the total — so it explains the subtraction. Max's $4 + 3 = 7$ is true math, but its total is $7$ , not $11$ , so it does not explain $11 - 4 = 7$ .
1. 1Look at the subtraction $11 - 4 = 7$ . To explain it with addition, the addition fact must use the same three numbers — $11$ , $4$ , and $7$ — and have $11$ as the total.
2. 2Check Pat's fact: $4 + 7 = 11$ . The arithmetic is true, and the total is $11$ with parts $4$ and $7$ — the same numbers as in the subtraction. Pat's explanation is correct.
3. 3Check Max's fact: $4 + 3 = 7$ . The arithmetic is true, BUT the total is $7$ , not $11$ . Max's fact does not use the same three numbers as $11 - 4 = 7$ , so it cannot explain the subtraction. Max's explanation is wrong.
4. 4Pat is correct, Max is not. The answer is "Only Pat."
Common mistake. A common mistake is thinking any true addition fact explains the subtraction. Max's $4 + 3 = 7$ is true math, but its total is $7$ , not $11$ . To explain $11 - 4 = 7$ , the addition fact must have the same total of $11$ — and use the same three numbers as the subtraction.
The idea underneath. Every subtraction has a related addition fact made from the same three numbers. The subtraction $11 - 4 = 7$ is explained by $4 + 7 = 11$ (or $7 + 4 = 11$ ) because both use the numbers $11$ , $4$ , and $7$ , with $11$ as the total.
3On level
Liam was given $11 - 4$ and wrote this related addition:
$\displaystyle 11 + \underline{\phantom{00}} = 4$
Select the statement that best describes Liam's sentence.
A
Liam used the difference instead of the number being subtracted.
B
Liam put the blank in the wrong place.
C
Liam used the wrong number as the total. The total should match the starting amount in the subtraction.
D
Liam's sentence is correct.
Show the answer and how to solve it
Liam used the wrong number as the total. For $11 - 4$ , the correct related addition is $4 + \underline{\phantom{00}} = 11$ — the starting amount $11$ is the total, and $4$ (the number being subtracted) is the first number. Liam wrote $11 + \underline{\phantom{00}} = 4$ , putting $11$ as the first number and $4$ as the total instead — he swapped their roles.
1. 1Look at the subtraction. The starting amount is $11$ and we are taking away $4$ .
2. 2The related addition asks: $4$ plus what number equals $11$ ? So the correct related addition is:
3. 3Now look at what Liam wrote:
4. 4Liam wrote $11 + \underline{\phantom{00}} = 4$ . The total of the addition should match the starting amount in $11 - 4$ — the starting amount is $11$ . But Liam put $11$ as the FIRST NUMBER and $4$ as the TOTAL — he swapped their roles. The correct related addition is $4 + \underline{\phantom{00}} = 11$ . So the choice that says 'Liam used the wrong number as the total' best describes his sentence.
Common mistake. A common mistake is reading Liam's $11 + \underline{\phantom{00}} = 4$ and trying to find a number that works. No whole number added to $11$ gives $4$ , because $11$ is already bigger than $4$ . That impossibility is the clue: Liam swapped which number is the total and which is the first number.
The idea underneath. For a subtraction like $11 - 4$ , the related addition is $4 + \underline{\phantom{00}} = 11$ . The starting amount in the subtraction ( $11$ ) becomes the TOTAL of the addition, and the number being subtracted ( $4$ ) becomes the first number in the addition sentence.
4Stretch
Use addition to subtract.
$\displaystyle 13 - 7 = \underline{\phantom{00}}$
$\displaystyle 7 + \underline{\phantom{00}} = 13$
The same number goes in both blanks. What is the number?
Show the answer and how to solve it
Answer. 6
The number is $6$ . The same number fills both blanks: $13$ - $7$ = $6$ and $7$ + $6$ = $13$ .
1. 1Look at the addition equation. You need a number that, when added to $7$ , makes $13$ .
2. 2Think about the addition fact:
3. 3Since $7$ + $6$ = $13$ , you know that $13$ - $7$ = $6$ . The same number $6$ fills both blanks.
Common mistake. A common mistake is typing $7$ (the number being subtracted) or $13$ (the larger number). The blank stands for what is added to $7$ to make $13$ , which is $6$ .
The idea underneath. Addition and subtraction are connected. If you know that $7$ + $6$ = $13$ , then you also know that $13$ - $7$ = $6$ .