These are some key words to look for when solving a math word problem. Knowing key words will help determine which operation is necessary to solve the problem. When solving word problems, it is helpful to underline or circle these key words to better understand what information the problem is giving you and to understand what exactly is being asked.
Here is a link to the original source: http://datadeb.files.wordpress.com/2009/11/mathoperationsteachersnotes.png
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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.
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
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.
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Word Problem by Problem Type BUNDLE
Product on sale
$38.80
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Multiplication and Division Word Problems
$19.75
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Two-Step Word Problems Number Puzzles – OA8
$3.75
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Multiplication Division Word Problems Number Puzzles – OA3
$3.75
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Addition and Subtraction Word Problems by Problem Type
$24.75
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.
18 Responses
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YES! I totally agree! The book we read this yer and did most of our PD on was very similar to this!
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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.
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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!
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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.
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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!
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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.
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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.
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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?
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Never mind…I got it!
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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.
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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.
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Thanks so much for the reply. What you explained makes perfect sense. I can visualize it now to try and replicate with my kiddos.
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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?
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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).
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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.
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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.
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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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Lesson Question:How can identifying key words help students solve mathematical word problems? Lesson Overview:In this lesson, students will take turns acting as «math coaches» who will assist other students in solving word problems by identifying key words that usually indicate specific mathematical operations. Length of Lesson:One hour to one hour and a half Instructional Objectives:Students will:
Materials:
Links:
Warm-up:Solving an authentic word problem:
Instruction:Brainstorming key words that indicate mathematical equations:
Mathematical Operations and Key Words
Creating key word flash cards:
Playing the role of «math coach»:
Wrap-up:Sharing word problem answers and strategies:
Extending the Lesson:
Assessment:
Educational Standards:Benchmarks for Mathematics Standard 1. Uses a variety of strategies in the problem-solving process
Click here to read more articles from Lesson Plans. |
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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?
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).
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:
- add
- altogether
- both
- combine
- in all
- increase
- increased by
- larger
- larger than
- longer
- longer than
- more
- more than
- perimeter
- plus
- sum
- together
- total
Subtraction Key Words
Here are some examples of subtraction key words:
- change
- decreased
- difference
- fewer
- gave away
- How many more…?
- How many less…?
- left
- left over
- less
- less than
- minus
- remain
- shorter than
- smaller than
- take away
Multiplication Key Words
Here are some examples of multiplication key words:
- area
- cubed
- double
- each
- groups
- per
- product
- quadruple
- rows
- squared
- times
- triple
Division Key Words
Here are some examples of division key words:
- average
- divide
- each
- equal group
- fourth
- half
- quarter
- quotient
- ratio
- share
- separate
- split
- third
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.
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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!
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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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In working with word problems, there are some words or phrases that give clues as to how the problem should be solved. The most common words or phrases are as follows.
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Add
- Sum—as in the sum of 2, 3, and 6 …
- Total—as in the total of the first six payments …
- Addition—as in a recipe calls for the addition of five pints …
- Plus—as in three liters plus two liters …
- Increase—as in her pay was increased by $15 …
- More than—as in this week the enrollment was eight more than last week …
- Added to—as in if you added $3 to the cost …
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Subtract
- Difference—as in what is the difference between …
- Fewer—as in there were fifteen fewer men than women …
- Remainder—as in how many are left or what quantity remains …
- Less than—as in a number is five less than another number …
- Reduced—as in the budget was reduced by $5,000 …
- Decreased—as in if he decreased the speed of his car by ten miles per hour …
- Minus—as in some number minus 9 is …
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Multiply
- Product—as in the product of 8 and 5 is …
- Of—as in one‐half of the group …
- Times—as in five times as many girls as boys …
- At—as in the cost of ten yards of material at 70¢ a yard is …
- Total—as in if you spend $15 a week on gas, what is the total for a three‐week period …
- Twice—as in twice the value of some number …
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Divide
- Quotient—as in the final quotient is …
- Divided by—as in some number divided by 12 is …
- Divided into—as in the group was divided into …
- Ratio—as in what is the ratio of …
- Half—as in half the profits are … (dividing by 2)
As you work a variety of word problem types, you will discover more “clue” words.
A final reminder: Be sensitive to what each of these questions is asking. What time? How many? How much? How far? How old? What length? What is the ratio?