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Teaching Math Word Problem Key Words (Free Cheat Sheet)

By Jeannette Tuionetoa on November 20, 2023

Tackling word problems in math can be challenging for kids to learn. We called them story problems when I was in school. If your kids are learning math key words so they can solve word problems, they you’ll find these free cheat sheets and worksheets for word problem key words helpful. 

Math Word Problem Keywords free cheat sheets graphing paper with a circle and text overlay

Math Word Problem Key Words

There is no doubt that mathematical operations using words are difficult for kids. They go from counting numbers to doing math equations with numbers.

Then all of a sudden… there are words, just words . All of a sudden algebraic expressions and mathematical operations are POOF – words.

The lack of numbers and shift in mindset can completely throw off a lot of students. If kids have difficulty with reading, then that is yet another struggle for kids as they try to learn basic problems in math.

Teaching students about challenging math keywords just got easier! Be sure to download our free math key words cheat sheet at the end of this post. 

Why do some kids struggle with word problems?

A key proponent in different operations in math is learning the key words that prompt kids to understand which operation skill they need to use to solve the problem.

This means that they should master regular math problems first and be able to read with comprehension. You will shortly find that if these two skills aren’t somewhat mastered first, then word problems will become an issue.

Many times math is a subject best taught in sequential order. If one step is missed, then the future steps falter. This is much like how it is when teaching word problems.

The best thing for your children is for them to first:

  • Be able to read well.
  • Understand math concepts and phrases.
  • Know to not rush, but focus on math key words, identify relevant information, and understand the text.
  • Get to know the keywords for math word problems

What are keywords for math word problems?

Key words in mathematical word operations are the words or phrases that will signal or show a student which type of math operation to choose in order to solve the math word problem.

The keywords for math word problems used in operations are a strategy that helps the math problem make sense and draw connections to how it can be answered.

Basically, when using key words, students must decipher whether they need to solve the math equation via addition, subtraction, multiplication, or division.

What are the common keywords for math word problems?

Thankfully, there are math key words that our children can learn that help them work through their word problems. They are prompts that point them in the right direction.

Just like a different language needs words translated for comprehension, students translate the words… into math .

Keywords for Math Word Problems

Learning these math keywords will help with problem solving:

Addition Math Key Words:

  • increased by
  • larger than
  • in addition to
  • how much in all

Subtraction Math Key Words:

  • how many more
  • how many less
  • shorter than
  • smaller than

Key Words for Multiplication Word Problems:

  • multiplied by
  • double/twice

Key Words used for Division Word Problems:

  • equal group
  • how many in each

You can print off a free math key words cheat sheet that has the above math key words for word problems and add it to your homeschool binder . Find the download link at the bottom of this post. 

How can we help kids learn keywords for solving numberless word problems?

Teach kids steps for solving word problems until it becomes a habit or they get comfortable with the steps. First, they can look for the important information and write those down. (Read the problem carefully). Next, kids need to define or find the variables in the math equation.

From the keywords, kids can now determine what math operation to use. Translate the words to math. Then, kids can solve the math equation. This is where the skills of solving numbered equations are important.

Finally, students have to put their answers in the form of a word sentence. NOTE: Many times kids think after solving the equation they are done. However, the key to making sure they understand that word problems need word answers.

Different Strategies to Familiarize Keywords in Word Operations

You can use some of these keywords for math word problems as vocabulary words in your homeschool.

Students can display subtraction, addition, multiplication, and multiplication handy reference posters on a bulletin board in your homeschool area. Students can also just list them on dry erase boards . These are perfect visual reminders for what keywords go with what math word problems.

Your students can also keep their keywords for math word problems with them as they study. They can place the list of keywords in a math folder or in an anchor chart – and then in their math folder.

Kids can keep the keyword poster sets in their math notebooks or keep them in a word problem journal .

Their strategy for learning word problem keywords all depends on how they best absorb information.

Students may do well using a combination of these methods. Either way, all of these different strategies can be used to get them comfortable in identifying the route to solve math word equations.

black upper background with white mathematical formulas. a girl doing math work and text overlay

Math Word Problem Keywords Cheat Sheets & Teaching Aids:

We created a free pdf download Word Problem Key Words Cheat Sheet that you can find at the bottom of this post. It’s great to use as a reference for math word problems.

Word Problem Clue Words

Get a Clue Free Download – Check out these word problem clue word handouts and posters to help your students with word problems. There 5 pages in all that will be handy for your kids in trying to find the correct answer while using the correct operation.

Addition and Subtraction Word Problem Keywords

Subtraction Keywords/Addition Keywords – Until your kids memorize keywords and what they mean, this freebie can help. Grab these simple black and white printable signs. They will help kids look for keywords like larger numbers for subtraction word problems or addition keywords like in addition to . 

Story Problem Key Words

Words to Math – Keywords in math problems are essentially turning words into math. This graphic organizer printable is a quick reference for your students to use with numberless math word problems. Place them in a notebook chart or your homeschool classroom wall as a visual reminder.

Word Problem Key Words Poster

Key Word Posters for Math Problems – Grab these word problem keyword handy reference posters for subtraction, addition, division, and multiplication. Each poster has its specific theme and specific words to solve all problem types. Kids will enjoy having practiced with these math key words posters.

Word Problem Key Words Worksheets

Fun Key Word Sorting Activity – Your kids have now studied some keywords for math word problems helpful for problem solving in mathematical operations. Use this word problem sorting activity to test their knowledge in a fun engaging way. Add this fun activity to your test prep materials.

World Problems Worksheets with Key Words – These word problems worksheets use key phrases to help your students identify the phrases that will help them determine which math operation to use.

Word Problem Key Words for Math

Math word problems are probably the first opportunity students get to understand how math relates to real world situations. The applications can be relevant in their real life experiences like going to the market.

However, the benefit to word problems doesn’t stop there…

With word problems, students develop their higher-order thinking and critical thinking skills.

Different types of word problems guide your students to applying math various math concepts at the same time. They have to know basic number sense, basic algebra skills, and even geometry when they attempt multiplication word problems.

If we do it the right way, kids won’t see word problems as a dreadful experience in math. Understanding word problems is a learning curve and doesn’t come easily to kids.

Identify Learning Gaps

Another important aspect of word problems is that they tell a parent/teacher if a child needs help in areas like reading comprehension or math number operations skills. This type of word math is a great evaluation of your student’s thinking processes.

We can, however, help make it a better experience for them by teaching it the right way.

Free Math Key Words Cheat Sheet Instant Download

You won’t want to miss our free Word Problem Key Words Cheat Sheet PDF download for different ways kids see keywords in various types of problems in mathematics. This math tool is everything your student needs and the perfect resource to reference keywords in math operations.

Includes the keywords that will help your children solve and recognize word problems for:

  • Subtraction
  • Multiplication

Instant Download: Math Word Problems Keywords Cheat Sheet

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key words for solving math word problems

Jeannette is a wife, mother and homeschooling mom. She has been mightily, saved by grace and is grateful for God’s sovereignty throughout her life’s journey. She has a Bachelor in English Education and her MBA. Jeannette is bi-lingual and currently lives in the Tongan Islands of the South Pacific. She posts daily freebies for homeschoolers!

key words for solving math word problems

Be sure to check out the open and go homeschool curriculum and resources over at www.dailyskillbuilding.com

key words for solving math word problems

"Key Words and Catch Phrases" for Word Problems

Addition Words

2. Altogether

Subtraction Words

1. Difference

3. How many more

4. How much more

6. Less: Debra bought apples for $3.20 and oranges for $4.23. How much less did the apples cost?

10. Subtract

10. Words ending with "er"; higher, longer, faster, heavier, larger, shorter, slower, farther, etc. Example: Jean's apple weighs 100 grams, and Karen's apple weighs 80 grams. How much heavier is Jean's apple?

Multiplication Words

1. Times : Maria ran around the track 5 times. It took her 5 minutes to run around the track. How many minutes did she run?

2. Every : Kim buys 2 apples everyday . How many apples does she buy in a week?

3. At this rate: Ed reads 25 words per minute. At this rate , how many words does he read in one hour?

Division Words

1. Each: Ken has 75 pencils and 15 boxes. How many pencils should he pack in each box so each customer gets the same number of pencils?

key words for solving math word problems

  • My Preferences
  • My Reading List
  • Math Word Problems
  • Study Guides
  • Keywords for Mathematical Operations
  • Keywords for Change in Order
  • Keywords Indicating Equality
  • Solving Simple Linear Equations

To begin, you translate English phrases into algebraic expressions. An algebraic expression is a collection of numbers, variables , operations, and grouping symbols. You will translate an unknown number as the variable x or n . The grouping symbols are usually a set of parentheses, but they can also be sets of brackets or braces.

In translating expressions, you want to be well acquainted with basic keywords that translate into mathematical operations: addition keywords, subtraction keywords, multiplication keywords, and division keywords, which are covered in the four following sections.

Addition keywords

Some common examples of addition keywords are as follows:

  • SUM OF_____ AND _____
  • TOTAL OF _____ AND _____
  • _____ PLUS _____
  • _____ INCREASED BY _____
  • INCREASE OF

The first two keywords (SUM and TOTAL) are called leading keywords because they lead the expression. The second two keywords (PLUS and INCREASED BY) are keywords that indicate the exact placement of the plus sign. The last four keywords can be found in word problems and may indicate addition.

When an expression begins with the leading keywords SUM or TOTAL, the leading keyword defines the corresponding AND. The plus sign then physically replaces the AND in the expression.

Example 1: Translate the following: the sum of five and a number

The following steps help you translate this problem:

1. Underline the words before and after AND when it corresponds to the leading keyword SUM OF.

  • the sum of five and a number

2. Circle the leading keyword and indicate the corresponding AND that it defines.

3. Translate each underlined expression and replace AND with a plus sign.

  • The expression translates to 5 + x .

Example 2: Translate the following: the total of a number and negative three

Use the following steps to translate this problem:

1. The keyword TOTAL OF is a leading keyword that defines AND, so underline the words before and after AND: “a number” and “negative three.”

  • the total of a number and negative three
  • The expression translates to x + −3.

Example 3: Translate the following: the sum of seven and negative four

Translate this example in the following way:

1. The word SUM OF is a leading keyword that defines AND, so underline the words before and after AND: “seven” and “negative four.”

  • the sum of seven and negative four
  • The expression translates to 7 + −4.

Reminder: The AND keyword translates to mean “plus” because the leading keyword is SUM OF. With other leading keywords (discussed in the following sections), AND can mean other things. Also notice that you do not simplify the expression and get “3” for the answer because you are just translating words into symbols and not performing the math.

Two other keywords on the addition keyword list, PLUS and INCREASED BY, can be correctly translated by the direct translation strategy. In the direct translation strategy, you translate each word into its corresponding algebraic symbol, one at a time, in the same order as written, as shown in Example 4.

Example 4: Translate the following: a number increased by twenty‐four

  • The expression translates to x + 24.

Some additional keywords, such as GAIN, MORE, INCREASE OF, and RAISE, are commonly found in story problems, as in Example 5.

Example 5: Translate the following story problem into a mathematical expression about the weight of the linebacker: The defensive linebacker weighed two hundred twenty‐two pounds at the beginning of spring training. He had a gain of seventeen pounds after working out with the team for four weeks.

  • The expression translates to 222 + 17.

Note: Not all numbers mentioned in a word problem should be included in the mathematical expression. The number “four” is just interesting fact, but it is not information you need in order to write an expression about the linebacker's weight.

You may also be wondering why the answer isn't 239 pounds. That's because the question asks you to translate the story problem into a mathematical expression, not to evaluate the expression.

Example 6: Translate the following word problem into a mathematical expression about the cashier's current hourly wage: A cashier at the corner grocery was earning $6.25 an hour. He received a raise of 25 cents an hour.

  • The expression translates to 6.25 + 0.25.

Note: The hourly wage is stated in dollars, and the raise is stated in cents. Any time you are adding two numbers that have units , make sure both numbers are measured with the same units; if they aren't, convert one of the numbers to the same units as the other. Having both numbers measured with the same units is called homogeneous units. In this example, you convert his raise, the 25 cents, to $0.25 because his hourly wage is measured in dollars, not cents, so the raise must also be in dollars.

Subtraction keywords

Subtraction keywords also include leading keywords, keywords that can be translated one word at a time, and keywords that are found in story problems. Look at the following list of subtraction keywords:

  • DIFFERENCE BETWEEN _____ AND _____
  • _____ MINUS _____
  • _____ DECREASED BY _____

One subtraction keyword (DIFFERENCE BETWEEN) is a two‐part expression that begins with a leading keyword that defines the corresponding AND. You can use the same methods of underlining and circling the keywords shown in the preceding section to translate these expressions.

Example 7: Translate the following: the difference between four and six

Here is how you translate Example 7:

1. Because the keyword DIFFERENCE BETWEEN is a leading keyword that defines the corresponding AND, underline the words before and after AND: “four” and “six.”

  • the difference between four and six

3. Translate each underlined expression and replace AND with a minus sign.

  • The expression translates to 4 – 6.

Note: AND is not always translated to mean addition. Here, the DIFFERENCE BETWEEN is the leading keyword that defines the AND to mean subtraction.

Other subtraction keywords, such as MINUS and DECREASED BY, use the direct translation strategy. Example 8 is a subtraction word problem that is translated one keyword at a time, in the exact order of the expression.

Example 8: Translate the following: twenty‐four decreased by a number

  • The expression translates to 24 – x .

In a story problem, you may find the subtraction keywords LOSS, LESS, FEWER, and TAKE AWAY, as shown in Example 9.

Example 9: Translate the following word problem into a mathematical expression about the current value of materials at the job site: A construction company stored $1,253 worth of materials at the job site. The company suffered a loss of $300 due to storm damage.

  • The expression translates to 1,253 – 300.

Multiplication keywords

Some common examples of multiplication keywords are as follows:

  • MULTIPLY _____ BY _____
  • PRODUCT OF _____ AND _____
  • _____ TIMES _____
  • DOUBLE _____
  • TWICE _____
  • TRIPLE _____
  • PERCENT OF _____
  • FRACTION OF _____

For two of the multiplication keywords, MULTIPLY and PRODUCT OF, a leading keyword defines the corresponding BY or AND, as shown in Example 10.

Example 10: Translate the following: the product of seven and a number

1. Because PRODUCT OF is a leading keyword that corresponds to AND, underline the words before and after AND: “seven” and “a number.”

  • the product of seven and a number

3. Translate each underlined expression and replace AND with a times sign.

  • The expression translates to 7 × x .

Note: Keep in mind that AND does not always indicate addition. The keyword PRODUCT OF defines the AND in this expression to mean multiplication.

A multiplication expression that is translated by the direct translation method is shown in Example 11.

Example 11: Translate the following: a number times fifteen

The expression translates to x × 15.

Some multiplication keywords, such as DOUBLE, TWICE, and TRIPLE, translate into a number and the operation of multiplication, as shown in Examples 12 and 13.

Example 12: Translate the following: twice a number

The expression translates to 2 × x .

Example 13: Translate the following word problem into a mathematical expression: Jennifer had $15 dollars in the bank. Over the next two weeks she doubled her money.

The expression translates to 2 × 15.

One of the keywords that indicates multiplication is OF. In word problems, however, you may see more than one use of the word “of.” The only OF that indicates multiplication is the one that follows the keyword PERCENT, the percent sign, the keyword FRACTION, or a fraction. See Examples 14 and 15.

Example 14: Translate the following: twenty five percent of four hundred dollars

The expression translates to 0.25 × 400.

Note: Remember that a percent is changed to a decimal before multiplying.

Example 15: Translate the following: one‐third of twenty‐seven

key words for solving math word problems

Division keywords

Some common examples of division keywords are as follows:

  • QUOTIENT OF _____ AND _____
  • DIVIDE _____ BY _____
  • _____ DIVIDED BY _____
  • DIVIDED EQUALLY

The keywords PRODUCT OF and QUOTIENT OF are difficult for some people to differentiate. Here is a hint to help you remember which one indicates division and which one indicates multiplication: QUOTIENT is a “harder” word than “PRODUCT,” and division is a “harder” operation than multiplication.

Remember: Leading keywords define the corresponding AND or BY to mean divide, usually designated with the symbol ÷.

Example 16: Translate the following: the quotient of seven and a number

1. Because the keyword QUOTIENT OF is a leading keyword that defines AND, underline the words before and after AND: “seven” and “a number.”

  • the quotient of seven and a number

3. Translate each underlined expression and replace AND with a division sign.

  • The expression translates to 7 ÷ n .

Note: Here, the keyword QUOTIENT OF defines AND to mean division.

Example 17: Translate the following: divide negative thirty‐six by nine

1. Because the word DIVIDE is a leading keyword that defines the BY, underline the words before and after BY: “negative thirty‐six” and “nine.”

  • divide negative thirty‐six by nine

2. Circle the leading keyword and indicate the corresponding BY that it defines.

3. Translate each underlined expression and replace BY with a division sign.

key words for solving math word problems

Note: The first number goes in the numerator when using a fraction bar to indicate division. The number in the numerator (the −36) goes inside the “house” when using the long division symbol.

Some division keywords can be translated one word at a time. Instead, you just follow the sentence and replace with algebraic notations as you go along.

Example 18: Translate the following: a number divided by 16

key words for solving math word problems

Often, in story problems, the keyword that indicates division is PER. When a story problem asks for the speed of a vehicle in miles per hour, set up the expression to divide the number of miles by the number of hours. You not only directly translate “miles” ÷ “hours,” but also identify the number of miles and number of hours by finding them elsewhere in the problem. See Example 19.

Example 19: Translate the following word problem into a mathematical expression about speed: It takes three hours to travel 150 miles to grandmother's house. How do you find your average speed in miles per hour?

You find “miles” ÷ “hours” in the question. In the first part of the word problem, you find the number of miles, 150 miles, and the number of hours, three hours.

The expression translates to 150 ÷ 3.

Previous Keywords for Change in Order

Next Keywords Indicating Equality

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Elementary math word problem key words and their limitations.

When you tell your students you will be working on word problems, do you hear a chorus of groans? If so, you are not alone! Teaching students how to solve math word problems tends to not be the most exciting math exercise in an elementary math curriculum (especially not learning about word problem key words and how they can be used to solve problems). They also tend to be very challenging for students. No wonder many students don’t like them!

In order for students to become proficient in mathematics, however, they need to apply their math learning to real life situations , which can be achieved through word problems. This experience should not be about following rote procedures and computing correct responses. When solving these types of problems, it is important for students to apply multiple strategies to make sense of the problem and solve it. These experiences should be grounded in strategy application and problem solving, rather than simply computation.

Identifying word problem key words is one of many strategies elementary students can use to help them solve single and multi-step word problems. Additionally, students need access to anchor charts, tools, and manipulatives that will equip them with the resources they need for these problem solving experiences. Using keywords for math word problems is just one piece of the puzzle!

This blog post will answer the following questions:

  • What are word problem key words?
  • What are some examples of keywords for addition word problems?
  • Can you share some examples of keywords for subtraction word problems?
  • What are some examples of keywords for multiplication word problems?
  • Can you share some examples of keywords for division word problems?
  • What are the limitations of using keywords to solve word problems?
  • Is using word problem keywords an effective strategy?

key words for solving math word problems

What are Word Problem Key Words?

Word problem key words are words or phrases that signal which operations (addition, subtraction, multiplication, or division) are needed in order to solve a math word problem.

Using keywords for math word problems (often referred to as clue words and phrases) is a strategy to make sense of and solve word problems. It is the idea of training the brain to look for specific words and phrases to determine what mathematical operations are needed. Here is an example of this strategy in practice:

Erin reads the problem: Pat has 3 red shirts. He has 2 blue shirts. How many red and blue shirts does he have in all? After reading through the problem once, Erin rereads the problem but this time she is looking specifically for the clue words and phrases she has learned. She highlights or underlines the phrase “in all.” She has learned in class that “in all” signals to the reader that they need to add. This strategy has helped her make sense of the problem (which in this case means that the addition operation is needed), set up an equation (3 + 2 = ?), and solve for the answer (5 shirts).

a teacher showing students how to use word problem key words in math

Common Math Word Problem Key Words and Phrases

Below is a list of key words and phrases that students can use to solve addition, subtraction, multiplication, and division word problems. If you teach the younger grades, you’ll find the list of addition and subtraction key words helpful. If you teach the older grades, you’ll find those helpful, as well as the multiplication and division key words.

Addition Key Words

Here are some examples of addition key words :

  • increased by
  • larger than
  • longer than

Subtraction Key Words

Here are some examples of subtraction key words :

  • How many more…?
  • How many less…?
  • shorter than
  • smaller than

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Multiplication Key Words

Here are some examples of multiplication key words :

Division Key Words

Here are some examples of division key words :

  • equal group

elementary students solving word problems digitally

Limitations of Using Keywords to Solve Word Problems

When students are learning how to solve word problems, it is beneficial for them to be exposed to, directly taught, and given practice with key words (also sometimes written as word problem keywords or keywords for math word problems). However, students need to understand that problems can be solved in many different ways. This is just one tool in their toolkit.  It is not always the most effective strategy to solve a given word problem. For example, students should not be trained to always subtract when they see the word less because they could use a missing addend from addition to solve.  This strategy should be used along with other strategies (e.g. visualization). As students progress through their math education and come across more challenging word problems, this strategy will become less effective. As a result, your students need to be equipped with an abundance of diverse strategies.

Math Resources for 1st-5th Grade Teachers

If you need printable and digital math resources for your classroom, then check out my time and money-saving math collections below!

Free Elementary Math Resources

We would love for you to try these word problem resources with your students. It offers them opportunities to practice applying word problem key words strategies, as well as other problem solving strategies. You can download word problem worksheets specific to your grade level (along with lots of other math freebies) in our free printable math resources bundle using this link: free printable math activities for elementary teachers .

Check out my monthly word problem resources !

  • 1st Grade Word Problems
  • 2nd Grade Word Problems
  • 3rd Grade Word Problems
  • 4th Grade Word Problems
  • 5th Grade Word Problems

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Strategies for Solving Word Problems – Math

key words for solving math word problems

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:

key words for solving math word problems

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:

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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.

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key words for solving math word problems

No More Keywords for Math Word Problems

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key words for solving math word problems

The use of math keywords focuses on looking at the words of a word problem in isolation and not in the context of the problem. In this post, I share four reasons why using keywords for math word problems fail students .

There are 125 sheep and 5 dogs in a flock. How old is the shepherd?  

1st Student: “I can’t solve this because it doesn’t say anything about the shepherd.” 

2nd Student: “120 years old because 125 minus the 5 dogs in a flock.” 

3rd Student: “25.” [The student’s work shows 125 divided by 5].

4th Student: “25” [The student’s work shows 125 divided by 5].

5th Student: “25” [The student’s work shows 125 divided by 5].

6th Student: “It doesn’t tell you.” 

7th Student: “130” [The student’s work shows the sum of 125 and 5.]

8th Student: “65” [The student’s work shows (125 + 5) ÷ 2.]

9th Student: “25.” When asked to explain her solution, the student responded, “Because it doesn’t say the difference, or the sum, or the product.” 

Of the 32 eighth-grade students asked to solve this problem, only 8 of them were able to give a response indicating they were able to read the problem, make sense of it, and determine there was not enough information to solve it.   

While the results of this scenario are quite shocking, this kind of formulaic thinking when it comes to solving word problems is all too common. 

In fact, when another mathematics educator tried a similar activity with her first graders, her results were just as astounding. (See the original post and video here . )

So, what’s the problem?

Using Keywords For Math Word Problems

Our students have been trained to look for math keywords, or clues, to what operation they are expected to perform to solve a math word problem. While I completely understand that teachers have perfected the use of keywords over the years in order to provide a strategy that would prove successful both in the classroom and on standardized tests, the use of keywords does not require students to think critically about a problem or allow them to make sense of the situation.

On a recent search in Pinterest, I was not surprised to find a plethora of pins related to using keywords for math word problems. The picture below shows a list of all the keywords that I found– many of which, I disagree with the placement or inclusion of.

This poster shows an example of keywords for math word problems.

As a teacher, I can’t imagine what it would feel like to help my students memorize all of these terms. How are they going to learn them– with a weekly quiz?

I think not.

Why Not Keywords?

But using keywords for math word problems works just fine for me you say?

Van de Walle and Lovin (2006) and Van de Walle, Karp, and Bay-Williams (2012) offer four reasons to remove the use of keywords from our work with students:

1. Keywords can be Dangerous!

Many authors and resource creators use keywords in ways that differ from the way students expect them to be used which leads students to an incorrect solution strategy pathway. Add to that the use of multiple-meaning words and our students can become quickly overwhelmed and confused.

Consider the following problem: Julie left $9 on the table. Her brother left $6 on the table. How much money was left on the table? Use of the word “left” might indicate to some that the solution to this problem is obtained with subtraction; however, this is an addition situation because two quantities are being joined together. 

(Find more “Keyword Fails” here .)

2. Use of Keywords Misses the Big Picture

The use of math keywords focuses on looking at the words in isolation and not in the context of the problem.

“Mathematics is about reasoning and making sense of situations” (Van de Walle & Lovin, 2006, p. 70); therefore, students should analyze the structure of the problems in the context not just dissect them for keywords.

When students begin to view problem situations in this way, they can identify the bigger picture and make connections between problem situations and the necessary solution strategy required to solve the problem.

3. What If There’s No Keyword?

Many problems, especially as students begin to advance to more sophisticated work, have no keywords.

Consider the following problem: Dominique had 10 flower petals. Four were green and the rest were orange. How many orange flower petals does Dominique have?  

Because this problem does not contain keywords, students who rely on this approach will not have a strategy on which to rely, which will most likely result in a new word, like “rest” being added to the subtraction word list.

4. Will Keywords Support Students Long-Term?

While teachers in the younger grades claim to have great success using keywords for math word problems, the use of keywords does not work with more advanced problems or those with more than one step.

Therefore, students who do not attend to the meaning of a problem while solving it will be unsuccessful in completing the problem because they will miss the intermediate steps needed to lead to the final result.

This is a quote about using tricks to learn math.

Making Sense of Problems

The first Mathematical Practice Standard of the Common Core State Standards for Math describe mathematically proficient students as those who can: 

  • Explain the meaning of a problem
  • Plan a solution pathway rather than jumping to a solution
  • Continually check for reasonableness and ask, “Does this make sense?” 

These three skills are essential to solving math word problems successfully.

But, how do we help students develop them?

Using Tricks To Replace Thinking

Tina Cardone, the author of Nix the Tricks , a guide to avoiding non-conceptually developmental short-cuts, suggests having students think about the words of the problem as a whole and focus on what is happening in the problem in context.

Students can accomplish this by visualizing the situation and creating a mental picture of the actions that are taking place. Once they understand the actions, students can then connect the actions to symbols.

After students have experience with a variety of problem situations, some patterns will begin to emerge as students begin to recognize recurring themes, such as joining, part-part-whole, separating, comparing, equal groups, sharing, and measuring.

Throughout the year, teachers can record the different situations students encounter on an anchor chart. Then replace that old, out-dated math keywords poster with the brand-spanking-new operation situations poster.

This poster shows how the operation situations can be used to replace keywords for math word problems.

Want to know more about the operation situations and strategies to help with math word problems ?

Download the free poster above using the form below and click here to learn more about strategies to help with math word problems.

What strategies do you use to emphasize making sense of word problems with your students? Share your ideas in the comments section below. 

  • Common Core State Standards for Math
  • https://gfletchy.com/2015/01/12/teaching-keywords-forget-about-it/
  • http://nixthetricks.com/
  • http://tjzager.com/2014/10/18/making-sense/
  • Van de Wall, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). Elementary and middle school mathematics: Teaching developmentally. Boston, MA: Pearson.
  • Van de Wall, J. A. and Lovin, L. H. (2006). Teaching student-centered mathematics: Grades 3 – 5. Boston, MA: Pearson.

key words for solving math word problems

Shametria Routt Banks

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8 Responses

Love the Analyzing Word Problems poster!

Thank you SOOOOO very much. I always thought that lists of key words were incomplete and had so much crossover … and needed to be used in context. You have combined all of this in a clear and concise way. LOVE IT!

Hi Patricia!

I’m so glad you found the post useful!

~ Shametria

Hi. As a non math teacher,I really like this approach. Word problems were the hated vegetable that went with a main course I hated and couldn’t cut. I was disappointed, though,that so many links didn’t work. I’m not sure how old the post is, so that may be the problem. But thanks for teaching me to teach them.

I’m so glad you found the post helpful! I went through the post and all the links work; however, you may have read it at a time when I was updating the connecting posts and they were in draft form. My apologies about that. All the links do work though, so I encourage you to take another look. If you have any questions, please contact me at [email protected] . Thank you!

What about EL learners? I have third grade newcomers who have zero language and have to work through word problems.

Interesting concept and makes sense… I tell my students to think about the action that is taking place to help them determine the operation needed.

Hi LaChone! Love that you don’t focus on keywords– such a gamechanger!

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Translating Word Problems: Keywords

Keywords Examples

The hardest thing about doing word problems is using the part where you need to take the English words and translate them into mathematics. Usually, once you get the math equation, you're fine; the actual math involved is often fairly simple. But figuring out the actual equation can seem nearly impossible. What follows is a list of hints and helps. Be advised, however: To really learn "how to do" word problems, you will need to practice, practice, practice.

How do I convert word problems into math?

  • Read the entire exercise.
  • Work in an organized manner.
  • Look for the keywords.
  • Apply your knowledge of "the real world".

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Algebra Word Problems

Step 1 in effectively translating and solving word problems is to read the problem entirely. Don't start trying to solve anything when you've only read half a sentence. Try first to get a feel for the whole problem; try first to see what information you have, and then figure out what you still need.

Step 2 is to work in an organized manner. Figure out what you need but don't have. Name things. Pick variables to stand for the unknows, clearly labelling these variables with what they stand for. Draw and label pictures neatly. Explain your reasoning as you go along. And make sure you know just exactly what the problem is actually asking for. You need to do this for two reasons:

  • Working clearly will help you think clearly, and
  • figuring out what you need will help you translate your final answer back into English.

Regarding point (a) above:

It can be really frustrating (and embarassing) to spend fifteen minutes solving a word problem on a test, only to realize at the end that you no longer have any idea what " x " stands for, so you have to do the whole problem over again. I did this on a calculus test — thank heavens it was a short test! — and, trust me, you don't want to do this to yourself. Taking fifteen seconds to label things is a better use of your time than spending fifteen minutes reworking the entire exercise!

Step 3 is to look for "key" words. Certain words indicate certain mathematica operations. Some of those words are easy. If an exercise says that one person "added" her marbles to the pile belonging to somebody else, and asks for how many marbles are now in the pile, you know that you'll be adding two numbers.

What are common keywords for word problems?

The following is a listing of most of the more-common keywords for word problems:

increased by more than combined, together total of sum, plus added to comparatives ("greater than", etc)

Subtraction:

decreased by minus, less difference between/of less than, fewer than left, left over, after save (old-fashioned term) comparatives ("smaller than", etc)

Multiplication:

of times, multiplied by product of increased/decreased by a factor of (this last type can involve both addition or subtraction and multiplication!) twice, triple, etc each ("they got three each", etc)

per, a out of ratio of, quotient of percent (divide by 100) equal pieces, split average

is, are, was, were, will be gives, yields sold for, cost

Note that "per", in "Division", means "divided by", as in "I drove 90 miles on three gallons of gas, so I got 30 miles per gallon". Also, "a" sometimes means "divided by", as in "When I tanked up, I paid $12.36 for three gallons, so the gas was $4.12 a gallon".

Warning: The "less than" construction, in "Subtraction", is backwards in the English from what it is in the math. If you need, for instance, to translate " 1.5 less than x ", the temptation is to write " 1.5 −  x ". Do not do this!

You can see how this is wrong by using this construction in a "real world" situation: Consider the statement, "He makes $1.50 an hour less than me." You do not figure his wage by subtracting your wage from $1.50 . Instead, you subtract $1.50 from your wage. So remember: the "less than" construction is backwards.

(Technically, the "greater than" construction, in "Addition", is also backwards in the math from the English. But the order in addition doesn't matter, so it's okay to add backwards, because the result will be the same either way.)

Also note that order is important in the "quotient/ratio of" and "difference between/of" constructions. If a problems says "the ratio of x and y ", it means " x divided by y ", not " y divided by x ". If the problem says "the difference of x and y ", it means " x  −  y ", not " y  −  x ".

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Some times, you'll be expected to bring your "real world" knowledge to an exercise. For instance, suppose you're told that "Shelby worked eight hours MTThF and six hours WSat". You would be expected to understand that this meant that she worked eight hours for each of the four days Monday, Tuesday, Thursday, and Friday; and six hours for each of the two days Wednesday and Saturday. Suppose you're told that Shelby earns "time and a half" for any hours she works over forty for a given week. You would be expected to know that "time and a half" means 1.5 times her base rate of pay; if her base rate is twelve dollars an hour, then she'd get 1.5 × 12 = 18 dollars for every over-time hour.

You'll be expected to know that a "dozen" is twelve; you may be expected to know that a "score" is twenty. You'll be expected to know the number of days in a year, the number of hours in a day, and other basic units of measure.

Probably the greatest source of error, though, is the use of variables without definitions. When you pick a letter to stand for something, write down explicitly what that latter is meant to stand for. Does " S " stand for "Shelby" or for "hours Shelby worked"? If the former, what does this mean, in practical terms? (And, if you can't think of any meaningful definition, then maybe you need to slow down and think a little more about what's going on in the word problem.)

Algebra Tutors

In all cases, don't be shy about using your "real world" knowledge. Sometimes you'll not feel sure of your translation of the English into a mathematical expression or equation. In these cases, try plugging in numbers. For instance, if you're not sure if you should be dividing or multiplying, try the process each way with regular numbers. For instance, suppose you're not sure if "half of (the unknown amount)" should be represented by multiplying by one-half, or by dividing by one-half. If you use numbers, you can be sure. Pick an easy number, like ten. Half of ten is five, so we're looking for the operation (that is, multiplication or division) that gives us an answer of 5 . First, let's try division:

ten divided by one-half:

10/(1/2) = (10/1)×(2/1) = 20

Well, that's clearly wrong. How about going the other way?

ten multiplied by one-half:

(10)×(1/2) = 10 ÷ 2 = 5

That's more like it! You know that half of ten is five, and now you can see which mathematical operations gets you the right value. So now you'd know that the expression you're wanting is definitely " (1/2) x ".

You have experience and knowledge; don't be afraid to apply your skills to this new context!

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key words for solving math word problems

Solving Word Questions

With LOTS of examples!

In Algebra we often have word questions like:

Example: Sam and Alex play tennis.

On the weekend Sam played 4 more games than Alex did, and together they played 12 games.

How many games did Alex play?

How do we solve them?

The trick is to break the solution into two parts:

Turn the English into Algebra.

Then use Algebra to solve.

Turning English into Algebra

To turn the English into Algebra it helps to:

  • Read the whole thing first
  • Do a sketch if possible
  • Assign letters for the values
  • Find or work out formulas

You should also write down what is actually being asked for , so you know where you are going and when you have arrived!

Also look for key words:

Thinking Clearly

Some wording can be tricky, making it hard to think "the right way around", such as:

Example: Sam has 2 dollars less than Alex. How do we write this as an equation?

  • Let S = dollars Sam has
  • Let A = dollars Alex has

Now ... is that: S − 2 = A

or should it be: S = A − 2

or should it be: S = 2 − A

The correct answer is S = A − 2

( S − 2 = A is a common mistake, as the question is written "Sam ... 2 less ... Alex")

Example: on our street there are twice as many dogs as cats. How do we write this as an equation?

  • Let D = number of dogs
  • Let C = number of cats

Now ... is that: 2D = C

or should it be: D = 2C

Think carefully now!

The correct answer is D = 2C

( 2D = C is a common mistake, as the question is written "twice ... dogs ... cats")

Let's start with a really simple example so we see how it's done:

Example: A rectangular garden is 12m by 5m, what is its area ?

Turn the English into Algebra:

  • Use w for width of rectangle: w = 12m
  • Use h for height of rectangle: h = 5m

Formula for Area of a Rectangle : A = w × h

We are being asked for the Area.

A = w × h = 12 × 5 = 60 m 2

The area is 60 square meters .

Now let's try the example from the top of the page:

tennis

Example: Sam and Alex play Tennis. On the weekend Sam played 4 more games than Alex did, and together they played 12 games. How many games did Alex play?

  • Use S for how many games Sam played
  • Use A for how many games Alex played

We know that Sam played 4 more games than Alex, so: S = A + 4

And we know that together they played 12 games: S + A = 12

We are being asked for how many games Alex played: A

Which means that Alex played 4 games of tennis.

Check: Sam played 4 more games than Alex, so Sam played 8 games. Together they played 8 + 4 = 12 games. Yes!

A slightly harder example:

table

Example: Alex and Sam also build tables. Together they make 10 tables in 12 days. Alex working alone can make 10 in 30 days. How long would it take Sam working alone to make 10 tables?

  • Use a for Alex's work rate
  • Use s for Sam's work rate

12 days of Alex and Sam is 10 tables, so: 12a + 12s = 10

30 days of Alex alone is also 10 tables: 30a = 10

We are being asked how long it would take Sam to make 10 tables.

30a = 10 , so Alex's rate (tables per day) is: a = 10/30 = 1/3

Which means that Sam's rate is half a table a day (faster than Alex!)

So 10 tables would take Sam just 20 days.

Should Sam be paid more I wonder?

And another "substitution" example:

track

Example: Jenna is training hard to qualify for the National Games. She has a regular weekly routine, training for five hours a day on some days and 3 hours a day on the other days. She trains altogether 27 hours in a seven day week. On how many days does she train for five hours?

  • The number of "5 hour" days: d
  • The number of "3 hour" days: e

We know there are seven days in the week, so: d + e = 7

And she trains 27 hours in a week, with d 5 hour days and e 3 hour days: 5d + 3e = 27

We are being asked for how many days she trains for 5 hours: d

The number of "5 hour" days is 3

Check : She trains for 5 hours on 3 days a week, so she must train for 3 hours a day on the other 4 days of the week.

3 × 5 hours = 15 hours, plus 4 × 3 hours = 12 hours gives a total of 27 hours

Some examples from Geometry:

Example: A circle has an area of 12 mm 2 , what is its radius?

  • Use A for Area: A = 12 mm 2
  • Use r for radius

And the formula for Area is: A = π r 2

We are being asked for the radius.

We need to rearrange the formula to find the area

Example: A cube has a volume of 125 mm 3 , what is its surface area?

Make a quick sketch:

  • Use V for Volume
  • Use A for Area
  • Use s for side length of cube
  • Volume of a cube: V = s 3
  • Surface area of a cube: A = 6s 2

We are being asked for the surface area.

First work out s using the volume formula:

Now we can calculate surface area:

An example about Money:

pizza

Example: Joel works at the local pizza parlor. When he works overtime he earns 1¼ times the normal rate. One week Joel worked for 40 hours at the normal rate of pay and also worked 12 hours overtime. If Joel earned $660 altogether in that week, what is his normal rate of pay?

  • Joel's normal rate of pay: $N per hour
  • Joel works for 40 hours at $N per hour = $40N
  • When Joel does overtime he earns 1¼ times the normal rate = $1.25N per hour
  • Joel works for 12 hours at $1.25N per hour = $(12 × 1¼N) = $15N
  • And together he earned $660, so:

$40N + $(12 × 1¼N) = $660

We are being asked for Joel's normal rate of pay $N.

So Joel’s normal rate of pay is $12 per hour

Joel’s normal rate of pay is $12 per hour, so his overtime rate is 1¼ × $12 per hour = $15 per hour. So his normal pay of 40 × $12 = $480, plus his overtime pay of 12 × $15 = $180 gives us a total of $660

More about Money, with these two examples involving Compound Interest

Example: Alex puts $2000 in the bank at an annual compound interest of 11%. How much will it be worth in 3 years?

This is the compound interest formula:

So we will use these letters:

  • Present Value PV = $2,000
  • Interest Rate (as a decimal): r = 0.11
  • Number of Periods: n = 3
  • Future Value (the value we want): FV

We are being asked for the Future Value: FV

Example: Roger deposited $1,000 into a savings account. The money earned interest compounded annually at the same rate. After nine years Roger's deposit has grown to $1,551.33 What was the annual rate of interest for the savings account?

The compound interest formula:

  • Present Value PV = $1,000
  • Interest Rate (the value we want): r
  • Number of Periods: n = 9
  • Future Value: FV = $1,551.33

We are being asked for the Interest Rate: r

So the annual rate of interest is 5%

Check : $1,000 × (1.05) 9 = $1,000 × 1.55133 = $1,551.33

And an example of a Ratio question:

Example: At the start of the year the ratio of boys to girls in a class is 2 : 1 But now, half a year later, four boys have left the class and there are two new girls. The ratio of boys to girls is now 4 : 3 How many students are there altogether now?

  • Number of boys now: b
  • Number of girls now: g

The current ratio is 4 : 3

Which can be rearranged to 3b = 4g

At the start of the year there was (b + 4) boys and (g − 2) girls, and the ratio was 2 : 1

b + 4 g − 2 = 2 1

Which can be rearranged to b + 4 = 2(g − 2)

We are being asked for how many students there are altogether now: b + g

There are 12 girls !

And 3b = 4g , so b = 4g/3 = 4 × 12 / 3 = 16 , so there are 16 boys

So there are now 12 girls and 16 boys in the class, making 28 students altogether .

There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1

And now for some Quadratic Equations :

Example: The product of two consecutive even integers is 168. What are the integers?

Consecutive means one after the other. And they are even , so they could be 2 and 4, or 4 and 6, etc.

We will call the smaller integer n , and so the larger integer must be n+2

And we are told the product (what we get after multiplying) is 168, so we know:

n(n + 2) = 168

We are being asked for the integers

That is a Quadratic Equation , and there are many ways to solve it. Using the Quadratic Equation Solver we get −14 and 12.

Check −14: −14(−14 + 2) = (−14)×(−12) = 168 YES

Check 12: 12(12 + 2) = 12×14 = 168 YES

So there are two solutions: −14 and −12 is one, 12 and 14 is the other.

Note: we could have also tried "guess and check":

  • We could try, say, n=10: 10(12) = 120 NO (too small)
  • Next we could try n=12: 12(14) = 168 YES

But unless we remember that multiplying two negatives make a positive we might overlook the other solution of (−14)×(−12).

Example: You are an Architect. Your client wants a room twice as long as it is wide. They also want a 3m wide veranda along the long side. Your client has 56 square meters of beautiful marble tiles to cover the whole area. What should the length of the room be?

Let's first make a sketch so we get things right!:

  • the length of the room: L
  • the width of the room: W
  • the total Area including veranda: A
  • the width of the room is half its length: W = ½L
  • the total area is the (room width + 3) times the length: A = (W+3) × L = 56

We are being asked for the length of the room: L

This is a quadratic equation , there are many ways to solve it, this time let's use factoring :

And so L = 8 or −14

There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!

So the length of the room is 8 m

L = 8, so W = ½L = 4

So the area of the rectangle = (W+3) × L = 7 × 8 = 56

There we are ...

... I hope these examples will help you get the idea of how to handle word questions. Now how about some practice?

Bright Hub Education

Identifying Keywords in Math Word Problems

Many students struggle with word problems as it seems they are intended to confuse you. The key to solving them is to figure out what the word problem is asking you to do, and break it down into a simple equation. Use this guide to identify keyword or phrases that will clue you into what the problem is asking you to do.

Addition Keywords

  • altogether; There were two blue eggs and three green eggs. How many eggs were there altogether ?
  • sum of; What is the sum of two plus two?
  • plus; What is the sum of two plus two?
  • total; What is the total of two plus two?
  • add; Add two and two.
  • together; Together , what two and two?
  • Combine; Combine two and two.

Subtraction Keywords

  • Take away; Take away four from five.
  • Subtract; Subtract four from five.
  • Minus; Five minus four is what?
  • From; Four from five is what?
  • Remain; How many remain after you take four from five?
  • Left; How many are left?

Multiplication Keywords

  • Product; What is the product of four and five?
  • Times; There are five times as many as there were.
  • Multiply; Multiply the numbers four and five.
  • As much (When preceded by a whole number, but not a fraction.);There was twice as much ice cream before you ate.
  • Some addition keywords are used in multiplication as well since multiplication is just another way of doing addition. For instance; There were four groups of fruit. There were 5 pieces in each group. How many were there altogether ?

Division Keywords

  • Divided by; Four divided by two is what?
  • Divide; Divide four by two.
  • of (when preceded by a fraction); Half of four is what?
  • As much (When preceded by a fraction.); I would like half as much as she had.
  • Into; Four goes into twenty how many times?

These are some of the most common math keywords used. Look for these keywords when you are trying to decided what the math question is actually asking you to do.

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How to REALLY Help Kids Solve Math Word Problems

Recently, I was working on multiplying and dividing by 2 with one of my kids. A constant refrain was, “What does multiply mean?” or “But remember, what does that division sign represent?”

As they started to grapple with these concepts and play with manipulatives and pictures and equations, I tried to make sure we always came back to the why. But why are you counting by 2’s to get the answer? And why are we splitting our set into groups of 2? Or 2 equal groups?

Even after all that work, and a high level of confidence in solving basic problems, when we began to work through math word problems, what do you think they did?

Pulled out all the numbers and added. Yes, added. Even for division.

After spending so much time talking about multiplication and division and practicing with hands on manipulatives and drawing pictures …the gut response to a word problem was to pull out the numbers without thinking and add them all together !

Is this ever true of your kids? Are they “number pluckers?” Or do they feel confident solving math word problems of every shape and form?

If you’re looking for help teaching kids to solve word problems , here are some tips and ideas for you!

Do you teach your kids to rely on keywords as they solve word problems? Do they still struggle? This post explains the problem with relying on keywords to solve word problems, plus ideas to help kids make sense of problems. Plus, it includes a set of free printable templates!

The Goal of Math Instruction

I think this begs the question, “Why are we doing this anyway?? Does it really matter if kids can solve word problems? Why can’t we just teach the facts?”

Well, I believe that ultimately our goal is not to produce quick and efficient machines (that’s what calculators are for), but rather to raise up strong problem solvers .

To help develop critical thinkers, and kids who apply logical reasoning and think outside the box.

I love this quote from S.Y. Gillan from the book, “ Problems Without Figures :”

Every problem in arithmetic calls for two distinct and widely different kinds of work: first, the solution, which involves a comprehension of the conditions of the problem and their relation to one another; second, the operation. First, we decide what to do ; this requires reasoning. Then we do the work; this is merely a mechanical process…Adding, subtracting, multiplying and dividing do not train the power to reason, but deciding in a given set of conditions which of these operations to use and why, is the feature of arithmetic which requires reasoning.

Do you hear what he’s saying? We’re not just teaching kids to do the work : the actual process of adding 2 numbers together. We’re teaching kids to reason and then apply their reasoning to solve problems .

The Problem with Relying On Keywords in Math Word Problems

As we spend intentional time helping kids make sense of word problems, we have to help them make sense of the situation . That means we have to move away from relying on keywords . Why?

1. Relying on keywords can lead kids astray:

Even though we, as teachers, give kids lists of keywords with the very best of intentions, this is actually not helpful if they’re used in a different way than kids are used to.

Here’s an example. Say kids are given the following word problem:

Ben has eighteen toy cars. He has seven less than his brother Andy. How many toy cars does Andy have?

Immediately, kids see two numbers: 18 and 7. They then see the keyword “less,” and what operation do we typically associate that keyword with? Subtraction .

Therefore, kids complete the problem by subtracting 7 from 18 for an answer of 11 .

What’s the problem here?

Well, in this situation, we actually need to add to find the final solution . Have you ever seen “less” listed on a keyword chart under addition? I haven’t!

2. Not all math word problems include keywords:

Second, what about those problems that present a situation without an actual keyword? If kids are entirely dependent on keywords, they’ll just be lost!

Here’s a great article that explains the problem with keywords and includes a helpful exercise to help kids think about the situation.

Although each word problem includes the term “total,” they all require a different operation to solve it, forcing kids to think about the situation.

Read: Solving Math Word Problems Without Keywords .

3. Real life math doesn’t include keywords:

Finally, looking for keywords is not practical advice for real world problem solving. When our kids come against a situation in their life that requires math, there will be no keywords.

Just messy, real life.

So what can we do?

Well first, here are some questions you can ask and encourage your kids to ask as they seek to understand the situation rather than pluck out keywords or numbers:

  • How would you describe the situation in your own words?
  • How do you picture this problem in your mind?
  • Can you draw a picture or model to represent this situation?

The goal is to really probe kids and force them to think about and picture the situation .

Yes, this takes more practice and work than plucking out numbers and keywords. But remember the end goal and press on!

Second, I have some math word problem solving templates that you can use to help your kids think about the situation, draw the situation and then do the actual calculations.

key words for solving math word problems

There are a few different templates here, so I hope you find one that will meet your needs!

The goal of these templates is to help kids draw a picture of the situation and use that to come up with a logical plan to solve.

We don’t want kids to throw logic and reasoning out the window. We want to encourage them to make reasonable decisions and strategies as they work out solutions .

Some include space to check their answer as well.

Simply enter your email in the form below and the math word problem templates will be sent your way!

Bethany, These resources are great! I enjoy reading the tips and references even more!! As an educator coming back to teaching math after not doing so for several years, I feel empowered! Thank you for your selflessness. I am very appreciative and so are my students.

Aw thank you so much for your kind words Charlene! I’m so glad you’re finding lots of great ideas and resources! I look forward to creating and sharing more in the future. 🙂

These are so helpful Thankyou 🙂

Dear Math Geek Mama,

I want to say Thank You for your endless resources and wisdom. I came upon this particular “Math Talk” at a time when I am teaching “Math Boot Camp” and assigned the higher level scholars. I am working on solving performance tasks which really are word problems and application and more!

You really made me think about keywords which is a huge focus of mine when I ask what the number clues are and the word(s) that tells what to do with those numbers. You are absolutely right that keywords can mean different things and are not absolute.

I really like your real to life examples, logic, and resources. I truly hope to purchase from you and not just use your freebies. You are more than generous and I thank you!

Mrs. Felicia Barlow

Hi Felicia!

Thank you so much for sharing your experiences and how this made you think more about keywords! They’re certainly not all bad, but I just think we have to be sure kids aren’t relying ONLY on keywords. And I’m so glad you’re able to find lots of fun resources here, I love sharing them. 🙂

Thank you for the templates

thank you this has been very insightful.

Bethany, Thank you, I hope you don’t mind if I grab your freebie, sometimes I help my grandkids with their math so I am here looking at how you are teaching math now-a-days. I remember doing grouping and sorting with my story problems as a child some 50 years ago. I guess maybe things haven’t changed . There was a time period I think teaching kind of got a bit lost but in some ways it seems to be getting back to the basics of teaching kids how to think. Thank you again I think this will help me with the kids. Have a great week. Martha

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  • How do you solve word problems?
  • To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
  • How do you identify word problems in math?
  • Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
  • Is there a calculator that can solve word problems?
  • Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
  • What is an age problem?
  • An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

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Solving word problem chart

1. Understand the Problem by Paraphrasing

2. identify key information and variables, 3. translate words into mathematical symbols, 4. break down the problem into manageable parts, 5. draw diagrams or visual representations, 6. use estimation to predict answers, 7. apply logical reasoning for unknown variables, 8. leverage similar problems as templates, 9. check answers in the context of the problem, 10. reflect and learn from mistakes.

Have you ever observed the look of confusion on a student’s face when they encounter a math word problem ? It’s a common sight in classrooms worldwide, underscoring the need for effective strategies for solving math word problems . The main hurdle in solving math word problems is not just the math itself but understanding how to translate the words into mathematical equations that can be solved.

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Generic advice like “read the problem carefully” or “practice more” often falls short in addressing students’ specific difficulties with word problems. Students need targeted math word problem strategies that address the root of their struggles head-on. 

A Guide on Steps to Solving Word Problems: 10 Strategies 

One of the first steps in tackling a math word problem is to make sure your students understand what the problem is asking. Encourage them to paraphrase the problem in their own words. This means they rewrite the problem using simpler language or break it down into more digestible parts. Paraphrasing helps students grasp the concept and focus on the problem’s core elements without getting lost in the complex wording.

Original Problem: “If a farmer has 15 apples and gives away 8, how many does he have left?”

Paraphrased: “A farmer had some apples. He gave some away. Now, how many apples does he have?”

This paraphrasing helps students identify the main action (giving away apples) and what they need to find out (how many apples are left).

Play these subtraction word problem games in the classroom for free:

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Students often get overwhelmed by the details in word problems. Teach them to identify key information and variables essential for solving the problem. This includes numbers , operations ( addition , subtraction , multiplication , division ), and what the question is asking them to find. Highlighting or underlining can be very effective here. This visual differentiation can help students focus on what’s important, ignoring irrelevant details.

  • Encourage students to underline numbers and circle keywords that indicate operations (like ‘total’ for addition and ‘left’ for subtraction).
  • Teach them to write down what they’re solving for, such as “Find: Total apples left.”

Problem: “A classroom has 24 students. If 6 more students joined the class, how many students are there in total?”

Key Information:

  • Original number of students (24)
  • Students joined (6)
  • Looking for the total number of students

Here are some fun addition word problems that your students can play for free:

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The transition from the language of word problems to the language of mathematics is a critical skill. Teach your students to convert words into mathematical symbols and equations. This step is about recognizing keywords and phrases corresponding to mathematical operations and expressions .

Common Translations:

  • “Total,” “sum,” “combined” → Addition (+)
  • “Difference,” “less than,” “remain” → Subtraction (−)
  • “Times,” “product of” → Multiplication (×)
  • “Divided by,” “quotient of” → Division (÷)
  • “Equals” → Equals sign (=)

Problem: “If one book costs $5, how much would 4 books cost?”

Translation: The word “costs” indicates a multiplication operation because we find the total cost of multiple items. Therefore, the equation is 4 × 5 = $20

Complex math word problems can often overwhelm students. Incorporating math strategies for problem solving, such as teaching them to break down the problem into smaller, more manageable parts, is a powerful approach to overcome this challenge. This means looking at the problem step by step rather than simultaneously trying to solve it. Breaking it down helps students focus on one aspect of the problem at a time, making finding the solution more straightforward.

Problem: “John has twice as many apples as Sarah. If Sarah has 5 apples, how many apples do they have together?”

Steps to Break Down the Problem:

Find out how many apples John has: Since John has twice as many apples as Sarah, and Sarah has 5, John has 5 × 2 = 10

Calculate the total number of apples: Add Sarah’s apples to John’s to find the total,  5 + 10 = 15

By splitting the problem into two parts, students can solve it without getting confused by all the details at once.

Explore these fun multiplication word problem games:

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Diagrams and visual representations can be incredibly helpful for students, especially when dealing with spatial or quantity relationships in word problems. Encourage students to draw simple sketches or diagrams to represent the problem visually. This can include drawing bars for comparison, shapes for geometry problems, or even a simple distribution to better understand division or multiplication problems .

Problem: “A garden is 3 times as long as it is wide. If the width is 4 meters, how long is the garden?”

Visual Representation: Draw a rectangle and label the width as 4 meters. Then, sketch the length to represent it as three times the width visually, helping students see that the length is 4 × 3 = 12

Estimation is a valuable skill in solving math word problems, as it allows students to predict the answer’s ballpark figure before solving it precisely. Teaching students to use estimation can help them check their answers for reasonableness and avoid common mistakes.

Problem: “If a book costs $4.95 and you buy 3 books, approximately how much will you spend?”

Estimation Strategy: Round $4.95 to the nearest dollar ($5) and multiply by the number of books (3), so 5 × 3 = 15. Hence, the estimated total cost is about $15.

Estimation helps students understand whether their final answer is plausible, providing a quick way to check their work against a rough calculation.

Check out these fun estimation and prediction word problem worksheets that can be of great help:

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When students encounter problems with unknown variables, it’s crucial to introduce them to logical reasoning. This strategy involves using the information in the problem to deduce the value of unknown variables logically. One of the most effective strategies for solving math word problems is working backward from the desired outcome. This means starting with the result and thinking about the steps leading to that result, which can be particularly useful in algebraic problems.

Problem: “A number added to three times itself equals 32. What is the number?”

Working Backward:

Let the unknown number be x.

The equation based on the problem is  x + 3x = 32

Solve for x by simplifying the equation to 4x=32, then dividing by 4 to find x=8.

By working backward, students can more easily connect the dots between the unknown variable and the information provided.

Practicing problems of similar structure can help students recognize patterns and apply known strategies to new situations. Encourage them to leverage similar problems as templates, analyzing how a solved problem’s strategy can apply to a new one. Creating a personal “problem bank”—a collection of solved problems—can be a valuable reference tool, helping students see the commonalities between different problems and reinforcing the strategies that work.

Suppose students have solved a problem about dividing a set of items among a group of people. In that case, they can use that strategy when encountering a similar problem, even if it’s about dividing money or sharing work equally.

It’s essential for students to learn the habit of checking their answers within the context of the problem to ensure their solutions make sense. This step involves going back to the original problem statement after solving it to verify that the answer fits logically with the given information. Providing a checklist for this process can help students systematically review their answers.

Checklist for Reviewing Answers:

  • Re-read the problem: Ensure the question was understood correctly.
  • Compare with the original problem: Does the answer make sense given the scenario?
  • Use estimation: Does the precise answer align with an earlier estimation?
  • Substitute back: If applicable, plug the answer into the problem to see if it works.

Problem: “If you divide 24 apples among 4 children, how many apples does each child get?”

After solving, students should check that they understood the problem (dividing apples equally).

Their answer (6 apples per child) fits logically with the number of apples and children.

Their estimation aligns with the actual calculation.

Substituting back 4×6=24 confirms the answer is correct.

Teaching students to apply logical reasoning, leverage solved problems as templates, and check their answers in context equips them with a robust toolkit for tackling math word problems efficiently and effectively.

One of the most effective ways for students to improve their problem-solving skills is by reflecting on their errors, especially with math word problems. Using word problem worksheets is one of the most effective strategies for solving word problems, and practicing word problems as it fosters a more thoughtful and reflective approach to problem-solving

These worksheets can provide a variety of problems that challenge students in different ways, allowing them to encounter and work through common pitfalls in a controlled setting. After completing a worksheet, students can review their answers, identify any mistakes, and then reflect on them in their mistake journal. This practice reinforces mathematical concepts and improves their math problem solving strategies over time.

3 Additional Tips for Enhancing Word Problem-Solving Skills

Before we dive into the importance of reflecting on mistakes, here are a few impactful tips to enhance students’ word problem-solving skills further:

1. Utilize Online Word Problem Games

A word problem game

Incorporate online games that focus on math word problems into your teaching. These interactive platforms make learning fun and engaging, allowing students to practice in a dynamic environment. Games can offer instant feedback and adaptive challenges, catering to individual learning speeds and styles.

Here are some word problem games that you can use for free:

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2. Practice Regularly with Diverse Problems

Word problem worksheet

Consistent practice with a wide range of word problems helps students become familiar with different questions and mathematical concepts. This exposure is crucial for building confidence and proficiency.

Start Practicing Word Problems with these Printable Word Problem Worksheets:

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3. Encourage Group Work

Solving word problems in groups allows students to share strategies and learn from each other. A collaborative approach is one of the best strategies for solving math word problems that can unveil multiple methods for tackling the same problem, enriching students’ problem-solving toolkit.

Conclusion 

Mastering math word problems is a journey of small steps. Encourage your students to practice regularly, stay curious, and learn from their mistakes. These strategies for solving math word problems are stepping stones to turning challenges into achievements. Keep it simple, and watch your students grow their confidence and skills, one problem at a time.

Frequently Asked Questions (FAQs)

How can i help my students stay motivated when solving math word problems.

Encourage small victories and use engaging tools like online games to make practice fun and rewarding.

What's the best way to teach beginners word problems?

Begin with simple problems that integrate everyday scenarios to make the connection between math and real-life clear and relatable.

How often should students practice math word problems?

Regular, daily practice with various problems helps build confidence and problem-solving skills over time.

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120 Math Word Problems To Challenge Students Grades 1 to 8

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Written by Marcus Guido

Hey teachers! 👋

Use Prodigy to spark a love for math in your students – including when solving word problems!

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You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.

A jolt of creativity would help. But it doesn’t come.

Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.

This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes.

There are 120 examples in total.

The list of examples is supplemented by tips to create engaging and challenging math word problems.

120 Math word problems, categorized by skill

Addition word problems.

A teacher is teaching three students with a whiteboard happily.

Best for: 1st grade, 2nd grade

1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total?

2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now?

3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total?

5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies?

6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?

7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now?

8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total?

Subtraction word problems

Best for: 1st grade, second grade

9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left?

10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing?

11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

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Practice math word problems with Prodigy Math

Join millions of teachers using Prodigy to make learning fun and differentiate instruction as they answer in-game questions, including math word problems from 1st to 8th grade!

12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half?

13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now?

14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month?

15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left?

16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left?

Multiplication word problems

A hand holding a pen is doing calculation on a pice of papper

Best for: 2nd grade, 3rd grade

17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have?

18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total?

19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?

20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total?

21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn?

Division word problems

Best for: 3rd grade, 4th grade, 5th grade

22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag?

23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on?

24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total?

25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost?

26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible?

Mixed operations word problems

A female teacher is instructing student math on a blackboard

27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now?

28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?

29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have?

30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag?

Ordering and number sense word problems

31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?

32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?

33. Composing Numbers: What number is 6 tens and 10 ones?

34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I?

35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points?

Fractions word problems

A student is drawing on a notebook, holding a pencil.

Best for: 3rd grade, 4th grade, 5th grade, 6th grade

36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar?

37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait?

38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total?

39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink?

40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total?

41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left?

42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete?

43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use?

44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction.

45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make?

46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number.

Decimals word problems

Best for: 4th grade, 5th grade

47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total?

48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left?

49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked?

50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower?

51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo?

52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week?

Comparing and sequencing word problems

Four students are sitting together and discussing math questions

Best for: Kindergarten, 1st grade, 2nd grade

53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?

54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?

55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs?

56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers?

57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20?

58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36?

59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April?

Time word problems

66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her?

69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school?

70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for?

71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home?

Money word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade

60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total?

61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left?

62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times?

63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost?

64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total?

65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left?

67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional.

68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year?

Physical measurement word problems

A girl is doing math practice

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade

72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler?

73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres?

74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years?

75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year?

A tablet showing an example of Prodigy Math's battle gameplay.

76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink?

77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get?

78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy?

79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total?

80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres?

81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction?

Ratios and percentages word problems

Best for: 4th grade, 5th grade, 6th grade

82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have?

83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers?

84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players?

85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport?

86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population?

87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there?

88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?

Probability and data relationships word problems

Two students are calculating on a whiteboard

Best for: 4th grade, 5th grade, 6th grade, 7th grade

89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased?

90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1?

91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction.

92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni?

93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test?

94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal?

95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y .

Geometry word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade

96. Introducing Perimeter:  The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter?

97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total?

98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume?

99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw?

100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter?

101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area?

102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw?

103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm?

104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy?

105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle?

106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it?

107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it?

108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it?

109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides?

110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units?

111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side?

112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter?

113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield?

114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius?

Variables word problems

A hand is calculating math problem on a blacboard

Best for: 6th grade, 7th grade, 8th grade

115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent?

116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored.

117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast.

118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored.

119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.

120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours?

How to easily make your own math word problems & word problems worksheets

Two teachers are discussing math with a pen and a notebook

Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do:

  • Link to Student Interests:  By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
  • Make Questions Topical:  Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
  • Include Student Names:  Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
  • Be Explicit:  Repeating keywords distills the question, helping students focus on the core problem.
  • Test Reading Comprehension:  Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
  • Focus on Similar Interests:  Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
  • Feature Red Herrings:  Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.

A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones.

Final thoughts about math word problems

You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students.

Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments.

The result?

A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach.

key words for solving math word problems

  • HOW IT WORKS
  • INSTITUTIONAL SALES

Creating key word flash cards:

  • Have a student count out the number of index cards that the class determined in the warm up problem and distribute four cards to each student.
  • Direct students to create four flash cards — one for each of the four mathematical operations. On the blank side of each card, they should boldly write an operation and its symbol (i.e., +, -, x, where is the division symbol?), and on the reverse, lined sign they should list the key words associated with that operation. (Students should base these flash cards on the table you created on the front board.)

Playing the role of "math coach":

  • Organize the class into small groups of no more than three to four students in each group, and explain that they will be using their new flash cards as visual aids in math coaching!
  • Distribute a "Solving Word Problems through Key Words" sheet to a student in each group and explain that the student with the sheet will act as the reader and recorder during the first round. The reader and recorder's job is to read a word problem aloud and to allow his fellow "math coaches" to advise him on which mathematical operation to follow in solving the problem.
  • Advise the math coaches in the class to listen to the word problem closely, to advise the reader and recorder to underline any key words in the problem that they detect, and to follow the flash card mathematical operation that they decide to "flash."
  • Direct groups to complete the "Solving Word Problems through Key Words" sheet, alternating the role of reader and recorder so that each student has at least one or two turns in that role.

Sharing word problem answers and strategies:

  • Invite students to the front of the classroom to explain their group's word problem strategies and how key words led to determining which mathematical operations to use in each problem.
  • For homework, assign students the task of writing some of their own word problems containing some of the key words discussed in class but not previously used on the "Solving Word Problems through Key Words" sheet.

Extending the Lesson:

  • To further challenge students, you could give them additional word problems that challenge them to interpret the same key words in somewhat confusing contexts (e.g., "I have eight jelly beans, which is three fewer than my brother has. How many jelly beans does my brother have?") Or, you could also introduce word problems involving multiple mathematical operations  (e.g., "A 6000 seat stadium is divided into 3 sections. There are 2000 seats in Section 1, and there are 1500 more seats in Section 2 than in Section 3. How many seats are in Section 2?")

Assessment:

  • Check whether or not groups accurately solved each of the ten word problems and underlined appropriate key words in the "Solving Word Problems through Key Words" sheet.
  • Assess students' original word problems to see if they appropriately incorporated key words to indicate specific mathematical operations.

Educational Standards :

Benchmarks for Mathematics

Standard 1.     Uses a variety of strategies in the problem-solving process

Level II (Grades 3-5) 1. Uses a variety of strategies to understand problem situations (e.g., discussing with peers, stating problems in own words, modeling problem with diagrams or physical objects, identifying a pattern)  2. Represents problems situations in a variety of forms (e.g., translates from a diagram to a number or symbolic expression) 3. Understands that some ways of representing a problem are more helpful than others 4. Uses trial and error and the process of elimination to solve problems 5. Knows the difference between pertinent and irrelevant information when solving problems  6. Understands the basic language of logic in mathematical situations (e.g., "and," "or," "not")  7. Uses explanations of the methods and reasoning behind the problem solution to determine reasonableness of and to verify results with respect to the original problem  Level III (Grades 6-8) 1. Understands how to break a complex problem into simpler parts or use a similar problem type to solve a problem 2. Uses a variety of strategies to understand problem-solving situations and processes (e.g., considers different strategies and approaches to a problem, restates problem from various perspectives)  3. Understands that there is no one right way to solve mathematical problems but that different methods (e.g., working backward from a solution, using a similar problem type, identifying a pattern) have different advantages and disadvantages 4. Formulates a problem, determines information required to solve the problem, chooses methods for obtaining this information, and sets limits for acceptable solutions  5. Represents problem situations in and translates among oral, written, concrete, pictorial, and graphical forms  6. Generalizes from a pattern of observations made in particular cases, makes conjectures, and provides supporting arguments for these conjectures (i.e., uses inductive reasoning)  7. Constructs informal logical arguments to justify reasoning processes and methods of solutions to problems (i.e., uses informal deductive methods)  8. Understands the role of written symbols in representing mathematical ideas and the use of precise language in conjunction with the special symbols of mathematics

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key words for solving math word problems

Math Word Problems

Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a particular question. For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8.

There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:

  • Question : Understand what the question is asking. What operation or operations do you need to use to solve this question? Ask for help to understand the question if you can't do it on your own.
  • Estimate : Use an estimation strategy, so you can check your answer for reasonableness in the evaluate step. Try underestimating and overestimating, so you know what range the answer is supposed to be in. Be flexible in rounding numbers if it will make your estimate easier.
  • Strategize : Choose a strategy to solve the problem. Will you use mental math, manipulatives, or pencil and paper? Use a strategy that works for you. Save the calculator until the evaluate stage.
  • Calculate : Use your strategy to solve the problem.
  • Evaluate : Compare your answer to your estimate. If you under and overestimated, is the answer in the correct range. If you rounded up or down, does the answer make sense (e.g. is it a little less or a little more than the estimate). Also check with a calculator.

Most Popular Math Word Problems this Week

Easy Multi-Step Word Problems

Arithmetic Word Problems

key words for solving math word problems

  • Addition Word Problems One-Step Addition Word Problems Using Single-Digit Numbers One-Step Addition Word Problems Using Two-Digit Numbers
  • Subtraction Word Problems Subtraction Facts Word Problems With Differences from 5 to 12
  • Multiplication Word Problems One-Step Multiplication Word Problems up to 10 × 10
  • Division Word Problems Division Facts Word Problems with Quotients from 5 to 12
  • Multi-Step Word Problems Easy Multi-Step Word Problems

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14 Effective Ways to Help Your Students Conquer Math Word Problems

If a train leaving Minneapolis is traveling at 87 miles an hour…

Word Problems WeAreTeachers

Word problems can be tricky for a lot of students, but they’re incredibly important to master. After all, in the real world, most math is in the form of word problems. “If one gallon of paint covers 400 square feet, and my wall measures 34 feet by 8 feet, how many gallons do I need?” “This sweater costs $135, but it’s on sale for 35% off. So how much is that?” Here are the best teacher-tested ideas for helping kids get a handle on these problems.

1. Solve word problems regularly

key words for solving math word problems

This might be the most important tip of all. Word problems should be part of everyday math practice, especially for older kids. Whenever possible, use word problems every time you teach a new math skill. Even better: give students a daily word problem to solve so they’ll get comfortable with the process.

Learn more: Teaching With Jennifer Findlay

2. Teach problem-solving routines

Word Problems Teacher Trap

There are a LOT of strategies out there for teaching kids how to solve word problems (keep reading to see some terrific examples). The important thing to remember is that what works for one student may not work for another. So introduce a basic routine like Plan-Solve-Check that every kid can use every time. You can expand on the Plan and Solve steps in a variety of ways, but this basic 3-step process ensures kids slow down and take their time.

Learn more: Word Problems Made Easy

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3. Visualize or model the problem

key words for solving math word problems

Encourage students to think of word problems as an actual story or scenario. Try acting the problem out if possible, and draw pictures, diagrams, or models. Learn more about this method and get free printable templates at the link.

Learn more: Math Geek Mama

4. Make sure they identify the actual question

key words for solving math word problems

Educator Robert Kaplinsky asked 32 eighth grade students to answer this nonsensical word problem. Only 25% of them realized they didn’t have the right information to answer the actual question; the other 75% gave a variety of numerical answers that involved adding, subtracting, or dividing the two numbers. That tells us kids really need to be trained to identify the actual question being asked before they proceed. 

Learn more: Robert Kaplinsky

5. Remove the numbers

key words for solving math word problems

It seems counterintuitive … math without numbers? But this word problem strategy really forces kids to slow down and examine the problem itself, without focusing on numbers at first. If the numbers were removed from the sheep/shepherd problem above, students would have no choice but to slow down and read more carefully, rather than plowing ahead without thinking. 

Learn more: Where the Magic Happens Teaching

6. Try the CUBES method

key words for solving math word problems

This is a tried-and-true method for teaching word problems, and it’s really effective for kids who are prone to working too fast and missing details. By taking the time to circle, box, and underline important information, students are more likely to find the correct answer to the question actually being asked.

Learn more: Teaching With a Mountain View

7. Show word problems the LOVE

Word Problems Jennifer Findlay

Here’s another fun acronym for tackling word problems: LOVE. Using this method, kids Label numbers and other key info, then explain Our thinking by writing the equation as a sentence. They use Visuals or models to help plan and list any and all Equations they’ll use. 

8. Consider teaching word problem key words

key words for solving math word problems

This is one of those methods that some teachers love and others hate. Those who like it feel it offers kids a simple tool for making sense of words and how they relate to math. Others feel it’s outdated, and prefer to teach word problems using context and situations instead (see below). You might just consider this one more trick to keep in your toolbox for students who need it.

Learn more: Book Units Teacher

9. Determine the operation for the situation

key words for solving math word problems

Instead of (or in addition to) key words, have kids really analyze the situation presented to determine the right operation(s) to use. Some key words, like “total,” can be pretty vague. It’s worth taking the time to dig deeper into what the problem is really asking. Get a free printable chart and learn how to use this method at the link.

Learn more: Solving Word Problems With Jennifer Findlay

10. Differentiate word problems to build skills

key words for solving math word problems

Sometimes students get so distracted by numbers that look big or scary that they give up right off the bat. For those cases, try working your way up to the skill at hand. For instance, instead of jumping right to subtracting 4 digit numbers, make the numbers smaller to start. Each successive problem can be a little more difficult, but kids will see they can use the same method regardless of the numbers themselves.

Learn more: Differentiating Math 

11. Ensure they can justify their answers

key words for solving math word problems

One of the quickest ways to find mistakes is to look closely at your answer and ensure it makes sense. If students can explain how they came to their conclusion, they’re much more likely to get the answer right. That’s why teachers have been asking students to “show their work” for decades now.

Learn more: Madly Learning

12. Write the answer in a sentence

key words for solving math word problems

When you think about it, this one makes so much sense. Word problems are presented in complete sentences, so the answers should be too. This helps students make certain they’re actually answering the question being asked… part of justifying their answer.

Learn more: Multi-Step Word Problems

13. Add rigor to your word problems

key words for solving math word problems

A smart way to help kids conquer word problems is to, well… give them better problems to conquer. A rich math word problem is accessible and feels real to students, like something that matters. It should allow for different ways to solve it and be open for discussion. A series of problems should be varied, using different operations and situations when possible, and even include multiple steps. Visit both of the links below for excellent tips on adding rigor to your math word problems.

Learn more: The Routty Math Teacher and Alyssa Teaches

14. Use a problem-solving rounds activity.

Word Problems Teacher Trap 3

Put all those word problem strategies and skills together with this whole-class activity. Start by reading the problem as a group and sharing important information. Then, have students work with a partner to plan how they’ll solve it. In round three, kids use those plans to solve the problem individually. Finally, they share their answer and methods with their partner and the class. Be sure to recognize and respect all problem-solving strategies that lead to the correct answer.

Learn more: Teacher Trap

Like these word problem tips and tricks? Learn more about Why It’s Important to Honor All Math Strategies .

Plus, 60+ Awesome Websites For Teaching and Learning Math .

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Sat / act prep online guides and tips, the complete guide to sat math word problems.

feature_words-1

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:

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

body_sat_math_sample_question_1

We can solve this problem by translating the information we're given into algebra. We know the individual price of each salad and drink, and the total revenue made from selling 209 salads and drinks combined. So let's write this out in algebraic form.

We'll say that the number of salads sold = S , and the number of drinks sold = D . The problem tells us that 209 salads and drinks have been sold, which we can think of as this:

S + D = 209

Finally, we've been told that a certain number of S and D have been sold and have brought in a total revenue of 836 dollars and 50 cents. We don't know the exact numbers of S and D , but we do know how much each unit costs. Therefore, we can write this equation:

6.50 S + 2 D = 836.5

We now have two equations with the same variables ( S and D ). Since we want to know how many salads were sold, we'll need to solve for D so that we can use this information to solve for S . The first equation tells us what S and D equal when added together, but we can rearrange this to tell us what just D equals in terms of S :

Now, just subtract S from both sides to get what D equals:

D = 209 − S

Finally, plug this expression in for D into our other equation, and then solve for S :

6.50 S + 2(209 − S ) = 836.5

6.50 S + 418 − 2 S = 836.5

6.50 S − 2 S = 418.5

4.5 S = 418.5

The correct answer choice is (B) 93.

body_sat_math_sample_question_2

This word problem asks us to solve for one possible solution (it asks for "a possible amount"), so we know right away that there will be multiple correct answers.

Wyatt can husk at least 12 dozen ears of corn and at most 18 dozen ears of corn per hour. If he husks 72 dozen at a rate of 12 dozen an hour, this is equal to 72 / 12 = 6 hours. You could therefore write 6 as your final answer.

If Wyatt husks 72 dozen at a rate of 18 dozen an hour (the highest rate possible he can do), this comes out to 72 / 18 = 4 hours. You could write 4 as your final answer.

Since the minimum time it takes Wyatt is 4 hours and the maximum time is 6 hours, any number from 4 to 6 would be correct.

body_Latin

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.

body_sat_math_sample_question_3

To solve this problem, we'll need to know both Armand's and Tyrone's situations, so let's look at them separately:

Armand: Armand sent m text messages each hour for 5 hours, so we can write this as 5m —the number of texts he sent per hour multiplied by the total number of hours he texted.

Tyrone: Tyrone sent p text messages each hour for 4 hours, so we can write this as 4 p —the number of texts he sent per hour multiplied by the total number of hours he texted.

We now know that Armand's situation can be written algebraically as 5m , and Tyrone's can be written as 4 p . Since we're being asked for the expression that represents the total number of texts sent by Armand and Tyrone, we must add together the two expressions:

The correct answer is choice (C) 5m + 4 p

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.

body_sat_math_sample_question_4

Let's try to think about this problem in terms of x . If Type A trees produced 20% more pears than Type B did, we can write this as an expression:

x + 0.2 x = 1.2 x = # of pears produced by Type A

In this equation, x is the number of pears produced by Type B trees. If we add 20% of x (0.2 x ) to x , we get the number of pears produced by Type A trees.

The problem tells us that Type A trees produced a total of 144 pears. Since we know that 1.2 x is equal to the number of pears produced by Type A, we can write the following equation:

1.2 x = 144

Now, all we have to do is divide both sides by 1.2 to find the number of pears produced by Type B trees:

x = 144 / 1.2

The correct answer choice is (B) 120.

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 . )

body_SAT_word_problem_5

This is a case of a problem that is difficult to show visually, since x is not a set degree value but rather a value greater than 55; thus, it must be presented as a word problem.

Since we know that x must be an integer degree value greater than 55, let us assign it a value. In this case, let us call x 56°. (Why 56? There are other values x could be, but 56 is guaranteed to work since it's the smallest integer larger than 55. Basically, it's a safe bet!)

Now, because x = 56, the next angle in the triangle—2 x —must measure the following:

Let's make a rough (not to scale) sketch of what we know so far:

body_triangle_ex_1

Now, we know that there are 180° in a triangle , so we can find the value of y by saying this:

y = 180 − 112 − 56

One possible value for y is 12. (Other possible values are 3, 6, and 9. )

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.

body_sat_math_sample_question_6

This question might sound tricky at first, but it's actually quite simple.

We know tha t P is the number of phones Kathy has left to fix, and d is the number of days she has worked in a week. If she's worked 0 days (i.e., if we plug 0 into the equation), here's what we get:

P = 108 − 23(0)

This means that, without working any days of the week, Kathy has 108 phones to repair. The correct answer choice, therefore, is (B) Kathy starts each week with 108 phones to fix.

body_juggle

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

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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):

body_sat_math_sample_question_7_2

If you often have trouble visualizing problems such as these, draw it out. We know that we're dealing with a circle since our focus is a pizza. We also know that the pizza weighs 3 pounds.

Because we'll need to solve the weight of each slice in ounces, let's first convert the total weight of our pizza from pounds into ounces. We're given the conversion (1 pound = 16 ounces), so all we have to do is multiply our 3-pound pizza by 16 to get our answer:

3 * 16 = 48 ounces (for whole pizza)

Now, let's draw a picture. First, the pizza is divided in half (not drawn to scale):

body_sat_math_sample_question_7_diagram_1

We now have two equal-sized pieces. Let's continue drawing. The problem then says that we divide each half into three equal pieces (again, not drawn to scale):

body_sat_math_sample_question_7_diagram_2

This gives us a total of six equal-sized pieces. Since we know the total weight of the pizza is 48 ounces, all we have to do is divide by 6 (the number of pieces) to get the weight (in ounces) per piece of pizza:

48 / 6 = 8 ounces per piece

The correct answer choice is (C) 8.

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!

body_ready-1

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

1. No Calculator

body_sat_math_test_question_1

2. Calculator OK

body_sat_math_test_question_2

3. Calculator OK

body_sat_math_test_question_3

4. Calculator OK

body_sat_math_test_question_4

Answers: C, B, A, 1160

Answer Explanations

1. For this problem, we have to use the information we're given to set up an equation.

We know that Ken spent x dollars, and Paul spent 1 dollar more than Ken did. Therefore, we can write the following equation for Paul:

Ken and Paul split the bill evenly. This means that we'll have to solve for the total amount of both their sandwiches and then divide it by 2. Since Ken's sandwich cost x dollars and Paul's cost x + 1, here's what our equation looks like when we combine the two expressions:

Now, we can divide this expression by 2 to get the price each person paid:

(2 x + 1) / 2

But we're not finished yet. We know that both Ken and Paul also paid a 20% tip on their bills. As a result, we have to multiply the total cost of one bill by 0.2, and then add this tip to the bill. Algebraically, this looks like this:

( x + 0.5) + 0.2( x + 0.5)

x + 0.5 + 0.2 x + 0.1

1.2 x + 0.6

The correct answer choice is (C) 1.2 x + 0.6

2. You'll have to be familiar with statistics in order to understand what this question is asking.

Since Nick surveyed a random sample of his freshman class, we can say that this sample will accurately reflect the opinion (and thus the same percentages) as the entire freshman class.

Of the 90 freshmen sampled, 25.6% said that they wanted the Fall Festival held in October. All we have to do now is find this percentage of the entire freshmen class (which consists of 225 students) to determine how many total freshmen would prefer an October festival:

225 * 0.256 = 57.6

Since the question is asking "about how many students"—and since we obviously can't have a fraction of a person!—we'll have to round this number to the nearest answer choice available, which is 60, or answer choice (B).

3. This is one of those problems that is asking you to define a value in the equation given. It might look confusing, but don't be scared—it's actually not as difficult as it appears!

First off, we know that t represents the number of seconds passed after an object is launched upward. But what if no time has passed yet? This would mean that t = 0. Here's what happens to the equation when we plug in 0 for t :

h (0) = -16(0)2 + 110(0) + 72

h (0) = 0 + 0 + 72

As we can see, before the object is even launched, it has a height of 72 feet. This means that 72 must represent the initial height, in feet, of the object, or answer choice (A).

4. You might be tempted to draw a diagram for this problem since it's talking about a pool (rectangle), but it's actually quicker to just look at the numbers given and work from there.

We know that the pool currently holds 600 gallons of water and that water has been hosed into it at a rate of 8 gallons a minute for a total of 70 minutes.

To find the amount of water in the pool now, we'll have to first solve for the amount of water added to the pool by hose. We know that 8 gallons were added each minute for 70 minutes, so all we have to do is multiply 8 by 70:

8 * 70 = 560 gallons

This tells us that 560 gallons of water were added to our already-filled, 600-gallon pool. To find the total amount of water, then, we simply add these two numbers together:

560 + 600 = 1160

The correct answer is 1160.

body_sleepy-1

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.

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Check out our best-in-class online SAT prep program . We guarantee your money back if you don't improve your SAT score by 160 points or more.

Our program is entirely online, and it customizes what you study to your strengths and weaknesses . If you liked this Math strategy guide, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next.

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Courtney scored in the 99th percentile on the SAT in high school and went on to graduate from Stanford University with a degree in Cultural and Social Anthropology. She is passionate about bringing education and the tools to succeed to students from all backgrounds and walks of life, as she believes open education is one of the great societal equalizers. She has years of tutoring experience and writes creative works in her free time.

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Math Word Problems Worksheets

Word problems worksheets for kindergarten to grade 5.

Our word problems worksheets are best attempted after a student is familiar with the underlying skill. We include many mixed word problems or word problems with irrelevant data so that students must think about the problem carefully rather than just apply a formulaic solution.

Choose your grade / topic:

Kindergarten:

         Addition word problems

         Subtraction word problems

Grade 1 word problems

Grade 2 word problems

Grade 3 word problems

Grade 4 word problems

Grade 5 word problems

Topics include:

Kindergarten addition word problems

  • Simple word problems with 1-digit addition

Kindergarten subtraction word problems

  • Simple word problems with 1-digit subtraction

Grade 1 word problems worksheets

  • Single digit addition word problems
  • Addition with sums 50 or less
  • Adding 3 or more numbers
  • Subtracting 1-digit numbers
  • Subtracting numbers under 50
  • Mixed addition & subtraction
  • Time and elapsed time
  • Counting money word problems
  • Measurement word problems (lengths)
  • Writing fractions from a story
  • Mixed word problems

Grade 2 word problems worksheets

  • 1,2 and 3-digit addition word problems
  • 1,2 and 3-digit subtraction
  • Mixed addition and subtraction
  • Multiplication within 25
  • Lengths - adding / subtracting / comparing (customary and metric)
  • Time and elapsed time (1/2 hour intervals)
  • Time and elapsed time (5 minute intervals)
  • Counting money (coins and bills)
  • Writing fractions word problems
  • Comparing fractions

Grade 3 word problems worksheets

  • Simple addition word problems (numbers under 100)
  • Addition in columns (numbers under 1,000)
  • Mental subtraction
  • Subtraction in columns (2-3 digits)
  • Simple multiplication (1-digit by 1 or 2-digit)
  • Multiplying multiples of 10
  • Multiplication in columns
  • Simple division
  • Long division with remainders (numbers 1-100)
  • Mixed multiplication and division word problems
  • Identifying, comparing and simplifying fractions
  • Adding and subtracting fractions (like denominators)
  • Length word problems
  • Time word problems (nearest 1 minute)
  • Mass and weight word problems
  • Volume and capacity word problems
  • Word problems with variables

Grade 4 word problems worksheets

  • Four operations (addition, subtraction, multiplication, division)
  • Estimating and rounding
  • Writing and comparing fractions
  • Multiplying fractions by whole numbers
  • Adding and subtracting decimals (up to 3 terms)
  • Length word problems (customary and metric units)
  • Time word problems (including am vs pm)
  • Money word problems (with decimal notation)
  • Shopping word problems

Grade 5 word problems worksheets

  • Mixed 4 operations (addition, subtraction, multiplication, division)
  • Estimating and rounding word problems (based on the 4 operations)
  • Add and subtract fractions and mixed numbers (like and unlike denominators)
  • Multiplying and dividing fractions
  • Mixed operations with fractions (add, subtract, multiply, divide)
  • Decimals word problems (add, subtract, multiply)
  • Mass and weight word problems (oz, lbs / gm, kg)
  • Variables and expressions word problems
  • Variables and equations word problems
  • Volume of rectangular prism
  • GCF / LCM word problems

Related topics

Fractions worksheets

Geometry worksheets

key words for solving math word problems

Sample Word Problems Worksheet

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key words for solving math word problems

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Reading Ranch Tutorial Centers

Reading Comprehension and Math Word Problems: Enhancing Problem-Solving Skills

Reading comprehension and math word problems are two key components of a solid educational foundation. Many students often face challenges when understanding complex texts and solving word problems. This article explores the relationship between reading comprehension and math word problems and how students can develop efficient strategies to excel in both areas.

key words for solving math word problems

Understanding the basics of reading comprehension is crucial for learners, as it equips them with the necessary skills to decipher meaning from age-appropriate texts. Similarly, when solving mathematical word problems, students must utilize their comprehension abilities to interpret and extract relevant information from the problem. By applying reading comprehension strategies to word problems, learners can boost their problem-solving skills and excel in subjects that require textual analysis.

Bridging the gap between reading comprehension and word problem-solving is achievable by equipping students with the right tools and techniques. Students can benefit from learning strategies that can be applied across different subjects, ensuring a well-rounded education. The following sections of the article offer valuable insights into using these strategies and commonly asked questions.

Key Takeaways

Strengthening reading comprehension skills supports success in math word problems.

Application of comprehension strategies improves problem-solving across various subjects.

Learners should focus on versatile techniques for a well-rounded education.

Understanding the Basics of Reading Comprehension

Reading comprehension is a critical skill for all students, as it enables them to grasp the meaning and significance of text. Students can develop their reading comprehension by focusing on accuracy, understanding the context, and applying the acquired information.

In the context of reading comprehension, accuracy refers to the ability of students to read words and sentences correctly. It is essential for students to have a solid foundation in phonics and vocabulary in order to improve their reading accuracy. To achieve this, they can frequently practice reading texts that are appropriate to their level and gradually increase the difficulty as they gain confidence.

The next aspect of reading comprehension is understanding the context in which a text is written. This requires the students to comprehend the meaning of individual words and phrases and their relationships within the text. To enhance their contextual understanding, students should learn to identify the main ideas, supporting details, and implicit information present in a text.

Additionally, students should consciously try to apply the information they have comprehended. This can be achieved by summarizing, discussing, or even responding to questions related to the text. By actively engaging with the material, students are more likely to retain the information and improve their overall reading comprehension.

Providing students with various types of texts, such as fiction, non-fiction, and poetry, can help them enhance their comprehension skills. Exposure to different genres allows them to encounter diverse language styles, themes, and structures, which in turn contributes to the development of their cognitive abilities.

Reading comprehension is an essential skill that not only improves a student’s academic performance but also contributes to their overall development. With continued practice, patience, and effort, students are capable of enhancing their comprehension skills, enabling them to better understand and appreciate the world around them.

Understanding Word Problems

Mathematics in word problems.

Word problems are essential in mathematics, as they present real-life situations where math is required to find a solution. They involve various mathematical operations, such as addition, subtraction, multiplication, and division. Geometry word problems may also include concepts like area, volume, or angle measures. Solving these problems is crucial for developing a deeper understanding of mathematical concepts and enhancing problem-solving skills.

Relevance of Word Problems

Math word problems are highly relevant in daily life as well as in various professions. They help students develop critical thinking and decision-making abilities. In subjects like science, engineering, and finance, mathematical word problems often serve as the foundation for complex problem-solving tasks. Thus, mastering word problems is critical for success in both academic and professional settings.

Challenges in Word Problems

Solving word problems can be challenging for multiple reasons:.

  • Language Processing: Students must first understand the problem’s context, which sometimes requires them to process challenging vocabulary or complex sentence structures.
  • Identifying Operations: Once the problem is understood, students need to identify the appropriate mathematical operation(s) (add, subtract, multiply, divide) and apply them to the given numbers.
  • Working with Fractions: Dividing fractions and solving problems that involve fractions can be particularly tricky for some learners.
  • Decoding: Translation of a problem from words to mathematical notation may be an obstacle for certain students.

Despite the challenges, learning to solve mathematical word problems is essential in developing mathematical literacy and problem-solving abilities. By practicing and mastering various types of word problems, students can build confidence in their mathematical skills and apply them in real-life situations.

Strategies to Solve Word Problems Identifying Key Words

To effectively solve mathematical word problems, it is important to identify key words within the text. These words often indicate the operation to perform or provide crucial information for solving the problem. Common key words for addition include sum , total , more , and added to , while subtraction problems often include words like difference , less , fewer , and minus . Multiplication and division problems may contain key words like times , product , divided by , and quotient . Recognizing these words can help guide the problem-solving process.

Problem-Solving Framework

A structured problem-solving framework can aid in approaching these types of problems systematically. Following a simple four-step process can improve students’ ability to find solutions:

  • Understand the problem: Read the problem carefully, identifying the key information and unknowns.
  • Devise a plan: Determine the appropriate operation(s), using the key words and other contextual clues.
  • Implement the plan: Perform the necessary calculations, ensuring accuracy and understanding of each step.
  • Review the solution: Check the solution against the original problem statement to ensure it is reasonable and complete.

Applying this framework to each word problem will build confidence and increase success in problem-solving.

Using Visual and Manipulative Resources

Visual representations and manipulatives can be extremely beneficial in helping students understand and solve word problems. For example, using diagrams, tables, or number lines can help visualize the problem, making it easier to identify the necessary steps for solving.

  • Diagrams : Sketching simple diagrams can clarify relationships between values and simplify complex problems. Examples include bar models, area models, and Venn diagrams.
  • Tables : Organizing data into a table can illustrate patterns, highlight relationships, and streamline calculations.
  • Number Lines : Using a number line can help visualize addition, subtraction, multiplication, and division operations, making it easier to grasp the concept of a given problem.

Similarly, manipulatives such as counters, fraction strips, or base-ten blocks can provide a hands-on approach to understanding abstract concepts and visualizing mathematical relationships. Students can physically manipulate these tools to explore, discover, and demonstrate their understanding of the problem-solving process.

In conclusion, using strategic approaches like identifying key words, employing a problem-solving framework, and incorporating visual representations and manipulatives can greatly enhance the ability to tackle complex math word problems, ultimately leading to a more successful and enjoyable learning experience.

Reading Comprehension and Word Problem Solving in Different Subjects

Math and science.

Reading comprehension is crucial in math and science subjects, as it involves understanding complex concepts and word problems. Students must be able to interpret the information given and apply mathematical and scientific principles to solve problems accurately. This involves breaking down the problem into smaller parts, identifying key terms and variables, and selecting the appropriate formulas or methods to use.

  • Math: In math, word problems can involve a wide range of topics, such as algebra, geometry, and calculus. Students need to decipher the context, translate it into mathematical expressions, and solve for the desired variables.
  • Science: Science subjects like physics, chemistry, and biology also require reading comprehension skills. Students need to understand scientific texts, grasp experiment procedures, and analyze data presented in various formats (tables, graphs, etc.).

Narrative and Social Studies

Reading comprehension and word problem-solving skills are also essential in understanding the context and drawing accurate conclusions in narrative and social studies subjects.

  • Narrative: In literature, reading comprehension involves analyzing the plot, characters, and themes, as well as understanding the author’s purpose and perspective. Additionally, it requires deciphering figurative language, symbolism, and other literary devices.
  • Social Studies: In subjects like history and geography, students need to read and comprehend texts about different cultures, political systems, and historical events. They may need to analyze primary and secondary sources, compare different perspectives, and evaluate the reliability of the information provided.

Both math/science and narrative/social studies subjects require strong reading comprehension skills to navigate and solve word problems or understand complex concepts successfully. By honing these skills, students can improve their overall academic performance and develop a more comprehensive understanding of various topics across different disciplines.

Application of Reading Comprehension Strategies

Reading comprehension strategies are essential for understanding and solving math word problems. By applying these strategies, students can significantly improve their ability to analyze and solve complex problems.

Firstly, identifying the main idea of a problem helps students focus on the most important information. This involves recognizing the key elements of the given problem and disregarding any unnecessary details. For example, in a problem about calculating the total price of items, the main idea is to find the product of the quantity and the unit price.

Visualizing the problem is another effective strategy. By creating a mental or physical image of the problem, students can better understand the relationships between the different elements involved. This may include drawing a diagram or sketch, or even using physical objects to represent the components of the problem.

Utilizing context clues can help students infer meaning and fill in any gaps in their understanding. Context clues can come in the form of definitions, examples, or descriptions that help to clarify unfamiliar terms or concepts. This is particularly helpful for problems with complex or technical language.

Making connections to prior knowledge or experiences allows students to apply previously learned concepts to new problems. This encourages critical thinking and fosters a deeper understanding of the subject matter. When confronted with a math word problem that uses similar concepts or ideas, students can draw on their past experiences to approach the problem confidently.

Another strategy is asking questions while reading through the problem. This practices active engagement with the text and promotes comprehension. Students should pose questions to themselves, such as “What is the problem asking?” or “What information is necessary for solving this problem?”. By doing so, they are better equipped to identify important information and organize their approach in a logical manner.

 In summary, incorporating reading comprehension strategies into math word problems enables students to better decipher complex problems, recognize important information, and develop critical thinking skills. By mastering these strategies, students are well on their way to becoming confident and proficient problem solvers.

Frequently Asked Questions

What are effective strategies for solving math word problems.

To solve math word problems effectively, try the following strategies:

  • Read the problem carefully and identify critical information.
  • Visualize the problem by drawing a model or diagram.
  • Translate words into mathematical expressions or equations.
  • Determine the proper operations to apply.
  • Solve the equation step by step, continuously checking for accuracy.
  • Verify the solution by plugging it back into the original problem.

How can I improve my child's reading comprehension skills for math?

To help your child enhance their reading comprehension skills in math, consider these approaches:

  • Encourage regular reading to develop vocabulary and language skills.
  • Discuss word problems, exploring how language and math concepts are connected.
  • Practice breaking problems down into smaller, more manageable parts.
  • Teach strategies for identifying key words and phrases that signal mathematical operations.
  • Provide opportunities to practice problem-solving in a variety of contexts.

What is the impact of reading comprehension on problem-solving in mathematics?

Reading comprehension greatly impacts problem-solving in mathematics, as it enables students to understand and interpret word problems accurately. Strong reading comprehension skills allow students to identify relevant information, choose appropriate strategies, and apply mathematical concepts to arrive at the correct solution.

How can teachers support special education students with word problems?

Teachers can support special education students in tackling math word problems by:

  • Providing clear instructions and explanations.
  • Using visual aids and manipulatives to represent mathematical concepts.
  • Breaking problems down into smaller steps.
  • Encouraging students to use personal strategies, such as highlighting keywords or drawing diagrams.
  • Offering additional practice opportunities and targeted interventions as needed.

What is the correlation between reading comprehension competence and mathematical problem-solving skills?

There is a strong correlation between reading comprehension competence and mathematical problem-solving skills. Improved reading comprehension fosters better understanding of word problems and the ability to select appropriate strategies to solve them. Consequently, increased proficiency in reading comprehension contributes to enhanced math performance.

Can you provide examples of common math word problems and their solutions?

Sure, here are two examples:

  • Problem: Sarah has 12 apples, and she wants to share them equally between her and two friends. How many apples does each person get?

Solution: Divide the total number of apples (12) by the number of people (3):

12 ÷ 3 = 4.

Each person gets 4 apples.

  • Problem: A rectangular garden is 18 meters long and 4 meters wide. What is the perimeter of the garden?

Solution: Add the lengths of all sides:

(18 + 4) x 2 = 22 x 2 = 44.

The perimeter of the garden is 44 meters.

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IMAGES

  1. This key math words chart for problem solving will help students know

    key words for solving math word problems

  2. Solving Word Problems Chart Grade 2-8

    key words for solving math word problems

  3. Key Words for Solving Word Problems

    key words for solving math word problems

  4. Key Words for Solving Math Word Problems by Teach Laugh Run

    key words for solving math word problems

  5. Math Problem Solving Key Words by Hillary Kiser

    key words for solving math word problems

  6. Word Problems in Math

    key words for solving math word problems

VIDEO

  1. Steps to solve a math word problem #maths #mathsday

  2. Solving Word Problems

  3. Word Problems Part 2

  4. 1.5 Video Notes

  5. Solving Math word problem

  6. Step 2 Estimate the Answer to the Word Problems

COMMENTS

  1. Teaching Math Word Problem Key Words (Free Cheat Sheet)

    Key words in mathematical word operations are the words or phrases that will signal or show a student which type of math operation to choose in order to solve the math word problem. The keywords for math word problems used in operations are a strategy that helps the math problem make sense and draw connections to how it can be answered.

  2. PDF Key Words for Solving Word Problems

    Key Words for Solving Word Problems The hardest part of solving a word problem is actually understanding the problem and determining the operation (or operations) that needs to be performed. Listed below are a few of the most commonly used key words in word problems and the operations that they signal.

  3. Key Words

    Do you want to improve your skills in solving word problems? Learn how to use key words and catch phrases to identify the operations and strategies needed for different types of problems. This webpage provides a list of common words and phrases for addition, subtraction, multiplication, division, fractions, and more. You can also find examples and practice problems to test your understanding.

  4. How to Know which Operations to Use in Word Problems

    Addition word problem worksheets. Starting in kindergarten, we've created addition word problems for students to practice. By grade 3, we've compiled mixed number word problems with addition as well. Here's an example of word problems of addition with sums of 50 or less from our grade 1 word problem section:

  5. Keywords for Mathematical Operations

    The first step in solving a word problem is always to read the problem. You need to be able to translate words into mathematical symbols, focusing on keywords that indicate the mathematical procedures required to solve the problem—both the operation and the order of the expression. In much the same way that you can translate Spanish into English, you can translate English words into symbols ...

  6. Elementary Math Word Problem Key Words and Their Limitations

    Word problem key words are words or phrases that signal which operations (addition, subtraction, multiplication, or division) are needed in order to solve a math word problem. Using keywords for math word problems (often referred to as clue words and phrases) is a strategy to make sense of and solve word problems.

  7. Strategies for Solving 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.

  8. No More Keywords for Math Word Problems

    In this post, I share four reasons why using keywords for math word problems fail students. There are 125 sheep and 5 dogs in a flock. How old is the shepherd? 1st Student: "I can't solve this because it doesn't say anything about the shepherd.". 2nd Student: "120 years old because 125 minus the 5 dogs in a flock.".

  9. How to turn word problems into math

    MathHelp.com. Step 1 in effectively translating and solving word problems is to read the problem entirely. Don't start trying to solve anything when you've only read half a sentence. Try first to get a feel for the whole problem; try first to see what information you have, and then figure out what you still need.

  10. Solving Word Questions

    Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents. ... Also look for key words: When you see Think; ... and there are many ways to solve it. Using the Quadratic Equation Solver we get −14 and 12. Check −14: −14(−14 + 2) = (−14)× ...

  11. Identifying Keywords in Math Word Problems

    Identifying Keywords in Math Word Problems. Many students struggle with word problems as it seems they are intended to confuse you. The key to solving them is to figure out what the word problem is asking you to do, and break it down into a simple equation. Use this guide to identify keyword or phrases that will clue you into what the problem ...

  12. How to REALLY Help Kids Solve Math Word Problems

    Although each word problem includes the term "total," they all require a different operation to solve it, forcing kids to think about the situation. Read: Solving Math Word Problems Without Keywords. 3. Real life math doesn't include keywords: Finally, looking for keywords is not practical advice for real world problem solving.

  13. Word Problems Calculator

    An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

  14. Keywords for Word Problems, Free PDF Download

    Keywords for Word Problems. With our Keywords for Word Problems lesson plan, students learn how to identify keywords in word problems that refer to specific mathematic operations (multiplication, division, addition, and subtraction) in order to help them decide how to solve word problems. Categories: Downloadable, Mathematics Tags: 1st Grade ...

  15. 10 Best strategies for solving math word problems in 2024

    6. Use Estimation to Predict Answers. Estimation is a valuable skill in solving math word problems, as it allows students to predict the answer's ballpark figure before solving it precisely. Teaching students to use estimation can help them check their answers for reasonableness and avoid common mistakes.

  16. 120 Math Word Problems To Challenge Students Grades 1 to 8

    Feature Red Herrings: Including unnecessary information introduces another problem-solving element, overwhelming many elementary students. A key to differentiated instruction, word problems that students can relate to and contextualize will capture interest more than generic and abstract ones. Final thoughts about math word problems

  17. Using Key Words to Unlock Math Word Problems

    Instructional Objectives: Students will: brainstorm key words that usually indicate specific mathematical operations. create flash cards to review the relationships between key words and operations. coach one another in collectively solving mathematical word problems. synthesize their knowledge of word problems by writing some of their own.

  18. The Problem with Using Keywords to Solve Word Problems

    Teaching students to look for keywords in word problems teaches them to bypass the context of the word problem. Students don't read the problem for understanding and instead, look for specific words that might help them solve the problem. Not all keywords work in all instances. Math problem-solving words provide a pathway, but not a ...

  19. Math Word Problems

    Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math ...

  20. 14 Effective Ways to Help Your Students Conquer Math Word Problems

    3. Visualize or model the problem. Encourage students to think of word problems as an actual story or scenario. Try acting the problem out if possible, and draw pictures, diagrams, or models. Learn more about this method and get free printable templates at the link. Learn more: Math Geek Mama. 4.

  21. The Complete Guide to SAT Math Word Problems

    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.

  22. Math Word Problem Worksheets

    Grade 5 word problems worksheets. Mixed 4 operations (addition, subtraction, multiplication, division) Estimating and rounding word problems (based on the 4 operations) Add and subtract fractions and mixed numbers (like and unlike denominators) Multiplying and dividing fractions. Mixed operations with fractions (add, subtract, multiply, divide)

  23. Reading Comprehension and Math Word Problems: Enhancing Problem-Solving

    In conclusion, using strategic approaches like identifying key words, employing a problem-solving framework, and incorporating visual representations and manipulatives can greatly enhance the ability to tackle complex math word problems, ultimately leading to a more successful and enjoyable learning experience.