Helping With Math.com logo for mobile
Custom Search

Multi-Step Math Word Problems

Home > By Subject > Math Word Problems > Multi-Step Word Problems

In multi-step math word problems, one or more problems have to be solved in order to get the information needed to solve the question being asked. This lesson will provide help and guidance that will help solve these types of problems.

Read the tips and guidance and then work through the two multi-step word problems in this lesson with your children. Try the two worksheets that are listed within the lesson (you will also find them at the bottom of the page.)

Solving Multi-Step Word Problems

Word problems are fun and challenging to solve because they represent actual situations that happen in our world.

In any word problem, the true challenge is deciding which operation to use. In multi-step word problems, there may be two or more operations, and you must solve them in the correct order to be successful.

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.

Before rushing to solve the problem, it is worth your time to slow down and clarify your understanding. Be sure you know what is being asked, what you already know from the problem, and what you need to know in order to solve the question being asked.

Use a highlighter on written problems to identify words that tell you what you are solving, and give you clues about which operations to choose. Make notes in the margins by these words to help you clarify your understanding of the problem.

Multi-Step Word Problem: Example #1

Discuss with your children how one danger when solving this type of problem is stopping too soon – after answering only the first part of the problem.

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 have left to read?

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 have left to read?

260 pages tells you the total pages to be read.

35 pages is the amount read on Monday.

40 pages is the amount read on Tuesday.

How many pages does he have left to read? is the question you are being asked.

Most students recognize that they need to add together 35 + 40 to get the pages read so far. The danger is you might think you can stop there.

Adding 35 + 40 will tell you that Steven has read 75 pages so far, but if you go back to check the question you are being asked, you will see that your answer does not match what you are being asked. You will have to take another step to get there.

Steven has read 75 pages so far, but you are being asked what he has left to read, not what he has already read. To get your final answer, you must subtract what he has read from the total pages to be read:  260 75.  Steven has 185 pages left to read.

260 75 = 185

It’s important to clearly show that you understand what your answer means. Instead of just writing 185, write:

Steven has 185 pages left to read.

Whenever you finish a math problem of any kind, always go back to the original problem. Think: “What is the question I am being asked?”  Make sure that your final answer is a reasonable answer for the question you are being asked.

I was asked, “How many pages does he have left to read?” My answer is: Steven has 185 pages left to read.

My answer is reasonable because it tells how many pages Steven still needs to read. I added together 35 and 40 to find out the total pages he had already read, and subtracted from the total pages in the book. The number he has left should be less than the total in the book, since he’s already read some. 185 is smaller than 260. My answer makes sense.

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 (working with words). 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.

Multi-Step Word Problem: Example #2

You might find that this problem is more difficult that the one above.

A man bought a dozen boxes, each with 24 highlighter pens inside, for $8 each box. He repacked five of these boxes into packages of six highlighters each, and sold them for $3 per package. He sold the rest of the highlighters separately at the rate of three pens for $2. How much profit did he make?

  • A dozen boxes tells you he had 12 boxes.
  • Each with 24 tells you the number of highlighters in each box.
  • $8 each box tells you the amount he paid for all the highlighters.
  • Repacked five boxes into packages of six highlighters each separates 5 sets of 24 away from the original 12 sets of 24.
  • $3 per package is the selling price of the separated sets.
  • The rest is the 7 sets of 24 still left after separating away the 5 sets.
  • Three pens for $2 is the selling price of those 7 sets.

How much profit did he make? is ultimately the question you are being asked. Profit is the amount earned from all sales, minus the amount spent to buy the highlighters.

  • There are 12 boxes, and each cost the man $8 to buy. 12 x $8 is $96, so the man spent $96 to buy all the highlighters. 
  • He separated 5 boxes of 24 away from the original 12 boxes, and made new packages with six highlighters in each package. 5 x 24 = 120, so he repacked 120 highlighters in all.
  • 120 ÷ 6 = 20, so he had 20 new packages. He sold each for $3. 20 x $3 = $60, so he has earned $60 so far. 
  • He still had 7 of his original boxes of 24.  7 x 24 = 168, so he had 168 highlighters still to sell.
  • He sold them in sets of 3 for $2 each set. 168 ÷ 3 = 56 sets, and 56 x $2 = $112. He earned $112 from selling the 7 boxes.
  • Then we must add together the two amounts he earned. $60 plus $112 is $172, so he earned $172 from all his sales.

The danger is stopping here, because it took so long to get to this point, that it feels like the end. Don’t forget that the question asks you how much profit he earned. Profit is the amount earned minus the amount spent to buy the highlighters.

  • He spent $96 and earned $172, so $172 - $96 tells you his profit, $76.

It’s important to clearly show that you understand what your answer means.

Instead of just writing $76, write:

The man made $76 profit.

Remember, whenever you finish a math problem, always go back to the original problem. Think: “What is the question I am being asked?”  Make sure that your final answer is a reasonable answer for the question you are being asked.

I was asked, “How much profit did he make?” My answer is:  The man made $76 profit.

My answer is reasonable because it tells the man’s profit. I figured out the total he had spent, $96, and subtracted it from the total earned, $172. Profit should be smaller than money earned, since the cost of the highlighters has to be taken out. $76 is smaller than $172. My answer makes sense.

 

The first problem we did was relatively simple, while the second was much more complicated. All multi-step problems require you to slow down and think clearly.

Remember: you won’t know if your answer is reasonable if you don’t understand what you are being asked to solve. Take time to highlight and make notes before you solve the problem, and always go back to the original problem when you finish to make sure you really answered the question you were being asked.

Multi-Step Math Word Problem Worksheets

Click the links below and get your children to try the worksheets that will allow for practice with the multi-step word problems.

 

 

Help Wanted with survey

Please consider helping us with an online survey which is part of an academic research project. The survey should not take longer than 10 minutes. Learn more about it here.

Sign-up For Updates

Safesubscribe logo
Follow HelpingWithMath.com on TwitterVisit the HelpingWithMath.com Facebook Page