Download Article
Download Article
You can solve many real world problems with the help of math. In order to familiarize students with these kinds of problems, teachers include word problems in their math curriculum. However, word problems can present a real challenge if you don’t know how to break them down and find the numbers underneath the story. Solving word problems is an art of transforming the words and sentences into mathematical expressions and then applying conventional algebraic techniques to solve the problem.
-
1
Read the problem carefully.[1]
A common setback when trying to solve algebra word problems is assuming what the question is asking before you read the entire problem. In order to be successful in solving a word problem, you need to read the whole problem in order to assess what information is provided, and what information is missing.[2]
-
2
Determine what you are asked to find. In many problems, what you are asked to find is presented in the last sentence. This is not always true, however, so you need to read the entire problem carefully.[3]
Write down what you need to find, or else underline it in the problem, so that you do not forget what your final answer means.[4]
In an algebra word problem, you will likely be asked to find a certain value, or you may be asked to find an equation that represents a value.- For example, you might have the following problem: Jane went to a book shop and bought a book. While at the store Jane found a second interesting book and bought it for $80. The price of the second book was $10 less than three times the price of he first book. What was the price of the first book?
- In this problem, you are asked to find the price of the first book Jane purchased.
Advertisement
-
3
Summarize what you know, and what you need to know. Likely, the information you need to know is the same as what information you are asked to find. You also need to assess what information you already know. Again, underline or write out this information, so you can keep track of all the parts of the problem. For problems involving geometry, it is often helpful to draw a sketch at this point.[5]
- For example, you know that Jane bought two books. You know that the second book was $80. You also know that the second book cost $10 less than 3 times the price of the first book. You don’t know the price of the first book.
-
4
Assign variables to the unknown quantities. If you are being asked to find a certain value, you will likely only have one variable. If, however, you are asked to find an equation, you will likely have multiple variables. No matter how many variables you have, you should list each one, and indicate what they are equal to.[6]
-
5
Look for keywords.[7]
Word problems are full of keywords that give you clues about what operations to use. Locating and interpreting these keywords can help you translate the words into algebra.[8]
- Multiplication keywords include times, of, and factor.[9]
- Division keywords include per, out of, and percent.[10]
- Addition keywords include some, more, and together.[11]
- Subtraction keywords include difference, fewer, and decreased.[12]
- Multiplication keywords include times, of, and factor.[9]
Advertisement
-
1
Write an equation. Use the information you learn from the problem, including keywords, to write an algebraic description of the story.[13]
-
2
Solve an equation for one variable. If you have only one unknown in your word problem, isolate the variable in your equation and find which number it is equal to. Use the normal rules of algebra to isolate the variable. Remember that you need to keep the equation balanced. This means that whatever you do to one side of the equation, you must also do to the other side.[14]
-
3
Solve an equation with multiple variables. If you have more than one unknown in your word problem, you need to make sure you combine like terms to simplify your equation.
-
4
Interpret your answer. Look back to your list of variables and unknown information. This will remind you what you were trying to solve. Write a statement indicating what your answer means.[15]
Advertisement
-
1
Solve the following problem. This problem has more than one unknown value, so its equation will have multiple variables. This means you cannot solve for a specific numerical value of a variable. Instead, you will solve to find an equation that describes a variable.
- Robyn and Billy run a lemonade stand. They are giving all the money that they make to a cat shelter. They will combine their profits from selling lemonade with their tips. They sell cups of lemonade for 75 cents. Their mom and dad have agreed to double whatever amount they receive in tips. Write an equation that describes the amount of money Robyn and Billy will give to the shelter.
-
2
Read the problem carefully and determine what you are asked to find.[16]
You are asked to find how much money Robyn and Billy will give to the cat shelter. -
3
Summarize what you know, and what you need to know. You know that Robyn and Billy will make money from selling cups of lemonade and from getting tips. You know that they will sell each cup for 75 cents. You also know that their mom and dad will double the amount they make in tips. You don’t know how many cups of lemonade they sell, or how much tip money they get.
-
4
Assign variables to the unknown quantities. Since you have three unknowns, you will have three variables. Let
equal the amount of money they will give to the shelter. Let equal the number of cups they sell. Let equal the number of dollars they make in tips.
-
5
Look for keywords. Since they will “combine” their profits and tips, you know addition will be involved. Since their mom and dad will “double” their tips, you know you need to multiply their tips by a factor of 2.
-
6
Write an equation. Since you are writing an equation that describes the amount of money they will give to the shelter, the variable
will be alone on one side of the equation.
-
7
Interpret your answer. The variable
equals the amount of money Robyn and Billy will donate to the cat shelter. So, the amount they donate can be found by multiplying the number of cups of lemonade they sell by .75, and adding this product to the product of their tip money and 2.
Advertisement
Add New Question
-
Question
How do you solve an algebra word problem?
Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary’s College.
Academic Tutor
Expert Answer
Carefully read the problem and figure out what information you’re given and what that information should be used for. Once you know what you need to do with the values they’ve given you, the problem should be a lot easier to solve.
-
Question
If Deborah and Colin have $150 between them, and Deborah has $27 more than Colin, how much money does Deborah have?
Let x = Deborah’s money. Then (x — 27) = Colin’s money. That means that (x) + (x — 27) = 150. Combining terms: 2x — 27 = 150. Adding 27 to both sides: 2x = 177. So x = 88.50, and (x — 27) = 61.50. Deborah has $88.50, and Colin has $61.50, which together add up to $150.
-
Question
Karl is twice as old Bob. Nine years ago, Karl was three times as old as Bob. How old is each now?
Let x be Bob’s current age. Then Karl’s current age is 2x. Nine years ago Bob’s age was x-9, and Karl’s age was 2x-9. We’re told that nine years ago Karl’s age (2x-9) was three times Bob’s age (x-9). Therefore, 2x-9 = 3(x-9) = 3x-27. Subtract 2x from both sides, and add 27 to both sides: 18 = x. So Bob’s current age is 18, and Karl’s current age is 36, twice Bob’s current age. (Nine years ago Bob would have been 9, and Karl would have been 27, or three times Bob’s age then.)
See more answers
Ask a Question
200 characters left
Include your email address to get a message when this question is answered.
Submit
Advertisement
Video
-
Word problems can have more than one unknown and more the one variable.
-
The number of variables is always equal to the number of unknowns.
-
While solving word problems you should always read every sentence carefully and try to extract all the numerical information.
Show More Tips
Advertisement
References
About This Article
Article SummaryX
To solve word problems in algebra, start by reading the problem carefully and determining what you’re being asked to find. Next, summarize what information you know and what you need to know. Then, assign variables to the unknown quantities. For example, if you know that Jane bought 2 books, and the second book cost $80, which was $10 less than 3 times the price of the first book, assign x to the price of the 1st book. Use this information to write your equation, which is 80 = 3x — 10. To learn how to solve an equation with multiple variables, keep reading!
Did this summary help you?
Thanks to all authors for creating a page that has been read 56,462 times.
Reader Success Stories
-
James Carson
Sep 13, 2019
«I think this is amazing because it explains how and what you need to do.This helped me in algebra, and I recommend…» more
Did this article help you?
Solving Word Problems in Mathematics
What Is a Word Problem? (And How to Solve It!)
Learn what word problems are and how to solve them in 7 easy steps.
Real life math problems don’t usually look as simple as 3 + 5 = ?. Instead, things are a bit more complex. To show this, sometimes, math curriculum creators use word problems to help students see what happens in the real world. Word problems often show math happening in a more natural way in real life circumstances.
As a teacher, you can share some tips with your students to show that in everyday life they actually solve such problems all the time, and it’s not as scary as it may seem.
As you know, word problems can involve just about any operation: from addition to subtraction and division, or even multiple operations simultaneously.
If you’re a teacher, you may sometimes wonder how to teach students to solve word problems. It may be helpful to introduce some basic steps of working through a word problem in order to guide students’ experience. So, what steps do students need for solving a word problem in math?
Steps of Solving a Word Problem
To work through any word problem, students should do the following:
1. Read the problem: first, students should read through the problem once.
2. Highlight facts: then, students should read through the problem again and highlight or underline important facts such as numbers or words that indicate an operation.
3. Visualize the problem: drawing a picture or creating a diagram can be helpful.
Students can start visualizing simple or more complex problems by creating relevant images, from concrete (like drawings of putting away cookies from a jar) to more abstract (like tape diagrams). It can also help students clarify the operations they need to carry out. (next step!)
4. Determine the operation(s): next, students should determine the operation or operations they need to perform. Is it addition, subtraction, multiplication, division? What needs to be done?
Drawing the picture can be a big help in figuring this out. However, they can also look for the clues in the words such as:
– Addition: add, more, total, altogether, and, plus, combine, in all;
– Subtraction: fewer, than, take away, subtract, left, difference;
– Multiplication: times, twice, triple, in all, total, groups;
– Division: each, equal pieces, split, share, per, out of, average.
These key words may be very helpful when learning how to determine the operation students need to perform, but we should still pay attention to the fact that in the end it all depends on the context of the wording. The same word can have different meanings in different word problems.
Another way to determine the operation is to search for certain situations, Jennifer Findley suggests. She has a great resource that lists various situations you might find in the most common word problems and the explanation of which operation applies to each situation.
5. Make a math sentence: next, students should try to translate the word problem and drawings into a math or number sentence. This means students might write a sentence such as 3 + 8 =.
Here they should learn to identify the steps they need to perform first to solve the problem, whether it’s a simple or a complex sentence.
6. Solve the problem: then, students can solve the number sentence and determine the solution. For example, 3 + 8 = 11.
7. Check the answer: finally, students should check their work to make sure that the answer is correct.
These 7 steps will help students get closer to mastering the skill of solving word problems. Of course, they still need plenty of practice. So, make sure to create enough opportunities for that!
At Happy Numbers, we gradually include word problems throughout the curriculum to ensure math flexibility and application of skills. Check out how easy it is to learn how to solve word problems with our visual exercises!
Word problems can be introduced in Kindergarten and be used through all grades as an important part of an educational process connecting mathematics to real life experience.
Happy Numbers introduces young students to the first math symbols by first building conceptual understanding of the operation through simple yet engaging visuals and key words. Once they understand the connection between these keywords and the actions they represent, they begin to substitute them with math symbols and translate word problems into number sentences. In this way, students gradually advance to the more abstract representations of these concepts.
For example, during the first steps, simple wording and animation help students realize what action the problem represents and find the connection between these actions and key words like “take away” and “left” that may signal them.
From the beginning, visualization helps the youngest students to understand the concepts of addition, subtraction, and even more complex operations. Even if they don’t draw the representations by themselves yet, students learn the connection between operations they need to perform in the problem and the real-world process this problem describes.
Next, students organize data from the word problem and pictures into a number sentence. To diversify the activity, you can ask students to match a word problem with the number sentence it represents.
Solving measurement problems is also a good way of mastering practical math skills. This is an example where students can see that math problems are closely related to real-world situations. Happy Numbers applies this by introducing more complicated forms of word problems as we help students advance to the next skill. By solving measurement word problems, students upgrade their vocabulary, learning such new terms as “difference” and “sum,” and continue mastering the connection between math operations and their word problem representations.
Later, students move to the next step, in which they learn how to create drawings and diagrams by themselves. They start by distributing light bulbs equally into boxes, which helps them to understand basic properties of division and multiplication. Eventually, with the help of Dino, they master tape diagrams!
To see the full exercise, follow this link.
The importance of working with diagrams and models becomes even more apparent when students move to more complex word problems. Pictorial representations help students master conceptual understanding by representing a challenging multi-step word problem in a visually simple and logical form. The ability to interact with a model helps students better understand logical patterns and motivates them to complete the task.
Having mentioned complex word problems, we have to show some of the examples that Happy Numbers uses in its curriculum. As the last step of mastering word problems, it is not the least important part of the journey. It’s crucial for students to learn how to solve the most challenging math problems without being intimidated by them. This only happens when their logical and algorithmic thinking skills are mastered perfectly, so they easily start talking in “math” language.
These are the common steps that may help students overcome initial feelings of anxiety and fear of difficulty of the task they are given. Together with a teacher, they can master these foundational skills and build their confidence toward solving word problems. And Happy Numbers can facilitate this growth, providing varieties of engaging exercises and challenging word problems!
Math word problems can be painful. And not just in the “I’m emotionally tired” kind of painful. We’re talking about the “my head hurts, I’m exhausted, that took too much work, I don’t know what’s next, I’m emotionally tired” kind of painful.
And it’s not as if somehow when you’re studying you can avoid math word problems. You can’t. They’ll always be there. And you always have to learn math in school.
Don’t let math word problems give you a headache. Use these simple steps to solve every math word problem with ease (well – as much ease as you can have when solving math problems. We get it – it’s never totally easy. It’s math…).
1. Get acquainted with the math word problem
There is an interesting difference between math word problems and simply solving an equation: math word problems don’t give you the equation.
Instead, they give you headaches. So much of math is about solving equations properly. If you don’t have the equation, it’s hard to solve it.
That means you have a few steps before you can actually solve your math word problem. But before we try to break it down, it’s best to just try to figure out what this problem is about – generally speaking. Just get to know the problem. Read through it once or twice. You don’t have to figure everything out at this point – just give the problem a nice handshake. You won’t solve it until you are at least familiar with the situation.
2. Answer 3 questions about the specific math word problem:
After you know a bit about the problem before you, we’re going to ask three questions about it. You can ask these three questions of any word problem, in any type of math. It’s a simple process, but it will break down all the important elements of any math problem.
a) For what am I looking?
This is the biggest question. It shapes your entire time answering the question. Take the following situation for example:
A plane leaves Toronto, Ontario (Canada), heads to Newark, New Jersey, and then heads to Seattle, Washington. Along the way to Seattle, a storm forces the plane to head north in order to get around it. The plane ends up crossing the Canadian border, but then has some engine trouble. When the plane is at 30,000 feet, an engine fails, and the plane has to attempt an emergency landing. Unfortunately, the plane crashes… and it does so directly on the Canada-United States border. Where will they bury the survivors?
We’ll let you think about that question for a few minutes. You can see the answer at the bottom of this post if you’re curious. But I recommend rechecking the most important detail before you guess: “For what I am looking?”
Don’t get lost in details. Get the question right before anything else. You must know what your math word problem is asking.
If you don’t know what you are looking for, you’ll end up missing it every time.
b) What do I need in order to find the answer?
After you know what you’re being asked, you can then think about what it will take to get that answered. You should have some idea at this point of the equation that will be needed to find a solution.
Specifically, we’re talking about equations here and the most important variables.
If you know what you are looking for and you can then name the pieces you need to find, even the most difficult problems become extremely manageable.
For a simple example, let’s say you’ve been given a question and you realize you are being asked how tall a ladder you’ll need to paint a wall (I know, weird problem – but just go with it).
After discovering what’s being asked of you – the length of the ladder – you realize that the Pythagorean Theorem is what you’ll need to solve it. This means our final question needed to solve this math word problem will be super easy.
c) What do I already have?
You know the question. You know what you need in order to solve it. Now you can simply fill in the equation with what you have already been given.
Don’t get lost in unimportant details. Math word problems are notorious for giving you too many details. That’s why this step is the last of the three questions.
Some students try to figure out what all they have first. They read the problem, write out all the details they have been given, and then expect to solve it from there. Instead, they often experience detail-overload.
But you will save yourself an enormous amount of time if you know you are looking to answer first. Knowing the question is more important than knowing what details you have. Only when you know the question you are answering and what you need in order to answer it can you then find the right details to answer it correctly.
3. Plug and chug
You can probably guess this step. You know the right question. You know the right equation. You’ve found the needed details.
Plug and chug. Simply enter your values into your equation, and crank out the right answer by solving the problem.
Don’t forget to label you answer, too! If you know what you’re looking for, your answer should be in the right units. But it’s always wise to double check.
Let us know what you think! Is this how you solve math word problems?
(Looking for the answer to the Canada-United States question? Well, the answer is nowhere. You don’t bury survivors)
function gtag(){dataLayer.push(arguments);}
gtag(‘js’, new Date());
gtag(‘config’, ‘UA-1492395-8’);
Skip to content
- Home
- Blog
- Free Resources
- Courses
- TpT Shop
-
View Larger Image
5 Strategies to Learn to Solve Math Word Problems
A critical step in math fluency is the ability to solve math word problems. The funny thing about solving math word problems is that it isn’t just about math. Students need to have strong reading skills as well as the growth mindset needed for problem-solving. Strong problem solving skills need to be taught as well. In this article, let’s go over some strategies to help students improve their math problem solving skills when it comes to math word problems. These skills are great for students of all levels but especially important for students that struggle with math anxiety or students with animosity toward math.
Signs of Students Struggling with Math Word Problems
It is important to look at the root cause of what is causing the student to struggle with math problems. If you are in a tutoring situation, you can check your students reading level to see if that is contributing to the issue. You can also support the student in understanding math keywords and key phrases that they might need unpacked. Next, students might need to slow their thinking down and be taught to tackle the word problem bit by bit.
How to Help Students Solve Math Word Problems
Focus on Math Keywords and Mathematical Key Phrases
The first step in helping students with math word problems is focusing on keywords and phrases. For example, the words combined or increased by can mean addition. If you teach keywords and phrases they should watch out for students will gain the cues needed to go about solving a word problem. It might be a good idea to have them underline or highlight these words.
Cross out Extra Information
Along with highlighting important keywords students should also try to decipher the important from unimportant information. To help emphasize what is important in the problem, ask your students to cross out the unimportant distracting information. This way, it will allow them to focus on what they can use to solve the problem.
Encourage Asking Questions
As you give them time to read, allow them to have time to ask questions on what they just read. Asking questions will help them understand what to focus on and what to ignore. Once they get through that, they can figure out the right math questions and add another item under their problem-solving strategies.
Draw the Problem
A fun way to help your students understand the problem is through letting them draw it on graph paper. For example, if a math problem asks a student to count the number of fruits that Farmer John has, ask them to draw each fruit while counting them. This is a great strategy for visual learners.
Check Back Once They Answer
Once they figured out the answer to the math problem, ask them to recheck their answer. Checking their answer is a good habit for learning and one that should be encouraged but students need to be taught how to check their answer. So the first step would be to review the word problem to make sure that they are solving the correct problem. Then to make sure that they set it up right. This is important because sometimes students will check their equation but will not reread the word problem and make sure that the equation is set up right. So always have them do this first! Once students believe that they have read and set up the correct equation, they should be taught to check their work and redo the problem, I also like to teach them to use the opposite to double check, for example if their equation is 2+3=5, I will show them how to take 5 which is the whole and check their work backwards 5-3 and that should equal 2. This is an important step and solidifies mathematical thinking in children.
Mnemonic Devices
Mnemonic devices are a great way to remember all of the types of math strategy in this post. The following are ones that I have heard of and wanted to share:
CUBES Word Problem Strategy
Cubes is a mnemonic to remember the following steps in solving math word problems:
C: Circle the numbers
U: Underline the question
B: Box in the key words
E: Eliminate the information
S: Solve the problem & show your work
RISE Word Problem Strategy
Rise is another way to explain the steps needed to solve problems:
R: Read and reread
I: Illustrate what is being asked
S: Solve by writing your equation or number sentences
E: Explain your thinking
COINS Word Problem Strategy
C: Comprehend the questions
O: Observe the data
I: Illustrate the problem
N: Write the number sentence (equation)
S: Solve
Understand -Plan – Solve – Check Word Problem Strategy
This is a simple step solution to show students the big picture. I think this along with one of the mnemonic devices helps students with better understanding of the approach.
Understand: What is the question asking? Do you understand all the words?
Plan: What would be a reasonable answer? In this stage students are formulating their approach to the word problem.
Solve: What strategies will I use to solve this problem? Am I showing my thinking? Here students use the strategies outlined in this post to attack the problem.
Check: Students will ask themselves if they answered the question and if their answer makes sense.
If you need word problems to use with your classroom, you can check out my word problems resource below.
Teaching students how to approach and solve math word problems is an important skill. Solving word problems is the closest math skill that resembles math in the real world. Encouraging students to slow their thinking, examine and analyze the word problem and encourage the habit of answer checking will give your students the learning skills that can be applied not only to math but to all learning. I also wrote a blog post on a specific type of math word problem called cognitively guided instruction you can read information on that too. It is just a different way that math problems are written and worth understanding to teach problem solving, click here to read.
Selma2021-10-13T10:24:53+00:00
Share This Story, Choose Your Platform!
Related Posts
Page load link
Ok
Math word problems can be tricky and often challenging to solve. Employing the SQRQCQ method can make solving math word problems easier and less intimidating. The SQRQCQ method is particularly useful for children with learning disabilities and can be used effectively in special education programs. SQRQCQ is an abbreviation for Survey, Question, Read, Question, Compute, and Question.
Step 1 — SURVEY the Math Problem
The first step to solving a math word problem is to read the problem in its entirety to understand what you are being asked to solve. After you read it, you can decide the most relevant aspects of the problem that need to be solved and what aspects are not relevant to solving the problem. The idea here is to get a general understanding.
Step 2 — QUESTION
Once you have an idea of what you’re attempting to solve, you need to determine what formulas, steps, or equations should be utilized in order to find the correct answer. It is impossible to find an answer if you can’t determine what needs to be solved. Basically, what are the questions being asked by the problem?
Step 3 — REREAD
Now that you’ve determined what needs to be solved, reread the problem and pay close attention to specific details. Determine which aspects of the problem are interrelated. Identify all relevant facts and information needed to solve the problem. As you do, write them down.
Step 4 — QUESTION
Now that you’re familiar with specific details and how different facts and information within the problem are interrelated, determine what formulas or equations must be used to set up and solve the problem. Be sure to write down what steps or operations you will use for easy reference.
Step 5 — COMPUTE
Use the formulas and/or equations identified in the previous step to complete the calculations. Be sure to follow the steps you outlined while setting up an equation or using a formula. As you complete each step, check it off your list.
Step 6 — QUESTION
Once you’ve completed the calculations, review the final answer and make sure it is correct and accurate. If it does not appear logical, review the steps you took to find the answer and look for calculation or set-up errors. Recalculate the numbers or make other changes until you get an answer that makes sense.
How does SQRQCQ help students with learning disabilities?
Math word problems tend to be especially challenging for Learning Disabled (LD) students. LD students often lack «Concept Imagery», or the ability to visualize the whole problem by creating a complete mental image. They often jump right into calculations and computations without understanding what the problem is asking or what they’re looking for.
LD students may also struggle to understand the words or wording within math word problems correctly. The inability to correctly interpret and understand wording greatly impacts their math reasoning skills and often leads them to making the wrong calculations and arriving incorrect conclusions.
Remembering and manipulating information and details in their working memory is another challenge some LD students face as they try to see the whole picture. Slow processing of information, followed by frustration and anxiety, will often lead LD students to try and get through math word problems as quickly as possible – which is why they often jump straight into computations in their attempt to make it to the finish line as quickly as possible.
SQRQCQ is a metacognitive guide that provides LD students with a logical order for solving math word problems. It provides just enough direction to guide them through the reasoning process without overwhelming them. SQRQCQ is also a mnemonic that is easy for students to remember and which they can fall back on when completing homework or taking tests.
Read also:
— A Guide for Studying Math
Does your child fear math word problems? He or she is not alone. When words take over, it seems like all logic goes out the window. Do not fear, there is a process. Using some simple steps, your child will master how to translate words into numbers, and easily solve those equations.
Solving a math word problem involves four steps:
1. Read through the question and set up a word equation (we’ll show you how in a minute).
2. Put numbers in place of the words to set up a regular math equation.
3. Now, solve the math equations.
4. Focus on answering the problem the question asks.
The easiest way to show this process is in a few examples. The most important part is not to try to get to the answer too fast, but rather to write down each piece of information. One solution will leads to another, and then another.
Example 1: addition and subtraction
John has four fewer pieces of candy than Bob. Bob has 18 candies. How many candies do John and Bob have together?
1. So let’s start: the initial step of the word problem is a fact finding mission.
From reading the problem, we know the following:
Bob = 18 (candies)
John + 4 = Bob
2. Put the numbers in in place of the words.
Bob = 18 – 4 = ?
3. Solve the math equation.
Bob = 18 – 4 = 14
4. Focus on answering the problem.
The problems wants to know how many candies the two boys have together.
You need to know:
John + Bob = ?
John 14 + Bob 18 = ?
14 + 18 = 32
John and Bob have 32 candy pieces.
Example 2: multiplication and division
Here’s an example that involves multiplication and division:
The height of a house is half as long as its width, and the width of the house is 80 feet. How tall is the house?
From the word equation, you know the following:
Width = 80
Height = Width ÷ 2
Plug in numbers for the words:
Height = Width 80 ÷ 2 = 40
The height of the house is 40 feet.
Example 3: multiple equations
Sometimes the word problem requires setting up more than one equation.
The express train is moving three times faster than the local train. If the local train is going 25 miles per hour, what’s the difference in speed between the express train and the local train?
Here are the facts:
Local = 25
Express = 3 x Local
Plug in the information you need:
Express = 3 x 25 Local = 75
However, the question asks you to find the difference in speed between the express train and the local train. Finding the difference between two numbers is subtraction:
Express – Local = ?
Plug in the information you’ve already found:
Express 75 – Local 25 = 50
The difference in speed between the express train and the local train is 50 miles per hour.
K5 offers free math word problem worksheets for grade 1 – 5. Go to our math worksheet pages, click on your grade, and then on the word problems link. Here’s the link to our grade 3 math word problems worksheets.
Become a Member
This content is available to members only.
Join K5 to save time, skip ads and access more content.
Learn More
The techniques and methods we apply to solve word problems in math will vary from problem to problem.
The techniques and methods we apply to solve a word problem in a particular topic in math will not work for another word problem found in some other topic.
For example, the methods we apply to solve the word problems in algebra will not work for the word problems in trigonometry.
Because, in algebra, we will solve most of the problems without any diagram. But, in trigonometry, for each word problem, we have to draw a diagram. Without diagram, always it is bit difficult to solve word problems in trigonometry.
Even though we have different techniques to solve word problems in different topics of math, let us see the steps which are most commonly used.
The following steps would be useful to solve word problems in Mathematics.
Step 1 :
Understanding the question is more important than any other thing. That is, always it is very important to understand the information given in the question rather than solving.
Step 2 :
If it is possible, we have to split the given information. Because, when we split the given information in to parts, we can understand them easily.
Step 3 :
Once we understand the given information clearly, solving the word problem would not be a challenging work.
Step 4 :
When we try to solve the word problems, we have to introduce «x» or «y» or some other alphabet for unknown value (=answer for our question). Finally we have to get value for the alphabet which was introduced for the unknown value.
Step 5 :
If it is required, we have to draw picture for the given information. Drawing picture for the given information will give us a clear understanding about the question.
Step 6 :
Using the alphabet introduced for unknown value, we have to translate the English statement (information) given in the question as mathematical equation.
In translation, we have to translate the following English words as the corresponding mathematical symbols.
of —-> x (multiplication)
am, is, are, was, were, will be, would be —-> = (equal)
Step 7 :
Once we have translated the English Statement (information) given in the question as mathematical equation correctly, 90% of the work will be over. The remaining 10% is just getting the answer. That is solving for the unknown.
Example :
The age of a man is three times the sum of the ages of his two sons and 5 years hence his age will be double the sum of their ages. Find the present age of the man.
Answer :
Step 1 :
Let us understand the given information. There are two information given in the question.
1. The age of a man is three times the sum of the ages of his two sons. (At present)
2. After 5 years, his age would be double the sum of their ages. (After 5 years)
Step 2 :
Target of the question :
Present age of the man = ?
Step 3 :
Introduce required variables for the information given in the question.
Let x be the present age of the man.
Let y be the sum of present ages of two sons.
Clearly, the value of x to be found.
Because that is the target of the question.
Step 4 :
Translate the given information as mathematical equation using x and y.
First information :
The age of a man is three times the sum of the ages of his two sons.
Translation :
The Age of a man —-> x
is —-> =
Three times sum of the ages of his two sons —-> 3y
Equation related to the first information using x and y is
x = 3y —-(1)
Second Information :
After 5 years, his age would be double the sum of their ages.
Translation :
Age of the man after 5 years —-> (x + 5)
Sum of the ages of his two sons after 5 years is
y + 5 + 5 = y + 10
(Because there are two sons, 5 is added twice)
Double the sum of ages of two sons —-> 2(y + 10)
would be —-> =
Equations related to the second information using x and y is
x + 5 = 2(y + 10) —-(2)
Step 5 :
Solve equations (1) & (2).
From (1), substitute 3y for x in (2).
3y + 5 = 2(y + 10)
3y + 5 = 2y + 20
y = 15
Substitute 15 for y in (1).
x = 3(15)
x = 45
So, the present age of the man is 45 years.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Last Updated on May 31, 2022 by Thinkster
When I was a middle school teacher, I used to ask my students how their other classes were going and what they had learned that day. On the days they shared that their math lesson focused on word problems, the accompanying grumbles and groans were clear indicators that they were far from happy with that day’s lesson.
I used to wonder what it was that really irked my students about word problems. After all, the same students that grumbled and groaned were the ones that used procedural, analytical, and thinking skills in science, language arts, and social studies.
Not only did they use these skills in other classes, but many of these students used these skills incredibly well and successfully!
If my own students could easily write a response on the effects of colonialism in Latin America, something that requires them to use strong thinking skills, then why did they struggle to use similar thinking skills with math word problems? Or worse, why did they think it was hard to solve math word problems?
The trouble is that many students typically associate math with computational problems and ‘quick facts’. Some hold onto a perception that analytical and critical thinking skills should be saved for essays or lab reports.
This is definitely not the case!
A strong math curriculum emphasizes developing analytical and conceptual thinking skills in students. These types of math problems require students to carefully plan, solve, and then check their work.
Students want to quickly work through their math problems, which often means that they make careless mistakes or struggle to understand what the problem is asking them to solve.
This can lead to massive frustration and why many students vehemently vocalize that they, “hate math word problems”.
There are two ways to combat this animosity and boost confidence when tackling math word problems. One, by ensuring your child knows different strategies and problem-solving tricks. Two, by having them practice different types of word problems frequently.
Thinkster Math tutors work with many students who struggle with math word problems. Together, we’ve compiled a list of our favorite tips and practice questions that you can use with your child.
Have your child organize their thinking
Before your child jumps in to try and solve a math word problem, they need to plan. This is often the step that students try and skip because they’re eager to finish their work quickly.
Not taking the time to carefully plan and dissect a word problem, though, can have your child feeling flustered when trying to solve it.
The planning process is incredibly important. It’s why authors take the time to outline and develop a plot before jumping in and writing a two hundred page novel. Planning allows for clarity and cohesive thoughts to develop.
This same planning process applies to math word problems.
As a first step, have your child identify what the problem is asking them to solve. Then, they should identify keywords and important details that are required to solve the problem. They can use highlighters, colored pencils, or even just a pen to underline or circle important information.
Identifying and understanding keywords and the order of operations in a word problem is a critical step!
Some kids also get confused by the different keywords and phrases used in word problems. In fact, some phrases might even have two meanings!
For example, using the words “increases by” could require using either addition or multiplication to solve the problem:
“There are 10 apples in a basket. The number of apples in the basket increases by 15. How many apples are there in all?”
“Johnny expects to pay $20 for his food, but the total bill increases by 7% because of tax. How much does Johnny need to pay?”
In the first word problem, your child simply adds 10 and 15 to get the answer. The second word problem requires multiplying $20 by 0.07, then adding that amount to $20.
These are two problems that use the same keyword, but require very different steps for solving!
This is why it’s great to practice keyword recognition with your child, and you can make flashcards for extra practice. For more helpful examples of keywords that your child should be able to identify, check out this link.
Encouraging your child to take the time to plan and organize their thinking by dissecting word problems helps them identify the details and operations required to solve. Finding this information helps your child as they start the next step of visualizing and illustrating the problem.
Solving math word problems with pictures
After your child identifies keywords within problems, the next step is to plan. There are many different types of strategies that your child can use. Creating illustrations, graphs, and diagrams are the most popular.
This is because many students are visual learners and benefit from using illustrations to help solve word problems. In fact, visual learners make up 65% of the students in a classroom.
Some math problems come with pictures or images for your child to refer to. For example:
This helps students learn and understand ways that they can organize their thinking to solve word problems.
Students also work with many word problems that do not come with any visuals or diagrams. This is why it’s a great idea to encourage your child to create their own images to help!
Here’s an example of how to use illustration to plan and solve a word problem:
There are 12 hens in a coop. Each hen lays 4 eggs a week. At the end of the week, Simon equally distributes and packs the eggs into 6 boxes. How many eggs are there in each box?
To solve this problem, your child will need to first calculate how many total eggs there are. Once they calculate 48 eggs (12 hens x 4 eggs each), they need to take this amount and divide it among 6 boxes. Your child can draw six boxes, then draw eggs into the boxes to visually represent how many eggs there are in each box.
Your child will develop strong problem-solving strategies as they grow accustomed to using charts and illustrations. This is also something that will help them as they tackle problems that involve patterns.
Solving math word problems with patterns
Another type of word problem that students encounter are problems with patterns.
For some students, these types of problems may seem difficult at first, especially if they are not taking the time to organize their thinking. But those that do take the time to use charts and visuals will find that there really is nothing to fear with pattern word problems!
Let’s try the following problem:
A bakery sells a different number of cakes each month. In March they sell 3 cakes, in April they sell 9 cakes, and in May they sell 27 cakes. If this pattern continues, how many cakes will they sell in July?
It’s not easy to try and figure out the answer mentally! This is why creating a chart helps students organize their thinking to reach the correct answer.
Once this information is displayed carefully, your child should be able to spot that they actually need to do two calculations. The word problem requires them to determine the number of cakes sold in July, but they can’t reach the answer without first determining how many cakes are sold in June.
Taking the time to carefully organize the data ensures that they do not miss this important step!
Here is another pattern word problem that you can have your child try to solve:
Robert adds chlorine tablets to a swimming pool every day to help keep it clean as more people come over to swim. On Monday he adds 3 tablets, on Tuesday he adds 5 tablets and on Wednesday he adds 7 tablets. If the pattern continues, how many chlorine tablets does he add on Thursday?
As your child solves the problem, make sure they underline keywords and important details, then organize their thinking with a chart! This is a great way to make sure they slow down when approaching the problem to minimize the risk of careless mistakes.
Solving math word problems with distractors
For students that try to sprint through solving word problems, distractors are often the reason they trip.
Which, quite honestly, is one of the reasons distractors are often thrown into word problems! They are meant to keep students on their toes and to ensure they are carefully reading what the problem is asking.
Distractors are words and information that are included in a problem, but really have nothing to do with it. It’s unnecessary information that students are expected to navigate around.
Thinkster Math CEO Raj Valli shares more on having students think on their feet with word problems that include distractors:
One tip that Thinkster tutors share with parents is to work on characterizing information and variables.
In the above video example, the problem requires students to determine how many fruits are in a basket. Characterizing all items in the basket and distinguishing between fruits and vegetables will ensure your child isn’t carelessly adding carrots into the final answer.
Here’s another example of a problem with a distractor that requires characterization:
A used car dealership has 91 cars and 29 trucks on the lot. Each day the dealership sells 13 cars. How many days would it take for all the cars to be sold?
A student that is rushing through the problem may add 91 and 29, then divide that amount by 13.
A student that takes the time to carefully dissect the problem will identify that there is a distractor.
As mentioned earlier, the first step is to understand what the word problem is answering. In this problem, your child needs to determine the number of days it takes to sell all cars at a dealership. By carefully characterizing the information, your child identifies that ‘29 trucks’ is information not needed to solve the problem.
Here is another word problem that you can have your child try solving:
Laura has invited 42 friends to her birthday. 18 friends are boys and 24 friends are girls. If she wants to give out 3 headbands to each of the girls, how many headbands will she have to buy?
Is your child able to pick out that “18 boys” is information not needed to solve the problem?
Having your child practice problems with distractors helps them spot this more quickly!
Get word problem practice and math help from an online math tutor
Along with following our tips and recommendations, one of the best ways for your child to grow more comfortable with solving word problems is by practicing.
A combination of exposure to different types of word problems along with frequent practice will help shift your child’s mentality when they tackle word problems. They should reach a point where they are no longer struggling, and instead have strong confidence when presented with a problem to solve.
While you can take the time to create your own word problems, there are online and digital tutoring programs, like Thinkster Math, that ensure your child is exposed to many different types of logical reasoning and critical thinking problems.
Thinkster Math’s world-class curriculum is packed with word problems!
We begin introducing word problems in our first-grade curriculum, which is on par with when students begin learning word problems in school. Introducing word problems at a young age ensures your child is developing strong problem-solving skills.
Thinkster also includes many real-world examples. Anchoring to real situations helps students understand and appreciate why they are solving word problems. It can also help them visualize what the problem is by asking them to solve it more easily.
Conclusion
Whether your child is grumbling and groaning about word problems at school or at home, it’s time to squash any frustration and animosity toward math word problems!
There are a few things that you can do at home to help your child grow more comfortable with word problems. Have them organize their thinking by marking problems with highlighters and work on keyword recognition.
It’s important to also have your child try different types of word problems so that they feel more prepared and ready to tackle what they’ll be learning in school! Try problems with and without visuals, patterns, and distractors to give them balanced preparation.
And remember, daily practice with a program like Thinkster Math can help! The combination of practice, video tutorials, and customized feedback can have your child become more confident in their ability to use using problem-solving strategies, and you will see incredible learning improvements in less than three months.
You can explore our curriculum and try more sample problems similar to the ones shared in this blog.
If you’re looking for to help your child, you can try Thinkster risk-free.
Thinkster provides a full-fledged platform (driven by AI, behavioral, and data science), as well as supplemental , help, , and more. Our Parent Insights App allows you to monitor your ‘s work and improvements at any time.
An elite, and system work together to help your go beyond just – we want them to master it.
Learn more about our curriculum and teaching style here.