problem solving key words

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Teaching Math Word Problem Key Words (Free Cheat Sheet)

Published: November 20, 2023

Contributor: Jeannette Tuionetoa

Disclosure: This post may contain affiliate links, meaning if you decide to make a purchase via my links, I may earn a commission at no additional cost to you. See my disclosure for more info.

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

Math Word Problem Key Words

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

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

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

Teaching students about challenging math keywords just got easier!

We have a FREE download of the Math Word Problems Keywords Cheat Sheet available for you at the bottom of this post. Keep scrolling to get your copy today!

Why do some kids struggle with word problems?

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

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

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

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

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

What are keywords for math word problems?

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

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

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

What are the common keywords for math word problems?

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

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

Keywords for Math Word Problems

Learning these math keywords will help with problem solving:

Addition Math Key Words:

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

Subtraction Math Key Words:

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

Key Words for Multiplication Word Problems:

• multiplied by
• double/twice

Key Words used for Division Word Problems:

• equal group
• how many in each

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

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

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

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

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

Different Strategies to Familiarize Keywords in Word Operations

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

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

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

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

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

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

Math Word Problem Keywords Cheat Sheets & Teaching Aids:

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

Word Problem Clue Words

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

Addition and Subtraction Word Problem Keywords

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

Story Problem Key Words

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

Word Problem Key Words Poster

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

Word Problem Key Words Worksheets

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

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

Word Problem Key Words for Math

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

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

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

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

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

Identify Learning Gaps

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

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

Free Math Key Words Cheat Sheet Instant Download

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

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

• Subtraction
• Multiplication

FREE Instant Download

Math Word Problems Keywords Cheat Sheet

• cheat sheets
• Instant Download

Jeannette Tuionetoa

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

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"Key Words and Catch Phrases" for Word Problems

Addition Words

2. Altogether

Subtraction Words

1. Difference

3. How many more

4. How much more

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

10. Subtract

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

Multiplication Words

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

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

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

Division Words

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

Reading & Math for K-5

• Kindergarten
• Learning numbers
• Comparing numbers
• Place Value
• Roman numerals
• Subtraction
• Multiplication
• Order of operations
• Drills & practice
• Measurement
• Factoring & prime factors
• Proportions
• Shape & geometry
• Data & graphing
• Word problems
• Children's stories
• Leveled Stories
• Sentences & passages
• Context clues
• Cause & effect
• Compare & contrast
• Fact vs. fiction
• Fact vs. opinion
• Main idea & details
• Story elements
• Conclusions & inferences
• Sounds & phonics
• Words & vocabulary
• Reading comprehension
• Early writing
• Numbers & counting
• Simple math
• Social skills
• Other activities
• Dolch sight words
• Fry sight words
• Multiple meaning words
• Prefixes & suffixes
• Vocabulary cards
• Other parts of speech
• Punctuation
• Capitalization
• Narrative writing
• Opinion writing
• Informative writing
• Cursive alphabet
• Cursive letters
• Cursive letter joins
• Cursive words
• Cursive sentences
• Cursive passages
• Grammar & Writing

Breadcrumbs

How to Know which Operations to Use in Word Problems

When working out what operation to use in a word problem, there are some key phrases students should look out for. Let’s take you through the key phrases and use them in examples.

Key phrases for addition word problems

Find the total. How many altogether? How many are there?

If asked the above, the word problem involves addition.

For example:

There are 14 goldfish in a water tank. Kerri put in 23 more goldfish in the tank. How many goldfish are there?

Answer: 14+ 23= 37. There are 37 goldfish in the tank.

Addition word problem worksheets

Starting in kindergarten, we’ve created addition word problems for students to practice. By grade 3, we’ve compiled mixed number word problems with addition as well.

Here’s an example of word problems of addition with sums of 50 or less from our grade 1 word problem section:

Key phrases for subtraction word problems

What is the difference? How many more? How many less?

If asked the above, the word problem involves subtraction.

For example: Mrs. Sheridan has 11cats. Mrs. Garrett has 24 cats. How many more cats does Mrs. Garrett have than Mrs. Sheridan?

Answer: 24 –11 = 13. She has 13 more cats.

Subtraction word problem worksheets

Starting in kindergarten, we’ve created subtraction word problem for every grade. By grade 3, you’ll find subtraction included in the mixed word problems as well.

In grade 2, students work on 1-3 digit subtraction word problems .

Key phrases for multiplication word problems

How many of the same thing repeated?

If asked the above, the word problem involves multiplication.

For example: Tyler, an animal rights advocate, decided to build his own animal sanctuary to protect different animals.

500 yards away there was the aquatic reserve for freshwater organisms. If there are 6 lakes in that region, each having 175 different fish, how many fish does he have in total?

(How many groups of 175 fish are repeated across 6 lakes.)

Answer: 6 x 175 = 1,050. He has a total of 1,050 fish.

Multiplication word problem worksheets

Starting in grade 3, students work on multiplication word problems .

Key phrases for division word problems

How many equal groups? If share evenly, how many…? The same number.

If asked the above, the word problem involves division.

For example: Sheila has started writing a list of the gifts that she plans to give to her family and friends this Christmas.

For her classmates, she made colorful paper stars which will be placed in small clear bottles. She was able to prepare 45 paper stars. How many stars will be placed in each bottle if Sheila has 9classmates?

Answer: 45 ÷ 9 = 5. There will be 5 stars placed in each bottle.

Division word problem worksheets

Starting in grade 3, we have division word problems for students to practice.

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Math Keywords for Problem Solving

Updated:  14 Aug 2024

Help your students decipher math word problems with a set of printable math keyword anchor charts.

Editable:  Google Slides

Non-Editable:  PDF

Pages:  5 Pages

• Curriculum Curriculum:  CCSS, TEKS

Grades:  2 - 5

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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...

CCSS.MATH.CONTENT.3.OA.D.8

Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including roundi...

CCSS.MATH.CONTENT.4.OA.A.2

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Math 2.4(C)

Solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms; and

Math 3.4(A)

Solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction;

Math 3.4(K)

Solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts.

Math 4.4(H)

Solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders.

Math 5.4(B)

Represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity;

Boost Problem-Solving with Word Problem Keywords!

Are your students struggling with word problems? It’s a common problem seen in math classrooms around the world, and we know teachers are always looking for new ways to teach students to identify the operations in problems before they begin to solve math problems. We’ve put together a handy set of printable anchor charts to help you get them started!

Use these posters in your classroom if your students need help making sense of word problems! These math keyword posters help students identify key words in word problems that indicate operations. There are four posters, one for each math operation (addition, subtraction, multiplication, division).

The posters also come in black and white, which can be printed on colored paper to save on ink! The one-page sheets are great for students to use as reference sheets in their math notebooks or shrink them and use them as bookmarks in their math workbooks.

Download and Print Your Math Keyword Charts

You’re just a click away from getting your new resources! Use the dropdown arrow on the Download button to select the Editable Google Slides resource file or the quick-print PDF version.

Lisamarie Del Valle, a teacher in Florida and Teach Starter collaborator contributed to this resource.

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Solving Word Questions

With LOTS of examples!

In Algebra we often have word questions like:

Example: Sam and Alex play tennis.

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

How many games did Alex play?

How do we solve them?

The trick is to break the solution into two parts:

Turn the English into Algebra.

Then use Algebra to solve.

Turning English into Algebra

To turn the English into Algebra it helps to:

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

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

Also look for key words:

When you see		Think
add, total, sum, increase, more, combined, together, plus, more than		+
minus, less, difference, fewer, decreased, reduced		−
multiplied, times, of, product, factor		×
divided, quotient, per, out of, ratio, percent, rate		÷
maximize or minimize		geometry formulas
rate, speed		distance formulas
how long, days, hours, minutes, seconds		time

Thinking Clearly

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

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

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

Now ... is that: S − 2 = A

or should it be: S = A − 2

or should it be: S = 2 − A

The correct answer is S = A − 2

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

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

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

Now ... is that: 2D = C

or should it be: D = 2C

Think carefully now!

The correct answer is D = 2C

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

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

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

Turn the English into Algebra:

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

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

We are being asked for the Area.

A = w × h = 12 × 5 = 60 m 2

The area is 60 square meters .

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

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

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

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

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

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

Which means that Alex played 4 games of tennis.

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

A slightly harder example:

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

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

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

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

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

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

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

So 10 tables would take Sam just 20 days.

Should Sam be paid more I wonder?

And another "substitution" example:

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

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

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

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

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

The number of "5 hour" days is 3

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

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

Some examples from Geometry:

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

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

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

We are being asked for the radius.

We need to rearrange the formula to find the area

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

Make a quick sketch:

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

We are being asked for the surface area.

First work out s using the volume formula:

Now we can calculate surface area:

An example about Money:

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

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

$40N + $(12 × 1¼N) = $660

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

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

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

More about Money, with these two examples involving Compound Interest

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

This is the compound interest formula:

So we will use these letters:

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

We are being asked for the Future Value: FV

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

The compound interest formula:

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

We are being asked for the Interest Rate: r

So the annual rate of interest is 5%

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

And an example of a Ratio question:

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

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

The current ratio is 4 : 3

Which can be rearranged to 3b = 4g

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

b + 4 g − 2 = 2 1

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

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

There are 12 girls !

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

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

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

And now for some Quadratic Equations :

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

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

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

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

n(n + 2) = 168

We are being asked for the integers

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

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

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

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

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

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

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

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

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

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

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

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

And so L = 8 or −14

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

So the length of the room is 8 m

L = 8, so W = ½L = 4

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

There we are ...

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

How do you solve word problems in math?

Master word problems with eight simple steps from a math tutor!

Author Amber Watkins

Published April 2024

• Key takeaways
• Students who struggle with reading, tend to struggle with understanding and solving word problems. So the best way to solve word problems in math is to become a better reader!
• Mastery of word problems relies on your child’s knowledge of keywords for word problems in math and knowing what to do with them.
• There are 8 simple steps each child can use to solve word problems- let’s go over these together.

Table of contents

• How to solve word problems

Lesson credits

As a tutor who has seen countless math worksheets in almost every grade – I’ll tell you this: every child is going to encounter word problems in math. The key to mastery lies in how you solve them! So then, how do you solve word problems in math?

In this guide, I’ll share eight steps to solving word problems in math.

How to solve word problems in math in 8 steps

Step 1: read the word problem aloud.

For a child to understand a word problem, it needs to be read with accuracy and fluency! That is why, when I tutor children with word problems, I always emphasize the importance of reading properly.

Mastering step 1 looks like this:

• Allow your child to read the word problem aloud to you. 
• Don’t let your child skip over or mispronounce any words. 
• If necessary, model how to read the word problem, then allow your child to read it again. Only after the word problem is read accurately, should you move on to step 2.

Step 2: Highlight the keywords in the word problem

The keywords for word problems in math indicate what math action should be taken. Teach your child to highlight or underline the keywords in every word problem. 

Here are some of the most common keywords in math word problems: 

• Subtraction words – less than, minus, take away
• Addition words – more than, altogether, plus, perimeter
• Multiplication words – Each, per person, per item, times, area 
• Division words – divided by, into
• Total words – in all, total, altogether

Let’s practice. Read the following word problem with your child and help them highlight or underline the main keyword, then decide which math action should be taken.

Michael has ten baseball cards. James has four baseball cards less than Michael. How many total baseball cards does James have? 

The words “less than” are the keywords and they tell us to use subtraction .

Step 3: Make math symbols above keywords to decode the word problem

As I help students with word problems, I write math symbols and numbers above the keywords. This helps them to understand what the word problem is asking.

Let’s practice. Observe what I write over the keywords in the following word problem and think about how you would create a math sentence using them:

Step 4: Create a math sentence to represent the word problem

Using the previous example, let’s write a math sentence. Looking at the math symbols and numbers written above the word problem, our math sentence should be: 10 – 5 = 5 ! 

Each time you practice a word problem with your child, highlight keywords and write the math symbols above them. Then have your child create a math sentence to solve. 

Step 5: Draw a picture to help illustrate the word problem

Pictures can be very helpful for problems that are more difficult to understand. They also are extremely helpful when the word problem involves calculating time , comparing fractions , or measurements . 

Step 6: Always show your work

Help your child get into the habit of always showing their work. As a tutor, I’ve found many reasons why having students show their work is helpful:

• By showing their work, they are writing the math steps repeatedly, which aids in memory
• If they make any mistakes they can track where they happened
• Their teacher can assess how much they understand by reviewing their work
• They can participate in class discussions about their work

Step 7: When solving word problems, make sure there is always a word in your answer!

If the word problem asks: How many peaches did Lisa buy? Your child’s answer should be: Lisa bought 10 peaches .

If the word problem asks: How far did Kyle run? Your child’s answer should be: Kyle ran 20 miles .

So how do you solve a word problem in math?

Together we reviewed the eight simple steps to solve word problems. These steps included identifying keywords for word problems in math, drawing pictures, and learning to explain our answers. 

Is your child ready to put these new skills to the test? Check out the best math app for some fun math word problem practice.

Parents, sign up for a DoodleMath subscription and see your child become a math wizard!

Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring elementary through college level math. "Knowing that my work in math education makes such an impact leaves me with an indescribable feeling of pride and joy!"

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Introduction to Word Problems

These lessons, with videos, examples, solutions and worksheets, help Grade 5 students learn how to solve word problems.

Related Pages More Grade 5 Math Word Problems More Lessons for Grade 5 Math Math Worksheets

The following diagram gives some examples of word problems keywords or clue words. Scroll down the page for more examples and solutions of word problems.

Introduction to Word Problem Terms

Problem Solving Strategies

Explain the meanings of the four basic operations–addition, subtraction, multiplication and division–so that you can understand how to solve word problems correctly.

Helpful hints for solving word problems

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Fun teaching resources & tips to help you teach math with confidence

How to REALLY Help Kids Solve Math Word Problems

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

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

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

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

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

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

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

The Goal of Math Instruction

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

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

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

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

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

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

The Problem with Relying On Keywords in Math Word Problems

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

1. Relying on keywords can lead kids astray:

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

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

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

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

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

What’s the problem here?

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

2. Not all math word problems include keywords:

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

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

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

Read: Solving Math Word Problems Without Keywords .

3. Real life math doesn’t include keywords:

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

Just messy, real life.

So what can we do?

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

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

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

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

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

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

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

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

Some include space to check their answer as well.

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

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

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

These are so helpful Thankyou 🙂

Dear Math Geek Mama,

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

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

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

Mrs. Felicia Barlow

Hi Felicia!

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

Thank you for the templates

thank you this has been very insightful.

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

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Strategies for Solving Word Problems – Math

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

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

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

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

1. read the entire word problem.

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

2. Think About the Word Problem

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

Here are the questions:

A. what exactly is the question.

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

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

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

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

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

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

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

C. What information do I already have?

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

3. Write on the Word Problem

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

• Circle any numbers you’ll use.
• Lightly cross out any information you don’t need.
• Underline the phrase or sentence which tells exactly what you’ll need to find.

4. Draw a Simple Picture and Label It

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

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

5. Estimate the Answer Before Solving

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

6. Check Your Work When Done

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

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

7. Practice Word Problems Often

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

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

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

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

This 3rd grade math task cards bundle has word problems in almost every one of its 30 task card sets..

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

CLICK HERE to take a look at 3rd grade:

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

CLICK HERE to see 4th grade:

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

CLICK HERE to take a look at 5th grade:

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

3rd Grade: Rounding Whole Numbers Task Cards

4th Grade: Convert Fractions and Decimals Task Cards

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

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How can identifying key words help students solve mathematical word problems? 3-8 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. One hour to one hour and a half Students will: to download] for "Solving Math Word Problems" on "Translating Word Problems" in the problem let them know that they needed to the two numbers in order to determine the number of index cards needed for the class (i.e., ).               add(ed) to all together both combined in all increase by more than perimeter plus sum total decreased by difference fewer than how many more left less less than minus remaining take away a area multiplied by of per product of rate times triple twice divided half how many each out of percent quarter quotient of percent Creating key word flash cards: Have a student count out the number of index cards that the class determined in the warm up problem and distribute four cards to each student. Direct students to create four flash cards — one for each of the four mathematical operations. On the blank side of each card, they should boldly write an operation and its symbol (i.e., +, -, x, where is the division symbol?), and on the reverse, lined sign they should list the key words associated with that operation. (Students should base these flash cards on the table you created on the front board.) Playing the role of "math coach": Organize the class into small groups of no more than three to four students in each group, and explain that they will be using their new flash cards as visual aids in math coaching! Distribute a "Solving Word Problems through Key Words" sheet to a student in each group and explain that the student with the sheet will act as the reader and recorder during the first round. The reader and recorder's job is to read a word problem aloud and to allow his fellow "math coaches" to advise him on which mathematical operation to follow in solving the problem. Advise the math coaches in the class to listen to the word problem closely, to advise the reader and recorder to underline any key words in the problem that they detect, and to follow the flash card mathematical operation that they decide to "flash." Direct groups to complete the "Solving Word Problems through Key Words" sheet, alternating the role of reader and recorder so that each student has at least one or two turns in that role. Sharing word problem answers and strategies: Invite students to the front of the classroom to explain their group's word problem strategies and how key words led to determining which mathematical operations to use in each problem. For homework, assign students the task of writing some of their own word problems containing some of the key words discussed in class but not previously used on the "Solving Word Problems through Key Words" sheet. Extending the Lesson: To further challenge students, you could give them additional word problems that challenge them to interpret the same key words in somewhat confusing contexts (e.g., "I have eight jelly beans, which is three fewer than my brother has. How many jelly beans does my brother have?") Or, you could also introduce word problems involving multiple mathematical operations  (e.g., "A 6000 seat stadium is divided into 3 sections. There are 2000 seats in Section 1, and there are 1500 more seats in Section 2 than in Section 3. How many seats are in Section 2?") Assessment: Check whether or not groups accurately solved each of the ten word problems and underlined appropriate key words in the "Solving Word Problems through Key Words" sheet. Assess students' original word problems to see if they appropriately incorporated key words to indicate specific mathematical operations. Educational Standards : Benchmarks for Mathematics Standard 1.     Uses a variety of strategies in the problem-solving process Level II (Grades 3-5) 1. Uses a variety of strategies to understand problem situations (e.g., discussing with peers, stating problems in own words, modeling problem with diagrams or physical objects, identifying a pattern)  2. Represents problems situations in a variety of forms (e.g., translates from a diagram to a number or symbolic expression) 3. Understands that some ways of representing a problem are more helpful than others 4. Uses trial and error and the process of elimination to solve problems 5. Knows the difference between pertinent and irrelevant information when solving problems  6. Understands the basic language of logic in mathematical situations (e.g., "and," "or," "not")  7. Uses explanations of the methods and reasoning behind the problem solution to determine reasonableness of and to verify results with respect to the original problem  Level III (Grades 6-8) 1. Understands how to break a complex problem into simpler parts or use a similar problem type to solve a problem 2. Uses a variety of strategies to understand problem-solving situations and processes (e.g., considers different strategies and approaches to a problem, restates problem from various perspectives)  3. Understands that there is no one right way to solve mathematical problems but that different methods (e.g., working backward from a solution, using a similar problem type, identifying a pattern) have different advantages and disadvantages 4. Formulates a problem, determines information required to solve the problem, chooses methods for obtaining this information, and sets limits for acceptable solutions  5. Represents problem situations in and translates among oral, written, concrete, pictorial, and graphical forms  6. Generalizes from a pattern of observations made in particular cases, makes conjectures, and provides supporting arguments for these conjectures (i.e., uses inductive reasoning)  7. Constructs informal logical arguments to justify reasoning processes and methods of solutions to problems (i.e., uses informal deductive methods)  8. Understands the role of written symbols in representing mathematical ideas and the use of precise language in conjunction with the special symbols of mathematics Article Topics: Key Words for Problem Solving Grades 6-12 School Leaders Have you entered to win this adorable math giveaway? ✨ 14 Effective Ways to Help Your Students Conquer Math Word Problems If a train leaving Minneapolis is traveling at 87 miles an hour… Word problems can be tricky for a lot of students, but they’re incredibly important to master. After all, in the real world, most math is in the form of word problems. “If one gallon of paint covers 400 square feet, and my wall measures 34 feet by 8 feet, how many gallons do I need?” “This sweater costs $135, but it’s on sale for 35% off. So how much is that?” Here are the best teacher-tested ideas for helping kids get a handle on these problems. 1. Solve word problems regularly This might be the most important tip of all. Word problems should be part of everyday math practice, especially for older kids. Whenever possible, use word problems every time you teach a new math skill. Even better: give students a daily word problem to solve so they’ll get comfortable with the process. Learn more: Teaching With Jennifer Findlay 2. Teach problem-solving routines There are a LOT of strategies out there for teaching kids how to solve word problems (keep reading to see some terrific examples). The important thing to remember is that what works for one student may not work for another. So introduce a basic routine like Plan-Solve-Check that every kid can use every time. You can expand on the Plan and Solve steps in a variety of ways, but this basic 3-step process ensures kids slow down and take their time. Learn more: Word Problems Made Easy [contextly_auto_sidebar] 3. Visualize or model the problem Encourage students to think of word problems as an actual story or scenario. Try acting the problem out if possible, and draw pictures, diagrams, or models. Learn more about this method and get free printable templates at the link. Learn more: Math Geek Mama 4. Make sure they identify the actual question Educator Robert Kaplinsky asked 32 eighth grade students to answer this nonsensical word problem. Only 25% of them realized they didn’t have the right information to answer the actual question; the other 75% gave a variety of numerical answers that involved adding, subtracting, or dividing the two numbers. That tells us kids really need to be trained to identify the actual question being asked before they proceed.  Learn more: Robert Kaplinsky 5. Remove the numbers It seems counterintuitive … math without numbers? But this word problem strategy really forces kids to slow down and examine the problem itself, without focusing on numbers at first. If the numbers were removed from the sheep/shepherd problem above, students would have no choice but to slow down and read more carefully, rather than plowing ahead without thinking.  Learn more: Where the Magic Happens Teaching 6. Try the CUBES method This is a tried-and-true method for teaching word problems, and it’s really effective for kids who are prone to working too fast and missing details. By taking the time to circle, box, and underline important information, students are more likely to find the correct answer to the question actually being asked. Learn more: Teaching With a Mountain View 7. Show word problems the LOVE Here’s another fun acronym for tackling word problems: LOVE. Using this method, kids Label numbers and other key info, then explain Our thinking by writing the equation as a sentence. They use Visuals or models to help plan and list any and all Equations they’ll use.  8. Consider teaching word problem key words This is one of those methods that some teachers love and others hate. Those who like it feel it offers kids a simple tool for making sense of words and how they relate to math. Others feel it’s outdated, and prefer to teach word problems using context and situations instead (see below). You might just consider this one more trick to keep in your toolbox for students who need it. Learn more: Book Units Teacher 9. Determine the operation for the situation Instead of (or in addition to) key words, have kids really analyze the situation presented to determine the right operation(s) to use. Some key words, like “total,” can be pretty vague. It’s worth taking the time to dig deeper into what the problem is really asking. Get a free printable chart and learn how to use this method at the link. Learn more: Solving Word Problems With Jennifer Findlay 10. Differentiate word problems to build skills Sometimes students get so distracted by numbers that look big or scary that they give up right off the bat. For those cases, try working your way up to the skill at hand. For instance, instead of jumping right to subtracting 4 digit numbers, make the numbers smaller to start. Each successive problem can be a little more difficult, but kids will see they can use the same method regardless of the numbers themselves. Learn more: Differentiating Math  11. Ensure they can justify their answers One of the quickest ways to find mistakes is to look closely at your answer and ensure it makes sense. If students can explain how they came to their conclusion, they’re much more likely to get the answer right. That’s why teachers have been asking students to “show their work” for decades now. Learn more: Madly Learning 12. Write the answer in a sentence When you think about it, this one makes so much sense. Word problems are presented in complete sentences, so the answers should be too. This helps students make certain they’re actually answering the question being asked… part of justifying their answer. Learn more: Multi-Step Word Problems 13. Add rigor to your word problems A smart way to help kids conquer word problems is to, well… give them better problems to conquer. A rich math word problem is accessible and feels real to students, like something that matters. It should allow for different ways to solve it and be open for discussion. A series of problems should be varied, using different operations and situations when possible, and even include multiple steps. Visit both of the links below for excellent tips on adding rigor to your math word problems. Learn more: The Routty Math Teacher and Alyssa Teaches 14. Use a problem-solving rounds activity. Put all those word problem strategies and skills together with this whole-class activity. Start by reading the problem as a group and sharing important information. Then, have students work with a partner to plan how they’ll solve it. In round three, kids use those plans to solve the problem individually. Finally, they share their answer and methods with their partner and the class. Be sure to recognize and respect all problem-solving strategies that lead to the correct answer. Learn more: Teacher Trap Like these word problem tips and tricks? Learn more about Why It’s Important to Honor All Math Strategies . Plus, 60+ Awesome Websites For Teaching and Learning Math . You Might Also Like Why Is Math Important? 7 Reasons To Convince Your Students You'll no longer be stumped when your students ask. Continue Reading Copyright © 2024. All rights reserved. 5335 Gate Parkway, Jacksonville, FL 32256 HW Guidelines Study Skills Quiz Find Local Tutors Demo MathHelp.com Join MathHelp.com Select a Course Below ACCUPLACER Math Math Placement Test PRAXIS Math + more tests 5th Grade Math 6th Grade Math Pre-Algebra College Pre-Algebra Introductory Algebra Intermediate Algebra College Algebra Translating Word Problems: Keywords Keywords Examples The hardest thing about doing word problems is using the part where you need to take the English words and translate them into mathematics. Usually, once you get the math equation, you're fine; the actual math involved is often fairly simple. But figuring out the actual equation can seem nearly impossible. What follows is a list of hints and helps. Be advised, however: To really learn "how to do" word problems, you will need to practice, practice, practice. How do I convert word problems into math? Read the entire exercise. Work in an organized manner. Look for the keywords. Apply your knowledge of "the real world". Content Continues Below MathHelp.com Algebra Word Problems Step 1 in effectively translating and solving word problems is to read the problem entirely. Don't start trying to solve anything when you've only read half a sentence. Try first to get a feel for the whole problem; try first to see what information you have, and then figure out what you still need. Step 2 is to work in an organized manner. Figure out what you need but don't have. Name things. Pick variables to stand for the unknows, clearly labelling these variables with what they stand for. Draw and label pictures neatly. Explain your reasoning as you go along. And make sure you know just exactly what the problem is actually asking for. You need to do this for two reasons: Working clearly will help you think clearly, and figuring out what you need will help you translate your final answer back into English. Regarding point (a) above: It can be really frustrating (and embarassing) to spend fifteen minutes solving a word problem on a test, only to realize at the end that you no longer have any idea what " x " stands for, so you have to do the whole problem over again. I did this on a calculus test — thank heavens it was a short test! — and, trust me, you don't want to do this to yourself. Taking fifteen seconds to label things is a better use of your time than spending fifteen minutes reworking the entire exercise! Step 3 is to look for "key" words. Certain words indicate certain mathematica operations. Some of those words are easy. If an exercise says that one person "added" her marbles to the pile belonging to somebody else, and asks for how many marbles are now in the pile, you know that you'll be adding two numbers. What are common keywords for word problems? The following is a listing of most of the more-common keywords for word problems: increased by more than combined, together total of sum, plus added to comparatives ("greater than", etc) Subtraction: decreased by minus, less difference between/of less than, fewer than left, left over, after save (old-fashioned term) comparatives ("smaller than", etc) Multiplication: of times, multiplied by product of increased/decreased by a factor of (this last type can involve both addition or subtraction and multiplication!) twice, triple, etc each ("they got three each", etc) per, a out of ratio of, quotient of percent (divide by 100) equal pieces, split average is, are, was, were, will be gives, yields sold for, cost Note that "per", in "Division", means "divided by", as in "I drove 90 miles on three gallons of gas, so I got 30 miles per gallon". Also, "a" sometimes means "divided by", as in "When I tanked up, I paid $12.36 for three gallons, so the gas was $4.12 a gallon". Warning: The "less than" construction, in "Subtraction", is backwards in the English from what it is in the math. If you need, for instance, to translate " 1.5 less than x ", the temptation is to write " 1.5 −  x ". Do not do this! You can see how this is wrong by using this construction in a "real world" situation: Consider the statement, "He makes $1.50 an hour less than me." You do not figure his wage by subtracting your wage from $1.50 . Instead, you subtract $1.50 from your wage. So remember: the "less than" construction is backwards. (Technically, the "greater than" construction, in "Addition", is also backwards in the math from the English. But the order in addition doesn't matter, so it's okay to add backwards, because the result will be the same either way.) Also note that order is important in the "quotient/ratio of" and "difference between/of" constructions. If a problems says "the ratio of x and y ", it means " x divided by y ", not " y divided by x ". If the problem says "the difference of x and y ", it means " x  −  y ", not " y  −  x ". Advertisement 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.) 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! URL: https://www.purplemath.com/modules/translat.htm Page 1 Page 2 Standardized Test Prep College math, homeschool math, share this page. Terms of Use About Purplemath About the Author Tutoring from PM Advertising Linking to PM Site licencing Visit Our Profiles No More Keywords for Math Word Problems Content and Standards 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. 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. Making Sense of Problems The first Mathematical Practice Standard of the Common Core State Standards for Math describe mathematically proficient students as those who can:  Explain the meaning of a problem Plan a solution pathway rather than jumping to a solution Continually check for reasonableness and ask, “Does this make sense?”  These three skills are essential to solving math word problems successfully. But, how do we help students develop them? Using Tricks To Replace Thinking Tina Cardone, the author of Nix the Tricks , a guide to avoiding non-conceptually developmental short-cuts, suggests having students think about the words of the problem as a whole and focus on what is happening in the problem in context. Students can accomplish this by visualizing the situation and creating a mental picture of the actions that are taking place. Once they understand the actions, students can then connect the actions to symbols. After students have experience with a variety of problem situations, some patterns will begin to emerge as students begin to recognize recurring themes, such as joining, part-part-whole, separating, comparing, equal groups, sharing, and measuring. Throughout the year, teachers can record the different situations students encounter on an anchor chart. Then replace that old, out-dated math keywords poster with the brand-spanking-new operation situations poster. Want to know more about the operation situations and strategies to help with math word problems ? Download the free poster above using the form below and click here to learn more about strategies to help with math word problems. What strategies do you use to emphasize making sense of word problems with your students? Share your ideas in the comments section below.  Common Core State Standards for Math https://gfletchy.com/2015/01/12/teaching-keywords-forget-about-it/ http://nixthetricks.com/ http://tjzager.com/2014/10/18/making-sense/ Van de Wall, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). Elementary and middle school mathematics: Teaching developmentally. Boston, MA: Pearson. Van de Wall, J. A. and Lovin, L. H. (2006). Teaching student-centered mathematics: Grades 3 – 5. Boston, MA: Pearson. Shametria Routt Banks Assessment Tools Critical Thinking Differentiation Math & Literature Math & Technology Math Routines Math Stations Virtual Learning Writing in Math You may also like... 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! Leave a Reply Cancel reply Your email address will not be published. Required fields are marked * This site uses Akismet to reduce spam. Learn how your comment data is processed . ©2024 The Routty Math Teacher.   All Rights Reserved.  Designed by Ashley Hughes. Privacy overview, grade level. Rating Count Price (Ascending) Price (Descending) Most Recent Math key words for word problems Key Words Used In Math Word Problems Math Bulletin Boards ( Math Talk, Word Problem Key Words , Math Facts) Math Wall Math Key Words Anchor Charts and Reference Posters for Word Problems Operations Key Words for Math Operations Posters Word Problems Math Operations Key Word Posters for Word Problems Signal Words for Add Subtract Identifying Operations in Word Problems Math Vocabulary Key Words Sort & Posters Math Key Words Graphic Organizer - Study Reference - Word Problems Math Key Words for Word Problems - Poster Math Word Problems with Key Words Math Key Words Sort - Basic Operations - Verbal Expressions - Word Problems Math Key Words For Word Problems : Student Reference Sheet (Anchor Chart) Free Addition & Subtraction Math Key Words Posters & Activity for Word Problems Free Multiplication & Division Math Key Words Posters for Word Problems Math Operations Key Word Posters | Word Problem Key Word Posters | Multistep FREE Key Math Words Anchor Chart for Word Problems Math Key Words Posters - Basic Operations - Verbal Expressions - Word Problems KEY WORDS USED IN MATH WORD PROBLEMS SPANISH & ENGLISH Math Key Words Task Cards for Word Problems Math Word Problem Anchor Chart - Key Words for Problem Solving for 4 Operations Math Word Problem Key Word Sorting Activity Key Words for Math Word Problems Math Word Problems Key Words Lists Posters Math Word Problem Key Words Math Word Problems Key Words Sort 1st grade 2nd grade We're hiring Help & FAQ Privacy policy Student privacy Terms of service Tell us what you think Choose Your Test Search Blogs By Category College Admissions AP and IB Exams GPA and Coursework The Complete Guide to SAT Math Word Problems A significant portion of the total digital SAT Math section will be word problems, meaning you'll need to create your own visuals and equations to solve for your answers. Though the actual math topics can vary, SAT word problems share a few commonalities, and we’re here to walk you through how to best solve them. This post will be your complete guide to SAT Math word problems. We'll cover how to translate word problems into equations and diagrams, the different types of math word problems you’ll see on the test, and how to go about solving your word problems on test day. Feature Image: Antonio Litterio /Wikimedia What Are SAT Math Word Problems? A word problem is any math problem based mostly or entirely on a written description. You will not be provided with an equation, diagram, or graph on a word problem and must instead use your reading skills to translate the words of the question into a workable math problem. Once you do this, you can then solve it. You will be given word problems on the digital SAT Math section for a variety of reasons. For one, word problems test your reading comprehension and your ability to visualize information. Secondly, these types of questions allow test makers to ask questions that'd be impossible to ask with just a diagram or an equation. For instance, if a math question asks you to fit as many small objects into a larger one as is possible, it'd be difficult to demonstrate and ask this with only a diagram. Translating Math Word Problems Into Equations or Drawings In order to translate your SAT word problems into actionable math equations you can solve, you’ll need to understand and know how to utilize some key math terms. Whenever you see these words, you can translate them into the proper mathematical action. For instance, the word "sum" means the value when two or more items are added together. So if you need to find the sum of a and b , you’ll need to set up your equation like this: a+b. Also, note that many mathematical actions have more than one term attached, which can be used interchangeably. Here is a chart with all the key terms and symbols you should know for SAT Math word problems: Sum, increased by, added to, more than, total of + Difference, decreased by, less than, subtracted from − Product, times, __ times as much, __ times as many (a number, e.g., “three times as many”) * or x Divided by, per, __ as many, __ as much (a fraction, e.g., “one-third as much”) / or ÷ Equals, is, are, equivalent = Is less than < Is greater than > Is less than or equal to ≤ Is greater than or equal to ≥ Now, let's look at these math terms in action using a few official examples: We can solve this problem by translating the information we're given into algebra. We know the individual price of each salad and drink, and the total revenue made from selling 209 salads and drinks combined. So let's write this out in algebraic form. We'll say that the number of salads sold = S , and the number of drinks sold = D . The problem tells us that 209 salads and drinks have been sold, which we can think of as this: S + D = 209 Finally, we've been told that a certain number of S and D have been sold and have brought in a total revenue of 836 dollars and 50 cents. We don't know the exact numbers of S and D , but we do know how much each unit costs. Therefore, we can write this equation: 6.50 S + 2 D = 836.5 We now have two equations with the same variables ( S and D ). Since we want to know how many salads were sold, we'll need to solve for D so that we can use this information to solve for S . The first equation tells us what S and D equal when added together, but we can rearrange this to tell us what just D equals in terms of S : Now, just subtract S from both sides to get what D equals: D = 209 − S Finally, plug this expression in for D into our other equation, and then solve for S : 6.50 S + 2(209 − S ) = 836.5 6.50 S + 418 − 2 S = 836.5 6.50 S − 2 S = 418.5 4.5 S = 418.5 The correct answer choice is (B) 93. This word problem asks us to solve for one possible solution (it asks for "a possible amount"), so we know right away that there will be multiple correct answers. Wyatt can husk at least 12 dozen ears of corn and at most 18 dozen ears of corn per hour. If he husks 72 dozen at a rate of 12 dozen an hour, this is equal to 72 / 12 = 6 hours. You could therefore write 6 as your final answer. If Wyatt husks 72 dozen at a rate of 18 dozen an hour (the highest rate possible he can do), this comes out to 72 / 18 = 4 hours. You could write 4 as your final answer. Since the minimum time it takes Wyatt is 4 hours and the maximum time is 6 hours, any number from 4 to 6 would be correct. Though the hardest SAT word problems might look like Latin to you right now, practice and study will soon have you translating them into workable questions. Typical SAT Word Problems Word problems on the SAT can be grouped into three major categories: Word problems for which you must simply set up an equation Word problems for which you must solve for a specific value Word problems for which you must define the meaning of a value or variable Below, we look at each world problem type and give you examples. Word Problem Type 1: Setting Up an Equation This is a fairly uncommon type of SAT word problem, but you’ll generally see it at least once on the Math section. You'll also most likely see it first on the section. For these problems, you must use the information you’re given and then set up the equation. No need to solve for the missing variable—this is as far as you need to go. Almost always, you’ll see this type of question in the first several questions on the SAT Math section, meaning that the College Board consider these questions easy. This is due to the fact that you only have to provide the setup and not the execution. It's stated that the vet recommends that, every day, the rabbit eat 25 calories per pound that it weighs, plus an additional 11 calories. Let's put this in terms of  x. If a rabbit weighs  x  pounds, then multiplying its weight in pounds by 25 calories yields 25x calories.  Adding the additional 11 calories gives us 25x + 11. The question states that  c  is the total number of calories that the vet recommends a rabbit eat each day. Put this all together, and you get: c = 25x +11. This means Answer Choice D is the correct answer. Word Problem Type 2: Solving for a Missing Value The vast majority of SAT Math word problem questions will fall into this category. For these questions, you must both set up your equation and solve for a specific piece of information. Most (though not all) word problem questions of this type will be scenarios or stories covering all sorts of SAT Math topics , such as averages , single-variable equations , and ratios . You almost always must have a solid understanding of the math topic in question in order to solve the word problem on the topic. Let's think about this problem in terms of x . If Scott has 400 employees, randomly selected 20 employees, then found that 16 of those 20 employees are enrolled in 3 professional development courses, then we know that 16/20 employees are in three courses, or 80% because 16/20 is 0.80 or 80/100. Because the employees were selected randomly, the best way to estimate how many of the 400 total employees are enrolled in exactly three professional development courses this year is to multiply 400 x 0.8. This gives us 320. Answer Choice B is the correct answer. You might also get a geometry problem as a word problem, which might or might not be set up with a scenario, too. Geometry questions will be presented as word problems typically because the test makers felt the problem would be too easy to solve had you been given a diagram, or because the problem would be impossible to show with a diagram. This is a case of a problem that is difficult to show visually, since x is not a set degree value but rather a value greater than 55; thus, it must be presented as a word problem. Since we know that x must be an integer degree value greater than 55, let us assign it a value. In this case, let us call x 56°. (Why 56? There are other values x could be, but 56 is guaranteed to work since it's the smallest integer larger than 55. Basically, it's a safe bet!) Now, because x = 56, the next angle in the triangle—2 x —must measure the following: Let's make a rough (not to scale) sketch of what we know so far: Now, we know that there are 180° in a triangle , so we can find the value of y by saying this: y = 180 − 112 − 56 One possible value for y is 12. (Other possible values are 3, 6, and 9. ) Word Problem Type 3: Explaining the Meaning of a Variable or Value This type of problem will show up at least once. It asks you to define part of an equation provided by the word problem—generally the meaning of a specific variable or number. Let's break this question down. The equation y - 5x = 6 represents the relationship between the number of suits that Kaylani made, x, and the total length of fabric that she purchased, y, in yards.  But what does the 6 represent? Let's get one of the variables by itself to see what the equation looks like then. Y is easier to isolate than x, so we'll do that. Adding 5x to both sides of the equation gives us y = 5x + 6 Because Kaylani made x suits and used 5 yards of fabric to make each suit, 5x represents the total amount of fabric she used to make the suits. Because y represents the total length of fabric Kaylani purchased, then the equation y = 5x + 6 shows us that Kaylani purchased 5x yards of fabric to make the suits, plus an additional 6 yards of fabric. Therefore, the best interpretation of 6 in this question is that Kaylani purchased 6  yards more fabric than she used to make the suits. The correct answer is Choice D. To help juggle all the various SAT word problems, let's look at the math strategies and tips at our disposal. SAT Math Strategies for Word Problems Though you’ll see word problems on the SAT Math section on a variety of math topics, there are still a few techniques you can apply to solve word problems as a whole. #1: Draw It Out Whether your problem is a geometry problem or an algebra problem, sometimes making a quick sketch of the scene can help you understand what exactly you're working with. For instance, let's look at how a picture can help you solve a word problem about a circle (specifically, a pizza): If you often have trouble visualizing problems such as these, draw it out. We know that we're dealing with a circle since our focus is a pizza. We also know that the pizza weighs 3 pounds. Because we'll need to solve the weight of each slice in ounces, let's first convert the total weight of our pizza from pounds into ounces. We're given the conversion (1 pound = 16 ounces), so all we have to do is multiply our 3-pound pizza by 16 to get our answer: 3 * 16 = 48 ounces (for whole pizza) Now, let's draw a picture. First, the pizza is divided in half (not drawn to scale): We now have two equal-sized pieces. Let's continue drawing. The problem then says that we divide each half into three equal pieces (again, not drawn to scale): This gives us a total of six equal-sized pieces. Since we know the total weight of the pizza is 48 ounces, all we have to do is divide by 6 (the number of pieces) to get the weight (in ounces) per piece of pizza: 48 / 6 = 8 ounces per piece The correct answer choice is (C) 8. As for geometry problems, remember that you might get a geometry word problem written as a word problem. In this case, make your own drawing of the scene. Even a rough sketch can help you visualize the math problem and keep all your information in order. #2: Memorize Key Terms If you’re not used to translating English words and descriptions into mathematical equations, then SAT word problems might be difficult to wrap your head around at first. Look at the chart we gave you above so you can learn how to translate keywords into their math equivalents. This way, you can understand exactly what a problem is asking you to find and how you’re supposed to find it. There are free SAT Math questions available online , so memorize your terms and then practice on realistic SAT word problems to make sure you’ve got your definitions down and can apply them to the actual test. #3: Underline and/or Write Out Important Information Even though the SAT is now digital, you're still allowed scratch paper to take notes and work out problems. The key to solving a word problem is to bring together all the key pieces of given information and put them in the right places. Make sure you write out all these givens on the diagram you’ve drawn (if the problem calls for a diagram) so that all your moving pieces are in order. One of the best ways to keep all your pieces straight is to underline your key information in the problem, and then write them out yourself before you set up your equation. So take a moment to perform this step before you zero in on solving the question. #4: Pay Close Attention to What's Being Asked It can be infuriating to find yourself solving for the wrong variable or writing in your given values in the wrong places. And yet this is entirely too easy to do when working with math word problems. Make sure you pay strict attention to exactly what you’re meant to be solving for and exactly what pieces of information go where. Are you looking for the area or the perimeter? The value of x, 2x, or y? It’s always better to double-check what you’re supposed to find before you start than to realize two minutes down the line that you have to begin solving the problem all over again. #5: Brush Up on Any Specific Math Topic You Feel Weak In You're likely to see both a diagram/equation problem and a word problem for almost every SAT Math topic on the test. This is why there are so many different types of word problems and why you’ll need to know the ins and outs of every SAT Math topic in order to be able to solve a word problem about it. For example, if you don’t know how to find an average given a set of numbers, you certainly won’t know how to solve a word problem that deals with averages! Understand that solving an SAT Math word problem is a two-step process: it requires you to both understand how word problems work and to understand the math topic in question. If you have any areas of mathematical weakness, now's a good time to brush up on them—or else SAT word problems might be trickier than you were expecting! All set? Let's go! Test Your SAT Math Word Problem Knowledge Finally, it's time to test your word problem know-how against real SAT Math problems: Word Problems Answers:  A, A, B, A Aaaaaaaaaaand time for a nap. Key Takeaways: Making Sense of SAT Math Word Problems Word problems make up a significant portion of the SAT Math section, so it’s a good idea to understand how they work and how to translate the words on the page into a proper expression or equation. But this is still only half the battle. Though you won’t know how to solve a word problem if you don’t know what a product is or how to draw a right triangle, you also won’t know how to solve a word problem about ratios if you don’t know how ratios work. Therefore, be sure to learn not only how to approach math word problems as a whole, but also how to narrow your focus on any SAT Math topics you need help with. You can find links to all of our SAT Math topic guides here to help you in your studies. What’s Next? Want to brush up on SAT Math topics? Check out our individual math guides to get an overview of each and every topic on SAT Math . From polygons and slopes to probabilities and sequences , we've got you covered! Running out of time on the SAT Math section? We have the know-how to help you beat the clock and maximize your score . Been procrastinating on your SAT studying? Learn how you can overcome your desire to procrastinate and make a well-balanced prep plan. Trying to get a perfect SAT score? Take a look at our guide to getting a perfect 800 on SAT Math , written by a perfect scorer. 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Courtney scored in the 99th percentile on the SAT in high school and went on to graduate from Stanford University with a degree in Cultural and Social Anthropology. She is passionate about bringing education and the tools to succeed to students from all backgrounds and walks of life, as she believes open education is one of the great societal equalizers. She has years of tutoring experience and writes creative works in her free time. Ask a Question Below Have any questions about this article or other topics? Ask below and we'll reply! 433 COMMENTS Teaching Math Word Problem Key Words (Free Cheat Sheet) Teaching Math Word Problem Key Words (Free Cheat ... "Key Words and Catch Phrases" for Word Problems 10. Words ending with "er"; higher, longer, faster, heavier, larger, shorter, slower, farther, etc. Example: Jean's apple weighs 100 grams, and Karen's apple weighs 80 grams. How much heavier is Jean's apple? Multiplication Words. 1. Times: Maria ran around the track 5 times. It took her 5 minutes to run around the track. How many minutes did ... PDF 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 in all increased by plus sum together total Subtraction Words change decreased by difference fewer or fewer than how many are left (or have left) PDF Key Words for Solving Word Problems Key Words for Solving Word Problems The hardest part of solving a word problem is actually understanding the problem and determining the operation (or operations) that needs to be performed. Listed below are a few of the most commonly used key words in word problems and the operations that they signal. How to Know which Operations to Use in Word Problems Subtraction word problem worksheets. Starting in kindergarten, we've created subtraction word problem for every grade. By grade 3, you'll find subtraction included in the mixed word problems as well. In grade 2, students work on 1-3 digit subtraction word problems. Key phrases for multiplication word problems. How many of the same thing ... Math Keywords for Problem Solving These math keyword posters help students identify key words in word problems that indicate operations. There are four posters, one for each math operation (addition, subtraction, multiplication, division). The posters also come in black and white, which can be printed on colored paper to save on ink! The one-page sheets are great for students ... Solving Word Questions Turning English into Algebra. To turn the English into Algebra it helps to: Read the whole thing first; Do a sketch if possible; Assign letters for the values; Find or work out formulas; You should also write down what is actually being asked for, so you know where you are going and when you have arrived!. Also look for key words: How Do You Solve Word Problems in Math? Step 2: Highlight the keywords in the word problem. The keywords for word problems in math indicate what math action should be taken. Teach your child to highlight or underline the keywords in every word problem. Here are some of the most common keywords in math word problems: Subtraction words- less than, minus, take away. Identifying Key Words in Math Problems Wisc-Online is a creation of Wisconsin's Technical Colleges and maintained by Fox Valley Technical College. Wisc-Online by Fox Valley Technical College is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. In this learning activity you'll read key words that direct you to add, subtract, multiply, or divide. Introduction to Word Problems These lessons, with videos, examples, solutions and worksheets, help Grade 5 students learn how to solve word problems. The following diagram gives some examples of word problems keywords or clue words. Scroll down the page for more examples and solutions of word problems. Introduction to Word Problem Terms. How to REALLY Help Kids Solve Math Word Problems 1. Relying on keywords can lead kids astray: Even though we, as teachers, give kids lists of keywords with the very best of intentions, this is actually not helpful if they're used in a different way than kids are used to. Here's an example. Say kids are given the following word problem: Ben has eighteen toy cars. Strategies for Solving Word Problems 1. Read the Entire Word Problem. Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too. 2. Word Problems Worksheets Mixed Word Problems with Key Phrases Worksheets These Word Problems Worksheets will produce addition, multiplication, subtraction and division problems using clear key phrases to give the student a clue as to which type of operation to use. These word problems worksheets are appropriate for 4th Grade, 5th Grade, 6th Grade, and 7th Grade. Using Key Words to Unlock Math Word Problems Instructional Objectives: Students will: brainstorm key words that usually indicate specific mathematical operations. create flash cards to review the relationships between key words and operations. coach one another in collectively solving mathematical word problems. synthesize their knowledge of word problems by writing some of their own. key words for problem solving 12. $5.00. PDF. Problem Solving - Key Words to Solve Math Story Problems is a set of color coded math key word cards that can help your students interpret and solve word problems. Mounted on key rings as a quick reference tool, this resource helps students choose the right operation based on the key words used. Key Words for Problem Solving Key Words for Problem Solving . Key Words for Problem Solving Foldable Organizer. Click on the folders to visit additonal math pages at Book Units Teacher. These math topics have more than one webpage. Click the links below the folders to go to individual pages. Free Math Solving Problem Key Words Teaching Resources Math operations key word practice for problem solvingA set of 28 task cards for identifying math key words.Each card identifies a word or phrase that would be commonly found in word problems.Students need to determine if that word represents an addition or subtraction math operations key word.A task card recording sheet and answer key is provided in this file**Take a peek at the other task ... 14 Effective Ways to Help Your Students Conquer Math Word Problems 14 Effective Ways to Help Your Students Conquer Math ... Results for problem solving key words These Key Words For Solving Word Problems - All Operations (addition, subtraction, multiplication, division) game cards are a part of the Mix & Match series. Any game board can be used with any set of game cards. The directions to each game board are exactly the same so the students can interchange any game board and game cards without any issues. How to turn word problems into math 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. No More Keywords for Math Word Problems 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 ... math key words for word problems Key Words Used In Math Word Problems {Poster/Anchor Chart with Cards for Students} A Poster/anchor chart to put on your Math Vocabulary board to use as a reference. Along with cards to use as bookmarks for a quick reference. Also included is a 24inch x 36inch (poster size) JPEG file, so you can . The Complete Guide to SAT Math Word Problems The Complete Guide to SAT Math Word Problems 6.7: Applications Involving Quadratic Equations The key phrase, "their product is \(96\)," indicates that we should multiply and set the product equal to \(96\). \(n\cdot (2n-4)=96\) Once we have the problem translated to a mathematical equation, we then solve. In this case, we can solve by factoring. The first step is to write the equation in standard form: assignment essay homework paper phd report resume review speech thesis