2nd Grade One- and Two-Step Word Problems Lesson: Notes and Examples (Free PDF)

Q: What if the unknown is at the start?

Write an equation with a ? at the start, such as ? + 26 = 90. Then think of the whole and the part you know, and subtract: 90 - 26 = 64.

2nd grade word problems lesson – Maths PDF

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This 2nd grade word problems lesson covers one- and two-step word problems (Common Core 2.OA.A.1), with a free PDF to print.

Key takeaway: This lesson helps Grade 2 students solve one-step and two-step word problems within 100.

Topic: One- and Two-Step Word Problems (2nd grade)
Content: One-page lesson with a definition, a worked example and key facts
Standards: 2.OA.A.1
Answers: Explanations included
Format: Free printable PDF, US Letter, black and white

A word problem is a short story that asks a math question. To solve one within 100, decide whether things are joined, removed, put together, taken apart, or compared. Then draw a bar model, write an addition or subtraction sentence, and solve. Two-step problems use the answer from the first step in the second step.

This lesson helps Grade 2 students solve one-step and two-step word problems within 100. First, children learn five story types: add to, take from, put together, take apart, and compare. Then they use bar models and equations with a question mark for the unknown.

Next, the lesson shows how to compare two amounts by subtracting. Also, it teaches how to solve two-step problems, where the first answer feeds the second step. Finally, it shows how to check that the answer makes sense. Plan about 15 minutes, with counters or a bar model template.

Grade 2 · Common Core State Standards: 2.OA.A.1

Key facts in this 2nd grade word problems lesson

Key facts

Five story types: add to, take from, put together, take apart, and compare.
Next, a bar model shows the parts and the whole so you can see which number is missing.
More than and fewer than mean comparing: subtract the smaller number from the larger.
Then, a two-step problem needs two math sentences; the first answer feeds the second.
Also, a ? or a letter can stand for the unknown number in an equation.

What is a word problem?

A word problem is a short story with numbers in it. The story ends with a question. Your job is to figure out what is happening and then add or subtract.

Word problem

A word problem uses a story to ask a math question. In Grade 2 the numbers stay within 100, and you solve with adding or subtracting.

Priya has 34 red beads and 25 blue beads. How many beads does she have in all? Draw the two parts side by side and the whole above them.

A bar model shows two parts and the whole.

The whole is the sum: \(34 + 25 = 59\). Priya has 59 beads.

What kinds of stories can you solve?

Most stories fit one of five types. Name the type and the math gets easier.

Type	What happens	Example
Add to	Something joins the group	\(45 + 20 = 65\)
Take from	Something leaves the group	\(80 – 30 = 50\)
Put together	Two parts make a whole	\(32 + 17 = 49\)
Take apart	A whole splits into parts	\(60 = 24 + ?\)
Compare	How many more or fewer?	\(71 – 48 = 23\)

When something leaves, hop backward on a number line. Starting at 85 and taking away 30 lands on 55.

Taking away moves left on the number line: 85 – 30 = 55.

To compare two amounts, line up two bars. The gap between them is the difference. Words like more than and fewer than tell you to compare.

To compare, find the gap between the two bars: 71 – 48 = 23.

How do you solve a two-step problem?

A two-step problem needs two math sentences. The answer to the first step is used in the second step.

Read the story and say it in your own words.
Find the question. Circle what you must find.
Draw a bar model for the first step and solve it.
Use that answer in a second bar model and solve.
Check: does the answer make sense in the story?

Worked example. Diego has 46 stamps. His aunt gives him 28 more. Then he gives 15 stamps to a friend. How many stamps does Diego have now?

Step 1 (bottom): 46 + 28 = 74. Next, step 2 (top): 74 – 15 = 59.

Step 1: \(46 + 28 = 74\). Step 2: \(74 – 15 = 59\). Diego has 59 stamps.

A letter or a question mark can stand for the number you do not know yet, as in \(46 + ? = 74\). The unknown can be the start, the change, or the result.

2nd grade word problems lesson: questions and answers

How do I know whether to add or subtract?

Ask what happens in the story. If things join or two parts make a whole, add. If things leave or you compare two amounts, subtract. Drawing a bar model helps you see it.

What is a bar model?

A bar model is a drawing of rectangles that stand for numbers. Parts sit side by side and the whole is written above them. The missing number is shown with a ?.

What does it mean to compare in a word problem?

Comparing means finding how many more or how many fewer one amount is. Subtract the smaller number from the larger, as in \(71 – 48 = 23\).

How do I solve a two-step word problem?

Solve one small question first, then use that answer to solve the final question. Write one math sentence for each step and check that your last answer fits the story.

What if the unknown is at the start?

Write an equation with a ? at the start, such as \(? + 26 = 90\). Then think of the whole and the part you know, and subtract: \(90 – 26 = 64\).

Common mistakes with this 2nd grade word problems lesson

Students pick the operation from a key word. For example, the word left does not always mean subtract. Instead, picture the story and decide what happens.
Children solve only the first step of a two-step problem. As a result, they give a number that does not answer the question. Underline the question and check that your answer matches it.
In compare problems, students add the two numbers. Instead, find the difference by subtracting the smaller from the larger. Also, saying the steps aloud helps you spot a slip.

How to study this chapter

First, read the story twice. Then draw a bar model with the parts and the whole. Then check the result once more before moving on.
Write the equation with a question mark for the unknown. Also write the answer with a unit, such as 36 books.
Parents can ask what the question mark stands for before the child solves. That one question prevents many wrong operations.

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