# 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.

\$15-\$8 = x

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

\$15-\$8=\$7 Next, Sarah receives \$5 from her mom. This needs to be added to the remaining amount from step one. This is step two.

\$7 + 5 = t t represents the total of money Sarah has after her mom gave her \$5 .

\$7+5=\$12

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. ### What are two-step word problems? ## 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. ## How to solve two-step word problems In order to solve two-step word problems: 1. Identify the first step and write an equation. 2. Identify the second step and write an equation. 3. Solve the equations in order. 4. 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? 1. Identify the first step and write an equation. First, you need to find out the total number of pieces Hannah dumped into the bowl from her two bags. 78+92=x 2Identify 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. x+124=c 3Solve the equations in order. 78 + 92 = 170 170 + 124 = 294 There are a total of 294 pieces of candy in the bowl. 4Assess 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? 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. ### 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? 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. ### 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? 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. ### 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? 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. ### 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? 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. ### 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. ### 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?

\$304 \$192

\$382 \$202

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.

\begin{aligned} & \$287-\$ 56=\$231 \\\\ & \$ 231-\$39=\$ 192 \end{aligned}

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.

145-18 = 127

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?

42 bags

6 bags

48 bags

7 bags

This two-step word problem involves two different operations.

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.

24+18=42

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?

\$78 \$62

\$25.50 \$9.50

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.

\begin{aligned} & \$3.50 \times 5=\$ 17.50 \\\\ & \$17.50+\$ 8=\25.50 \end{aligned} 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? \$748

\$52 \$359

\42 This two-step word problem involves two different operations. 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. \begin{aligned} & 29 \times \ 12=\$348 \\\\ & \$ 400-\$348=\$ 52 \end{aligned}

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?

15 \mathrm{R}4

16

15

15 \cfrac{4}{7}

This two-step word problem involves two different operations.

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.

\begin{aligned} & 128-19=109 \\\\ & 109 \div 7=15 \mathrm{R} 4 \end{aligned}

## Two-step word problems FAQs

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.

How do I solve a two-step word problem?

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.

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