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
Do your students need some help learning those key words when trying to solve word problems? Here is a FREE set of Key Words to use for solving addition and subtraction word problems. (Multiplication and Division Key Words are below)
These are a perfect size to hang on your math wall or even on your word wall. Students will be able to tackle word problems with ease using these key words.
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Do you need some word problems to practice using key words? Here are some fun and engaging word problem task cards to use in your classroom.
2-Digit Addition and Subtraction Word Problem Task Cards includes: 30 task cards, recording sheet, an answer key, and a game board for a 2-4 Player game.
Use the Task Cards for:
- Small Group
- As part of your lesson
- Homework
- Warm-up activity
- Math Centers
- To play a game with the gameboard
- Partner or team activities
Need more of a challenge? Try 3 and 4-Digit Addition and Subtraction Word Problem Task Cards. It includes: 30 task cards, recording sheet, an answer key, and a game board for a 2-4 player game.
Both packs are bundled here if you need both of them:
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Looking for Multiplication and Division Key Words?
Click Here for your FREEBIE!
Here are some Word Problem Task Cards for Multiplication and Division: These task cards include: 30 task cards using single digit multiplication and division, recording sheets, an answer key, and a game board for a 2-4 player game.
Your students will be pros at problem solving with all this practice!
Thanks for stopping by today.
See you soon,
Here are more resources using Word Problems:
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Presentation on theme: «Word Problems Looking for Key Words!.»— Presentation transcript:
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Word Problems Looking for Key Words!
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Steps for Solving Word Problems
Read the problem twice! Look for key words! Draw a picture! Write a number sentence! Solve the problem! Check your answer to see if it makes sense!
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Addition Word Problems
Total How many altogether Sum How many in all
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Example of Addition Word Problem
Jason has 22 baseball cards. His mother decided to give him 18 more. How many baseball cards will Jason have in all? Answer: 40
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Subtraction Key Words How many more How many less How many fewer
What is the difference How much change (money)
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Meet Percy P. Porcupine This is my friend Percy!
Percy is friendly; however, what out for his quills! Your task is to help Percy solve some word problems using addition and subtraction!
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Wacky Waldo’s Animal Circus
Wacky Waldo is every bit of his name…WACKY! He is having some trouble with the animals in his circus! Your task is to help him solve some word problems and get his circus under control!
Mixed Operations with Key Phrases Word Problems
This word problems worksheet will produce addition, multiplication, subtraction and division problems using clear key phrases to give the student a clue as to which type of operation to use.
This word problems worksheet will produce ten problems per worksheet.
Operations Used in each Word Problem
Addition and Subtraction Problems
Addition and Multiplication Problems
Multiplication and Division Problems
Problems with All 4 Operations
Format for the Numbers Used in the Word Problems
Represent Numbers with Digits
Represent Numbers with Words
Mixture of Both Formats
Extra Information
Only provide the values needed for the problem
Sometimes add extra unnecessary information
Always include extra unnecessary information
Language for the Word Problems Worksheet
| English | German | Albanian |
| Spanish | Swedish | Italian |
| French | Turkish | Polish |
| Norwegian |
Memo Line for the Word Problems Worksheet
You may enter a message or special instruction that will appear on the bottom left corner
of the Word Problems Worksheet.
Word Problems Worksheet Answer Page
Include Word Problems Worksheet Answer Page
Now you are ready to create your Word Problems Worksheet by pressing the Create Button.
If You Experience Display Problems with Your Math Worksheet
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Click here for More Word Problems Worksheets
Solving word problems is hard. Word problem keywords seem like a logical solution but this strategy will make solving word problems even more difficult.
Like really, really hard.
In a world where reading comprehension, logical thinking, math computation, and visualization come together, word problems were born.
As teachers, we are interested in doing everything we can to make instruction make sense, come alive and “click” for our students. And, unfortunately, in the interest of the end goal, it can be very easy to try to teach tricks to our students. In the long run, however, this does SUCH a disservice!
Let’s look at the list of commonly taught word problem keywords and match it up to a progression of addition and subtraction word problems from K-2 to see if learning these keywords will serve a student well.
Common Word Problem Keywords
Keywords for addition often include:
add
sum
total
plus
and
in all
altogether
together
more
Subtraction often sounds like:
difference
take away
minus
fewer
less
took
gave away
leftover
difference
First up: Do the keywords hold up in Kindergarten?
CCSS.MATH.CONTENT.K.OA.A.2
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
So, the standards alone here really aren’t enough to determine what word problems look like at this level. To learn about what the standards “look like” you need to look into the progressions document. Have you seen this chart? I know it’s difficult to read, so I have included a link.
Basically, the chart lays out the different type of word problem and then, through the shading, explains which problem types are expected at each grade level.
Back to kindergarten now. The bulk of the problems are put together, take apart, add to and take from problems where the result is the missing piece. Looking at the questions, one by one:
4 bunnies sat on the grass. 5 more bunnies hopped over. How many bunnies are on the grass now?
The keyword indicates addition, addition of 4 + 5 will solve the problem.
10 apples were sitting on the table. I ate 4. How many are on the table now?
No keyword… you could argue that “ate” means take away so that’s subtraction but, in the world of keywords they really offer no help here.
2 green apples and 4 red apples are sitting on the table. How many apples are on the table?
Keyword indicated addition, the addition of 2 + 4 will solve the problem.
Grandma has 10 apples. How many can she put in the red vase and how many can she put in the blue vase?
This question is open-ended and contains no keywords.
Conclusion? In kindergarten, keywords are not misleading, however, they are not helpful in solving all types of word problems.
Do Word Problem Keywords Help in 1st Grade Word Problems?
CCSS.MATH.CONTENT.1.OA.A.1
Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.1
The “1” at the end of this standard is directing you to the chart that describes the problem types. Too bad they didn’t make the same note in the Kindergarten standard…. I digress…
So here you see we have unknowns in all positions in all types of word problems. The only real caveat here is that change problems where the start is missing and comparison problems where the language is intentionally misleading are saved for second.
Let’s go through a few problems:
6 bunnies were sitting on the grass.Some more bunnies hopped there.Then there were 12 bunnies. How many bunnies hopped over to the first 6 bunnies?
Keyword indicates addition. 6 + 12 does NOT solve the problem. A student needs to be quite flexible with situation and solution equations for this key word to make sense.
18 apples were on the table. I ate some apples. Then there were 10 apples. How many apples did I eat?
No keyword. If you were in the camp that said “ate” indicated subtraction before 18-10 will yield the correct answer.
14 apples are on the table. 7 are red and the rest are green. How many apples are green?
No keyword.
Lucy has 16 apples. Julie has 9 apples. How many more apples does Julie have than Lucy?
Keyword indicates addition. Addition will NOT solve this problem. Without any obvious action in this word problem, even a situation equation is a difficult argument for a 6 year old.
Lucy has 10 fewer apples than Julie. Julie has 18 apples. How many apples does Lucy have?
Key word indicates subtraction. Subtraction will solve the problem… but wait until 2nd grade…
Conclusion? In first grade, many problem do not have obvious keywords and those with keywords may be very misleading with a keyword leading to a situation equation rather than a solution equation. But when was the last time that you saw a “keywords” poster that said “Keywords for determining the operation in your situation equation!” I haven’t seen one yet.
If I haven’t yet convinced you that teaching keywords is doing a disservice to students, continue on to reading about 2nd grade.
Should word problem keywords be used to teach word problems in 2nd grade?
CCSS.MATH.CONTENT.2.OA.A.1
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1
I am not going to even TOUCH the multi-step nature of word problems at second grade. Obviously, with multiple steps, there may be multiple keywords for a student to sift through.
Here we add in the last 4 type of word problems.
Some bunnies were sitting on the grass. 19 more bunnies hopped there. Then there were 27 bunnies. How many bunnies were on the grass before?
Keyword “more” indicates addition. 19 + 27 will not solve the problem. Addition is appropriate only in a situation equation.
Some apples were on the table. I ate 7 apples. Then there were 45 apples. How many apples were on the table before?
No keyword unless we count “ate”. In that case, subtraction is appropriate.
Lucy has 19 fewer apples than Julie. Lucy has 36 apples. How many apples does Julie have?
Keyword indicates subtraction. Subtraction will NOT solve this problem. In fact, a solution equation using subtraction would have to look like J-19=36. How many of your students would have written that? In terms of pure key words most students would write 36 – 19 as Lucy was written directly before the word “fewer”. The keyword is very misleading in this problem!
Julie has 63 more apples than Lucy. Julie has 89 apples. How many apples does Lucy have?
Keyword indicates addition. Addition will NOT solve this problem. Most students, in an attempt to write a situation equation matching addition will write 89 + 63 = L as Julie’s name was written first. The keyword, again, is very misleading.
In fact, in the problem type diagram for the last 2 problems, the descriptions are “fewer suggests wrong operation” and “more suggests wrong operation”.
How To Teach Word Problems WITHOUT Key Words
This blog was filled with a whole lot of what NOT to do. But I have solutions as well! Check out these posts to see how you can think CRA, use numberless word problems, and even use measurement standards in order to help your students better understand word problems!
Want to get started with numberless word problems today? I have a free “Getting Started Guide” including questions so you can try this strategy today!
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I LOVED teaching third grade math! If I could have found a way to teach nothing but third grade math- I would have been in heaven.
I did not like math as a child. I just couldn’t understand WHY! I was THAT kid asking, “When will I use this?” “Why does that work?” My math teachers hated me. And because of that experience, I strive to give my third graders a better experience with math. In my classroom, we always talk about why they need to know it and why it works.
Third grade math is not easy though! They spend Kindergarten, 1st grade and 2nd grade working on addition and subtraction. Then in third grade, we are expected to teach multiplication and division to mastery. We double the number of operations that students have to be competent in and will see in word problems!
Using key words in word problems may have been a suitable strategy in previous years. However, students quickly realize that many of the addition key words can also be used in a multiplication problems. Many division key words look similar to multiplication key words. It isn’t easy! They NEED MORE THAN KEY WORDS! Students need to be taught a problem solving strategy that will work every time.
In my classroom, students are required to use a four step process anytime that they see a word problem. And they see them ALL the time!
You can read about my routine in the post below or listen to the podcast.
Read the problem.
It might seem obvious that we need to start the problem solving process by reading the problem, but the reality is that students want to start doing something with the numbers before they finish reading.
I require my students to set down their pencil or dry erase marker and read the entire problem. They focus more on the words when they don’t have a writing utensil.
I ask them to visualize what the problem is stating rather than trying to form a plan to solve.
I have found that they are much more successful when they really think about what they know BEFORE they start drawing and solving.
Reread while drawing a math model.
After my students have read through the entire problem once, they will begin rereading the problem.
This time, I ask that they just read one sentence or phrase at a time.
They should draw a math model as they read. The models tend to be much more accurate if students are only reading one piece of the problem at a time. However, sometimes they will get to the end of the problem and discover that their model is not going to help them solve. That’s okay! Use the power of the eraser!
I call them models rather than drawings because I want my students to understand that math models are not the same as a picture you might draw in art class. No one needs to be an artist in math class!
Models that my students might draw (because I have modeled them):
Equal Group Pictures
Tape Diagrams (also known as Bar Modeling)
Number Bonds
Arrays
Number Lines
Write an equation and solve.
Most students want to jump to writing an equation or number sentence, but in my class, it can’t be done until the model is drawn.
Once the model is drawn students can better understand what the unknown is and write a number sentence that will help them to accurately solve the word problem. I always remind my students that they need to examine the model before writing the equation.
After they solve the equation they need to ask if it is reasonable and then put it back into their model to check for accuracy.
Write the answer in a complete sentence.
I always require my students to write every word problem answer in a complete sentence. I teach my students to go back to the question and use part of the question in their answer. This increases the probability that students will actually answer the question that was asked.
I also require proper capitalization and punctuation because I believe that integrating writing into math will help students to be more successful in both subjects.
Do you need more suggestions for teaching your students to write during math? Check out THIS post for my five step process!
Free Posters & Notebook Activity
Would you like a free copy of my word problem strategy posters? How about a student notebook activity to help your students to learn the new strategy? Just drop your name and personal email address in the boxes below and I will send them to you right away!
I hope that this routine helps your students to be more successful with word problems!
