Made up word problems

Math word problems can be a challenge for young learners. It’s particularly daunting for students who are struggling with reading comprehension or learning English as a second language. One way to level the playing field is to teach word problems visually. All of the common word problem types, such as part-part-whole, comparison, joining, separating, multiplication and division, can be expressed with simple but effective images that illustrate the numerical relationships within the word problems.

various Thinking Blocks models

solving a multistep word problem

To overcome the limitations of the measuring blocks, I developed a system of virtual blocks that could be used to model almost any math word problem. These “thinking blocks” provided a powerful way to organize information and simplify problem solving. Thinking Blocks not only revealed what was to be solved, it illuminated the process as well. That was its superpower. Since then, Thinking Blocks has become a transformative math tool, teaching millions of students around the world how to model and solve word problems.

a three step approach

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Dynamically Created Word Problems

Here is a graphic preview for all of the word problems worksheets. You can select different variables to customize these word problems worksheets for your needs. The word problems worksheets are randomly created and will never repeat so you have an endless supply of quality word problems worksheets to use in the classroom or at home. Our word problems worksheets are free to download, easy to use, and very flexible.

These word problems worksheets are a great resource for children in 3rd Grade, 4th Grade, and 5th Grade.

Click here for a Detailed Description of all the Word Problems Worksheets.

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Words to Symbols Word Problems	Addition Word Problems Using 1 Digit with 2 Addends	Addition Word Problems Using 2 Digit with 2 Addends
Addition Word Problems Using 1 Digit with 3 Addends	Addition Word Problems Using 2 Digit with 3 Addends	Addition Word Problems 2 Digit Missing Addends
Subtraction Word Problems Using 1 Digit	Subtraction Word Problems Using 2 Digits	Addition and Subtraction Word Problems Using 1 Digit
Addition and Subtraction Word Problems Using 2 Digits	Addition and Subtraction Word Problems 2 Digits With No Regrouping	Addition and Subtraction Word Problems Using 3 Digits
Multi-Step Problems Addition and Subtraction	Multiplication Word Problems Using 1 Digit	Multiplication Word Problems Using Dozens
Multiplication Word Problems Using 2 Digits	Division Word Problems Using 1 Digit in Divisor	Division Word Problems Using Dozens in Divisor
Division Word Problems Using Multiple Digits in Divisor	Division Word Problems Dividing with Fractions	Multiplication and Division Word Problems Using 1 Digit
Mixed Operations Problems Using 1 or 2 Digits	One Step Equation Word Problems	Two Step Equation Word Problems
Multi-Step All Operations Word Problems	Fractions Word Problems Adding Two Fractions	Fractions Word Problems Adding Three Fractions
Fractions Word Problems Subtracting Fractions	Fractions Word Problems Adding Two Mixed Numbers	Fractions Word Problems Subtracting Two Mixed Numbers
U. S. Coins Word Problems Adding Coins Worksheets	Advanced Adding U. S. Coins Word Problems	U. S. Money Word Problems Adding Two Purchases
U. S. Money Word Problems Adding Three Purchases	U. S. Money Word Problems Change from a Purchase	Travel Time Word Problems
Reading a Calendar Word Problems	Elapsed Dates Word Problems	Ratios and Rate Word Problems
Percentage Word Problems	Mixed Operations with Key Phrases Word Problems	U.S. Money Change from a Purchase Multiplication Word Problems

Detailed Description for All Word Problems Worksheets

Words to Symbols Handout
This Word Problems Worksheet will produce a great handout to help students learn the symbols for different words and phrases in word problems.

Addition Word Problems Worksheets Using 1 Digit with 2 Addends
These addition word problems worksheets will produce 1 digit problems with two addends, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Addition Word Problems Worksheets Using 2 Digits with 2 Addends
These addition word problems worksheets will produce 2 digits problems with two addends, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Addition Word Problems Worksheets Using 1 Digit with 3 Addends
These addition word problems worksheets will produce 1 digit problems with three addends, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Addition Word Problems Worksheets Using 2 Digits with 3 Addends
These addition word problems worksheets will produce 2 digits problems with three addends, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Addition Word Problems Worksheets 2 Digits Missing Addends
These addition word problems worksheet will produce 2 digits problems with missing addends, with ten problems per worksheet. You may select between regrouping and non-regrouping type of problems. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Subtraction Word Problems Worksheets Using 1 Digit
These subtraction word problems worksheets will produce 1 digit problems, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Subtraction Word Problems Worksheets Using 2 Digits
These subtraction word problems worksheets will produce 2 digits problems, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Addition and Subtraction Word Problems Worksheets Using 1 Digit
These addition and subtraction word problems worksheets will produce 1 digit problems, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Addition and Subtraction Word Problems Worksheets Using 2 Digits
These addition and subtraction word problems worksheets will produce 2 digits problems, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Addition and Subtraction Word Problems Worksheets 2 Digits With No Regrouping
These addition and subtraction word problems worksheets will produce 2 digits problems with no regrouping and ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Addition and Subtraction Word Problems Worksheets Using 3 Digits
These addition and subtraction word problems worksheets will produce 3 digits problems, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Multi-Step Problems Addition and Subtraction
These multi-step addition and subtraction word problems worksheets will produce 10 problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Multiplication Word Problems Worksheets Using 1 Digit
These multiplication word problems worksheets will produce 1 digit problems, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Multiplication Word Problems Worksheets Using Dozens
These multiplication word problems worksheets will produce problems using dozens, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Multiplication Word Problems Worksheets Using 2 Digits
These multiplication word problems worksheets will produce 2 digits problems, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Division Word Problems Worksheets Using 1 Digit in Divisor
These division word problems worksheets will produce 1 digit divisor problems, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Division Word Problems Worksheets Using Dozens in Divisor
These division word problems worksheets will produce problems using dozens in the divisor, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Division Word Problems Worksheets Using Multiple Digits in Divisor
These division word problems worksheets will produce multiple digits in the divisor for the problems, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Dividing with Fractions Worksheets
These division Word Problems Worksheets will produce problems that focus on division with fractions. You have the option to select the range of denominators, as well as the types of fractions displayed. These word problems worksheets are appropriate for 4th Grade, 5th Grade, and 6th Grade.

Multiplication and Division Problems Using 1 Digit
These multiplication and division word problems worksheets will produce 1 digit problems, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Mixed Operations Word Problems Using 1 or 2 Digits
These mixed operations word problems worksheets will produce addition, multiplication, subtraction and division problems with 1 or 2 digit numbers. These word problems worksheets will produce ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

One Step Equation Word Problems
These equations worksheets will produce one step word problems. These worksheets will produce ten problems per worksheet. These word problems worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Two Step Equation Word Problems
These equations worksheets will produce two step word problems. These worksheets will produce ten problems per worksheet. These word problems worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Multi-Step All Operations Word Problems
These Word Problems worksheets will produce word problems involving all basic operations. You may choose the format of the answers. These word problems worksheets will produce ten problems per worksheet. These word problems worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Adding Two Fractions Word Problems
These fractions word problems worksheets will produce problems with the addition of two fractions. These word problems worksheets will produce ten problems per worksheet. These word problems worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Adding Three Fractions Word Problems
These fractions word problems worksheets will produce problems with the addition of three fractions. These word problems worksheets will produce ten problems per worksheet. These word problems worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Subtracting Fractions Word Problems
These fractions word problems worksheets will produce problems involving subtracting two fractions. These word problems worksheets will produce ten problems per worksheet. These word problems worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Adding Two Mixed Numbers Word Problems
These fractions word problems worksheets will produce problems involving adding two mixed numbers. These word problems worksheets will produce ten problems per worksheet. These word problems worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Subtracting Two Mixed Numbers Word Problems
These fractions word problems worksheets will produce problems involving subtracting two mixed numbers. These word problems worksheets will produce ten problems per worksheet. These word problems worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Adding U.S. Coins Word Problems
This U.S. coins word problems worksheet will produce coin addition problems. These worksheets will produce ten problems per worksheet. These word problems worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Advanced Adding U.S. Coins Word Problems
These Word Problems Worksheets will produce word problems that focus on adding up different denominations of US coin currency. You have the option to select any combination of pennies, nickels, dimes, quarters, and half dollars for each worksheet. These worksheets will produce ten problems per worksheet. These word problems worksheets are a good resource for students in the 5th Grade through the 8th Grade.

U.S. Money Adding Two Items Word Problems
These U.S. money word problems worksheest will produce purchase problems for adding two items. These worksheets will produce ten problems per worksheet. These word problems worksheets are a good resource for students in the 5th Grade through the 8th Grade.

U.S. Money Adding Three Items Word Problems
These U.S. money word problems worksheets will produce purchase problems for adding three items. These worksheets will produce ten problems per worksheet. These word problems worksheets are a good resource for students in the 5th Grade through the 8th Grade.

U.S. Money Change from a Purchase Word Problems
These U.S. money word problems worksheets will produce problems for calculating change from a purchase. These word problems worksheets will produce ten problems per worksheet. These word problems worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Travel Time Word Problems Worksheets
These time word problems worksheets produce problems for finding the duration, start, and end times of trips. Users may select the units of time to use in the problems. These word problems worksheets will produce ten problems per worksheet. These word problems worksheets are appropriate for students in the 5th Grade through the 8th Grade.

Reading a Calendar Word Problems Worksheets
These calendar worksheets will produce word problems revolving around reading and understanding a monthly calendar. You may select the month and the year within a range of the years 1800 to 3999. These word problems worksheets will produce nine problems per worksheet. These word problems worksheets are appropriate for students in the 5th Grade through the 8th Grade.

Elapsed Dates Word Problems Worksheets
These time word problems worksheets will produce questions with elapsed days, weeks, months, and years, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade.

Ratios and Rates Word Problems Worksheets
These ratio word problems worksheets will produce eight ratio and rates word problems for the students to solve. These ratio word problems worksheets are appropriate for 3rd Grade, 4th Grade, 5th Grade, 6th Grade, and 7th Grade.

Percentage Word Problems Worksheets
These Percentage Word Problems Worksheets will produce problems that focus on finding and working with percentages. You have the option to select the types of numbers, as well as the types of problem you want. These percentage word problems worksheets are appropriate for 3rd Grade, 4th Grade, 5th Grade, 6th Grade, and 7th Grade.

Mixed Word Problems with Key Phrases Worksheets
These Word Problems Worksheets will produce addition, multiplication, subtraction and division problems using clear key phrases to give the student a clue as to which type of operation to use. These word problems worksheets are appropriate for 4th Grade, 5th Grade, 6th Grade, and 7th Grade.

U.S. Money Change from a Purchase Multiplication Word Problems
These Word Problems Worksheets will produce problems that ask students to use multiplication to calculate the monetary value of a purchase and then find how much change is given from the purchase.

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About 25% of your total SAT Math section will be word problems, meaning you will have to create your own visuals and equations to solve for your answers. Though the actual math topics can vary, SAT word problems share a few commonalities, and we’re here to walk you through how to best solve them.

This post will be your complete guide to SAT Math word problems. We’ll cover how to translate word problems into equations and diagrams, the different types of math word problems you’ll see on the test, and how to go about solving your word problems on test day.

Feature Image: Antonio Litterio/Wikimedia

What Are SAT Math Word Problems?

A word problem is any math problem based mostly or entirely on a written description. You will not be provided with an equation, diagram, or graph on a word problem and must instead use your reading skills to translate the words of the question into a workable math problem. Once you do this, you can then solve it.

You will be given word problems on the SAT Math section for a variety of reasons. For one, word problems test your reading comprehension and your ability to visualize information.

Secondly, these types of questions allow test makers to ask questions that’d be impossible to ask with just a diagram or an equation. For instance, if a math question asks you to fit as many small objects into a larger one as is possible, it’d be difficult to demonstrate and ask this with only a diagram.

Translating Math Word Problems Into Equations or Drawings

In order to translate your SAT word problems into actionable math equations you can solve, you’ll need to understand and know how to utilize some key math terms. Whenever you see these words, you can translate them into the proper mathematical action.

For instance, the word «sum» means the value when two or more items are added together. So if you need to find the sum of a and b, you’ll need to set up your equation like this: a+b.

Also, note that many mathematical actions have more than one term attached, which can be used interchangeably.

Here is a chart with all the key terms and symbols you should know for SAT Math word problems:

Key Terms	Mathematical Action
Sum, increased by, added to, more than, total of	+
Difference, decreased by, less than, subtracted from	−
Product, times, __ times as much, __ times as many (a number, e.g., “three times as many”)	* or x
Divided by, per, __ as many, __ as much (a fraction, e.g., “one-third as much”)	/ or ÷
Equals, is, are, equivalent	=
Is less than	<
Is greater than	>
Is less than or equal to	≤
Is greater than or equal to	≥

Now, let’s look at these math terms in action using a few official examples:

Though the hardest SAT word problems might look like Latin to you right now, practice and study will soon have you translating them into workable questions.

Typical SAT Word Problems

Word problems on the SAT can be grouped into three major categories:

• Word problems for which you must simply set up an equation
• Word problems for which you must solve for a specific value
• Word problems for which you must define the meaning of a value or variable

Below, we look at each world problem type and give you examples.

Word Problem Type 1: Setting Up an Equation

This is a fairly uncommon type of SAT word problem, but you’ll generally see it at least once on the Math section. You’ll also most likely see it first on the section.

For these problems, you must use the information you’re given and then set up the equation. No need to solve for the missing variable—this is as far as you need to go.

Almost always, you’ll see this type of question in the first four questions on the SAT Math section, meaning that the College Board consider these questions easy. This is due to the fact that you only have to provide the setup and not the execution.

Word Problem Type 2: Solving for a Missing Value

The vast majority of SAT Math word problem questions will fall into this category. For these questions, you must both set up your equation and solve for a specific piece of information.

Most (though not all) word problem questions of this type will be scenarios or stories covering all sorts of SAT Math topics, such as averages, single-variable equations, and ratios. You almost always must have a solid understanding of the math topic in question in order to solve the word problem on the topic.

You might also get a geometry problem as a word problem, which might or might not be set up with a scenario, too. Geometry questions will be presented as word problems typically because the test makers felt the problem would be too easy to solve had you been given a diagram, or because the problem would be impossible to show with a diagram. (Note that geometry makes up a very small percentage of SAT Math.)

Word Problem Type 3: Explaining the Meaning of a Variable or Value

This type of problem will show up at least once. It asks you to define part of an equation provided by the word problem—generally the meaning of a specific variable or number.

To help juggle all the various SAT word problems, let’s look at the math strategies and tips at our disposal.

SAT Math Strategies for Word Problems

Though you’ll see word problems on the SAT Math section on a variety of math topics, there are still a few techniques you can apply to solve word problems as a whole.

#1: Draw It Out

Whether your problem is a geometry problem or an algebra problem, sometimes making a quick sketch of the scene can help you understand what exactly you’re working with. For instance, let’s look at how a picture can help you solve a word problem about a circle (specifically, a pizza):

As for geometry problems, remember that you might get a geometry word problem written as a word problem. In this case, make your own drawing of the scene. Even a rough sketch can help you visualize the math problem and keep all your information in order.

#2: Memorize Key Terms

If you’re not used to translating English words and descriptions into mathematical equations, then SAT word problems might be difficult to wrap your head around at first. Look at the chart we gave you above so you can learn how to translate keywords into their math equivalents. This way, you can understand exactly what a problem is asking you to find and how you’re supposed to find it.

There are free SAT Math questions available online, so memorize your terms and then practice on realistic SAT word problems to make sure you’ve got your definitions down and can apply them to the actual test.

#3: Underline and/or Write Out Important Information

The key to solving a word problem is to bring together all the key pieces of given information and put them in the right places. Make sure you write out all these givens on the diagram you’ve drawn (if the problem calls for a diagram) so that all your moving pieces are in order.

One of the best ways to keep all your pieces straight is to underline your key information in the problem, and then write them out yourself before you set up your equation. So take a moment to perform this step before you zero in on solving the question.

#4: Pay Close Attention to What’s Being Asked

It can be infuriating to find yourself solving for the wrong variable or writing in your given values in the wrong places. And yet this is entirely too easy to do when working with math word problems.

Make sure you pay strict attention to exactly what you’re meant to be solving for and exactly what pieces of information go where. Are you looking for the area or the perimeter? The value of x, 2x, or y?

It’s always better to double-check what you’re supposed to find before you start than to realize two minutes down the line that you have to begin solving the problem all over again.

#5: Brush Up on Any Specific Math Topic You Feel Weak In

You’re likely to see both a diagram/equation problem and a word problem for almost every SAT Math topic on the test. This is why there are so many different types of word problems and why you’ll need to know the ins and outs of every SAT Math topic in order to be able to solve a word problem about it.

For example, if you don’t know how to find an average given a set of numbers, you certainly won’t know how to solve a word problem that deals with averages!

Understand that solving an SAT Math word problem is a two-step process: it requires you to both understand how word problems work and to understand the math topic in question. If you have any areas of mathematical weakness, now’s a good time to brush up on them—or else SAT word problems might be trickier than you were expecting!

All set? Let’s go!

Test Your SAT Math Word Problem Knowledge

Finally, it’s time to test your word problem know-how against real SAT Math problems:

Word Problems

Answers: C, B, A, 1160

Answer Explanations

Aaaaaaaaaaand time for a nap.

Key Takeaways: Making Sense of SAT Math Word Problems

Word problems make up a significant portion of the SAT Math section, so it’s a good idea to understand how they work and how to translate the words on the page into a proper expression or equation. But this is still only half the battle.

Though you won’t know how to solve a word problem if you don’t know what a product is or how to draw a right triangle, you also won’t know how to solve a word problem about ratios if you don’t know how ratios work.

Therefore, be sure to learn not only how to approach math word problems as a whole, but also how to narrow your focus on any SAT Math topics you need help with. You can find links to all of our SAT Math topic guides here to help you in your studies.

What’s Next?

Want to brush up on SAT Math topics? Check out our individual math guides to get an overview of each and every topic on SAT Math. From polygons and slopes to probabilities and sequences, we’ve got you covered!

Running out of time on the SAT Math section? We have the know-how to help you beat the clock and maximize your score.

Been procrastinating on your SAT studying? Learn how you can overcome your desire to procrastinate and make a well-balanced prep plan.

Trying to get a perfect SAT score? Take a look at our guide to getting a perfect 800 on SAT Math, written by a perfect scorer.

Have friends who also need help with test prep? Share this article!

I really love doing Facebook LIVE presentations. I particularly enjoy it when I have the opportunity to talk about something that strikes a chord with homeschool parents. We did a Facebook LIVE video talking about working with students and mathematical word problems. It was like touching that third electrified rail in so far as how people feel about word problems! It would be fair to divide us into two groups:

1) Those who find word problems to be fascinating puzzles.
2) The rest of us, who really do not have an affection for word problems.

In the interest of true confession, I have never been a particular fan of mathematics. You can assign me the task of diagraming sentences all day long. In my opinion, word problems can be sometimes inscrutable.

Steve Demme (the author of Math-U-See) said to me once, “Well, Gretchen, you know when you solve math problems as an adult, they ARE word problems.” Point taken. While I would not say I love word problems to this day, I no longer have an adversarial relationship with them. One of the things I’ve always loved about Math-U-See is taking the sting out of word problems by making them a part of the daily lessons. What, however, do you do if you did not start your mathematical journey with Math-U-See?

We as parents have to be able to model for our children how to meet the challenge of word problems head on, and toward that end I want to share with you some of the tips that were shared in the Facebook LIVE video. I also have some things to say about math anxiety in adults.

You can also watch the video below, if you prefer.

Below you will find several tips to implement when working with word problems with your children. These tips are applicable, regardless of the age of your student, their mathematical experience, or even the level of Math-U-See in which they are working. As always, I am indebted to our tremendous customer service team. They are the contributors of much of my list here. You do know, of course, that being a member of the Demme Learning family means that you can call our team and ask for help if you are having a struggle. We want your success!

10 Ways to Make Word Problems Fun

1) Start With Fresh Eyes

If you are just completing a math lesson, and have already been at it for 15-20 minutes, take a break before you begin the word problems. Stand up and do some jumping jacks, have a snack, take a break. Then sit back down to the word problems.

2) Read the Word Problem All the Way Through First

Read the word problem all the way through first; don’t worry about the numbers in the word problem. Then ask yourself and your student, “do we understand what it’s all about”? Are there any new terms we are unsure of here? Are there words we don’t know?

3) Reread the Word Problem Again

Reread the word problem again; out loud is best. I know that reading out loud seems silly, but it is tremendously helpful.

4) Skip the Numbers

Sometimes in the reading out loud is it helpful to just skip the numbers altogether. Instead of reading the number, add some humor by saying “BEEP” instead of the number. Humor really DOES help learning! You can change the names of the people in the word problems to your children, their friends, or even their favorite super hero.

5) Circle Keywords

Are there keywords you can circle? “Sum”, “in all” and “all together” usually mean addition. “How many are left/remaining”, or “What is the difference” usually means subtraction. The word of is an important one as in “1/4 of 12” or “5/10 of a dollar” means you are being instructed to multiply. There are other key math words that may help you analyze a word problem – but be careful.

Depending on key words alone does not encourage students to think mathematically about a problem or use logic to reason toward a solution. Sometimes key words do not appear in problems, or additional operations may be required to find the final answer Encourage them to take the whole of the word problem in context. Make sure you both understand what the problem is asking before seeking out those individual words.

6) Rewrite the Word Problem

If word problems cause anxiety in your child, help them become the drafter of word problems. For example: 12-7= ? That is the computation. Have your student create a situation to accompany those numbers. Developing a proficiency in creating word problems really helps students develop confidence in analyzing them.

7) Word Problem Writers Are Sneaky

Remind your student that those who write word problems are a sneaky lot. They will put in information that is not necessary just to throw a student off track. If irrelevant information is a challenge for your student, try creating some word problems that contain unnecessary information. Help them become proficient in knowing what is not necessary – that is a life skill in and of itself!

Consult the Instruction Manual

If there is a lesson in the Math-U-See curriculum that is giving you a particular challenge, make very sure you have consulted the corresponding lesson pages in the instruction manual. We always provide instruction for the how as well as the why, and often, if a family is challenged with a lesson, we find that the answers they seek can be found in the lesson manual pages.

9) Review the Questions

Word problems need to be answered in words too. Make sure that you have answered the question in words. Further, does your answer make mathematical sense? Can you plug your answer back into the word problem and work it out to to see that it is indeed correct? Remember this step. This leads to frustration for a student who has worked hard, and perhaps not found the right answer.

10) Relax

Just like any skill, learning to negotiate word problems is something that happens over time. You are not going to be an overnight success (most of the time). But if you, as the parent, can stay affirmative and encouraging, you can make a tremendous difference for your student.

In conclusion, I realize that this blog post is long. The information will be helpful to you. If you still want more, we offer more help with word problems on our parent resource page:

Word Problem Tips [PDF]

We do need to have a conversation about what our math anxiety does to our children. Look for that blog post to come in the near future. We want you and your student to have success in all your mathematical endeavors!

A Picture is Worth a Thousand Words

“Today, we are going to solve math word problems.” When students hear this from their math teacher, their faces drop, sweat starts to form on their foreheads and they refuse to make eye contact. As a math teacher, I understand. I understand the anxiety and want to make the learning process with word problems more enjoyable. This is where reading, writing and, math collide and the real world of math begins. Let’s talk about how to solve word problems with pictures.

When students struggle with word problems in school, they also have difficulty tackling them for homework. Most students want the “one-size-fits-all” formula for word problems but unfortunately, that does not exist. However, drawing a picture will help students visualize the problem and will start advancing their learning stage from the concrete to the abstract. Let’s take a look at how to solve a word problem using pictures:

Steps for Solving Word Problems using Pictures

1. Read the entire problem: Get all the facts – Underline key word
2. Answer the question: What am I looking for?
3. Draw a picture or diagram: Visualize as a real world situation
4. Solve the problem: Set up the equation and solve
5. Check your solution: Is this answer reasonable?

Word Problem Examples – Example A

Cody has 6 pencils on his desk, Jonah has 4 more than Cody and Vinny has three less pencils than Jonah. How many pencils are there in all?

• Read the entire problem  √
• What am I looking for? How many pencils do Cody, Jonah and Vinny have altogether?  √
• Draw a picture or diagram √

• Solve the problem    √

      6 + 10 + 7 = 23 pencils

• Check your solution  √

      This answer is reasonable

Example B

There are 3 fish tanks labeled   X, Y, and Z. Y weighs 6 times as much as X and twice as much as Z. If Z is 36 lbs. heavier than X, find the total weight of X, Y and Z.

• Read the entire problem  √
• What am I looking for?  What is thetotal weight of fish tanks X, Y and Z?  √
• Draw a picture or diagram √

• Solve the problem    √

18 + 108 + 54 = 180 pounds

• Check your solution  √

      This answer is reasonable

Visualizing a word problem with pictures is a strategy that will help motivate many students to begin the process of solving them.  This works especially for students that may become bored by the excess amount of words instead of numbers or for those students who become overwhelmed by the information and want to break it down into a simpler form.   Another benefit of using pictures when solving word problems involves communicating the results.  The pictures act as justification for answers, make the problems easier to understand and therefore, secure the learning process.

Meet our Guest Blogger: Jan Rowe

Jan is one of Educational Connections’ top tutors. She has twelve years of classroom teaching experience and holds a Virginia and Florida teaching license in middle school mathematics and elementary education. Jan has been with Educational Connections for over a year, working with over twenty students. Her tutoring goal is to help each student understand their learning style so they can improve the speed and quality of that learning. When she is not tutoring or teaching, Jan loves to play scrabble, go hiking and play Frisbee with her new puppy.

It’s one thing to solve a math equation when all of the numbers are given to you but with word problems, when you start adding reading to the mix, that’s when it gets especially tricky.

The simple addition of those words ramps up the difficulty (and sometimes the math anxiety) by about 100!

How can you help your students become confident word problem solvers? By teaching your students to solve word problems in a step by step, organized way, you will give them the tools they need to solve word problems in a much more effective way.

Here are the seven strategies I use to help students solve word problems.

1. Read the Entire Word Problem

Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too.

2. Think About the Word Problem

Students need to ask themselves three questions every time they are faced with a word problem. These questions will help them to set up a plan for solving the problem.

Here are the questions:

A. What exactly is the question?

What is the problem asking? Often times, curriculum writers include extra information in the problem for seemingly no good reason, except maybe to train kids to ignore that extraneous information (grrrr!). Students need to be able to stay focused, ignore those extra details, and find out what the real question is in a particular problem.

B. What do I need in order to find the answer?

Students need to narrow it down, even more, to figure out what is needed to solve the problem, whether it’s adding, subtracting, multiplying, dividing, or some combination of those. They’ll need a general idea of which information will be used (or not used) and what they’ll be doing.

This is where key words become very helpful. When students learn to recognize that certain words mean to add (like in all, altogether, combined), while others mean to subtract, multiply, or to divide, it helps them decide how to proceed a little better

Here’s a Key Words Chart I like to use for teaching word problems. The handout could be copied at a smaller size and glued into interactive math notebooks. It could be placed in math folders or in binders under the math section if your students use binders.

One year I made huge math signs (addition, subtraction, multiplication, and divide symbols) and wrote the keywords around the symbols. These served as a permanent reminder of keywords for word problems in the classroom.

If you’d like to download this FREE Key Words handout, click here:

C. What information do I already have?

This is where students will focus in on the numbers which will be used to solve the problem.

3. Write on the Word Problem

This step reinforces the thinking which took place in step number two. Students use a pencil or colored pencils to notate information on worksheets (not books of course, unless they’re consumable). There are lots of ways to do this, but here’s what I like to do:

• Circle any numbers you’ll use.

• Lightly cross out any information you don’t need.

• Underline the phrase or sentence which tells exactly what you’ll need to find.

4. Draw a Simple Picture and Label It

Drawing pictures using simple shapes like squares, circles, and rectangles help students visualize problems. Adding numbers or names as labels help too.

For example, if the word problem says that there were five boxes and each box had 4 apples in it, kids can draw five squares with the number four in each square. Instantly, kids can see the answer so much more easily!

5. Estimate the Answer Before Solving

Having a general idea of a ballpark answer for the problem lets students know if their actual answer is reasonable or not. This quick, rough estimate is a good math habit to get into. It helps students really think about their answer’s accuracy when the problem is finally solved.

6. Check Your Work When Done

This strategy goes along with the fifth strategy. One of the phrases I constantly use during math time is, Is your answer reasonable? I want students to do more than to be number crunchers but to really think about what those numbers mean.

Also, when students get into the habit of checking work, they are more apt to catch careless mistakes, which are often the root of incorrect answers.

7. Practice Word Problems Often

Just like it takes practice to learn to play the clarinet, to dribble a ball in soccer, and to draw realistically, it takes practice to become a master word problem solver.

When students practice word problems, often several things happen. Word problems become less scary (no, really).

They start to notice similarities in types of problems and are able to more quickly understand how to solve them. They will gain confidence even when dealing with new types of word problems, knowing that they have successfully solved many word problems in the past.

If you’re looking for some word problem task cards, I have quite a few of them for 3rd – 5th graders.

This 3rd Grade Math Task Cards Bundle has word problems in almost every one of its 30 task card sets.

There are also specific sets that are dedicated to word problems and two-step word problems too. I love these because there’s a task card set for every standard.

CLICK HERE to take a look at 3rd grade:

This 4th Grade Math Task Cards Bundle also has lots of word problems in almost every single of its 30 task card sets. These cards are perfect for centers, whole class, and for one on one.

CLICK HERE to see 4th grade:

This 5th Grade Math Task Cards Bundle is also loaded with word problems to give your students focused practice.

CLICK HERE to take a look at 5th grade:

Want to try a FREE set of math task cards to see what you think?

3rd Grade: Rounding Whole Numbers Task Cards

4th Grade: Convert Fractions and Decimals Task Cards

5th Grade: Read, Write, and Compare Decimals Task Cards

Thanks so much for stopping by!

Solving word problems in elementary school is an essential part of the math curriculum. Here are over 30 math word problems to practice with children, plus expert guidance on how to solve them.

This blog is part of our series of blogs designed for teachers, schools and parents supporting home learning.

What is a word problem?

A word problem in math is a math question written as one sentence or more that requires children to apply their math knowledge to a ‘real-life’ scenario. 

This means that children must be familiar with the vocabulary associated with the mathematical symbols they are used to, in order to make sense of the word problem. 

For example:

Isn’t brilliant arithmetic enough?

In short, no. Students need to build good reading comprehension, even in math. Overtime math problems become increasingly complex and require students to possess deep conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. 

As students progress through their mathematical education, they will need to be able to apply mathematical reasoning and develop mathematical arguments and proofs using math language. They will also need to be dynamic, applying their math knowledge to a variety of increasingly sophisticated problems. 

To support this schools are adopting a ‘mastery’ approach to math

“Teaching for mastery”, is defined with theses component: 

• Math teaching for mastery rejects the idea that a large proportion of people ‘just can’t do math’.  
• All students are encouraged by the belief that by working hard at math they can succeed. 
• Procedural fluency and conceptual understanding are developed in tandem because each supports the development of the other. 
• Significant time is spent developing deep knowledge of the key ideas that are needed to support future learning. The structure and connections within the mathematics are emphasized, so that students develop deep learning that can be sustained.

(The Essence of Maths Teaching for Mastery, 2016)

Mastery helps children to explore math in greater depth

Fluency in arithmetic is important; however, with this often lies the common misconception that once a child has learned the number skills appropriate to their grade level/age, they should be progressed to the next grade level/age of number skills. 

The mastery approach encourages exploring the breadth and depth of these math concepts (once fluency is secure) through reasoning and problem solving. 

How to teach children to solve word problems? 

Here are two simple strategies that can be applied to many word problems before solving them.

1. What do you already know?
2. How can this problem be drawn/represented pictorially?

Let’s see how this can be applied to word problems to help achieve the answer.

Solving a simple word problem

There are 28 students in a class.

The teacher has 8 liters of orange juice.

She pours 225 milliliters of orange juice for every student.

How much orange juice is left over?

1. What do you already know?

• There are 1,000ml in 1 liter
• Pours = liquid leaving the bottle = subtraction
• For every = multiply
• Left over = requires subtraction at some point

2. How can this problem be drawn/represented pictorially?

The bar model, also known as strip diagram, is always a great way of representing problems. However, if you are not familiar with this, there are always other ways of drawing it out. 

Read more: What is a bar model

For example, for this question, you could draw 28 students (or stick man x 28) with ‘225 ml’ above each one and then a half-empty bottle with ‘8 liters’ marked at the top.

Now to put the math to work. This is a 5th grade multi-step problem, so we need to use what we already know and what we’ve drawn to break down the steps.

Solving a more complex, mixed word problem

Mara is in a bookshop.

She buys one book for $6.99 and another that costs $3.40 more than the first book.

She pays using a $20 bill.

What change does Mara get? (What is the remainder?)

1. What do you already know?

• More than = add
• Using decimals means I will have to line up the decimal points correctly in calculations
• Change from money = subtract

2. How can this problem be drawn/represented pictorially?

See this example of bar modelling for this question:

Now to put the math to work using what we already know and what we’ve drawn to break down the steps.

Mara is in a bookshop. 

She buys one book for $6.99 and another that costs $3.40 more than the first book. 1) $6.99 + ($6.99 + $3.40) = $17.38

She pays using a $20 bill.

What change does Mara get? 2) $20 – $17.38 = $2.62

Math Word Problems For Kindergarten to Grade 5

The more children learn about math as they go through elementary school, the trickier the word problems they face will become.

Below you will find some information about the types of word problems your child will be coming up against on a year by year basis, and how word problems apply to each elementary grade. 

Word problems in kindergarten

Throughout kindergarten a child is likely to be introduced to word problems with the help of concrete resources (manipulatives, such as pieces of physical apparatus like coins, cards, counters or number lines) to help them understand the problem.

An example of a word problem for kindergarten would be

Chris has 3 red bounce balls and 2 green bounce balls. How many bounce balls does Chris have in all?

Word problems 1st grade

First grade is a continuation of kindergarten when it comes to word problems, with children still using concrete resources to help them understand and visualize the problems they are working on

An example of a word problem for first grade would be:

A class of 10 children each have 5 pencils in their pencil cases. How many pencils are there in total?

Word problems in 2nd grade

In second grade, children will move away from using concrete resources when solving word problems, and move towards using written methods. Teachers will begin to demonstrate the adding and subtracting within 100, adding up to 4- two-digit numbers at a time.

This is also the year in which 2-step word problems will be introduced. This is a problem which requires two individual calculations to be completed.

Second grade word problem: Geometry properties of shape

Shaun is making shapes out of plastic straws.

At the vertices where the straws meet, he uses blobs of modeling clay to fix them together

Here are some of the shapes he makes:

Shape	Number of straws	Number of blobs of modeling clay
A	4	4
B	3	3
C	6	6

One of Sean’s shapes is a triangle. Which is it? Explain your answer.

Answer: shape B as a triangle has 3 sides (straws) and 3 vertices, or angles (clay)

Second grade word problem: Statistics

2nd grade is collecting pebbles. This pictogram shows the different numbers of pebbles each group finds.

Word problems in 3rd grade

At this stage of their elementary school career, children should feel confident using the written method for addition and subtraction. They will begin multiplying and dividing within 100. 

This year children will be presented with a variety of problems, including 2-step problems and be expected to work out the appropriate method required to solve each one. 

3rd grade word problem: Number and place value

My number has four digits and has a 7 in the hundreds place.

The digit which has the highest value in my number is 2.

The digit which has the lowest value in my number is 6.

My number has 3 fewer tens than hundreds.

What is my number?

Answer: 2,746

Word problems in 4th grade

One and two-step word problems continue in fourth grade, but this is also the year that children will be introduced to word problems containing decimals.

Fourth grade word problem: Fractions and decimals

Stan, Frank and John are washing their cars outside their houses.

Stan has washed 0.5 of his car.

Frank has washed 1/5 of his car.

Norm has washed 2/5 of his car.

Who has washed the most?

Explain your answer.

Answer: Stan (he has washed 0.5 whereas Frank has only washed 0.2 and Norm 0.4)

Word problems in 5th grade

In fifth grade children move on from 2-step word problems to multi-step word problems. These will include fractions and decimals.

Here are some examples of the types of math word problems in fifth grade will have to solve.

5th grade word problem – Ratio and proportion

The Angel of the North is a large statue in England. It is 20 meters tall and 54 meters wide. 

Ally makes a scale model of the Angel of the North. Her model is 40 centimeters tall. How wide is her model?

Answer: 108cm

Fifth grade word problem – Algebra

Amina is making designs with two different shapes.

She gives each shape a value.

Calculate the value of each shape.

Answer: 36 (hexagon) and 25. 

Fifth grade word problem: Measurement

There are 28 students in a class.

The teacher has 8 liters of orange juice.

She pours 225 milliliters of orange juice for every student.

How much orange juice is left over?

Answer: 1.7 liters or 1,700ml

Topic based word problems

The following examples give you an idea of the kinds of math word problems your child will encounter in elementary school

Place value word problem fourth grade

This machine subtracts one hundredth each time the button is pressed. The starting number is 8.43. What number will the machine show if the button is pressed six times? Answer: 8.37

Download free number and place value word problems for grades 2, 3, 4 and 5

Addition and subtraction word problem grade 2

Sam has 64 sweets. He gets given 12 more. He then gives 22 away. How many sweets is he left with? Answer: 54

Download free addition and subtraction word problems for for grades 2, 3, 4 and 5

Addition word problem grade 2

Sammy thinks of a number. He subtracts 70. His new number is 12. What was the number Sammy thought of? Answer: 82

Subtraction word problem fifth grade

The temperature at 7pm was 4oC. By midnight, it had dropped by 9 degrees. What was the temperature at midnight? Answer: -5oC

Multiplication word problem third grade

Eggs are sold in boxes of 12. The egg boxes are delivered to stores in crates. Each crate holds 9 boxes. How many eggs are in a crate? Answer: 108

Download free multiplication word problems for grades 2, 3, 4 and 5. 

Division word problem fifth grade

A factory produces 3,572 paint brushes every day. They are packaged into boxes of 19. How many boxes does the factory produce every day? Answer: 188

Download free division word problems for grades 2, 3, 4 and 5. 

Free resource: Use these four operations word problems to practice addition, subtraction, multiplication and division all together.

Fraction word problem fourth grade

At the end of every day, a chocolate factory has 1 and 2/6 boxes of chocolates left over. How many boxes of chocolates are left over by the end of a week? Answer: 9 and 2/6 or 9 and 1/3

Download free fractions and decimals word problems for grades 2, 3, 4 and 5. 

Money word problem second grade 

Lucy and Noor found some money on the playground at recess. Lucy found 2 dimes and 1 penny, and Noor found 2 quarters and a dime. How many cents did Lucy and Noor find? Answer: Lucy = $0.21, Noor = $0.60; $0.21 + $0.61 = $0.81

Area word problem 3rd grade

A rectangle measures 6cm by 5cm.

What is its area? Answer: 30cm2

Perimeter word problem 3rd grade

The swimming pool at the Sunshine Inn hotel is 20m long and 7m wide. Mary swims around the edge of the pool twice. How many meters has she swum? Answer: 108m

Ratio word problem 5th grade (crossover with measurement)

A local council has spent the day painting double yellow lines. They use 1 pot of yellow paint for every 100m of road they paint. How many pots of paint will they need to paint a 2km stretch of road? Answer: 20 pots

PEMDAS word problem fifth grade

Draw a pair of parentheses in one of these calculations so that they make two different answers. What are the answers?

50 – 10 × 5 =

50 – 10 × 5 =

Volume word problem fifth grade

This large cuboid has been made by stacking shipping containers on a boat. Each individual shipping container has a length of 6m, a width of 4m and a height of 3m. What is the volume of the large cuboid? Answer: 864m3

Remember: The word problems can change but the math won’t 

It can be easy for children to get overwhelmed when they first come across word problems, but it is important that you remind them that while the context of the problem may be presented in a different way, the math behind it remains the same. 

Word problems are a good way to bring math into the real world and make math more relevant for your child. So help them practice, or even ask them to turn the tables and make up some word problems for you to solve.