subtraction and addition problem solving

Word Problems Involving Addition and Subtraction

Word problems involving addition and subtraction are discussed here step by step.

There are no magic rules to make problem solving easy, but a systematic approach can help to the problems easily. 

Word problems based on addition are broadly of two types: (a) When objects of two or more collections are put together.  For example:

Amy has 20 lemon sweets and 14 orange sweets. What is the total number of sweets Amy has?  (b) When an increase in number takes place. 

For example:

Victor has 14 stamps. His friend gave him 23 stamps. How many stamps does Victor have in all? The key words used in problems involving addition are:

s um; total; in all; all together.

Word problems based on subtraction are of several types: (a) Partitioning : Take away, remove, given away.

(b) Reducing : Find out how much has been given away or how much remains.

(c) Comparison : More than / less than.

(d) Inverse of addition : How much more to be added. The key words to look out for in a problem sum involving subtraction are: take away; how many more ; how many less ; how many left ; greater ; smaller.

1. The girls had 3 weeks to sell tickets for their play. In the first week, they sold 75 tickets. In the second week they sold 108 tickets and in the third week they sold 210 tickets. How may tickets did they sell in all? Tickets sold in the first week = 75

Tickets sold in the second week = 108

Tickets sold in the third week = 210

Total number of tickets sold = 75 + 108 + 210 = 393

Answer: 393 tickets were sold in all.

2. Mr. Bose spent $450 for petrol on Wednesday. He spent $125 more than that on Thursday. How much did he spend on petrol on those two days. This problem has to be solved in two steps.

Step 1: Money spent for petrol on Thursday

450 + 125 = $575 Step 2: Money spent for petrol on both days

450 + 575 = $1025

Examples on word problems on addition and subtraction:

1. What is the sum of 4373, 4191 and 3127? Solution: The numbers are arranged in columns and added.

Therefore, sum =11,691

2. What is the difference of 3867 and 1298?

Solution: The numbers are arranged in columns and subtracted:

Therefore, difference = 2569

3. Subtract 4358 from the sum of 5632 and 1324. Solution: Sum of 5632 and 1324

Difference of 6956 and 4358

Therefore, 2598 is the answer.

4. Find the number, which is

(i) 1240 greater than 3267.

(ii) 1353 smaller than 5292. Solution: (i) The number is 1240 more than 3267

Therefore, the number = 3267 + 1240 or = 4507 (ii) The number is 1353 less than 5292

= 5292 – 1353 or

5. The population of a town is 16732. If there are 9569 males then find the number of females in the town. Solution:

6. In a factory there are 35,675 workers. 10,750 workers come in the first shift, 12,650 workers in the second shift and the rest come in the third shift. How many workers come in the third shift? Solution: Number of workers coming in the first and second shift

= 10750 + 12650 = 23400

Therefore, number of workers coming in the third shift = 35675 - 23400 = 12275

Related Concept

● Word Problems on Addition

● Subtraction

● Check for Subtraction and Addition

● Word Problems Involving Addition and Subtraction

● Estimating Sums and Differences

● Find the Missing Digits

● Multiplication

● Multiply a Number by a 2-Digit Number

● Multiplication of a Number by a 3-Digit Number

● Multiply a Number

● Estimating Products

● Word Problems on Multiplication

● Multiplication and Division

● Terms Used in Division

● Division of Two-Digit by a One-Digit Numbers

● Division of Four-Digit by a One-Digit Numbers

● Division by 10 and 100 and 1000

● Dividing Numbers

● Estimating the Quotient

● Division by Two-Digit Numbers

● Word Problems on Division

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Addition and Subtraction Word Problems Worksheets

What makes our pdf worksheets on addition and subtraction word problems indispensable is the fact that they give students tons of practice in the real-life application of key math aspects. Children in kindergarten through grade 5 will wrap their head around the given scenarios and identify the operation required. Choose from 1-digit, 2-digit, 3-digit, and multi-digit addition and subtraction; instantly review the work using the included answer key. Our free worksheets help build a liking for the topic!

Addition and Subtraction Word Problems | Within 10

Ready to redefine your practice sessions involving finding sums and differences? This section will make a great addition to your repertoire. Begin your addition and subtraction within 10 here!

• Download the set

Addition and Subtraction Word Problems | Within 20

Get printable word problems for kindergarten, 1st grade, and 2nd grade students here. Work through engaging situations involving addition and subtraction of numbers within 20.

2-Digit Addition and Subtraction Word Problems | Without Regrouping

A wealth of addition and subtraction word problems without regrouping await! Test the knowledge acquired and review skills in finding the sum or difference of double-digit numbers.

2-Digit Addition and Subtraction Word Problems | With Regrouping

Ride on our printable worksheets that help children practice regrouping through a solid mix of real-life scenarios. Practice borrowing and carry forwarding while performing both operations.

3-Digit and 2-Digit Addition and Subtraction Word Problems

Watch how grateful the aspiring mathematicians in grade 2 and grade 3 are to word problems for helping them ease into this topic. Mastery in adding and subtracting 3-digit and 2-digit numbers begins here!

3-Digit Addition and Subtraction Word Problems

Put passion into your practice sessions with our addition and subtraction word problems within 1000. The carefully-chosen scenarios provide tons of support so skills thrive in no time.

Multi-Digit Addition and Subtraction Word Problems

There's no such thing as 'enough practice' when it comes to solving addition and subtraction word problems. The key is to continue the prepping with our pdfs for the 4th grade and 5th grade students.

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Solving Multi-Step Addition and Subtraction Word Problems

Solving multi-step addition and subtraction word problems can help students see the relationship between operations, as well as practice their calculations.  When I teach subtraction, I also like to show how students can use addition to check their work!  Students often think that they are done when they arrive at the answer, but it is my mission to show them that they can do just one more step to check and make sure their work is correct.  Addition and subtraction work together to help each other out.

The Art of Check Writing

Although the art of writing a check and balancing a checkbook is going away, those processes still have great value for practicing addition and subtraction.  I like to present math problems with money, budgets and purchasing items, but these days students tell me just to “charge it to a card”.  I have been tempted to find my old carbon copy paper receipts and bring them into class.  Just the other week, we had our lawnmower repaired.  The man ran a small, old business and he wrote out all of the receipts and transactions by hand, using the box with carbon copy receipts.  He wrote down the price of the parts, added the taxes and charges, and summed it up – BY HAND!  The only thing missing for a good math problem was writing the word form onto a check.

Set up Shop in Your Classroom

So I thought, why not create a shop in my classroom!  Students can be the shopkeepers and the customers, but no charge cards allowed!  Shopkeepers would have to write the receipt, and the customers would have to write a check for the exact amount.  The students would have to read scenarios and decide what to buy.  I could even give them a budget or a sales goal and they would have to periodically check the difference by subtracting.  It would be a lesson embedded in real life addition and subtraction word problems.

Set up for Solving Multi-Step Addition and Subtraction Word Problems

• Print or create price tags from page 6 of the worksheet for the list of items located pages 7-10.
• Set up “items” and pictures around the room. There are pictures provided on pages 7-10 on the worksheet , but you can always supplement or creatively add items of your own.
• Set up 5 shopkeeper stations with blank copies of “Receipts.” (See worksheet page 3)
• Set up each shop with a Sales Record to keep track of sales and income. Each shop has a distinct sales goal, such as $99, $250, $400, $505, $888.
• $99 – Bargain Basement
• $250 – Quarter Millie’s Party Store
• $400 – Four Double Zero
• $505 – 505 Faves
• $888 – Great Eights
• Provide each student with 6 blank checks and 1 balance sheet. (See worksheet pages 4-5.)
• Provide each student with a copy of the Addition and Subtraction Worksheet .
• If you have little bells or signs, you can set up the shopkeeper with things like an “Open/Closed” sign or “Ring bell for service”.

Launch the Solving Multi-Step Addition and Subtraction Word Problems

If you have time, set up some open/closed shop signs to create the feel of a store in the classroom.  You can even have students create a checkbook with their checks.

Introduce the activity by saying “Today we are going to go shopping!”  Explain that everyone will rotate through and get a chance to run a shop as well as go shopping for items on the worksheet.  The students will not actually pick up items and keep them, but you can have things on display or just have photos and a price list.

Explain the vocabulary and show an example of each: (All are found on the worksheet .)

this is used to write an exact amount of money.  It takes the money out of your bank account and gives it to the store or person it is written to when cashed at the bank.

Balance Sheet

This is a record of how much money you have and how much you spend.  The balance is the amount of money people have to spend.  Use the balance sheet to keep track of the money.  Tell the students that everyone starts with a balance of $445.00. The shoppers can write a brief description of what they buy in the white rows and then subtract the amount spent from the balance.  Explain that the students can do the subtraction vertically in the balance column.  The shaded rows show the running balance, and the white rows show how much is spent each time.  Subtract any money spent to get the new balance.Tell your students “When you reach zero – you are out of money!”

This is a set amount of money made from selling goods that sales people try to reach.  If you have a sales goal, you can subtract any sales to see how much more money you need to reach the goal.

This lists the items being purchased and how much they each cost.  The receipt also gives the total cost of the purchase.  It is a record to show the sale.

Use this scenario to model the work students will do:

“You walk into the store Four Double Zero and  decide to buy headphones for $125 and a case for $34.  What is your purchase price?”

Together, work through the addition.  Remind the students that BOTH the customer and the shopkeeper must do the addition.  Then the shopkeeper tells the customer what to pay.  (There are no taxes or charges unless indicated in the problem on the worksheet).

Pass Out Student Checkbooks

Give every student their checks or checkbook.  Use the first blank check to write the demo check together.  Every check must have:

• The name of the store or person you are writing the check to
• The purchase amount in word form
• The purchase amount in standard form
• The Memo line – items purchased

Then demonstrate the following:

• The customer must subtract: $455 – $159
• The Storekeeper must subtract it from the Sales Goal $400- $159

After the demo, space the students out among the stores.  Assign 1-2 students as shopkeepers at each shop and have the remaining students walk around and shop using the worksheet scenarios.

You can provide 5-10 minutes of shopping and then switch roles, or you can walk around and switch out shopkeepers as you see fit.

• Each student has a Budget of $455 for their entire shopping trip.
• The scenarios on the worksheet ask students to buy at least 2 items from each shop. Some of the word problems are set, others have a choice of items.
• Customers indicate the items and say the prices. The shopkeeper writes the prices and adds them up.  The Customer also adds them up and they check.
• Once the price is determined, the customer writes a check using standard and word form and the name of the store, then signs and dates it.
• The customer then subtracts the purchase from his/her running balance.
• The shopkeeper cashes the check, adds it to the sales list and subtracts it from the sales goal for that shop.
• Customers must check their balance after each purchase. Customers will keep a running balance throughout their shopping experience.
• Shopkeepers must check their Sales goals and how much more money they need after each customer. Shopkeepers can keep a running total while they are in charge of that shop.  However, when a new shopkeeper comes in, they must start with the original sales goal when subtracting.
• Depending on the class size, start each shop with 1-2 shopkeepers. Then have the remaining students go around to the available shopkeepers and work through their transactions.  Switch roles when appropriate.

Reflection on Solving Multi-Step Addition and Subtraction Word Problems

Walk around and help the shopkeepers and the customers as they work through the purchasing process.

At the end, share what people decided to buy and talk about the processes of making a transaction.

Ask questions such as:

• Which store did you like the best?
• Did you ever add up the numbers and get a different sum than the shopkeeper/customer? How did you resolve the price issue?
• Why do you need to subtract your purchases from the budget?
• How did you keep track of your purchases?
• Did any shopkeepers reach their sales goal before leaving their “shift”?
• In the end, how could you check the total amount of purchases you made today? Did you stay under budget?
• Did anyone go over their budget?
• Have students create a price list of items and write 4 of their own word problems. Give them a sales goal and come up with 4 different ways to reach that goal.  Can they hit the goal exactly?
• Research prices of items, but make sure the students find whole numbers.  (Many times ticket prices tend to be whole numbers).  Ask how much money the school would need to budget if the class went on a trip to that theater, sports game, or show.

FREE Solving Multi-Step Addition and Subtraction Word Problems Worksheets and Resources

These are all PDF Files. They will open and print easily. The Student Edition Files are labeled SE and the Teacher Editions Files are labeled TE. Click the links below to download the different resources.

2-4 Assignment SE – Solving Multi-Step Addition and Subtraction Word Problems 2-4 Assignment TE – Solving Multi-Step Addition and Subtraction Word Problems( Members Only ) 2-4 Bell Work SE – Solving Multi-Step Addition and Subtraction Word Problems (PDF) 2-4 Bell Work TE – Solving Multi-Step Addition and Subtraction Word Problems ( Members Only ) 2-4 Exit Quiz SE – Solving Multi-Step Addition and Subtraction Word Problems  (PDF) 2-4 Exit Quiz TE – Solving Multi-Step Addition and Subtraction Word Problems ( Members Only ) 2-4 Exit Quiz SE – Solving Multi-Step Addition and Subtraction Word Problems  (PDF) 2-4 Guided Notes TE – Solving Multi-Step Addition and Subtraction Word Problems ( Members Only ) 2-4 Interactive Notebook – Solving Multi-Step Addition and Subtraction Word Problems  (PDF) 2-4 Lesson Plan – Solving Multi-Step Addition and Subtraction Word Problems  (PDF) 2-4 Online Activities – Solving Multi-Step Addition and Subtraction Word Problems ( Members Only ) 2-4 Slide Show – Solving Multi-Step Addition and Subtraction Word Problems  (PDF)

Solving Multi-Step Addition and Subtraction Word Problems Worksheets and Resources

To get the Editable versions of these files Join us inside the Math Teacher Coach Community! This is where we keep our full curriculum of 4th Grade Math Lessons and Activities.

2-4 Assignment Student Edition ( Doc – Members Only ) 2-4 Assignment Teacher Edition ( Doc – Members Only ) 2-4 Bell Work Student Edition ( Doc – Members Only ) 2-4 Bell Work Teacher Edition ( Doc – Members Only ) 2-4 Exit Quiz Student Edition ( Doc – Members Only ) 2-4 Exit Quiz Teacher Edition ( Doc – Members Only ) 2-4 Guided Notes Student Edition ( Doc – Members Only ) 2-4 Guided Notes Teacher Edition ( Doc – Members Only ) 2-4 Interactive Notebook ( Doc – Members Only ) 2-4 Lesson Plan ( Doc – Members Only ) 2-4 Online Activities ( Doc – Members Only ) 2-4 Slide Show ( PPT – Members Only )

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Don’t Forget to Pin this Activity on Multi-Step Addition and Subtraction Word Problems…

Want to see the rest of the activities for unit 2 – multi-digit whole number addition and subtraction.

• 2-1  Multi-Digit Whole Number Addition
• 2-2  Solving Two-Step Addition Word Problems
• 2-3  Multi-Digit Whole Number Subtraction
• 2-4  Solving Two-Step Subtraction Word Problems
• 2-5  Solving Multi-Step Addition and Subtraction Word Problems
• 2-6  Creating Word Problems Involving Addition and Subtraction

If you enjoyed the read, don’t forget to check out more of our blogs on PreCalculusCoach , GeometryCoach , Algebra2Coach , Algebra1Coach , and PreAlgebraCoach !

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Addition and subtraction

Here you will learn strategies on how to add and subtract, including using visual models, the number line, and algorithms.

Students will first learn about addition and subtraction in kindergarten, continue to add and subtract larger numbers in 2 nd and 3 rd grade, and learn the standard algorithm in 4 th grade. In 7 th grade, students learn to add and subtract with integers and then rational numbers.

What are addition and subtraction?

Addition is the operation of combining two or more numbers together. Subtraction is the operation of taking away from a number.

Students as early as pre-k have a basic, informal understanding of addition and subtraction. By the end of Kindergarten, students can operate within 10, heavily relying on models like counters or 10 frames to solve.

By the end of first grade, students should be able to add and subtract fluently within 20. As students work on repeatedly adding and subtracting with single digit numbers, they deepen their number sense around the operations by solving in different ways.

This includes beginning to build number bonds.

For example,

• Seeing 5+4 and knowing the sum is 9 without having to solve.
• Seeing 9-4 and knowing the difference is 5 without having to solve.

This aids students as they go into 2 nd and 3 rd grade and learn to add and subtract multi-digit numbers (within 1,000 ). At this level, students are still relying on number relationships, properties of operations, place value ideas, models, etc. to solve.

When adding 3- digit numbers, students may combine each place value of the addends separately.

Hundreds \hspace{1.1cm} Tens \hspace{1.2cm} Ones

200 + 100 \hspace{1cm} 30 + 40 \hspace{1cm} 5 + 9 \hspace{1cm}

= 300 \hspace{1.5cm} = 70 \hspace{1.3cm} = 14

And then add in the partial sums:

300+70+14=384

When subtracting numbers that are larger, students may use what they know about place value to solve.

The distance from 781-395 is the same as 786-400, it is just shifted up 5 on the number line.

Now solve 786-400 by taking away 4 hundreds.

786-400=386, so 781-395=386.

Once students have developed a flexible understanding of multi-digit addition and multi-digit subtraction in 2 nd grade and 3 rd grade, they learn the standard algorithm in 4 th grade.

It is important to consider the place value of each digit and line up the corresponding digits in each number.

In 5 th grade and 6 th grade, students continue to add and subtract with whole numbers and apply these strategies to decimal operations.

See also: Adding and subtracting decimals

In 7 th grade, students learn to add and subtract integers and rational numbers.

You can add and subtract integers using visual models or a number line.

Step-by-step guide: Adding and subtracting integers

You can also add and subtract rational numbers using visual models or a number line.

[FREE] Addition and Subtraction Worksheet (Grade 2 to 7)

Use this quiz to check your grade 2, 3, 4 and 7 students’ understanding of addition and subtraction. 15+ questions with answers covering a range of 2nd, 3rd, 4th and 7th grade addition and subtraction topics to identify areas of strength and support!

Common Core State Standards

How does this apply to 2 nd grade math, 3 rd grade math, 4 th grade, and 7 th grade math?

• Kindergarten – Operations and Algebraic Thinking (K.OA.A.2) Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
• Grade 1 – Operations and Algebraic Thinking (1.OA.C.6) Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8+6=8+2+4=10+4=14 ); decomposing a number leading to a ten (e.g., 13-4=13-3-1=10-1=9 ); using the relationship between addition and subtraction (e.g., knowing that 8+4=12, one knows 12-8=4 ); and creating equivalent but easier or known sums (e.g., adding 6+7 by creating the known equivalent 6+6+1=12+1=13 ).
• Grade 2 – Operations and Algebraic Thinking (2.OA.A.1) Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
• Grade 2 – Numbers and Operations in Base Ten (2.NBT.B.5) Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
• Grade 3 – Numbers and Operations in Base Ten (3.NBT.A.2) Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
• Grade 4 – Numbers and Operations in Base Ten (4.NBT.A.4) Fluently add and subtract multi-digit whole numbers using the standard algorithm.
• Grade 7- The Number System (7.NS.A.1) Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
• Grade 7- The Number System (7.NS.A.3) Solve real-world and mathematical problems involving the four operations with rational numbers.

How to add and subtract

There are a lot of ways to add and subtract. For more specific step-by-step guides, check out the individual pages linked in the “What are addition and subtraction?” section above or read through the examples below.

Addition and subtraction examples

Example 1: two digit addition.

Solve 34 + 58.

Choose a strategy.

You can use a model of the tens and ones.

Combine the tens and ones.

You can create one new group of ten from 10 ones.

This leaves 9 tens and 2 ones, which is 92.

So, 34+58=92.

Example 2: three digit subtraction

Solve 340-291.

You can use a number line to count up to 340 from 291.

The difference between 291 and 340 is 49.

So, 340-291=49.

Example 3: addition with the algorithm

Add 4,297 + 381 with the algorithm.

Stack the numbers and line up the place values.

Add each column from right to left and regroup the numbers when necessary.

Write your final answer and check to make sure your answer is reasonable.

You can estimate to decide if your answer is reasonable.

4,297 rounds to 4,300.

381 rounds to 400.

4,300+400=4,700, so the answer should be close to 4,700. Since 4,678 is close, the answer is reasonable.

4,297+381=4,678

Example 4: subtraction word problem with the algorithm

After the harvest, a farmer has 2,148 pears. 213 of the pears are rotten and cannot be sold. If the farmer sells the rest, how many pears will she sell?

Write an equation that represents the word problem.

2,148 - 213 = ⬜

Subtract each column from right to left and exchange for a \bf{10} when necessary.

2,148 rounds to 2,000.

213 rounds to 200.

2,000-200=1,800, so the answer should be close to 1,800. Since 1,935 is close, the answer is reasonable.

2,148-213=1,935

Example 5: subtracting integers with models

Subtract: -4 -(-6)=?

Represent the problem with counters, identifying zero pairs with addition or adding zero pairs when necessary for subtraction.

-4 - (-6) starts with -4 and removes -6. Add 2 zero pairs in order to remove -6.

The answer is the leftover counters.

There are two positive counters left.

Example 6: adding rational numbers with the algorithm

Solve -34 \cfrac{2}{3}+\left(-567 \cfrac{3}{4}\right) .

Make sense of the calculation – relating to positive numbers when necessary.

-34 \cfrac{2}{3}+\left(-567 \cfrac{3}{4}\right) combines two negative amounts, which do not create zero pairs.

This means the answer will be even more negative. You can use the algorithm for addition to see what the total amount is.

Use an algorithm.

\begin{aligned}& 34 \frac{2}{3}+567 \frac{3}{4} \\\\ & =34 \frac{2 \times 4}{3 \times 4}+567 \frac{3 \times 3}{4 \times 3} \\\\ & =34 \frac{8}{12}+567 \frac{9}{12} \\\\ & =601 \frac{17}{12} \text { or } 602 \frac{5}{12}\end{aligned}

Decide if the final answer is positive or negative.

Adding two negative numbers results in a negative number. For example, if you started on the number line and went back 34 \cfrac{2}{3} and then you went back 567 \cfrac{3}{4} more, you are further down the negative side of the number line.

-34 \cfrac{2}{3}+\left(-567 \cfrac{3}{4}\right)=-602 \cfrac{5}{12}

Teaching tips for addition and subtraction

• Sufficient time using place value blocks, 100 s charts, grids and other interactive manipulatives should be provided to students when they are first learning to operate with any new set of numbers. The Common Core Standards intentionally allow time for students to develop an understanding of the operation, before learning how to use the algorithm.
• When students are first learning, encourage them to make connections between addition problems and subtraction problems. As students learn how to operate with any new set of numbers (whole, integer, or rational), it is crucial that they see the connection, as this opens the door to solving strategies, helps them make sense of the algorithms, and can be used to decide if an answer is reasonable. Understanding this relationship is also important for later topics like solving equations.
• When choosing printable math worksheets, look for resources that have missing numbers in all parts of the equation (start unknown, change unknown, result unknown). This helps students develop flexible ideas about the operations and can help prevent mindlessly grabbing numbers from word problems.
• Instead of giving students subtraction worksheets that have dozens of questions to solve, prioritize worksheets that allow students to solve in more than one way and that encourage them to consider the reasonableness of their answer. While there may be times that students are expected to solve in a larger quantity (for example, when learning the algorithm or completing a math review packet), the majority of student work should focus on depth not breadth.

Easy mistakes to make

• Not considering the place value of numbers when solving When using strategies to solve, students may choose a strategy they do not fully understand, causing them to misuse place value. For example, 56 + 78 Thinking that they can just add 5+6+7+8.
• Thinking subtraction always leads to a smaller number (and vice versa with addition) Students often create this false idea because subtracting a larger number from a smaller number or adding negative numbers are not addressed in elementary school. As students begin to operate with integers, it is important to consistently ask them to make sense of an equation before operating. This may be explaining the operation in their own words or using a model to show what is happening.

• Not making sense of operations with rational numbers By the time students operate with rational numbers, they will have learned many algorithms. Though algorithms can be useful, if used in a rush it is easy to make mistakes. Encourage students to think about a reasonable answer before solving. This can help them catch mistakes.

Practice addition and subtraction questions

1. Solve 39 + 46.

This leaves 8 tens and 5 ones, which is 85.

2. Solve 763-594.

You can use a number line to count up to 594 from 763.

The difference between 594 and 763 is 169.

So, 763-594=169.

3. Solve 5,621 + 3,570.

To use the standard algorithm, stack the numbers and line up the place values.

5,621 rounds to 6,000.

3,570 rounds to 4,000.

6,000+4,000=10,000, so the answer should be close to 10,000.

Since 9,191 is close, the answer is reasonable.

5,621+3,570=9,191

4. Jerome has 18,341 points in a game. Yasmine has 8,239 points in the same game. How many more points does Jerome have?

18,341-8,239 = ⬜

To solve with the standard algorithm, stack the numbers and line up the place values.

18,341 rounds to 18,000.

8,239 rounds to 8,000.

18,000-8,000=10,000, so the answer should be close to 10,000.

Since 10,102 is close, the answer is reasonable.

18,341-8,239=10,102

5. Subtract: -12-3= \, ?

-12-3 starts with -12 and removes 3 positives. Add 3 zero pairs in order to remove 3.

There are 15 negative counters left.

You can also think of this as the distance from 3 to -12.

6. Solve -84.4+391.02= \, ?.

-84.4 + 391.02 combines negative and positive values, which creates zero pairs. This means that -84.4+391.02=391.02-84.4, so you can use the standard algorithm to solve.

Adding a smaller negative number to a larger positive results in a positive answer.

-84.4+321.02=306.62

Addition and subtraction FAQs

Regrouping is when you are adding and have more than 10 ones, tens, hundreds, etc. and you need to regroup to create a new group of ten, hundred, etc. For example, if you add 27 + 18, you will have 3 tens and 15 ones. You regroup 10 of the ones to be a new group of ten, so you are left with 4 tens and 5 ones, or 45.

Exchanging is when you are subtracting and you do not have enough ones, tens, hundreds, etc. to take away and you need to exchange for a new group of ten, hundred, etc. For example, if you subtract 27 - 18, you start with 7 ones and need to take away 8. There are not enough, so you exchange one of the tens in 27 for ones. Then you have 1 ten and 17 ones. Now you can subtract 8 ones from 17 ones, leaving 9 ones.

In 4 th grade students learn to add and subtract fractions with common denominators. In fifth grade they learn to add and subtraction fractions with uncommon denominators. Then in 7 th grade they are expected to add and subtract negative fractions. See also: Adding and subtracting fractions

The next lessons are

• Multiplication and division
• Types of numbers
• Rounding numbers
• Adding and subtracting rational numbers
• Adding and subtracting negative numbers
• Add and subtract within 100
• Standard algorithm addition

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[FREE] Common Core Practice Tests (3rd to 8th Grade)

Prepare for math tests in your state with these 3rd Grade to 8th Grade practice assessments for Common Core and state equivalents.

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Basic Addition & Subtraction Facts Online practice for grades 1-2

On this page, you can practice the basic addition and subtraction facts with single-digit addends (such as 4 + 5, 9 + 7, 9 − 4, 12 − 8).

You can practice addition facts, subtraction facts, and missing addend problems (missing number additions).

For first grade, choose basic facts where the sum is 10 or less, and for second grade, choose basic facts where the sum is 20 or less. Additionally you can select timed or untimed practice and the number of practice problems.

Further options for addition only include: adding with zero, doubles, doubles plus one, nine trick (or adding with 9), and the eight-trick (or adding with 8).

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Addition and Subtraction Word Problems Worksheets

Addition and subtraction word problems worksheets are necessary for students to build upon the basic addition and subtraction skill of arithmetic. Word problems in mathematics refer to the information presented through ordinary storytelling, and students have to understand and transform it into mathematical equations.

Benefits of Addition and Subtraction Word Problems Worksheets

The benefit of addition and subtraction word problems worksheets is that students understand how to comprehend the given information in the word problems and write it in mathematical notation in order to solve it further. These worksheets also help students practice addition and subtraction operation with single, two-digit as well as three-digit numbers. These maths worksheets have a variety of problems containing simple problems with examples from everyday life.

Download Addition and Subtraction Word Problems Worksheet PDFs

Addition and Subtraction word problems worksheets are simple and easy to work with, students can download the PDF format of these worksheets to practice at their own pace.

☛ Check Grade wise Addition and Subtraction Word Problems Worksheets

• Grade 2 Addition Word Problems Worksheets
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Addition & Subtraction Word Problems

Related Topics: More Math Word Problems Math Worksheets

How to solve addition and subtraction two-step word problems? These examples of addition and subtraction word problems and solutions will illustrate how to use the block diagrams (Singapore Math) method and tape diagrams (Common Core Math) to solve word problems. Go to Math Word Problems for more examples.

How to use bar models to solve addition and subtraction word problems? Examples:

• The Toyota car factory makes 7,736 cars a day. It makes 1,372 more cars a day than the Honda car factory. a) How many cars does the Honda factory make each day? b) If the Honda factory sells 3,459 cars today, how many cars will the Honda factory have left?
• A high school has 4,268 students. It has 768 less students than the college. a) How many students does the college have? b) How many students do both schools have altogether?
• The Chicago tribune, a newspaper, prints 483 papers on Tuesday. The newspaper prints 87 fewer newspapers on Thursday. a) How many newspapers does the paper print on Thursday? b) How many papers does the Chicago Tribune print on both Tuesday and Thursday?

What is a Tape Diagram? A tape diagram is a drawing that looks like a segment of tape, used to illustrate number relationships. It is also known as strip diagrams, bar model, fraction strip, or length model.

How to use tape diagrams in Part-whole Model and Additive Comparison Model problems? Examples:

• The office supply closet had 25,473 large paperclips, 13,648 medium paperclips and 15,306 small paperclips. How many paperclips were in the closet?
• Raffle tickets were sold for a school fundraiser to parent, teachers, and students. 563 tickets were sold to teachers. 888 mire tickets were sold to students than to teachers. 904 tickets were sold to parents. a) About how many tickets were sold to parents, teachers, and students? Round each number to the nearest hundred to find your estimate. b) Exactly how many tickets were sold to parents, teachers, and students? c) Assess the reasonableness of your answer in (b). Use your estimate from (a) to explain.
• During the month of March 68,025 pounds of king crab were caught. If 15,614 pounds were caught in the first week of March, how many pounds were caught in the rest of the month?

How to model and solve an addition or subtraction word problem involving two changes? Example: Danny has 40 Star Fleet cards. He lost 17 cards at the park. He bought 13 cards at the store. How many cards did Danny have then?

How to model and solve a part-whole addition word problem involving two parts Singapore Math - Addition and Subtraction with Two Parts Part-Whole Model with two parts - Finding the whole. Example: Dylan paid $5 for a book. He had $19 left. How much money did Dylan have at first?

How to model and solve a part-whole addition word problem involving three parts? Singapore Math - Addition and Subtraction with Three Parts Example: Sam is reading a book. He read 9 pages yesterday and 5 pages today. If he reads 12 more pages, he will finish the book. How many pages are in Sam’s book?

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Problem Solving - Addition and Subtraction

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Problem Structures for Addition & Subtraction

Quick pop quiz. How many problem structures are there for addition and subtraction problems?

If you said somewhere around 15 structures, you’re in the right ballpark. Unfortunately, students are often exposed to only the simplest structures. As teachers, we need to have an understanding of all the structures and teach them to our students in a methodical way.

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“…teachers who are not aware of the variety of situations and corresponding structures may randomly offer problems to students without the proper sequencing to support students; full grasp of the meaning of the operations.” (Van de Walle et al)

The charts below were adapted from Elementary and Middle School Mathematics: Teaching Developmentally (Van de Walle et al), a phenomenal book for developing your own understanding of math.

The addition/subtraction structures are grouped into three main types: Change, Part/Part/Whole, and Comparison. For each type, there are multiple structures, depending on what information is known and unknown.

Change Problems

One of the first things you might notice is that the structures are not designated as addition or subtraction. While we typically think of  joining as addition and  separating as subtraction, you’ll see from the chart that is not always the case.  Result Unknown is the simplest and most familiar structure. You might think of these as classic addition and subtraction problems. As we move across the chart, the problems become increasingly complex, and we see that the Change Unknown and  Start Unknown structures can be interpreted as either addition or subtraction.

An appropriate way to introduce the problems is to start with the simplest,  Result Unknown , problems. Start with Join problems and allow students to practice solving just that type of problem. Help students focus on the meaning of each number in the problem, in terms of Change , Start , or Result . Drawing models is a good strategy for helping students analyze and visualize each problem. Next, introduce Separate problems, again giving them practice with just that type. Then it’s time to mix them up, so students have to determine the appropriate structure, based on the problem.

Now start to move across the chart, using the same process. Introduce the next structure (Join, Change Unknown ), practice the structure, and then mix it in with the others they already know. Keep in mind that this process takes time. If you’re a second-grade teacher, make a schedule for introducing the structures throughout the school year. Use numbers appropriate to the students’ computation skills.

Part-Part-Whole

Part-Part-Whole problems are very similar to Change. The subtle difference is that often there is no action in these problems, which makes them a little more abstract for students. The Whole Unknown structure is a very simple addition problem. In the One Part Unknown structure, we know the total and one of the parts, but we are missing the other part. This is also commonly called a Missing Addend problem. We often solve this type of problem using subtraction, but a counting-up strategy works well also. A really interesting structure is Both Parts Unknown. It’s a word problem application of knowing all the combinations for a number !

As students are introduced to more of the structures, remember that it’s just as important that they generate problems as solve them. I love an activity I call You Write the Story . Give students an equation and have them write a story to go with it and draw a model for their story.

One other note about Change and Part-Part-Whole problems, while these examples all have two addends, you can also use more than two addends to provide more of a challenge. Think: There are 425 students in the cafeteria. One hundred twenty-seven students are 5th graders, 146 are 4th graders, and the rest are 3rd graders. How many 3rd graders are in the cafeteria?

Finally, we have Comparison problems, which involve comparing two quantities–a larger quantity and a smaller one. They can also be written using either more or  fewer.  Fewer is by far more difficult for students. We want to make sure we introduce comparison subtraction using manipulatives to help students understand the structure. See this pos t for more information.

There you have it! All the structures for addition and subtraction problems. You can download your own copy of the tables showing the structures using the button below.

I look forward to hearing how you will teach these structures in your classroom, so be sure to leave a comment!

Resources for problem structures

Morrow-Leong, K., Moore, S. D., & Gojak, L. (2021). Mathematize it!: Going beyond key words to make sense of word problems , grades K-2 or grades 3-5 . Thousand Oaks, CA: Corwin.

Carpenter, Thomas P., et al. (2015) Children’s Mathematics: Cognitively Guided Instruction . Heinemann.

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Great post! I’ve been reading the Mathematize IT: Making Sense books also.

Do you have a post for Problem Structures of multiplication and division?I saw the book, but I was hoping you had something more like this post for multiplication and division.

I follow all your posts! Thank you for helping me become a better teacher❤️

Thanks for your kind comments! I don’t have a post, but I do have a document with all the structures for all operations . Enjoy!

This is a great visual! Thanks for sharing.

Awesome blog and charts! I did notice that “amount” is misspelled in the last chart in the red boxes.

Well, yes it is! Thanks so much for calling it to my attention. I’ll get it corrected straight away.

Late to the game but I LOVE THIS!

What are your thoughts on multistep problems as it relates to these structures?

That would be another, and trickier, step! Being able to comprehend what’s happening in the problem is key. Check out this post on the 3 Reads Protocol for a great strategy for improving comprehension.

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Addition Subtraction Practice Zone

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How to Solve Addition Problems

In this post, we are going to learn to analyze, think about, and solve addition problems. Usually, failure in mathematics comes from not understanding the problems that we are given. This is why we are going to analyze 5 problems which require addition to solve.

Addition Problems nº 1

There were 8 cars in the parking lot of a hotel. 5 more cars have entered the parking lot. How many cars are in the parking lot now?

This is the simplest type of problem that we can encounter: it is a short statement, with only 2 facts which have the same units: 8 cars and 5 cars. Now the only thing left for us to think about is what operation we have to do. To do this, we are going to think about if in the beginning there were 8 cars and later 5 more cars enter the parking lot, are there now more or fewer cars than in the beginning? The answer to this question is that there are now more cars than in the beginning. Therefore, the operation that we need to do is ADDITION.

Now there are 13 cars in the parking lot.

Addition Problems nº 2

The walls of Catherine’s class are full of drawings! Today I went to see the class and on the wall to the right, I counted 5 drawings and on the wall to the left 7 more. How many drawings in total are there on the walls of Catherine’s class?

Although this problem is simple, it is a little more complicated than the previous problem because it is longer, but it only has 2 facts which also have the same units: 5 drawings and 7 drawings. Before thinking about the operation that we have to do, we are going to reason through the statement: in order to count how many drawings there are in total, we could collect them and put them all on the same wall and then count them. The number that we would obtain would be greater than 5 and greater than 7 too. Thus, the operation we have to use is ADDITION.

There are 12 drawings in total.

Addition Problems nº 3

Mary has 4 candies that her grandmother gave to her when she was visiting. Richard has 2 more candies than Mary because he bought some and later realized that he had more in his house. How many candies does Richard have?

In this problem, we have to compare two quantities: Mary has 4 candies and Richard has 2 more candies than Mary. Let’s think. Does Richard have more or fewer candies than Mary? If Richard has 2 candies more than Mary, this means that he has more candies. So the operation that we need to carry out is ADDITION.

Richard has 6 candies.

Addition Problems nº 4

Yesterday many kids went to eat breakfast in the school dining hall and drank all the juice. If they had served 5 liters less of juice yesterday, they would have served as many liters as they did today. Today they served 6 liters of juice. How many liters of juice did they serve yesterday?

In this problem we have to match two quantities: today they served 6 liters of juice and yesterday if they had served 5 liters less, they would have served the same amount of liters as today. We have to decide whether they served more or less juice yesterday than today. As we are told that to match today’s quantity they would have had to serve 5 liters less, we deduce that yesterday they served more liters than today. Thus, the operation that we have to use is ADDITION.

Yesterday they served 11 liters of juice.

Addition Problems nº 5

During recess, I’ve been playing marbles with 4 friends. Since I have been careless, I have lost 3 marbles and now I am left with 6 marbles. How many marbles did I have before I began to play?

In this problem, we have 3 numerical facts: 4 friends, 3 marbles and 6 marbles. But be careful! Not all the facts help solve the problem. In this case, the number of friends that I have does not influence the number of marbles I had. So this fact is not relevant to the solution of the problem. We focus on the facts that interest us: I have lost 3 marbles and now I have 6 left. We have to reflect on the following question: before beginning to play did I have more or fewer marbles than I have now? If I lost marbles during the game, it means that I had more marbles before than I have now, so the operation we have to use is ADDITION.

Before playing, I had 9 marbles.

And that’s all for today’s post. We hope that you have enjoyed and learned from this post.

Next week we will continue with another post about problems.

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How to Teach Addition and Subtraction to Visual Thinking Kids

Demme Learning · August 21, 2024 · Leave a Comment

Picture this: Young students stare at math problems, their brows furrowed in concentration as they struggle to calculate solutions. Meanwhile, their peers are quickly writing down answers and moving easily through the material. 

What’s the difference? The struggling students are just as smart and intelligent as their peers … they just aren’t seeing numbers and equations in quite the same way. Instead, their minds long for images of physical objects, spatial relationships, and diagrams. These are visual thinking kids, and their learning process differs significantly from that of their more verbal peers. In the world of mathematics, where abstract concepts are the norm, visual learners often face challenges.

But what if we could transform these challenges into opportunities?

Visual thinking is more than just a learning preference; it’s a unique way of processing information. When it comes to mathematics, visual thinkers excel at seeing patterns and relationships. By tailoring math instruction to these students, we can tap into their potential and make mathematical concepts come alive for them. 

At Demme Learning, we utilize the “Build, Write, Say” method – a game-changer for teaching addition and subtraction to visual learners. This approach combines hands-on manipulation, written work, and verbal expression to create a multi-sensory learning experience. With proper preparation, thoughtful presentation, and regular practice, this method can revolutionize math education for visual thinkers.

Understanding Visual Thinking Kids

Visual thinking is a distinct learning style where students process information best through visualization and observation. Visual thinkers benefit from seeing concepts in action, unlike auditory or kinesthetic learners. They often possess a vivid imagination and can easily recall images, diagrams, and visual patterns.

Common characteristics of visual thinkers include:

• Strong spatial awareness
• Preference for charts, graphs, and diagrams
• Excellent memory for visual details
• Tendency to doodle or draw while thinking
• Strong visualization skills

Identifying these traits early is important for teachers and parents alike. By recognizing visual thinkers and applying visual thinking strategies, we can better support these students along their mathematical journey.

The Build, Write, Say Method

The Build, Write, Say method is an approach that caters specifically to visual thinkers and helps guide them toward math mastery . This method incorporates three key steps:

• Build : Use physical objects ( math manipulatives ) or visual aids to represent math problems.
• Write : Write out the math problems and solutions.
• Say : Verbally explain the process and the “why” behind it while building and writing.

This method is particularly effective for visual thinkers because it engages multiple senses and reinforces learning through different modalities. By physically manipulating objects, students can see the math concept come to life. Writing helps solidify the concept and saying it out loud reinforces understanding.

Teaching Addition and Subtraction to Visual Thinkers

Let’s apply the Build, Write, Say method to teach single-digit addition and subtraction:

• Use a pink 3-block to represent 3
• Place a light blue 5-block next to it to represent 5
• Show the sum by placing a brown 8-block underneath the 3 and 5 blocks
• Write : Have the student write out the problem: 3 + 5 = 8
• Say : Encourage the student to explain the process: “I have a pink 3-block. I’m adding a light blue 5-block. When I put them together, I see that it has the same length as the brown 8-block, so 3 plus 5 equals 8.”

For subtraction, use a similar approach. For instance, to teach 8 – 3:

• Build : Start with a brown 8-block, then invert a pink 3-block on top of it. Place a light blue 5-block next to the inverted 3-block to show the difference.
• Write : 8 – 3 = 5
• Say : “I start with a brown 8-block. I flip the pink 3-block over to show that I’m taking away 3. The difference is shown by the light blue 5-block. So, 8 minus 3 equals 5.”

This method, using color-coded blocks, helps visual learners create mental images that act as referents, making abstract ideas concrete and easier to grasp.

What Happens Inside the Student’s Brain

When visual learners engage with math using this method, several cognitive processes come into play. The visual cortex is heavily involved in processing the images of the manipulatives and written numbers, while the parietal lobe works on spatial relationships and number sense.

The Build, Write, Say method enhances understanding and retention by creating multiple neural pathways. As students build and manipulate objects, their motor cortex is engaged. Writing activates language areas and fine motor skills. Speaking out loud involves auditory processing areas. 

This multi-sensory approach strengthens connections between different parts of the brain and leads to deeper learning and better recall.

Tips for Parents and Educators

To effectively implement the Build, Write, Say method and support visual thinkers in math:

1) Use Diverse Visual Ads

Incorporate color coding, diagrams, and graphic organizers. For example, use different colors for tens and units in place value exercises.

2) Encourage Drawing

Let students draw pictures to represent problems. This can be especially helpful for word problems.

3) Utilize Technology

Many educational apps and programs offer visual representations of math concepts.  Math fact fluency  can be enhanced through visual games and activities.

4) Create Math Picture Books

Help students create their own books illustrating math concepts with drawings and explanations.

5) Use Real-World Examples

Connect math to visual experiences in daily life. For instance, use pizza slices to teach fractions.

6) Provide Plenty of Practice

Consistent practice is key.  Offer tips for struggling math students  to build confidence.

7) Incorporate Movement

Combine visual thinking with kinesthetic activities. For example, use  mud math activities  to make learning tangible and fun.

8) Be Patient

Allow students to process information at their own pace. Visual thinkers may need more time to “see” the problem before solving it.

Remember, every child is unique. What works for one visual learner may not work for another. Be prepared to adapt and find the methods that resonate best with each student.

The Value of Tailored Math Instruction

By understanding and catering to the needs of visual thinkers, we can transform math from a daunting subject into an engaging, even exciting, experience. The Build, Write, Say method, combined with various visual thinking strategies, opens up new pathways for comprehension and problem-solving.

As educators and parents, our role is to provide the tools and support that allow visual thinkers to thrive. By doing so, we’re not just teaching math – we’re nurturing creativity, boosting confidence, and laying the foundation for lifelong learning.

Want more math resources?  Check out The Guild! This free archive provides resources for building math skills and learning math facts.

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