1st Grade · 2nd Grade · 1.OA.A.1 · 2.OA.A.1

Addition and subtraction word problems in 1st and 2nd grade

Addition and subtraction word problems are short math stories that end with a question, such as how many are left or how many more. In 1st grade, your child solves them with numbers up to 20. In 2nd grade, the numbers go up to 100 and some problems take two steps.

What the standards say

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

1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

What it means, in plain words

Addition and subtraction word problems in 1st grade: five kinds of story 1.OA.A.1

Word problems in 1st grade come in five kinds of story. In some, more things arrive. In others, some things go away. Some stories put two groups together or split one group into two parts. The last kind compares two groups to find how many more or how many fewer.

The missing number can be anywhere in the story. Take 5 birds on a fence, when 4 more land. The story can ask how many birds there are now, how many landed or how many were there at first. The start and the change are harder to find, because the child cannot solve them in the order the story happens.

Children show the story with objects, a drawing or an equation. In the equation, a question mark stands for the missing number, as in $5 + ? = 9$ .

Your child should be able to:

Solve stories where things are added or taken away, with numbers up to 20
Solve stories that put groups together, split them or compare them
Find a missing number at the start, in the middle or at the end of a story
Write an equation with a question mark for the missing number

Example

Some ducks were on a pond. 6 more ducks swam over. Now there are 14 ducks. How many ducks were on the pond at first?

The missing number is the start, so write $? + 6 = 14$ .
Ask: what number plus 6 makes 14?
Count back 6 from 14: 13, 12, 11, 10, 9, 8.
$8 + 6 = 14$ , so there were 8 ducks on the pond at first.

Addition and subtraction word problems in 2nd grade: bigger numbers and two steps 2.OA.A.1

In 2nd grade the same kinds of story use numbers up to 100. Subtraction word problems now often need two-digit subtraction, and children draw a tape diagram to see the story. A tape diagram is a picture made of bars, one bar for each amount, so a child can see which part is missing.

The new part is the two-step problem. The story has two actions, and the answer to the first step is used in the second. Compare stories also get harder. "The red box has 8 fewer cards than the blue box" means the blue box has more, so finding the blue box needs an addition.

Your child should be able to:

Solve one-step stories with numbers up to 100
Solve two-step stories, using the answer to the first step in the second
Draw a tape diagram or write an equation with a question mark for the missing number
Decide whether to add or subtract in a compare story by asking which amount is bigger

Example

A bus has 34 people on it. At the first stop, 12 people get off. At the second stop, 25 people get on. How many people are on the bus now?

Step 1, people get off: $34 - 12 = 22$ .
Step 2, people get on: $22 + 25 = 47$ .
There are 47 people on the bus now.

Where children usually get stuck

For "Some cars were in a parking lot. 5 drove away. 8 cars are still there. How many cars were there at first?", your child writes $8 - 5 = 3$ .
The child picks the operation from a word like "away" instead of from the story. The cars at the start were the 8 still there plus the 5 that left, so the answer is 13.
What helps. Act it out with toy cars or spoons. Put out 8, bring back the 5 that drove away, and count all of them.
For "A jar had 9 buttons. Some more were added. Now it has 15 buttons. How many were added?", your child writes $9 + 15 = 24$ .
The child sees two numbers and the word "added" and adds them. But 15 is already the total, and the question asks for the gap between 9 and 15, which is 6.
What helps. Draw two bars, a short one for 9 and a long one for 15. Ask what piece would make the short bar as long as the long one.
In the bus story, your child answers 22.
The child stops as soon as one calculation is done, without checking it against the question. 22 is the number of people after the first stop, not the number on the bus now.
What helps. Before solving, ask your child to say the question out loud. After solving, read the question again and ask whether the number answers it.

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
Maya has 3 apples. Sam has 1 more apple than Maya. How many apples does Sam have?
A
1
B
4
C
2
D
3
Show the answer and how to solve it
Sam has $4$ apples because Sam has the same $3$ apples as Maya plus $1$ more, so $3 + 1 = 4$ .
1. 1Look at Maya's bar in the tape diagram. It shows 3 apples.
2. 2Look at Sam's bar. It matches Maya's 3 apples, plus 1 more apple.
3. 3Add the two parts to find Sam's total:
4. 4So Sam has 4 apples.
Common mistake. A common mistake is giving 1 as the answer. The 1 tells how many MORE apples Sam has than Maya — it is not Sam's total. To find Sam's total, add 1 to Maya's 3 apples.
The idea underneath. 'More than' means add. To find the bigger amount in a compare story, start with the smaller amount and add the difference.
2On level
Liam baked 19 cookies. His mom baked 24 more. How many cookies do they have in all?
cookies
Show the answer and how to solve it
Answer. 43
They have 43 cookies in all. We put the two amounts together: $19 + 24 = 43$ .
1. 1Liam has 19 cookies and his mom has 24. To find how many they have in all, put the two amounts together by adding 19 and 24.
2. 2Add the ones first: $9 + 4 = 13$ . That is more than $9$ , so write $3$ in the ones place and regroup $1$ ten into the tens column.
3. 3Now add the tens, including the regrouped ten: $1 + 2 + 1 = 4$ . Write $4$ in the tens place. So $19 + 24 = 43$ .
4. 4They have $43$ cookies in all.
Common mistake. A common mistake is forgetting to regroup when the ones add up to more than $9$ . Since $9 + 4 = 13$ , you must write $3$ in the ones place and carry $1$ over to the tens. Skipping the regroup gives a wrong tens digit.
The idea underneath. When the ones add up to 10 or more, you can swap 10 ones for 1 ten and move it to the tens column. This is the same trading idea you use when working with base-ten blocks.
3On level
There are 12 cats at the shelter. 5 are sleeping and the rest are awake. How many cats are awake?
cats
Show the answer and how to solve it
Answer. 7
The answer is 7. Since $5 + 7 = 12$ , taking the 5 sleeping cats away from the total of 12 leaves 7 awake cats.
1. 1Look at the story. There are 12 cats in all. 5 are sleeping, and the rest are awake. We need to find how many are awake.
2. 2The total of 12 cats is made of two parts: the sleeping ones and the awake ones. To find the awake part, take the 5 sleeping cats away from the total of 12.
3. 3There are 7 awake cats.
Common mistake. A common mistake is to add 12 and 5 and answer 17. Remember, the total of 12 already includes BOTH the sleeping cats and the awake cats — so to find the missing awake part, you take the known sleeping part away: $12 - 5 = 7$ .
The idea underneath. In a put-together story, the total includes BOTH parts. To find a missing part, take the known part away from the total.
4Stretch
Devontae had 73 books. He gave 28 to his teacher. Then he gave 19 to his friend Maya. How many books does Devontae have now?
books
Show the answer and how to solve it
Answer. 26
Devontae has $26$ books left after giving $28$ to his teacher and $19$ to his friend Maya.
1. 1Devontae started with $73$ books.
2. 2First, he gave $28$ books to his teacher. Take $28$ away from $73$ :
3. 3Then he gave $19$ more books to his friend Maya. Take $19$ away from $45$ :
4. 4So Devontae has $26$ books left.
Common mistake. A common mistake is stopping after the first subtraction and writing $45$ as the answer. The story has two take-away steps, so you must keep going and also subtract the $19$ books given to his friend Maya.
The idea underneath. A two-step take-away story takes things away one part at a time. Subtract the first amount, then subtract the second amount from what is left to find how much remains.