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- Middle School
- Expanding, Factoring, and Distributing Expressions

Keywords for Addition and Subtraction

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## Basics on the topic Keywords for Addition and Subtraction

In order to translate word problems into mathematical expressions, it is helpful to know certain keywords to look for which indicate which mathematical operations to use. Specifically, words like sum, total, increase, add, plus are commonly used for addition, as well as words like altogether, combine, more than, all, both, and so on. The same goes for subtraction: decrease, minus, fewer, take away, difference, left, less than, subtract, remain, and so on. Learn how to recognize keywords for addition and subtraction by helping Caulleen solve a mystery at her school, the Academy of Magic. Common Core Reference: CCSS.MATH.CONTENT.6.EE.A.2

## Transcript Keywords for Addition and Subtraction

At the Academy of Magic, Caulleen is hot on the trail of a breaking story for her school paper. According to rumors, the school's Switch Quitch Team has been experiencing an odd phenomenon: Brooms from the equipment room are going missing, only to mysteriously return a few hours later, as if nothing had happened! In order to crack this case, we will need to identify keywords for using addition and subtraction .

## How you turn keywords into mathematical expressions

Caulleen plans to start her investiagation by interviewing the Switch Quitch coach. She needs to start with the basics: who had access to the equipment room? The coach tells her that one of the new boys on the team is in charge of equipment. But he can't remember his name. But he knows the number of boys and girls on the team altogether is equal to 20. He knows this because the total sum of players on the team was 16 last year, but increased by 4 this year. How can we turn this information into mathematical equations so we can be sure of how many players are on the team?

## Keywords which are indicating Addition

When information about math operations is presented in a word problem format , look for keywords that indicate the correct operation to use. Let's start with the first fact the coach told us. The total number of boys and girls on the team is 20, altogether. The keywords 'total' and 'altogether' tell us that this is an addition problem. We don't know exactly how many boys and girls there were, but we can use the variables 'b' and 'g' to represent them. Finally, we know that the total number is 20, so that goes to the right of the equal sign. Let's move on to the second thing we learned. She told us that last year, the total sum of players on the team was 16 but increased by 4 this year. The words " total sum " and " increase " tell us that this is also an addition problem . We can use the variable 'p' to represent the players on the team. The number 16 tells us the number of players last year and 4 is the number we are increasing by.

## Keywords which are indicating subtraction

Hm...very interesting, but we're going to need some more clues to solve this mystery. Caulleen decides to talk to the Switch Quitch team captain to see what she knows about the missing brooms. The captain tells Caulleen there should be 20 brooms in the supply room, but today, that amount decreased by 3. Let's convert this to an algebraic expression . By focusing on the keyword decreased , we know to use subtraction . Now we can insert the number of brooms there should be and take away the number that are missing. That's another helpful clue, but still we aren't any closer to solving the mystery. But suddenly the team captain remembers that, actually, today there wasn't just brooms missing. There was one ball fewer than there normally in the equipment closet. Even though we don't know how many balls there normally are in the equipment closet, we can write this as an algebraic expressions. The keywords " fewer than " indicate that we should be using subtraction in our expression . We can use the variable 'n' to represent the number of balls that there usually are. Since there was one fewer than the number of balls there usually are, we can write this as the expression n - 1. Two more pieces have been added to the puzzle. But what does it all mean?

## Keywords overview - Addition and subtraction

Before we get back to Caulleen, remember that there are a lot of keywords that can be used to indicate addition and subtraction . For addition , Caulleen used the words total , sum , altogether , and increase . But we could also have used the words combine , plus , more than , or even just the word " and ". For subtraction , Caulleen used the words, fewer than , decrease , take away , and subtract . We also could have used less than , minus , and difference . Can you think of any others?

Back to the missing brooms. As she's going over her notes, Caulleen starts to hear a strange rustling sound coming from outside. Is someone playing Switch Quitch? It looks like those missing brooms are having fun without the students of the Academy of Magic. But actually, you know what? These guys are pretty good!

## Keywords for Addition and Subtraction exercise

Identify the keywords that indicate subtraction..

The expression describing the information above is given by $20-3$.

$1$ ball fewer means $-1$.

Further keywords which indicate subtraction are

Keep the keywords for subtraction pictured beside in mind in this exercise.

Using those keywords you can solve word problems:

- "There should be $20$ brooms in the supply room, but today there are $3$ less brooms in the supply room." ... this sentence translates to $20-3$ brooms in the supply room.
- "There was $1$ ball fewer than there normally are in the equipment closet."... this sentence translates to means $n-1$, where $n$ stants for the normal number of balls in the equipment closet.

## Decide if the keywords indicate addition or subtraction.

Let's have a look at an example: Paul has $20$ dollars more than Anne. Let $p$ be the amount Paul has, and let $a$ be the amount of money Anne has. We can then see that $p=a+20$.

Let's look at another example: Frank ate two pieces of cake less than Mary. Mary ate $3$ pieces of cake. We then know that Frank ate $3-2=1$ pieces of cake.

$+$ is the plus sign, while $-$ is the minus sign.

$+$ is the plus sign. So the following phrases indicate plus:

- altogether or one can also say in total
- and or plus are rather clear
- take away is another expression for subtract
- Subtraction means

## Explain how to transfer the word problem to an equation.

Check the word problems above for the keyword of addition or subtraction.

- $+$ is the sign for addition
- $-$ is the sign for subtraction

Let's have a look at another example:

The total sum of all spell books and wands is $35$.

- Total sum indicates addition .
- You have to assign variables to the unknown values; let's let $s$ stand for the number of spell books and $w$ for the number of wands.
- The sum of all spell books and wands can be written as $s+w$.
- The fact that this sum is equal to $35$ leads to the equation, $s+w=35$.

If you have to transform a word problem in a mathematical expression, you first have to decide which kind of operator you have to use.

Here we have to distinguish between addition and subtraction. The corresponding keywords are pictured beside.

So, let's have a look at the given examples for word problems. The keywords are written in bold:

- Last night the total of spell books in the classroom was $24$, but there were $5$ less in the classroom this morning.
- The difference between the students’ wands last night and this morning is $13$.

The value of the difference, $13$, is known. So we get the equation, $l-m=13$.

- Last but not least, the number of potion ingredients combined with the number of black cats increased by $3$.

## Decide how to express the word problems in the form of equations.

First think about which operation you need to use: addition or subtraction?

You don't have to solve the corresponding equations.

If you have to transform any word problem into a mathematical expression, you first have to decide which operations you need to use.

To help you decide which operations are needed, you can highlight the corresponding keywords:

- The difference between the number of boys ($x$) and girls ($y$) is $5$.
- The total sum of boys ($x$) and girls ($y$) is $45$.
- The number of wands $x$ is $5$ more than $45$.
- If you take away $5$ from the number of brooms $x$ you get $5$.

## Find all keywords that indicate addition.

Try to examine the corresponding expression. How can you recognize if you have to add or to subtract?

The expression for the information above, with $b$ representing the number of boys and $g$ representing the number of girls is $b+g=20$.

Keep these keywords pictured in mind.

It's better to keep the keywords for addition, pictured beside, in mind, as well as those for subtraction, so we can solve word problems.

Let's have a look at the examples above:

- Combining the number of boys and girls on the team gives $20$ members of the team altogether .
- The total sum of players on the team was $16$, but increased by $4$.

## Express the word problems as equations.

When constructing the expressions corresponding to the word problems given, units shouldn't be included.

Keywords like sum , add , combine , and more than indicate addition.

Keywords like minus , difference , fewer , and take away indicate subtraction.

First let's have a look at the temperature : the average temperature of the last year ($x$) increased by $2^\circ F$ to $92^\circ F$. So we have $x+5=92$.

Next, let the price of the Richard's preferred car be $x$, and let the price of his wife's preferred car be $y$. If Richard combines both prices he gets $23000$ dollars. Thus, we have $x+y=23000$.

Richard would like to buy a new broom: the Super Broom Number $1$ costs $450$ dollars, while Top Broom Highlevel's price is unknown, say $x$. The price $x$ is $5$ dollars fewer than the price of the Super Broom Number $1$. This leads to the equation $450-35=x$.

Last we examine the stock exchange together with Richard: the sum of $x$ and $y$ is given by the expression $x+y$. Next, minus $23$ - this gives us $x+y-23$. The keyword more than indicates that $x+y-23$ is equal to $z+45$, finally giving us the equation $x+y-23=z+45$.

Keywords for Multiplication

What is Factoring?

Keywords for Division

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## Addition and Subtraction Word Problems: Why We Should Avoid Math Keywords

I don’t know about you, but early in my career, I was encouraged to teach math keywords as a primary strategy for solving addition and subtraction word problems. Oh, how I wish I could have a do-over!

If you’re not sure why I want a do-over, and to leave math keywords at the door when teaching addition and subtraction word problems, let me explain.

## What Are Math Keywords

First, let’s tackle what keywords are before we talk about why we shouldn’t be teaching this way. Math keywords are essentially words that we associate with certain operations. It is a strategy that made its way into many classrooms (mine included) that teaches students to look for certain words to determine whether they should add or subtract.

What might this look like? Here is a list of commonly taught “keywords” for addition and subtraction: (Note “keywords” is in quotation marks because they are often not the key!)

## Math “Keywords” in Addition Word Problems

Math “keywords” taught in subtraction word problems.

- how many more
- how many less

Now that we have a common understanding of math keywords and how they are often used to teach addition and subtraction word problems, let’s talk about why it isn’t the best approach.

## A Closer Look at Addition and Subtraction Word Problems

Learning to solve addition and subtraction word problems via math keywords can be misleading! When we seek words over context, we are opening the door for misunderstanding. Let’s talk about two main problems:

- There is a slew of examples where the keyword doesn’t indicate the expected operation
- There are many more addition and subtraction word problems that don’t have any math keywords.

Let’s take a closer look:

## Where the Math Keyword Doesn’t Work

I put 5 flowers in the vase. Penelope put in more flowers. Then there were 9 flowers. How many flowers did Penelope put in the vase? The keyword “more” indicates that this problem should include addition, when, in fact, it requires subtraction.

Crayons come in packs of 8. If you buy 2 packs, how many crayons do you have i n all ? The keyword “in all” indicates that this problem should be solved by adding 8 + 2, when in fact it’s looking for repeated addition.

Damaris left $8 for the tip. Sadie left $7 for the tip. How much money was left for tips? The keyword “left” indicates subtraction, but here we are looking to add the two amounts together to find out the total.

Ella and Oscar have $15 altogether . Ella as $8. How much money does Oscar have? The keyword “altogether” implies addition will solve this problem when it really requires subtraction.

## When There Are No Math Keywords

When teaching students to rely on keywords to solve addition and subtraction word problems, we are setting them up to scratch their heads when there are no keywords to be found. What addition and subtraction word problems don’t include math keywords? Here are just a few:

There are 10 beads on a necklace. 4 are purple and the rest are blue. How many beads are blue?

How many tentacles do 3 octopuses have?

These are just two examples! If we teach students to be reliant on keywords, what are they supposed to do when they approach these kinds of problems? There are no keywords to guide them (and we already know that even if there were, they are unreliable). It’s just another reason to avoid this strategy altogether.

## Multi-Step Addition and Subtraction Word Problems

When we reach two-step and multi-step addition and subtraction word problems, students are faced with multiple keywords. Whether they all indicate the same operation, imply the use of multiple operations, or mislead students into thinking certain operations are required, it’s a mess!

When we teach students to rely on keywords to solve addition and subtraction word problems, when they get to multi-step word problems, they freeze. This is because we have taught them tricks instead of teaching them to comprehend. Those tricks only work sometimes in the most basic scenarios. When students encounter more complicated mathematical situations, they will need to rely on far more to break down the task.

## How to Teach Addition and Subtraction Word Problems Instead

Instead of teaching keywords, we should be encouraging our students to think about what the addition and subtraction word problems are asking. There is no substitution for thinking!

Here are some strategies I use to get them THINKING about the word problems:

## Make it Interactive

Allow students to move, act it out, draw it, or write/talk it out. This is not only great for building meaning, but it doubles as a way to incorporate movement into your lessons.

## Let Them Own It

Ask students to retell the word problem in their own way. Allow them to explain what’s happening. Giving them time to process the problem and make meaning of it will deepen their understanding.

## Focus on Meaning

Focus on what the operations MEAN. What are the big ideas of addition and subtraction? What do those concepts look like? Deep discussions about operations form a stronger foundation, without the cracks that keywords allow.

## Numberless Addition and Subtraction Word Problems

Numberless word problems do just what they say: It removes the numbers. This allows students to think about the context of the word problem instead of focusing on the numbers. Here are some examples:

Verity had _____ M&Ms. Marcus had _____ Skittles. How many pieces of candy did they have altogether?

There are _____ beads on a necklace. _______ are purple and the rest are blue. How many beads are blue?

Working through a variety of numberless word problems together allows students to experience the context of story problems. They build meaning and their own strategies for how deconstructing them!

This can also be used as a two-step approach to working through word problems:

- Remove the numbers and have a discussion about what is happening in the word problem.
- Bring the numbers back into the problem and let students solve it.

## Open-Ended Addition and Subtraction Word Problems

Use open-ended word problems (many can be found here) to get students thinking beyond solving! Open-ended problems often remove the numbers AND the question. Because there are so many possible answers (not all involving the same operation), students get to be part of the story creation. Here are some examples:

Verity had some M&M’s. Marcus had a different number of M&M’s. Use words, pictures, and/or numbers to share your ideas.

Imani’s necklace had some blue beads and some purple beads. Use words, pictures, and/or numbers to share your ideas.

If you want to get started with these, you can read all about how I introduce open-ended word problems HERE! You can also read more about how I use student math journals to understand their thinking HERE!

I hope this post has been helpful! Did this change the way you think about addition and subtraction word problems and/or how we use math keywords? I’d love to know if you’d share your thoughts in the comments! Happy Teaching!

## You May Also Enjoy These Posts:

## Reader Interactions

Thank you so much for this post. It shed new light on how I will teach number stories from now on.

This example really hit home. “I put 5 flowers in the vase. Penelope put in more flowers. Then there were 9 flowers. How many flowers did Penelope put in the vase? The keyword “more” indicates that this problem should include addition, when, in fact, it requires subtraction.” My math lesson on Thursday had a very similar word problem. The objective was to have students use subtraction to solve but all 16 students used addition to solve. When we met in our math groups and I tried to explain it as subtraction they could not grasp that concept (granted, it is only day 20 of school and they will eventually see the connection) but one student actually pointed out that the number story said “more” and that means add.” Thank you again. I will have all these points in mind when teaching math from now on.

What a new way to think about this! I can’t wait to put this new way of thinking in place.

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## Addition and Subtraction Word Problem Keywords

- Each word problem contains numbers which should be written down.
- Keywords in the word problem can help us to decide whether to add or subtract these numbers.
- The list above contains some common addition and subtraction keywords.
- If you see these words in the word problem, they may help you to decide whether to add or subtract the numbers that you have already written down.

- Phoebe has 12 cm of ribbon and Jack has 23 cm of ribbon.
- How much ribbon do they have altogether?
- The word ‘altogether’ tells us to add the two numbers to make a total.
- We can write the numbers of 12 and 23 with their digits above each other.
- Adding the units column, 2 + 3 = 5.
- Adding the tens column, 1 + 2 = 3.
- 12 + 23 = 35 and so, there is 35 cm of ribbon in total.

- Number Bonds to 20
- 2-Digit Column Addition
- Column Subtraction without Borrowing / Regrouping

## Mixed Addition and Subtraction Word Problems Worksheets and Answers

## Mixed Addition and Subtraction Word Problems

Addition and subtraction keywords.

- Together / Altogether
- Less / Fewer than
- How many are left / remain?
- Change – in money questions
- Words ending in ‘er’, such as shorter, longer, faster.

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## Maths / Numbers & Patterns / Word Problems / Addition & Subtraction

Browse our collection of addition and subtraction word problems with answer pages. These resources help teach real world examples of when we use addition and subtraction, and the key words that indicate addition and subtraction. Encourage students to highlight the important information in each word problem, including key words and figures. Addition key words include: ‘more’, ‘in all’, ‘total’, ‘altogether’. Subtraction key words include: ‘less’, ‘difference’, ‘minus’, ‘remain’. Learn different strategies to help solve word problems.

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Problem Solving Poster Set

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Problem Solving Operation Words Poster

A poster showing key words and phrase that mean addition, subtraction, multiplication and division.

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Elementary math word problem key words and their limitations.

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

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

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

This blog post will answer the following questions:

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

## What are Word Problem Key Words?

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

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

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

## Common Math Word Problem Key Words and Phrases

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

## Addition Key Words

Here are some examples of addition key words :

- increased by
- larger than
- longer than

## Subtraction Key Words

Here are some examples of subtraction key words :

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

## Multiplication Key Words

Here are some examples of multiplication key words :

## Division Key Words

Here are some examples of division key words :

- equal group

## Limitations of Using Keywords to Solve Word Problems

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

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## Free Elementary Math Resources

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

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- 2nd Grade Word Problems
- 3rd Grade Word Problems
- 4th Grade Word Problems
- 5th Grade Word Problems

- Read more about: ELEMENTARY TEACHING , MATH

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The answer to a subtraction problem is called the difference. The value being subtracted is called the subtrahend, and the value from which the subtrahend is being subtracted is called the minuend.

A number sentence is an equation or an inequality which is written with numbers and symbols rather than words. The term is most often used in the early grades when students are learning addition, subtraction, multiplication and division.

In math, a computation method is used to find an answer in regards to any given problem. The most common computation methods make up the majority of basic math functions including addition, subtraction, multiplication and division.

In order to translate word problems into mathematical expressions, it is helpful to know certain keywords to look for which indicate which mathematical

“I put 5 flowers in the vase. Penelope put in more flowers. Then there were 9 flowers. How many flowers did Penelope put in the vase? The

This video lesson introduces students to key words that suggest whether to add or subtract when solving word problems.

This math lesson workbook teaches students to solve one-step addition and subtraction word problems within 20. Students learn key

Addition and Subtraction Keywords · Subtract · Minus · Take away · Less / Fewer than · Difference · Decrease · How many are left / remain?

Discuss the words on the poster with the students and have them suggest word problems for addition or subtraction that use the key word. Using the Key Word

Subtraction Words. change. decreased by. difference. fewer or fewer

This handy set of word cards feature key vocabulary for this topic. Great for a variety of activities, your children can use them as inspiration during

Subtraction key words include: 'less', 'difference', 'minus', 'remain'. Learn different strategies to help solve word problems. Use the filter above to narrow

Division Key Words · average · divide · each · equal group · fourth · half · quarter · quotient; ratio; share; separate; split; third. elementary students

This word problems worksheet will produce addition, multiplication, subtraction and division problems using clear key phrases to give the student a clue as