What to expect in this article?
After reading this article, you will be able to analyze, process, and solve multi-step word problems. This lesson will provide help and guidance in solving these types of problems as it includes tips on how to solve a multi-step problem. There are two given examples wherein you can practice and guide your children in honing their mathematical skills. You can also read the common errors and misconceptions of students in solving multi-step problems. Furthermore, this article consists of links directed to worksheets – which you can find at the bottom of the page.
What is a multi-step word problem?
Math word problems are a critical component of the mathematics curriculum because they help students develop their mental abilities, improve logical analysis, and stimulate creative thinking. Word problems are fun and challenging to solve because they represent actual situations that happen in our world. More so, having the ability to solve math word problems significantly benefits one’s career and personal life.
To be able to solve any math word problem, children must be familiar with the mathematics language associated with the mathematical symbols they are accustomed in order to comprehend the word problem.
A multi-step math word problem is a type of problem wherein you need to solve one or more problems first in order to get the necessary information to solve the question being asked. It usually involves multiple operations and may also involve more than one strand of the curriculum. Say, for example, a multi-step word problem involving area and perimeter may also require the application of ratio and multiplication.
How to solve multi-step word problems?
In any word problem, the true challenge is deciding which mathematical operation to use. In solving multi-step word problems, there may be two or more operations that you need to work on, and you must solve them in the correct order to be able to get the correct answer. Since word problems describe a real situation in detail, the question being asked can get lost in all the information, especially in a multi-step problem.
To solve multi-step word problems, you may follow these strategy:
- Analyze and understand the problem.
- Break down each sentence of the problem and identify the clues.
- List all the information.
- Identify the unknown in the problem.
- Devise a plan or identify the mathematical operations you are going to use.
- Carry out the plan.
- Label your final answer.
Multi-Step Word Problem #1
Step 1: Break down each sentence of the problem and identify the information needed to solve the problem.
- The first sentence states that “Steven is reading a book that has 260 pages.” Hence, the total number of pages of that particular book is 260.
- The second statement says, “He read 35 pages on Monday night and 40 pages on Tuesday night.”
Step 2: Analyze the question of the problem and find the keyword for the unknown. The last sentence of the problem, “How many pages does he has left to read?” asks us how many more pages Steven needs to read. Hence, we are going to find the number of pages he still needs to read.
Step 3: Based on the second statement, Steven read 35 pages on a Monday night and 45 pages on a Tuesday night. Hence, we will use addition in getting the total number of pages he read for 2 nights. Thus,
35 + 40 = 75
Therefore, Steven read 75 pages in the span of two days. However, that is not the answer we are looking for.
Step 4: Since we are asked to get the number of pages he still needs to read, the first sentence on our problem shows us that there are 260 pages in the book. Hence, we need to subtract the number of pages Steven has read from the total number of pages of the book. Thus,
260 – 75 = 185
Therefore, Steven has 185 pages left to read.
Multi-Step Word Problem #2
Jesy bought a dozen of boxes, each containing 24 highlighter pens inside. Each box costs \$8. Jesy repacked five of these boxes into packages of six highlighters each and sold them for \$3 per package. She sold the rest of the highlighters at the price of three pens for \$2. How much profit did Jesy make?
Step 1: Break down each sentence of the problem and identify the information needed to solve the problem.
- The statement, “Jesy bought a dozen of boxes, each containing 24 highlighter pens inside,” tells us that there are a dozen of boxes that contains 24 highlighters. A dozen means there are 12 boxes.
- The second sentence, “Each box costs \$8”, means Jesy bought 12 boxes at \$8 each.
- “Jesy repacked five of these boxes into packages of six highlighters each and sold them for \$3 per package” means that Jesy separated 5 boxes from the original 12 boxes to be repacked at a package of six, which was sold at \$3 each.
- “She sold the rest of the highlighters at the price of three pens for \$2” means that Jesy sold the remaining highlighters and bundled it for 3 pens for \$2.
Step 2: Analyze the question of the problem and find the keyword. The last sentence of the problem, “How much profit did Jesy make?” asks us how much profit Jesy earned after repacking the highlighter pens. Profit is defined as the amount earned minus the amount spent to buy the highlighters.
Step 3: Based on the first statement, Jesy bought 12 boxes containing 24 highlighters. The follow-up statement that says, “Each box costs \$8” refers to the price of each box. In this particular statement, we can find the total expenditures of Jesy for the highlighter pens by simply multiplying the total number of boxes to \$8. Hence,
12 x \$8 = \$96
This means that Jesy spent \$96 to buy all the highlighters. However, that is not the question being asked. Hence, we need to work on the follow-up statements and find more clues to get Jesy’s profit in selling highlighters.
Step 4: The next statement says that “Jesy repacked five of these boxes into packages of six highlighters each and sold them for \$3 per package” means that Jesy separated 5 boxes from the dozen to be repacked at a package of six, which was sold at \$3 each. Based on this statement, we need to do three things:
- Find the total number of highlighters she got from separating 5 boxes;
- Find the total number of packages she made by repacking it by 6; and
- Find how much money she made by selling the sets of 6 at \$3.
Step 5: To find the total number of highlighters she got from separating 5 boxes, we simply multiply 5 by the number of highlighters inside the box. Based on the first statement, each box contains 24 highlighters. Hence,
5 x 24 = 120
This means Jesy repacked a total of 120 highlighter pens.
Step 6: To find the total number of packages she made by repacking 120 highlighter pens by 6, we will divide 120 by 6. Thus,
120 6 = 20
So, she was able to make 20 sets of 6 highlighter pens.
Step 7: The next thing we need to do is find how much money she made by selling the sets of 6 by \$3. This can be done by multiplying 20 sets by \$3. Hence,
20 x \$3 = \$60
Thus, Jesy made \$60 from the 20 sets of 6 highlighter pens.
Step 8: The third sentence, “She sold the rest of the highlighters at the price of three pens for \$2” means that Jesy sold the remaining highlighters and bundled it for 3 pens for \$2. From this statement, we need to work on four things first:
- Find the remaining number of boxes;
- Find the total number of highlighter pens she repacked;
- Find the number of sets she repacked by making sets of 3; and
- Find how much money Jesy made by selling packs of 3 at \$2.
Step 9: To find the remaining number of boxes, we need to go through some of the problem statements. Based on the first statement, we have 12 boxes, then 5 boxes were separated to make a highlighter set of 6. Hence, we will subtract 5 from 12.
12 – 5 = 7
So, we still have 7 remaining boxes.
Step 10: To find the total number of highlighter pens she repacked, we need to multiply the remaining 7 boxes to the number of highlighter pens inside the box. Going back to the information we already have, we know that there are 24 highlighter pens inside a box. Thus,
7 x 24 = 168
This means Jesy repacked a total of 168 highlighter pens.
Step 11: Find the number of sets Jesy made by repacking 168 highlighter pens by 3. This can be done by dividing 168 by 3. Hence,
168 3 = 56
Thus, Jesy was able to make 56 sets of 3 highlighter pens.
Step 12: Determine how much money Jesy made by selling each set for \$2. Hence,
56 x \$2 = \$112
This means Jesy made \$112 by selling 3 highlighter pens for \$2.
Step 13: The question asks us to determine the profit Jesy made by selling the highlighter pens. In order to find the profit, we need the information of:
- How much did Jesy spend on the highlighter. In Step 3, we found out that she paid \$96 on buying all the highlighter pens.
- How much money does Jesy make on selling packs of 6 highlighters for \$3. In Step 7, we already know that she made \$60; and
- How much money does Jesy make on selling sets of 3 highlighter pens for \$2. In Step 12, we found out that she made \$112.
Step 14: Before getting the profit Jesy made, we need to know the total money Jesy made in selling the highlighters. Hence, we will simply add the money of \$60 and \$112. Thus,
\$60 + \$112 = \$172
However, \$172 is not the profit Jesy made. This is just the money she was able to make in selling the highlighter pens.
Step 15: Lastly, we will subtract the money Jesy spent on buying the highlighters from the money she made by selling it to find the profit. Thus,
\$172 – \$96 = \$76
Therefore, Jesy made a profit of \$76 by selling the highlighter pens.
You can tell that there are lots of things to remember with a multi-step word problem, even when the problem itself is relatively easy. But that’s what makes these problems challenging: you get to use both sides of your brain – your logical math skills and your verbal language skills. That’s why they are often more fun to do than problems that are just numbers without the details and context that word problems give you. The better you understand how to solve them, the more fun they are to solve.
What are the common errors in solving multi-step word problems?
Mathematical word problems can be challenging to solve. To obtain the correct answer, children must read the words and carefully analyze the problem, determine the appropriate math operation, and then perform the calculations correctly. An error in working on one of the steps may result in a wrong answer.
Here’s a list of some errors students make when solving multi-step word problems:
- The most common error of students is stopping at one process if they solve one problem. Consider the same word problem about Steven.
“Steven is reading a book that has 260 pages. He read 35 pages on Monday night and 40 pages on Tuesday night. How many pages does he has left to read?”
Most students recognize that they need to add 35 and 40 together to get the total number of pages Steven has read so far. Most errors occur when students stop at one process. Adding 35 + 40 will tell you that Steven has read 75 pages so far, but if we go back to the question you are being asked, you will notice that 75 pages are not the answer you are being asked. Thus, we still need to take another step to get there. Steven has read 75 pages so far, but the questions asked us to solve the number of pages he has left to read. Hence, subtracting 75 from the total number of pages of the book makes much more sense.
- Students get confused with the mathematical operation to use. Even if children are strong readers, they may struggle to pick up on clues in word problems. These clues are phrases that instruct children on how to solve a problem, such as adding or subtracting. The children are then required to convert these phrases into a number sentence in order to solve word problems.
How to teach multi-step problems to children?
There are certain activities or practices that you can try with your child in order to develop their skills in solving multi-step problems.
- The first and most important skill in working with multi-step is being able to understand the problem clearly. Hence, practicing your child in slowly reading and visualizing problems is the first step in implementing our effective reading comprehension strategies.
- Practice your child in recognizing mathematics terms and vocabulary that are used in word problems. There are keywords or clues that we can easily spot in a word problem if we familiarize ourselves with these mathematical terms.
Let’s look at the sample words related to addition, subtraction, multiplication, and division.
|English Words||Mathematical Operation|
|take away |
However, some English words can sometimes be confusing as they may mean differently depending on the context.
Let’s look at the table below:
|English Word||Mathematical meaning||Example|
|more than||addition||What is 3 more than 2? This means, we 3 + 2.|
|inequality||9 is more than 3 – which means 9 > 3.|
|less than||subtraction||What is 12 less than 20? This question means we simply need to subtract 20 by 12. Hence, 20 – 12.|
|inequality||4 is less than 7 simply means 4 < 7.|
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