Word Problems Within 100: One and Two Steps

Quick answer

Second-grade story problems use the same kinds of stories as first grade — adding to, taking from, putting together, taking apart and comparing — with numbers up to 100, and some need two steps. A tape diagram shows the whole and its parts as lengths, so it shows whether to add or subtract: add parts to find a whole, subtract to find a missing part. In a two-step problem, the answer to the first step becomes a number in the second.

What you'll learn

Solve one-step word problems within 100 with the unknown in any position
Draw a tape diagram to show the parts and the whole
Solve two-step word problems within 100

Draw the story as a tape

A class has $38$ pencils. The teacher buys $27$ more. How many pencils are there now?

Draw a tape diagram: a strip with one part for each number. Make each part about as long as its number.

Thirty-eight and twenty-seven

Both parts are known. The whole is missing. So add:

38 + 27 = 30 + 20 + 8 + 7 = 50 + 15 = 65

There are $65$ pencils.

Why the tape tells you what to do

A tape always shows parts and a whole. The parts fit end to end to make the whole.

If the whole is the missing piece, add the parts.
If a part is the missing piece, subtract the known part from the whole.

So you never need to hunt for clue words. Draw the tape, find the question mark, and you know which to do.

Compare with two tapes

Ana has $45$ stickers. Ben has $28$ . How many more stickers does Ana have?

Ana's and Ben's stickers

Line the tapes up at the start. The part of Ana’s tape that sticks out past Ben’s is the difference.

$45 - 28 = 17$ . Ana has $17$ more stickers.

Two-step problems

Some problems need two steps. The answer to the first step is a number you use in the second.

Sam’s book has $60$ pages. He read $25$ pages on Monday and $18$ on Tuesday. How many pages are left?

Sixty pages

Step 1: find the pages he read. $25 + 18 = 43$ .

Step 2: take them from the whole book. $60 - 43 = 17$ .

$17$ pages are left.

Worked examples

Common mistakes

Practice problems

A farm has $47$ hens and $36$ ducks. How many birds is that in all?

Answer

$83$

Full solution

Both parts are known, so add. $40 + 30 = 70$ and $7 + 6 = 13$ . $70 + 13 = 83$ .
There are $72$ apples. $35$ are green and the rest are red. How many are red?

Answer

$37$

Full solution

The whole is $72$ and one part is $35$ . $72 - 35$ : count up from $35$ to $40$ ( $5$ ), then to $72$ ( $32$ ). $5 + 32 = 37$ .
Lily has $64$ beads. Max has $39$ . How many more beads does Lily have?

Answer

$25$

Full solution

The difference is bigger minus smaller: $64 - 39$ . $39 + 1 = 40$ , and $40 + 24 = 64$ . $1 + 24 = 25$ .
Some birds were in a tree. $18$ flew away. Now $27$ are left. How many birds were in the tree at first?

Answer

$45$

Full solution

$\square - 18 = 27$ . The start is the whole: $27 + 18 = 45$ .
Use the tape diagram. What number goes in place of the question mark?

Find the missing part

Answer

$34$

Full solution

The whole is $90$ and one part is $56$ . $90 - 56 = 34$ . Check: $56 + 34 = 90$ .
A shop had $80$ balloons. It sold $26$ in the morning and $31$ in the afternoon. How many are left?

Answer

$23$

Full solution

Step 1: $26 + 31 = 57$ sold. Step 2: $80 - 57 = 23$ left.
Kim has $15$ fewer cards than Jo. Jo has $52$ cards. How many cards does Kim have?

Answer

$37$

Full solution

Kim has fewer, so subtract: $52 - 15 = 37$ .
Tom had $43$ marbles. He won $19$ more, then gave $25$ to his sister. How many does he have now?

Answer

$37$

Full solution

Step 1: $43 + 19 = 62$ . Step 2: $62 - 25 = 37$ .
A class read $28$ books in May. In June they read $9$ more books than in May. How many books did they read in June?

Answer

$37$

Full solution

June is May’s number plus $9$ : $28 + 9 = 37$ .
“Ava has $50$ stamps. She uses $12$ and then buys $20$ more. How many does she have?” Ben answers $38$ . What went wrong?

Hint

How many steps does the story have?

Answer

He did only the first step. The answer is $58$ .

Full solution

Step 1: $50 - 12 = 38$ . That is how many she has after using some.

Step 2: she buys $20$ more. $38 + 20 = 58$ .

Frequently asked questions

What is a tape diagram?

A drawing of a strip cut into parts, with each part as long as the number it stands for. The whole strip is the total.

How does a tape diagram tell me whether to add or subtract?

If the whole is unknown, add the parts. If a part is unknown, subtract the known part from the whole.

What is a two-step word problem?

One that needs two number sentences. The answer to the first becomes part of the second.

How do I solve a compare problem?

Draw two tapes that start together. The part of the longer tape that sticks out is the difference: bigger minus smaller.

How do I check my answer?

Put it back into the story. If every number in the story still fits, the answer is right.

What to learn next

Standards alignment

This lesson covers the following Common Core State Standards for Mathematics.

CCSS.MATH.CONTENT.2.OA.A.1Operations and Algebraic ThinkingUse 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.

For teachersPrint problems onlyTick to print a blank worksheet; leave it clear to print the lesson with the full answer key.