two step problem solving worksheet

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Two-step word problems.

Two-step word problems have three numbers which must be operated on separately, and in the right order. They take much more understanding of the problem than simple word problems because they provide the information in a less structured form.

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Two step word problems

Two-step word problems

Here you will learn about two-step word problems, including how to solve a two-step word problem, how to represent these problems using equations, and how to assess the reasonableness of answers.

Students will first learn about two-step word problems as part of operations and algebraic thinking in 3 rd grade and will continue using this skill throughout elementary and middle school.

What are two-step word problems?

Two-step word problems are word problems or story problems that require two steps to find the answer. These two steps can involve the same operation or two different operations.

To solve a two-step word problem, you must read the problem carefully before identifying each of the two steps. After identifying the two steps, you can write an equation for each step. Then you will need to solve each equation in order before arriving at the final answer.

For example,

Sarah had \$15. She spent \$8 on a new book. Then her mom gave her \$5. How much money does she have now?

We can break down the problem into steps and write an equation.

Sarah starts with \$15, so this is the starting number.

Then she spends \$8 on a new book. This means you need to subtract \$8. This is step one .

x represents the amount of money Sarah has after buying the book.

Next, Sarah receives \$5 from her mom. This needs to be added to the remaining amount from step one. This is step two .

t represents the total of money Sarah has after her mom gave her \$5 .

Sarah has \$12 now.

You can also write an equation showing both steps and use the order of operations rules to solve.

After solving the problem, you should ask yourself: Is my answer reasonable?

You can use quick mental math or estimation to see if your answer is reasonable.

You can round the \$8 to \$10 to make the estimation easier.

\$15-\$10 + \$5 = \$10, so Sarah has about \$10 left. This means the answer of \$12 is reasonable.

Common Core State Standards

How does this relate to 3 rd grade math and 4 th grade math?

• Grade 3 – Operations and Algebraic Thinking (3.OA.D.8) Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
• Grade 4 – Operations and Algebraic Thinking (4.OA.A.3) Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

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How to solve two-step word problems

In order to solve two-step word problems:

Identify the first step and write an equation.

Identify the second step and write an equation.

Solve the equations in order.

Assess the reasonableness of your answer.

Two-step word problems examples

Example 1: two-step addition (same operation).

Hannah bought 2 bags of candy for trick-or-treaters. One bag had 78 pieces of candy and the other had 92 pieces of candy. Hannah’s friend came over and dumped another bag of candy in the bowl. This bag had 124 pieces of candy. How many pieces of candy are in the bowl altogether?

First, you need to find out the total number of pieces Hannah dumped into the bowl from her two bags.

2 Identify the second step and write an equation.

Next, you need to add the total pieces that Hannah’s friend dumped into Hannah’s total from the previous step.

3 Solve the equations in order.

There are a total of 294 pieces of candy in the bowl.

4 Assess the reasonableness of your answer.

You can use mental math or estimation to see if your answer is reasonable.

You can quickly round each number to 100, which gives you a total of 300 pieces of candy. This is close to the actual answer of 294, so the answer is reasonable.

Example 2: two-step problem (different operation)

A teacher ordered 8 new boxes of pencils for her classroom. Each box of pencils had 16 pencils. She decided to combine all of the pencils, and then split them evenly between the 4 student tables in the room. How many pencils will each table get?

First, you need to find the total number of pencils in all the boxes.

8 \times 16=x

Next, you need to divide the total number of pencils by the number of tables.

Each table will get 32 pencils.

8 \times 20= about 160 total pencils divided by 4 tables = about 40 pencils on each table. So the answer of 32 is reasonable.

Example 3: solving two-step word problems with fractions

A cookie recipe calls for \cfrac{1}{2} cup of white sugar and \cfrac{3}{4} cup of brown sugar.

The baker is making 6 batches of cookies. What is the total amount of sugar (white and brown) that will be used?

First, you need to add the amounts of sugar to find the total amount of sugar needed for 1 batch.

\cfrac{1}{2}+\cfrac{3}{4}=x

Next, you need to multiply the total amount of sugar by the number of batches being made.

x \times 6=s

7 \cfrac{1}{2} total cups of sugar will be needed for 6 batches of cookies.

\cfrac{1}{2} and \cfrac{3}{4} is a little more than 1 cup.

Since there will be 6, the answer will be more than 6 cups.

Therefore, the answer of 7 \cfrac{1}{2} cups is reasonable.

Example 4: solving two-step word problems with decimals

Chris makes \$12.50 an hour at his job at the roller skating rink. He worked 25 hours. After he got his paycheck, he spent \$65 on a new pair of shoes. How much money does he have left from his paycheck?

First, you need to find out how much money Chris’s paycheck was by multiplying the hourly rate by the number of hours he worked.

12.50 \times 25=x

Next, you need to subtract \$65 from the total paycheck amount.

Chris has \$247.50 left from his paycheck.

To estimate the amount of Chris’s paycheck, you can multiply 12 by 25. You could also multiply 12 by 30, but note this will be a high estimate.

12 \times 25=300-65 = \$235 which makes \$247.50 a reasonable answer.

Example 5: interpreting remainders in two-step division word problem

Five 5 th grade classes each have 24 students and 2 teachers attending a field trip. Each bus can hold 48 people. How many buses are needed to carry all of the students and teachers to the field trip?

First, you need to find out how many students and teachers are attending the field trip altogether. To do this, you will need to multiply 5 \times 26.

5 \times 26=x

Next, you need to divide the total number of people by the number of people each bus can carry.

x \div 48=b

Now that you have identified the steps, you can solve the equations in order.

For this problem, you will need to refer back to the question in order to interpret the remainder. It asks: How many buses are needed to carry all of the students and teachers to the field trip?

So in this word problem, the answer 2 \; R \, 34 represents 2 full buses with 34 people leftover. Since those 34 people also need a bus to ride to the field trip, you would round up the answer to 3 so that all people can attend the field trip.

3 buses are needed to carry all of the students and teachers to the field trip.

There are about 125 people attending the field trip (about 25 people \times 5 classes) and about 50 people can fit on a bus. 125 \div 50=2.5, so the answer of 3 buses is reasonable.

Example 6: interpreting remainders in two-step division word problems

Haruki had 39 books. He got 7 more books for his birthday. His bookshelf has 4 shelves. He wants to put the same number of books on each shelf and put the remaining books on top of his bookshelf. How many books will go on top of Haruki’s bookshelf?

First, you need to determine how many books Haruki has altogether.

So step 1 is to add to find the total number of books.

Next, you will need to divide the total number of books by the number of shelves Haruki has.

For this problem, you will need to refer back to the question in order to interpret the remainder. It asks: How many books will go on top of Haruki’s bookshelf?

So in this word problem, the remainder is your answer.

2 books will go on top of Haruki’s bookshelf.

Haruki has about 45 books that he wants to divide equally between 4 shelves, which means there would be about 11 books on each shelf with about 1 left over. So the answer of 2 books is reasonable.

Teaching tips for two-step word problems

• Begin with simple 2 -step word problems on math worksheets that involve familiar situations and basic operations. Gradually increase the complexity as learners gain confidence and understanding.
• Lesson plans should involve step-by-step problem-solving strategies, such as underlining important information, identifying keywords, and breaking the problem into smaller parts. Model how to solve each step before tackling the problem as a whole.
• Connect math word problems to real-life scenarios that are relevant and interesting to students. This can help them see the practical application of math and reasoning skills and increase engagement on word problem worksheets.
• Provide students with a template if needed to help them break down the problem into steps. You can also provide students with a printable answer key to check their work. If their answers do not match, they can go back to investigate and find the correct steps.
• Start with simple two-step word problems with 1 -digit numbers to allow students to focus on identifying the two steps. Then advance to 2 -digit and 3 -digit problems.

Easy mistakes to make

• Incorrect order of operations Students might perform operations in the wrong order, leading to incorrect solutions. It is imperative that students write their equations correctly to ensure the operations are performed in the correct order.
• Not checking the solution Sometimes, students may not take the time to review their solution to ensure it makes sense in the context of the problem. Checking the answer against the problem statement or using estimation to verify reasonableness can help catch errors.
• Missing a step or performing the steps in the wrong order Sometimes, students may misinterpret the problem statement, causing them to miss a step or mix up the order of steps. It’s crucial to carefully read and understand what the problem is asking for before attempting to solve it.

Related arithmetic lessons

• Skip counting
• Number sense
• Inverse operations
• Money word problems
• Calculator skills

Practice two-step word problem questions

1. Frankie has \$287 in her checking account. She spent \$56 on her phone bill and then spent \$39 at dinner. How much money is left in her account?

This is a two-step subtraction word problem, meaning each of the two steps involves subtraction.

1 st step: Subtract the amount spent on the phone bill.

2 nd step: Subtract the amount spent at dinner from what is left after step 1.

2. Elliot has 145 marbles in his collection. He lost 18 marbles and then bought 27 more. How many marbles does he have now?

154 marbles

190 marbles

136 marbles

100 marbles

This two-step word problem involves two different operations.

1 st step: Subtract the number of marbles Elliot lost.

2 nd step: Add the number of marbles Elliot bought to the total remaining marbles from step 1.

127 + 27 = 154 marbles

3. Mrs. Smith baked 24 cookies in the morning and 18 cookies in the afternoon. If she wants to pack them into bags of 6 cookies each, how many bags of cookies will she have in total?

1 st step: Find the total number of cookies Mrs. Smith baked.

2 nd step: Divide the total number of cookies by the number of cookies per bag to find the total number of bags.

42 \div 6=7 bags

4. Sarah has 15 comic books. She decides to buy 5 more comic books at the store. Each comic book costs \$3.50. If she also buys a poster for \$8, how much money will Sarah spend in total?

This two-step word problem involves two different operations. Also note that there is an extra bit of unnecessary information in the word problem (Sarah has 15 comic books).

1 st step: Determine the total cost of the comic books Sarah buys.

2 nd step: Add the amount spent on the poster to the total from step 1.

5. Libby is selling boxes of cookies for a fundraiser at her school. So far, she has sold 29 boxes of cookies for \$12 each. If she has a goal of raising \$400, how much more money does she need to earn?

1 st step: Multiply to find the amount Libby earned from selling 29 boxes of cookies.

2 nd step: Determine how much more money Libby needs to earn to reach her goal by subtracting the total from step 1 from her goal amount.

6. Georgio has 128 complete fossils in his collection. He donated 19 fossils to a local museum. He wants to arrange the rest of his fossils in a display case in his house. The display case has 7 shelves. If he wants to put the same number of fossils on each shelf, how many will go on each shelf?

1 st step: Subtract to find the number of fossils remaining after donating to the museum.

2 nd step: Determine how many fossils Georgio can put on each shelf by dividing the remaining fossils by the number of shelves.

Two-step word problems FAQs

To solve a two-step word problem, you must read the problem carefully before identifying each of the two steps. After identifying the two steps, you can write an equation. Then you will need to perform each step in the correct order before arriving at the final answer.

The next lessons are

• Properties of equality
• Types of numbers
• Rounding numbers
• Factors and multiples

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Algebraic Equations (Two-Step)

Practice solving two-step algebraic equations with these printable worksheets and task cards. Common Core Standard: 7.EE.B.4

Level: Basic Positive Whole Numbers

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Intermediate Level: Positive & Negative Integers

Advanced Level: Decimals, Exponents, & Parenthesis

If two-step equations are too advanced, go down a level and use these single-step equation resources.

We have a variety of algebra and pre-algebra topics for teaching students about independent/dependent variables, expressions, equations, and inequalities.

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Two-Step Word Problems (Grade 3)

Suggested learning target.

• I can choose the correct operation to perform the first computation, and choose the correct operation to perform the second computation in order to solve two-step word problems.
• I can write equations using a letter for the unknown number.
• I can decide if my answers are reasonable using mental math and estimation strategies including rounding.

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Multistep Worksheets

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Free Printable Solving 2 Step Equations Worksheets

Solving two-step equations is one of the most important skills that you need to master in studies of algebra. This is truly a skill that comes up over and over again throughout studies of mathematics. And that’s why I’ve put together this collection of solving 2 step equations worksheets for you!

These free printable worksheets will help you practice solving for the value of the unknown variables in linear equations. Practicing multi-step equations is important to help you develop foundational skills that will be built upon in further studies of mathematics. 

Throughout my career as a math teacher I have seen many students struggle with much more advanced equation solving as a result of missing foundations. Completing additional practice by using practice worksheets like those found below will help you avoid encountering further struggles down the road!

Let’s dig into this two step equations worksheet collection!

How to Solve Two-Step Equations

Two-step equations contain a combination of algebraic expressions that form math sentences. These types of equations require you to perform two steps in order to determine the value of the unknown variables.

If this is your first time solving a 2-step equation, don’t worry! Two-step equations are solved using a similar process to solving one-step equations. However, there is the obvious addition of an extra step. 

A 2-step equation problem will require you to apply  two  operations in order to determine the value of the variable that is unknown. You will be given two sides of the equation, an unknown variable, and a series of operations.

The first step is to identify the side of the equation that has the unknown variable on it. In simple terms, this will be whichever side has the “letter” on it. Your main goal will be to isolate this unknown variable.

The second step is to “undo” whatever the operations are that are keeping the variable from being isolated. To do this, we apply inverse operations. This is just a fancy way of saying “do the opposite of whichever operations are there”. Typically this involves completing order of operations in reverse.

After you have performed each step, you will be able to identify the value of the variable!

Solving Two-Step Equations Example

In order to help you get ready for the math worksheets linked below, I wanted to share an example of a two-step equation. Consider the following 2-step equation: 

As you can see, this equation has an unknown variable on the left hand side of the equation that is multiplied by 3 before being subtracted by 4. Because of this, unlike one-step equations, this equation cannot be solved in a single step.

To begin, we apply an inverse operation to “undo” the subtraction by 4. This inverse operation is addition by 4. We do this on both sides of the equation to ensure that we do not unbalance the equation:

$$3p-4+4=8+4$$

We now have a single step equation! Since the variable is multiplied by 3, the inverse operation will be to divide both sides by 3. This results in:

$$\frac{3p}{3}=\frac{12}{3}$$

We have now successfully solved this 2-step equation for the value of the unknown variable! 

Remember that you can always check your answer by taking the value of the variable and placing it back into the original equation. If the left hand side of the equation is equal to the right hand side, you have solved the equation correctly!

For example, replacing  p  with \(p = 4\) results in:

$$3(4)-4=8$$

So we can confirm that the equation was solved correctly! Checking your answer is a fun activity that can give you a boost of confidence if this is your first time solving a 2-step equation!

Solving 2 Step Equations Worksheets

Now that you have completed some additional practice using the example above, it’s time to dig into these solving 2 step equations worksheets! I have included a wide variety of problem types across three worksheets to help you develop a deep understanding of the equation solving process.

Solving Two-Step Equations: Positive and Negative Integers

The two step equations worksheet linked below is an excellent resource if this is your first time solving algebraic equations. Positive and negative integers are familiar to most mathematics students, so it makes sense to try solving these linear equations first!

After solving each equation, be sure to check the answer key to verify that you fully understand the process for solving two-step equations involving positive integers and negative integers.

​After you have had some time to practice with equations involving integers, move forward with decimals and fractions to deepen your understanding!

Download the PDF worksheet by clicking below!

Solving 2-Step Equations Involving Decimals

After you have spent some time familiarizing yourself with 2-step equations involving negative and positive integers, take a look at the following practice worksheets. Next up is a PDF worksheet that focuses on solving equations involving decimals.

You will see that the equations found in this PDF worksheet include decimal coefficients. The process that you use to solve these 2-step equations is exactly the same as the steps you completed previously.

I have included a wide variety of types of decimal answers throughout these problems. You will see examples of terminating decimals as well as non-terminating decimals !

Be sure to review the answer key after you complete each problem and take note of each type of decimal number!

Solving Two Step Equations Involving Fractions

The last of the practice worksheets that I have included focuses on solving equations involving fractions. These types of equations are the most challenging of this set. Fractions are something that many students find intimidating. However, the process to solve a two-step equation that contains fractions is the same!

After you complete this worksheet, check the answer key to make sure you fully understand how to solve 2-step equations involving fractions!

Using These Solving 2 Step Equations Worksheets

Equation solving is one of the most important skills that you can develop as a student who is studying mathematics. Whether you are learning to use algebra to solve real-world word problems or a tricky test question, understanding how to solve 2-step equations is your first step toward developing a strong foundation of basic algebra skills. 

And it is important to remember that you will need strong algebra skills as you move forward to start solving much more complex problems such as quadratic equations, linear inequalities , and exponential equations . 

I hope you found these practice worksheets to be useful additional practice problems as you work to deepen your understanding of two-step equation solving!

If you are looking to apply your understanding of linear equations to word problems, check out this linear equations word problems worksheet !

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Two-Step Equation Worksheets

Two-step equation worksheets have a huge collection of printable practice pages to solve and verify the equations involving integers, fractions and decimals. Also, a number of exercise pdfs on translating two-step equations, MCQs and word problems based on geometric shapes are given here for additional practice for 7th grade and 8th grade students. Some of them are offered free of cost!

Solving Two-Step Equations involving Whole Numbers

Kick into gear solving single-variable two-step equations involving positive coefficients with this practice set! Rearrange the equations to make the variable the subject, and solve for its whole-number value.

• Download the set

Solving Equations involving Integers

In these worksheets solve the two-step equations with integer coefficients. Numerous worksheets are available for practice.

Solving Equations involving Fractions

Solve the equations which have fractions as their coefficients. Arrive the solution to the equations in just two steps.

Solving Equations involving Decimals

Decimal coefficients are included in these printable two-step equation worksheets. Solve these equations to get the value of the unknown.

Solving Equations: Mixed Review

Solve these mixed equations which involve fractions, integers and decimals. Each pdf two-step equation worksheet has ten problems for a thorough practice.

Equation Word Problems Worksheets

Utilize this set of worksheets to guide students of grade 7 and grade 8 to solve an array of diligently prepared equation word problems.

(15 Worksheets)

Solve and Verify the Solution

In these 12 worksheets solve each two-step equation to find the unknown. Substitute the value of the variable in the given equation to verify the solution.

Multiple Choice Questions

Identify the correct two-step equation or value from the given multiple responses. Each pdf worksheet has eight questions for practice.

Translating Two-Step Equation

In these printable worksheets, translate the given phrases and/ or sentences into two-step equation.

Find me! Solve these interesting problems following the given hints. Ex. If you add 7 to three times of me, you get 34. What number am I?

Equations in Geometry: Type 1

The lengths of the sides of geometric figures are given in the form of expressions. Use the given inputs to find the value of the unknown variables.

Equations in Geometry: Type 2

The properties of the geometric shapes are the clues to solve these word problems. Figure out the two-step equation from the given expressions to find the value of the unknown.

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» Multi-step Equation

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• Two Step Problem

Two Step Problems Math Worksheets|Printables PDF for kids

Two step math calculation problems. Learn to solve different math operations like multiplication, addition, subtraction, division with math worksheets. Each problem has two operations like multiplication and addition in one problem, multiplication twice in a problem, division and multiplication in a problem so on.

You can see the preview of the worksheets before you download them so that you can check what you exactly want to download and print for your kids / students to practice. Once students have downloaded the worksheets then they one can check the answers provided at the end of the worksheets.

Improve math basic calculations with these two step problem worksheets. Once students have mastered in these worksheets then they are ready to proceed to oreder of operations worksheets. These worksheets are suitable for 2nd grade/level onwards.

Two Step Problems - 1

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Two Step Problems Worksheets

How to Solve Two-step Operation Problems - Not all mathematical problems have a single operation with them. At an early age, children are given simpler problems with only one mathematical operation to perform. These simple problems are necessary for developing the foundation for solving complex problems. Once children have a firm grip on solving a single-operation problem, they progress to solving multiple operations. The very next step to the single-operation problem is the two-step operation problem. These problems involve two operations and are solved following the rules of PEMDAS. According to this rule, we first solve for the parentheses followed by exponents. Next, we solve for multiplication and division in left to right order. Lastly, we solve for the addition and subtraction in left to right order. Example Problems: James had 12 chocolates; he then gives one to his friend John. One of his friends gave three of his chocolates to James. How many chocolates James have in total? The number of chocolates James has is equal to 12. He gives one to John. 12 -1 = 11, James receives three more chocolates from another friend. 11 + 3 = 14. The total number of chocolates James has is equal to 14.

Basic Lesson

Demonstrates the rule set to follow when performing arithmetic operations. Practice problems are provided. A set of rules for arithmetic operations are devised to perform calculations involving more than one arithmetic operation. Rule 1: First perform any calculations inside parentheses. Rule 2: Next perform all multiplications and divisions, working from left to right. Rule 3: Lastly, perform all additions and subtractions, working from left to right.

Intermediate Lesson

Explains how to attack the variables in a two-step order of operations problem. Practice problems are provided.

Independent Practice 1

Contains 20 two-step problems. The answers can be found below.

Independent Practice 2

Features another 20 two-step problems.

Homework Worksheet

12 two-step problems for students to work on at home. Example problems are provided and explained.

10 two-step problems. A math scoring matrix is included.

Homework and Quiz Answer Key

Answers for the homework and quiz.

Answers for the lesson and practice sheets.

Birthdays Rock!

Start with the number of your birth month. Multiply by 4. Add 13. Multiply by 100. Divide by 4. Subtract 200. Add the day of the month you were born. Multiply by 2. Subtract 40. Multiply by 50. Add to it the last 2 digits of the year you were born. Subtract 10,500.

2-step problem solving worksheets

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Free Printable Two-Step Word Problems Worksheets for 7th Grade

Math: Discover a collection of free printable two-step word problem worksheets, perfect for Grade 7 students. Enhance your students' problem-solving skills and mathematical understanding with these resources from Quizizz.

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Two-Step Word Problems worksheets for Grade 7 are an essential tool for teachers to help their students develop strong problem-solving skills in math. These worksheets focus on teaching students how to break down complex math word problems into two simpler steps, allowing them to better understand the process and apply their knowledge of addition, subtraction, multiplication, and division. By incorporating these worksheets into their lesson plans, teachers can provide their students with engaging and challenging math word problems that will improve their overall understanding of mathematical concepts. Furthermore, these Grade 7 worksheets are designed to align with the Common Core State Standards, ensuring that students are receiving a consistent and high-quality education in math.

In addition to Two-Step Word Problems worksheets for Grade 7, Quizizz offers a wide range of resources for teachers to enhance their students' learning experience in math. Quizizz is an online platform that allows teachers to create interactive quizzes, polls, and presentations, making it easier than ever to engage students and assess their understanding of math concepts. With Quizizz, teachers can easily customize their quizzes to include questions related to math word problems, addition word problems, and other relevant topics for Grade 7 students. Moreover, Quizizz provides teachers with valuable insights into their students' performance, allowing them to identify areas where students may need additional support or practice. By incorporating Quizizz into their classroom, teachers can create a more dynamic and effective learning environment for their Grade 7 students, ensuring they develop the skills necessary to excel in math.

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Solving Two-Step Problems 3rd Grade Math Worksheets

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Definition:

Solving any math problem  is not only accountable with one step or process, it may have a different procedure to arrive with the same answer.  Two-step process  is one way of solving a math problem in two equation, which can be in the means of addition, subtraction , multiplication and / or division.

A two-step math word problem requires you to solve two equations before you arrive to an answer. The problem might have two different operations (like multiplication and addition ), or it might have two of the same operation.

• Read the problems wholly and carefully
• Do a sketch to illustrate, if possible
• Assign or translate the words into numbers
• Read it carefully until you decide what you need to do, including which step to complete first.
• Re-read the problem if necessary.
• Work through the first step of the given scenario.
• Look at the important information in the problem, and turn that equation into an equation by translating words into operation.
• *Feel free to draw images to better picture-out the problem.

I had 12 chips. I gave my friend 2 of them. Then I bought another 4. How many chips do I have in all?

Solving Two-Step Problems

First step:  Subtract the total number of chips to the first given scenario. (12 – 2 = 10)

Second step:  Add the answer obtained from the first step to the second scenario. (10 + 4 = 14) : So, the girl has 14 chips in total.

Solving Two-Step Problems Worksheets

This is a fantastic bundle which includes everything you need to know about Solving Two-Step Problems across 15 in-depth pages. These are ready-to-use Common core aligned Grade 3 Math worksheets .

Each ready to use worksheet collection includes 10 activities and an answer guide. Not teaching common core standards ? Don’t worry! All our worksheets are completely editable so can be tailored for your curriculum and target audience.

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