Two-Step Word Problems Worksheets

Two-step word problems hide a question inside the question: children have to find one number before they can find the answer. The five PDFs on this page have six problems each that need two calculations, using all four operations, with space for each step, and every sheet has an answer key. They follow standards 3.OA.D.8 and 4.OA.A.3 of the Common Core standards for grade 3 operations and algebraic thinking, and the notes below show how to find the hidden question, how to check with an estimate and how to write the steps.

Plan the steps

Two-step problems hide a question inside the question. In “3 notebooks at $4 each, pay with $20, how much change?”, you first need the cost (3 × $4 = $12), then the change ($20 − $12 = $8). Asking “What do I need to find first?” is the key habit. Grade 3 children solve two-step problems with all four operations (Common Core 3.OA.D.8).

Two-step word problems worksheets: what is in the set

There are 5 two-step word problems worksheets on this page, and every one has an answer key except for any cut-out games. Every set has six problems that need two calculations, and the five sets mix all four operations.

Two step word problems: what they look like

Two step word problems ask one question, but the answer needs two calculations. The first calculation finds a number that the story does not give, and the second uses it to answer the question. The step that is hidden is often the one that children miss. Wikipedia’s article on word problems describes why these problems are important in school mathematics. This table shows eight problems, with the hidden step, the two number sentences and the answer:

Each of the eight problems uses two different operations. In the change, book and bead problems the first step finds an amount that is taken away from a total, so the second step subtracts it from the total and not the other way round. Reading the whole story before writing anything is the best habit.

Two step word problems grade 3: the standard 3.OA.D.8

For two step word problems grade 3, the standard is 3.OA.D.8. Children solve two-step problems with the four operations, write equations with a letter for the unknown, and judge whether answers are reasonable using mental math and estimation, including rounding. The Common Core standards for grade 3 operations and algebraic thinking list it with the other grade 3 standards. Each of the three parts is practiced on this page: the steps, the equation and the estimate. This table shows the equation with a letter for five stories:

The letter n is the hidden number that is left after the first step. A child who writes the equation first and then solves it in two steps is using algebra, even if they do not call it that. The addition and subtraction word problems and multiplication and division word problems pages have the one-step stories that come before.

Mixed operations word problems: sixteen pairs of steps

Mixed operations word problems can use any two of the four operations, and there are sixteen possible pairs, in order. Most of the problems in grade 3 use only some of them, but children should be ready for any. This table shows the sixteen pairs for the numbers 24, 4 and 2:

The table shows that the order of the operations changes the answer. (24 + 4) ÷ 2 is 14, but (24 ÷ 4) + 2 is 8. This is the reason why each step is written on its own line, and why the brackets matter when two steps are written together.

Multi step word problems: grade 4 and beyond

In grade 4, the multi step word problems can have more than two steps, and some have remainders that must be interpreted. Standard 4.OA.A.3 asks children to solve multistep problems with whole numbers and the four operations, including problems in which the remainder has to be interpreted. The Common Core standards for grade 4 operations and algebraic thinking describe the standard. This table shows four problems with the same division and different meanings of the remainder:

The same division, 50 ÷ 8, can give an answer of 6, 7 or 2, depending on the question. A good habit for children is to ask “what does the remainder mean here?” before writing the answer. The division with remainders and long division worksheets pages have the division skills.

4th grade word problems: estimating to check

In 4th grade word problems, the numbers are larger, and children check their answers with an estimate. To estimate a two-step problem, round each number to the nearest ten, and do the two steps with the rounded numbers. This table shows six problems, with the estimate and the exact answer:

An estimate is not an exact answer, and the question is only whether the exact answer is close. The estimate for 19 × 6 − 8 is 20 × 6 − 10 = 110, and the exact answer is 106, so the answer is reasonable. The estimating with rounding page has more practice with estimating, and the money worksheets pages use two-step problems with change.

Common mistakes with two-step word problems

The most common mistake is to stop after the first step. This table shows five mistakes, what went wrong and the fix:

Two-step word problems word problems

Two-step stories hide a question inside the question. Ask children to say the hidden question, write one number sentence for each step, and then answer in a sentence:

Games and activities for two-step word problems

Children learn two-step word problems best when they play with it. These games use things that are found at home or in a classroom:

• Hidden question: read a story and say only the hidden question, without any calculating
• Story chains: one child writes the first step, and a partner writes the second
• Make it two steps: take a one-step story and add a second question to it
• Shop and change: buy two items at a class shop with play money and find the change
• Estimate first: estimate each answer before calculating, and see who is closest
• Word problem bingo: a bingo card with answers, and calling cards with stories

Extra support and extra challenge with two-step word problems

For children who need more support: make sure that one-step stories are secure first, and do each problem as two separate one-step stories. Cover the second question until the first is answered. Write the first step on one line and the second on another, and draw a bar model if it helps. Do one sheet at a time with the answer key beside the work.

For children who need more challenge: ask for a story that needs three steps, for a story that fits the equation 3 × 4 + n = 20, and for a story where the remainder has to be rounded up in the last step. Making up their own two-step story, and swapping it with a friend, is a good challenge.

How to tell that a child is ready to move on from two-step word problems

Before moving on from two-step word problems, check that the child can do all four of these things:

1. The child says the hidden question before calculating.
2. The child writes one number sentence for each step.
3. The child answers the question that is asked, not the first step.
4. The child checks the answer with an estimate.

When all four are true, move on to the multi-step problems of grade 4, or return to the addition and subtraction word problems and multiplication and division word problems pages for any weak spots.

A 20-minute lesson on two-step word problems

A short lesson is the best way to introduce two-step word problems. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where two-step word problems fits across the grades

No skill stands alone. This table shows what children learn before and after two-step word problems, with the standard that goes with each step:

This page is the last of the whole-number word problem pages. The whole sequence is on the math word problems worksheets page.

Helping at home with two-step word problems

Parents do not need to be experts to help with two-step word problems. These suggestions work well, and each takes only a few minutes:

• Ask “what do you need to find first?” when a problem looks hard.
• Use real shopping: two items, then the change.
• Ask the child to read the question again before the answer is written.
• Estimate together, and ask “is it close?”.
• Check that the answer is for the question that was asked.

How to check progress in two-step word problems

A teacher or parent can check progress in two-step word problems with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for two-step word problems

Most children need about a week of short sessions for two-step word problems. This plan follows the order of the worksheets on this page:

When the plan for two-step word problems is complete, the child is ready for multi-step stories. The whole sequence is on the math word problems worksheets page.