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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:

keywords for problem solving

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 :

Subtraction Key Words

Here are some examples of subtraction key words :

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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 :

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 !

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keywords for problem solving

keywords for problem solving

The Problem with using Keywords to Solve Word Problems

When I first started teaching, I used to display lists of keywords for word problems that students could use to solve word problems. I thought this was the best idea ever. Give students something to look for when reading word problems to know when to add, subtract, multiply, or divide. Genius. Or so I thought.

Five years later, I learned about problem types and got deep into the work of Children’s Mathematics: Cognitively Guided Instruction (affiliate). I learned that students should be taught how to understand the context of a word problem not to look for keywords.

This revolutionized my thinking about how I was teaching word problems. I highly recommend the book because of the videos. It was so interesting to watch how children were solving problems and to see what was going on in their heads.

What are Keywords in Word Problems?

Word problem keywords are words or phrases that tell the students which operations (addition, subtraction, multiplication, or division) are needed to solve a word problem. Students are training their brains to look for specific words and phrases to determine what mathematical operations are needed.

Here is a list of common word problem keywords that students are taught to find for each operation:

Addition Keywords

add altogether both combine in all increase larger larger than longer longer than more more than perimeter plus sum together total

Subtraction Keywords

How many less…? How many more…? change decreased difference fewer gave away left leftover less less than minus remain shorter than smaller than take away

Multiplication Keywords

area cubed double each groups per product quadruple rows squared times triple

Division Keywords

average divide each equal group fourth half quarter quotient ratio share separate split third

Why shouldn’t teachers teach students to use keywords for word problems?

Word problems are a great way to engage students in mathematical thinking . The experience should not just be about finding keywords, following rote procedures, and computing correct responses.

While solving word problems it’s important for kids to apply multiple strategies so they can make sense out the problem while solving them. These experiences need grounding in mathematical strategies rather than calculations by finding the keywords.

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. Keywords for math word problems provide a pathway, but not a guaranteed way to solve the problem. Younger students will internalize the keywords and think that they always mean a specific operation.

How do I teach students to solve word problems without using keywords?

You can read all about how I teach math word problems and pick up a freebie of the word problems I use in my classroom in a previous blog post .

In this blog post, I’m going to give you a few examples as to why teaching students how to look for keywords just doesn’t work and sets students up for failure in the long run. Ready to get started?

A quick google search landed me on these definitions for addition and subtraction:

Addition: The total amount of two whole numbers combined. Subtraction: Removing objects from a collection.

Those are the most basic definitions I could find. Keep them in mind as we explore some addition and subtraction word problems and how keywords are used or not used for solving them.

Like I do for my classroom, I’m going to remove the numbers in the word problems so that you can concentrate on the words in the problem.  My  previous blog post gives you my purpose for removing the numbers.

Different Types of Word Problems

There are nine different types of word problems for addition and subtraction. Below are examples of each one and a brief explanation of why teaching students to use keywords can be problematic when solving word problems.

Join Problems

JRU (Join Result Unknown) There were _____ kids on the playground. ____ more kids came onto the playground. How many kids are on the playground?

JCU (Join Change Unknown) There were ____ kids on the playground. Some more kids came to the playground. Now there are ____ kids on the playground. How many kids came to the playground?

JSU (Join Start Unknown) Some kids were on the playground. ____ kids came on the playground. Now there are ____ kids on the playground. How many kids were on the playground at the beginning?

All of the above problems are join problems, which means that the operation is adding, although the unknown is in different places in each problem. The first two are the most basic problems that you would introduce to kindergarten and first graders. Even second graders solve these types of problems, but with more difficult number combinations.

Did you notice that none of the problems have traditional keywords? However, notice the verb phrase in all the problems that reveals that the problems are join problems are: came on . This set of words can be acted out in a classroom, even as simple as using hand motions.

When I set up students to understand the context of a problem. We act out the problem. I emphasize that students are looking for the action of a problem and an unknown.  Students can use any strategy to find the unknown. Some students may actually subtract for the last two problem types, but I’d bet that most of my students would count up from the start for the JCU problem.

When students can identify the action of the problem (which is the operation) and the unknown (what they are solving for) they are set for success.

Separate Problems

SRU (Separate Result Unknown) There were ___ kids on the playground. ____ kids went home. How many kids are left on the playground?

SCU (Separate Change Unknown) There were ___ kids on the playground. Some kids went home. Now there are ___ kids on the playground. How many kids went home?

SSU (Separate Start Unknown) There were some kids on the playground. ____ kids went home. Now there are ___ kids on the playground. How many kids were on the playground at the beginning?

Like the Join problems, these separate problems are best learned through identifying the action and placement of the unknown.  Number lines are one of the best tools I have found for teaching word problems.  Students can physically act out the math on a large number line or draw their own open number lines for larger numbers.

Part-Part-Whole Problems

WU There are ___ boys on the playground and ___ girls on the playground. How many kids are on the playground?

BAU (this is possible combinations, which is not often taught in the lower grades) There are ___ kids on the playground. How many could be boys and how many could be girls?

PU There are ___ kids on the playground. ___ of the kids are boys and the rest are girls. How many girls are on the playground?

Manipulatives are a great resource for part-part-whole problems.  As students begin to understand that one color of an object represents one part and another color another part, they can see how the parts come together and get broken apart.

Compare Problems

Compare word problems are the most difficult for students as it is all about comparing the relationship of the numbers.  It is the most abstract.

DU There are ___ boys and ___ girls on the playground. How many more boys than girls are there? (Change more to fewer or difference. It’s the same type of problem but gives students a chance to practice different vocabulary.

CQU There are __ more boys than girls on the playground. There are ___ girls on the playground. How many boys are on the playground? (Change the more to fewer for a variation).

RU There are ___ more boys than girls on the playground. There are ___ boys in the playground. How many girls are on the playground? (Again, change out more for fewer)

In all the examples above, can you pick out which keywords were used? Not many.  The point?  Students cannot depend on keywords to solve word problems and instead need to learn how to identify the action of the problem and figure out the unknown in the problem or what is missing in the word problem.

When can students use keywords to solve word problems?

Identifying the keywords in a problem can be one of many strategies that students use to help them solve single and multi-step word problems. However, it is not a strategy they should be taught before experiencing all of the other strategies across multiple types of word problems.

Keywords and their use should be discovered by students. Lists should be created with students as they discover the keywords. They should also note the instances when a specific keyword doesn’t work in a problem.

This type of thinking about word problems generally doesn’t happen until elementary students are in the upper grades. They need enough reading comprehension to step outside of the word problem and analyze how the words are used within it.

Another Resource for Teaching Students to Solve Word Problems

Another good book on the top is John Van De Walle’s Teaching Student-Centered Mathematics (affiliate). There are several books, some for K-2 and some for 3-5. If you’re a second and third-grade teacher I highly recommend checking out both books because you have kiddos that will spend the grad levels.

Why can't I teach students to use keywords to solve word problems? Find out why this practice is outdated and doesn't prepare our students for success. Teach students to be successful in solving word problems by understanding the problem itself.  Teaching ideas, aides, and strategies to teach your student addition & subtraction facts as well as the relationship of numbers. #math #secondgrade #learnmath #teachingkidsmath #teaching #kidslearn #addition #subtraction  #wordproblems

I’d love to hear about how you help your students solve word problems.  Do you have something that works really well for your kiddos?  Leave a comment and tell me about it below.

Free Addition & Subtraction Word Problems

Do you want a free sample of the word problems I use in my classroom?  Click here or the image below. FREE Sample of Word Problems by Problem Type

Easily Differentiate Word Problems by problem type and using different numbers in each problem throughout the year. Use small numbers (0-5) for Kinder, medium numbers (1-10) for first grade and larger numbers (0-100) for second grade. Great for interactive notebooks, math journals, and problem solving.

Teaching Resources for Word Problems

Are you looking for some resources to help you teach word problems? Check out the word problems resources below of on TpT .

Word Problem by Problem Type BUNDLE

More Ideas for Teaching Word Problems

Identifying word problem keywords is one of many strategies elementary students can use to help them solve single and multi-step word problems.

Here are more strategies and teaching resources on how to solve word problems.

Easily Differentiate Word Problems by problem type and using different numbers in each problem throughout the year. Use small numbers (0-5) for Kinder, medium numbers (1-10) for first grade and larger numbers (0-100) for second grade. Great for interactive notebooks, math journals, and problem solving.

5 Tips – How to Teach Students to Solve Word Problems

Facebook Live Compare Word Probelms

Compare Word Problems – How to Teach Students to Solve Them

Teach students to solve word problems by helping them read for the context of the problem. Here is a Facebook Live that I did explaining the three type of Join problems.

Join Word Problems – Word Problems by Problem Type

Teach students to solve word problems by helping them read for the context of the problem. Here is a Facebook Live that I did explaining the three types of Separate Word Problems.

Separate Word Problems – How to teach by problem type

keywords for problem solving

Why Numberless Word Problems Should be Part of Your Math Instruction

A word problem routine that helps students analyze the word problem, determine the equation, and choose a model. This structured routine gives students the tools to successfully solve word problems.

A Structured Word Problem Routine that Teaches Students to Analyze the Problem

Addition and Subtraction Word Problems by Problem Type allow you to differentiate the numbers for your students and teach them to look at the context of a problem before working with the numbers. Vocabulary cards to solve word problems.

Addition and Subtraction Word Problems by Problem Type Resource

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Teach Students to Compare Measurements

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Thankful Flapbook – A Perfect Thanksgiving Activity

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Making Waves: Sound Wave Properties Fourth Grade Science Stations

18 responses.

YES! I totally agree! The book we read this yer and did most of our PD on was very similar to this!

I have been researching and preaching the same message this year. It is amazing the difference it makes to teach students about word problems and their structure within problem types. My students actually “think” while they are solving the problems. Keep up the message and children will benefit.

At a conference several years ago, a speaker made the point that if students could create “verbal models” for word problems, they were able to generalize and solve all types of similar problems. The speaker was referring to Algebra 1-level problems, but it certainly could be used here. In a “verbal model,” you are allowed to use boxes, words and operation symbols, but not numbers. It’s hard to show here in this text-only mode, but the playground problems could be: [number of children on playground at start] + [number of children who came on] = [total number of children on playground]. This applies to all of the “join” problems; it’s just a matter of which “[box]” is the variable. I’ve used this very successfully with 7th and 8th grade Algebra 1 students!

Yes yes yes! I totally agree! I used to use those words too until I realized that it just confuses them! They think it’s their easy way out of actually understanding a word problem, and instead, they just look at the numbers and the key words and get the answers all wrong! Great post!

Our district provided a training a few weeks ago for our new math adoption, Go Math, that was being given by one of the authors Juli Dixion. Most of the staff from my school went and they were amazed. Several of the teachers in my group had posters and bookmarks with the key words and realized that they need to take them down. Once they saw the activity we did about the different types of word problems they understood why some of their students still were confused and had a hard time solving word problems. The presenters suggest that we try to create some of each type throughout our units so students can feel more secure. What a great workshop and there was a lot of information that I feel is going to lead to some great changes at my school this next year! Thank you for sharing.

HI, I am a home school parent and I have read every one comments. I have a 5th grader whom I struggle with teaching him the correct way to learn math, such as in geometry, or algebra. Also the books you all talked about, can they be checked out of a library? If anyone has a simply way of teaching these two things please help, I am up for all advice. Thank you!

I’m not sure if the books can be checked out from the library. Maybe if you have a teacher education program at a local university, that library might have the books, but they probably won’t be at a general, local library. Most libraries have online search systems, so it’s worth a look.

As for the correct way or a simple way to learn or teach geometry or algebra for fifth grade, I’m not sure I can offer much advice in that area. There’s some pretty complicated mathematical concepts in those two strands that need to be developed with a ton of hands-on application. There’s no easy answer or resources I can point you to that encompasses it all. As a homeschooler, you might want to look into a full program that has a scope and sequence of instruction for each grade level.

Shelitha, have you ever used Kahn Academy with your child? It is an online resource that is free and has video lessons and practice and the students earn coins/points. There is also Learn Zillion, another good online resource that is mostly free.

I, and my team, have been discussing this lately; this is the best explanation I’ve seen of how to help the kids. Thanks!

Question: (hope I’m not the only one) What do BAU, DU, CQU and RU stand for?

Never mind…I got it!

You have some great posts that are incredibly helpful for a first year math teacher like myself. Thank you for sharing your expertise with us all, that’s what teaching should be all about – sharing the knowledge for the sake of the children! I really like your anchor charts and strategies thought I had to admit it took me a while to understand the adding to subtract without using the number line to model. I wonder if all these strategies confuse students more in the long run. I would like to know if you go through every strategy on your anchor chart on one lesson or model one, have them practice and continue with the next one another day? I’m really just so new to all of this and it’s hard to imagine the process a skilled teacher like yourself goes through when I see these wonderful anchor charts. Thanks for your help.

Hi, Sandra,

We approach using different strategies in different ways. If a student is telling about how he / she solved a problem and uses a specific strategy, we will name the strategy and apply it to a variety of problems, like these Number Lines . If I am formally teach a specific strategy, I will only teach one a day, even one every few days with a lot of practice. However, if we pulled a math problem out of some work we’re doing and are solving it, I’ll generally just use a strategy that is logically for the math problem. This work with the number of pumpkin seeds is a great example of a math problem that we pulled from work we did in another content area. The anchor chart is something we create mid-way through the year to summarize the strategies we’ve learned so far. As students become more and more fluent at using a variety of strategies, we discuss how some are better for certain types of problems and that students needs to choose strategies that work best for them.

Thanks so much for the reply. What you explained makes perfect sense. I can visualize it now to try and replicate with my kiddos.

I am teaching math intervention to 3rd graders and I have struggled with the idea of giving them the CUBES strategy because those math action words don’t always appear in the problem OR it’s misleading. I love your article! Question: do you actually teach the students the terms for the types of problems (join change unknown, etc) or is that just for your teacher reference?

I’m not familiar with the CUBES strategy. To answer your question, it depends on the grade level. I tend to use the labels for what is happening in the problem, like start, change, result, or compare, more / less, part, whole. I don’t necessarily label problems as join problems with students, but we do talk about how the two groups are joined together (or whatever the action is within the problem).

This is not an either-or problem, but both-and. Using key words to solve word problems is one of many strategies that helps students to learn to comprehend and solve word problems. It may help some students to look for key words, and, if they are there and indicate the operation, then great. I have noticed that use of key words still persists in much Common Core-aligned material, in which cases the key words still traditionally indicate the operation needed to solve the word problems. But if there are no key words in word problems, then students may be taught OTHER strategies to help them comprehend them.

Thank you for your comment and feedback.

The problem arises when students are only taught to look for keywords and when keywords misdirect students or are not included in the word problem. I don’t consider teaching students to look for keywords to be a strategy as much as a shortcut that sometimes works. What you indicated above is that the teaching of keywords comes first and that the OTHER strategies , including the context of the word problem, come second. I would reverse that and teach context first and, if students discover patterns in the words, then have a discussion about similarities of words within certain problem types, with a warning that the generalization doesn’t always work. This way, students have ownership over the discovery of the pattern, it sticks with them in their long term memory, and they have a solid foundation of context.

Another thing to consider is that in elementary school we teach fairly easy word problems. Even the two-step and multi-step word problems aren’t too difficult. However, students encounter more difficult problems in middle and high school. Searching for keywords often doesn’t work with more complex problem.

Mind blowing! This makes so much sense, and especially how our math curriculum uses vocabulary now. This is so simple in teaching word problems! I unintentionally started doing this and now I have a why behind it! Great info.

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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?

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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:

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.)

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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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Math Key Words for Problem Solving {Notebook Anchor Chart}

Math Key Words for Problem Solving {Notebook Anchor Chart}

The Literacy Loft - Jessica Meyer

Math Word Problems for 3rd grade using Math Key Words for Problem Solving

Math Animal

Math Key Words Anchor Charts and Reference Posters for Word Problems

Caffeine Queen Teacher

Mix & Match Game Cards {Key Words For Solving Word Problems - All Operations}

Primarily Created

Problem Solving Strategies- CUBES and UPS CHECK

Creatively Teaching First

Key Words to Problem Solve ? Math Basic Operations Posters

The Laminating Co-Teacher

3rd Grade 160 Word Problems Math Problem Solving CCSS *All Standards*

Teaching in Walla Walla

Math CUBES Problem Solving & Math Key Words Bulletin Board Posters

count on kupe

Also included in:  Math Reference Bulletin Board Display Bundle

5th Grade 160 Word Problems Math Problem Solving CCSS *All Standards*

5th Grade 160 Word Problems Math Problem Solving CCSS *All Standards*

Math Word Problem Sets | Math Problem Solving

Math Word Problem Sets | Math Problem Solving

Cognitive Cardio Math

Also included in:  6th Grade Math Activities Resource Bundle

Linear Equations Word Problems TASK CARDS - Differentiated Activity

Linear Equations Word Problems TASK CARDS - Differentiated Activity

Math Byrd

Also included in:  Common Core Algebra 1 TASK CARDS - BUNDLE PRICE!

Fractions, Decimals, and Percents Word Problems | Problem Solving Activity

Fractions, Decimals, and Percents Word Problems | Problem Solving Activity

Also included in:  Fractions, Decimals, and Percents Activity Bundle | Math Centers

Key Words for Solving Word Problems

Key Words for Solving Word Problems

Kinney Kreations

Key Words for Solving Math Word Problems

Teach Laugh Run

Understanding Word Problems: Addition and Subtraction Key Words Unit

More than Math by Mo

2nd Grade 160 Word Problems Math Problem Solving CCSS *All Standards*

Problem Solving: Classroom Display

Problem Solving: Classroom Display

Gifted and Talented Teacher

4th Grade 160 Word Problems Math Problem Solving CCSS *All Standards*

Math Key Words for Word Problems - Poster

Math Key Words for Word Problems - Poster

Adrienne Mosiondz

Daily Math Word Problems Grades 3-4 Spiral Review

The Owl Spot

POWERS AND LAW OF EXPONENTS Word Problems -  Error Analysis  (Find the Error)

POWERS AND LAW OF EXPONENTS Word Problems - Error Analysis (Find the Error)

Exceeding the CORE

Also included in:  6th, 7th, 8th Grade Middle School MATH BUNDLE Standards Based

72 CGI word problems 4th grade-WITH KEY Common Core friendly

72 CGI word problems 4th grade-WITH KEY Common Core friendly

Stacy Harris

Comparing and Ordering Fractions Word Problems | Problem Solving Worksheets

Comparing and Ordering Fractions Word Problems | Problem Solving Worksheets

Also included in:  Fraction Activities Bundle | Comparing Adding Subtracting Multiplying Dividing

Steps for Solving Word Problems and Key Words for Addition and Subtraction

Steps for Solving Word Problems and Key Words for Addition and Subtraction

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keywords for problem solving

No More Keywords for Math Word Problems

keywords for problem solving

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: 

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. 

keywords for problem solving

Shametria Routt Banks

keywords for problem solving

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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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keywords for problem solving

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IMAGES

  1. Math Problem Solving Key Words by Hillary Kiser

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  2. Mathematics Problem Solving Keywords Poster

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  3. Key Words for Problem Solving

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  4. Problem Solving Words and Strategies ~ Use key words and steps to help your child solve word

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  6. Key Words for Problem Solving on Bookmark by Teacher's Hub

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VIDEO

  1. Class, Keyword, Method Introduction

  2. KEYWORDS

  3. Keywords Problem//Typing Suggestions Words Not Showing

  4. Stop using these words🚫#lawsofmaths#viralshort #mathstricks #easymaths #

  5. Using Keywords to Search

  6. How To Quickly Determine Keyword Difficulty Manually

COMMENTS

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    We need critical thinking, creative and logical approaches for solve problems. Generally, problem solving has a few steps such as Define the

  2. Elementary Math Word Problem Key Words and Their Limitations

    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

  3. The Problem with using Keywords to Solve Word Problems

    Word problem keywords are words or phrases that tell the students which operations (addition, subtraction, multiplication, or division) are needed to solve a

  4. Key Words Used in Math Word Problems

    Key Words Used in Math Word Problems. Addition Words. add. all together or altogether. and. both. combined. how many in all. how much.

  5. Math Problem Solving Key Words Posters

    Sep 17, 2013 - This packet includes two sets of problem solving key word posters for addition, subtraction, multiplication, and division.

  6. How to turn word problems into math

    What are common keywords for word problems? · Addition: increased by more than combined, together total of · Subtraction: decreased by minus, less difference

  7. Problem Solving Key Words Teaching Resources

    Helps students learn what key words to look for in math word problems for different operations. Helps students know how to solve

  8. No More Keywords for 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

  9. United 4 Math: Keywords for Problem Solving

    United 4 Math - Keywords for Problem Solving Focus - Keywords for Word Problems Grade Levels - 3-5 This lesson focuses on the most important

  10. 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.