problem solving addition subtraction

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Unit 2: Addition and subtraction

About this unit, basic addition and subtraction.

• Basic addition (Opens a modal)
• Basic subtraction (Opens a modal)
• Add and subtract: pieces of fruit (Opens a modal)
• Relating addition and subtraction (Opens a modal)
• Add within 5 7 questions Practice
• Subtract within 5 7 questions Practice
• Add within 10 7 questions Practice
• Subtract within 10 7 questions Practice
• Relate addition and subtraction 7 questions Practice
• Getting to 10 by filling boxes (Opens a modal)
• Adding to 10 (Opens a modal)
• Make 10 (grids and number bonds) 7 questions Practice
• Make 10 7 questions Practice

Addition and subtraction word problems within 10

• Addition word problems within 10 (Opens a modal)
• Subtraction word problems within 10 (Opens a modal)
• Addition word problems within 10 7 questions Practice
• Subtraction word problems within 10 7 questions Practice

Addition and subtraction within 20

• Adding within 20 using place value blocks (Opens a modal)
• Adding within 20 using ten frames (Opens a modal)
• Adding 7 + 6 (Opens a modal)
• Adding 8 + 7 (Opens a modal)
• Adding with arrays (Opens a modal)
• Subtracting different ways (Opens a modal)
• Subtract within 20 using a number line (Opens a modal)
• Subtract within 20 using place value blocks (Opens a modal)
• Subtract within 20 using ten frames (Opens a modal)
• Subtracting 14 - 6 (Opens a modal)
• Add within 20 visually 7 questions Practice
• Add within 20 7 questions Practice
• Adding with arrays 4 questions Practice
• Subtract within 20 visually 7 questions Practice
• Subtract within 20 7 questions Practice
• Find missing number (add and subtract within 20) 7 questions Practice
• Add & subtract within 20 7 questions Practice

Word problems within 20

• Addition and subtraction word problems: superheroes (Opens a modal)
• Addition and subtraction word problems: gorillas (Opens a modal)
• Addition and subtraction word problems 1 7 questions Practice
• Addition and subtraction word problems 2 7 questions Practice
• Add and subtract within 20 word problems 7 questions Practice

Word problems with "more" and "fewer"

• Comparison word problems: marbles (Opens a modal)
• Comparison word problems: roly-polies (Opens a modal)
• Word problems with "more" and "fewer" 2 7 questions Practice

Intro to addition with 2-digit numbers

• Adding 2-digit numbers without regrouping (Opens a modal)
• Adding 2-digit numbers without regrouping 1 (Opens a modal)
• Example: Adding 2-digit numbers (no carrying) (Opens a modal)
• Breaking apart 2-digit addition problems (Opens a modal)
• Regrouping to add 1-digit number (Opens a modal)
• Adding up to four 2-digit numbers 4 questions Practice
• Break apart 2-digit addition problems 4 questions Practice
• Regroup when adding 1-digit numbers 7 questions Practice

Intro to subtraction with 2-digit numbers

• Subtracting two-digit numbers without regrouping (Opens a modal)
• Subtracting 2-digit numbers without regrouping 1 (Opens a modal)
• Subtracting a 1-digit number with regrouping (Opens a modal)
• Subtract within 100 using place value blocks 4 questions Practice
• Subtract within 100 using a number line 4 questions Practice
• Subtract 1-digit numbers with regrouping 7 questions Practice

Strategies for adding and subtracting within 100

• Adding 53+17 by making a group of 10 (Opens a modal)
• Adding by making a group of 10 (Opens a modal)
• Strategies for adding 2-digit numbers (Opens a modal)
• Addition and subtraction with number lines (Opens a modal)
• Add 2-digit numbers by making tens 4 questions Practice
• Add 2-digit numbers by making tens 2 4 questions Practice
• Select strategies for adding within 100 4 questions Practice
• Add within 100 using a number line 4 questions Practice

Addition within 100

• Understanding place value when adding ones (Opens a modal)
• Understanding place value when adding tens (Opens a modal)
• Adding with regrouping (Opens a modal)
• Add within 100 using place value blocks 4 questions Practice

Subtraction within 100

• Subtracting with regrouping (borrowing) (Opens a modal)

Word problems within 100

• Adding and subtracting on number line word problems (Opens a modal)
• Adding two digit numbers on a number line (Opens a modal)
• Subtraction word problem: tennis balls (Opens a modal)
• Addition word problem: horses (Opens a modal)
• Subtraction word problem: snow (Opens a modal)
• Subtraction word problem: crayons (Opens a modal)
• Multi step addition word problem (Opens a modal)
• Multi-step subtraction word problem (Opens a modal)
• Add and subtract on the number line word problems 4 questions Practice
• Addition word problems within 100 4 questions Practice
• Subtraction word problems within 100 4 questions Practice
• 2-step addition word problems within 100 4 questions Practice
• 2-step subtraction word problems within 100 4 questions Practice

Adding 1s, 10s, and 100s

• Adding 10 or 100 (Opens a modal)
• Adding 1s, 10s, and 100s (Opens a modal)
• Adding 3-digit numbers (no regrouping) (Opens a modal)
• Add 10s and 100s (no regrouping) 4 questions Practice
• Add within 1,000 using place value blocks 4 questions Practice

Subtracting 1s, 10s, and 100s

• Subtracting 1, 10, or 100 (Opens a modal)
• Subtracting 1s, 10s, and 100s (Opens a modal)
• Subtracting 3-digit numbers (no regrouping) (Opens a modal)
• Subtract 10s and 100s (no regrouping) 7 questions Practice
• Subtract within 1,000 using place value blocks 4 questions Practice

Strategies for adding 2- and 3-digit numbers

• Breaking apart 3-digit addition problems (Opens a modal)
• Solving 3-digit addition in your head (Opens a modal)
• Addition using groups of 10 and 100 (Opens a modal)
• Adding and subtracting on number line (Opens a modal)
• Break apart 3-digit addition problems 4 questions Practice
• Add using groups of 10 and 100 4 questions Practice
• Add on a number line 4 questions Practice
• Select strategies for adding within 1000 4 questions Practice

Addition with regrouping within 1000

• Using place value to add 3-digit numbers: part 2 (Opens a modal)
• Adding 3-digit numbers (Opens a modal)
• Add within 1000 4 questions Practice

Subtraction with regrouping within 1000

• Worked example: Subtracting 3-digit numbers (regrouping) (Opens a modal)
• Worked example: Subtracting 3-digit numbers (regrouping twice) (Opens a modal)
• Worked example: Subtracting 3-digit numbers (regrouping from 0) (Opens a modal)
• Subtracting in your head (no regrouping) (Opens a modal)
• Subtract on a number line 4 questions Practice
• Subtract within 1000 4 questions Practice

Addition and subtraction missing value problems

• Missing numbers in addition and subtraction (Opens a modal)
• Missing number for 3-digit addition within 1000 (Opens a modal)
• Find the missing number (add and subtract within 100) 4 questions Practice
• Find the missing number (add and subtract within 1000) 4 questions Practice

Addition and subtraction greater than 1000

• Relate place value to standard algorithm for multi-digit addition (Opens a modal)
• Multi-digit addition with regrouping (Opens a modal)
• Multi-digit subtraction with regrouping: 6798-3359 (Opens a modal)
• Multi-digit subtraction with regrouping: 7329-6278 (Opens a modal)
• Multi-digit subtraction with regrouping twice (Opens a modal)
• Alternate mental subtraction method (Opens a modal)
• Adding multi-digit numbers: 48,029+233,930 (Opens a modal)
• Relate place value to standard algorithm for multi-digit subtraction (Opens a modal)
• Multi-digit subtraction: 389,002-76,151 (Opens a modal)
• Multi-digit addition 4 questions Practice
• Multi-digit subtraction 4 questions Practice

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
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• Word problems
• Children's stories
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• Cause & effect
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Addition & subtraction word problems

Add & subtract numbers < 50.

These grade 1 word problems worksheets involve the addition and subtraction of 1 and 2 digit numbers. Some problems have 3 or more terms.

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Addition & Subtraction Word Problems

Related Pages Math Worksheets Lessons for Fourth Grade Free Printable Worksheets

Printable “Addition/Subtraction Word Problems” Worksheets: Subtraction Word Problems Addition Word Problems Addition/Subtraction Word Problems

Addition Word Problems 2nd Grade Word Problems Add/Subtract Word Problems

Multi-digit Addition/Subtraction

Addition/Subtraction Word Problems Worksheets

In these free math worksheets, students practice how to solve addition/subtraction word problems.

How to solve addition/subtraction word problems? Solving addition or subtraction word problems involves breaking down the information given in the problem, identifying the key elements, and performing the appropriate mathematical operations.

• Read and understand the problem: Take your time to read the entire word problem carefully. Identify the key information about what is being added or subtracted.
• Identify keywords: Look for keywords that indicate addition or subtraction. These can be words like: Addition: total, sum, combined, altogether, plus Subtraction: left, remaining, difference, less, minus
• Determine what needs to be found: The word problem will often ask a question. Identify what you need to solve for (e.g., the total number of apples, the remaining cookies).
• Assign variables: Sometimes, assigning letters (variables) to represent unknown quantities can be helpful. This can make the problem easier to translate mathematically.
• Translate the problem into a math sentence (Draw diagrams if necessary): Use the information you gathered to write a mathematical equation that represents the situation. If it’s an addition problem, the sentence will involve adding the relevant quantities. If it’s a subtraction problem, the sentence will show the starting quantity minus what is being taken away.
• Solve the math sentence: Once you have the equation, perform the addition or subtraction to find the answer.
• Check your answer: Briefly re-read the problem and see if your answer makes sense in the context of the scenario.

Here are some additional tips: Pay attention to units: Make sure the units of the quantities you add or subtract are compatible (e.g., adding apples and oranges doesn’t make sense). Draw a diagram: Sometimes, a simple drawing can help visualize the problem and make it easier to solve. Start with simpler problems: If you’re new to word problems, practice with easier ones before tackling more complex ones.

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Addition/Subtraction Word Problems Worksheets .

More Addition/Subtraction Word Problems Worksheets

Printable (Answers on the second page.) Addition/Subtraction Worksheet #1 Addition/Subtraction Worksheet #2 Addition/Subtraction Worksheet #3 Addition/Subtraction Worksheet #4 Addition/Subtraction Worksheet #5 Addition/Subtraction Worksheet #6

Online Multi-digit Addition Word Problems Multi-digit Subtraction Word Problems

Related Lessons & Worksheets

Multi-digit Addition (eg. 12,456 + 3,376) Multi-digit Subtraction (eg. 32,406 - 4,375) Multi-digit Subtraction with Zeros (eg. 40,006 - 3,214)

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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.

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.

[FREE] Addition and Subtraction Check for Understanding (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!

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
• Add and subtract within 1000
• Adding and subtracting rational numbers
• Add and subtract within 100
• Add and subtract with the algorithm

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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

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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

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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 Word Problems Activities

Teach your child all about addition and subtraction word problems with amazing educational resources for children. These online addition and subtraction word problems learning resources break down the topic into smaller parts for better conceptual understanding and grasp. Get started now to make addition and subtraction word problems practice a smooth, easy and fun process for your child!

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Addition Word Problems

Represent 'Add To' Scenarios Game

Learn to solve math problems through our 'Represent 'Add To' Scenarios' game.

Solve 'Add To' Scenarios Game

Add more arrows to your child’s math quiver by solving 'Add To' scenarios.

Find the Sum Using Part-Part-Whole Model Worksheet

Combine math learning with adventure by solving to find the sum using 'Part-Part-Whole' model.

Write Equations Using Part-Part-Whole Model Worksheet

Learn number sense at the speed of lightning by writing equations using 'Part-Part-Whole' model.

Subtraction Word Problems

Represent 'Take Apart' Scenarios Game

Kids must represent 'Take Apart' scenarios to practice subtraction.

Solve 'Take Apart' Scenarios Game

Take the pressure off by simplifying subtraction by solving 'Take Apart' scenarios.

Subtract Using Part-Part-Whole Model Worksheet

Combine math learning with adventure by solving to subtract using 'Part-Part-Whole' model.

Solve Using Part-Part-Whole Model Worksheet

Learn subtraction at the speed of lightning by practicing to solve using 'Part-Part-Whole' model.

All Addition and Subtraction Word Problems Resources

Add within 5: Summer Word Problems Worksheet

Engaging summer-themed worksheet with word problems to enhance addition skills within 5.

Subtract within 5: Summer Word Problems Worksheet

A fun, summer-themed worksheet designed to enhance students' subtraction skills with problems up to 5.

Add within 5: Halloween Word Problems Worksheet

Spooky-themed worksheet for practicing addition within 5 through Halloween word problems.

Subtract within 5: Halloween Word Problems Worksheet

Spooky themed worksheet to master subtraction within 5 through fun Halloween word problems!

Represent 'Put Together' Scenarios Game

Have your own math-themed party by learning how to represent 'Put Together' scenarios.

Change Unknown Scenarios Game

Shine bright in the math world by learning how to change unknown scenarios.

Add within 5: Christmas Word Problems Worksheet

Engage in festive math fun with this Christmas-themed worksheet, adding numbers within 5.

Subtract within 5: Christmas Word Problems Worksheet

Engaging Christmas-themed worksheet for students to master subtraction within 5 through word problems.

Solve 'Put Together' Scenarios Game

Shine bright in the math world by learning how to solve 'Put Together' scenarios.

Word Problems to Subtract Multiples of 10 Game

Help your child take flight by learning how to solve word problems to subtract multiples of 10.

Add within 5: Shopping Word Problems Worksheet

Engaging worksheet with a shopping theme to help students master addition within 5 through word problems.

Subtract within 5: Shopping Word Problems Worksheet

Engaging subtraction worksheet with a shopping theme, helping students solve problems within 5.

Solve Count On Scenarios Game

Begin the exciting journey of becoming a math wizard by learning how to solve count on scenarios.

Solve Word Problems on Take From Scenarios Game

Enjoy the marvel of math-multiverse by learning to solve word problems on "Take From" scenarios.

Add within 5: Travel Word Problems Worksheet

This worksheet combines fun travel-themed scenarios with math problems, requiring students to add numbers within 5.

Subtract within 5: Travel Word Problems Worksheet

Travel-themed worksheet to enhance students' subtraction skills within 5 through word problems.

Solve 'Change Unknown' Scenarios Game

Begin the exciting journey of becoming a math wizard by solving 'Change Unknown' scenarios.

Solve Difference Unknown Scenarios Game

Kids must solve difference unknown scenarios to practice subtraction.

Add within 5: Sports Word Problems Worksheet

Engaging sports-themed worksheet designed to strengthen students' ability to add within 5.

Subtract within 5: Sports Word Problems Worksheet

Sports-themed worksheet designed to engage students in solving subtraction problems within 5.

Solve 'Count On' Word Problems Game

Take the first step towards building your math castle by solving 'Count On' word problems.

Solve Scenarios with 'Difference Unknown' Game

Shine bright in the math world by learning how to solve scenarios with 'Difference Unknown'.

Add within 5: Cooking Word Problems Worksheet

A fun, cooking-themed worksheet for students to practice addition within 5 with word problems.

Subtract within 5: Cooking Word Problems Worksheet

Whip up your subtraction skills with this cooking-themed worksheet, subtracting within 5!

Represent 'Add To' Word Problems Game

Take a deep dive into the world of math with our 'Represent 'Add To' Word Problems' game.

Solve Subtraction Word Problems Game

Enjoy the marvel of mathematics by exploring how to solve subtraction word problems.

Add within 5: Winter Word Problems Worksheet

Engage students with this Winter-themed worksheet, solving fun addition problems within 5.

Subtract within 5: Winter Word Problems Worksheet

Engaging winter-themed worksheet to practice subtraction within 5 through word problems.

Solve 'Add To' Word Problems Game

Unearth the wisdom of mathematics by learning how to solve 'Add To' word problems.

Represent 'Put Together' Word Problems Game

Unearth the wisdom of mathematics by learning how to represent 'Put Together' word problems.

Add within 5: Easter Word Problems Worksheet

Engaging Easter-themed worksheet focused on solving addition problems up to the number 5.

Subtract within 5: Easter Word Problems Worksheet

Engage in this Easter-themed worksheet, subtracting numbers within 5 through fun word problems.

Solve 'Put Together' Word Problems Game

Let your child see the world through math-colored shades by solving 'Put Together' word problems!

Word Problems to Add Multiples of 10 Game

Learn to solve word problems to add multiples of 10.

Add within 5: Thanksgiving Word Problems Worksheet

Thanksgiving-themed worksheet helping students solve word problems by adding within 5.

Subtract within 5: Thanksgiving Word Problems Worksheet

Engaging worksheet for students to solve Thanksgiving-themed subtraction problems within 5.

Word Problems to Add Tens to a 2-digit number Game

Make math learning fun by solving word problems to add tens to a 2-digit number.

Solve Word Problems on Add to Scenarios Game

Ask your little one to solve word problems on "Add to" scenarios to play this game.

Create and Solve Your Own Story Problem Worksheet

Help your child revise subtraction by creating and solving your own story problem.

Solve Word Problems on Put together Scenarios Game

Practice the superpower of addition by learning to solve word problems on "Put together" scenarios.

Subtract to Compare Game

Let your child see the world through math-colored shades by subtracting to compare.

Solve Addition Word Problems Worksheet

Assess your math skills by solving addition word problems in this worksheet.

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Differentiated Math Fact Practice

4th Grade Resources

Problem Solving: 11 Types of Addition and Subtraction Problems

When to Teach Problem Solving Skills

Let's Take a Problem Solving Journey

Did you know there are 11 types of addition and subtraction problems?

11 types of addition and subtraction problems, joining problem solving group.

• Sum Unknown
• Change Unknown
• Start Unknown

Separating Problem Solving Group

• Difference Unknown

Part - Part - Whole Problem Solving Group

• Whole Unknown
• Part Unknown

Comparing Problem Solving Group

• Larger Part Unknown
• Smaller Part Unknown

Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number.

Where should you begin?

What's Next?

Thank you so much for sharing this post for 11+ Exam Maths Word Problems . I’ve been looking for exactly this and you made it possible. Sending much gratitude.

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Addition and Subtraction

These activities are part of our Primary collections , which are problems grouped by topic.

These lower primary tasks all involve addition, subtraction or both.

Have a go at these upper primary activities which all involve addition, subtraction or both.

Powerful online learning at your pace

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.

This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally use and recommend.

“…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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1.6: Solving Equations by Addition and Subtraction

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• Page ID 22464

• David Arnold
• College of the Redwoods

Let’s start with the definition of a variable.

A variable is a symbol (usually a letter) that stands for a value that may vary

Next we follow with the definition of an equation.

An equation is a mathematical statement that equates two mathematical expressions.

The key difference between a mathematical expression and an equation is the presence of an an equals sign. So, for example,

2 + 3[5 − 4 · 2], x2 + 2x − 3, and x + 2y + 3

are mathematical expressions (two of which contain variables), while

3 + 2(7 − 3) = 11, x +3=4, and 3x = 9

are equations. Note that each of the equations contain an equals sign, but the expressions do not.

Next we have the definition of a solution of an equation.

What it Means to be a Solution

A solution of an equation is a numerical value that satisfies the equation. That is, when the variable in the equation is replaced by the solution, a true statement results.

Show that 3 is a solution of the equation x + 8 = 11.

Substitute 3 for x in the given equation and simplify.

\[ \begin{array}{rlrl}{x+8} & {=11} & {} & { \textcolor{red}{ \text { The given equation. }}} \\ {3+8} & {=11} & {} & {\textcolor{red}{ \text { Substitute } 3 \text { for } x .}} \\ {11} & {=11} & {} & {\textcolor{red}{ \text { Simplify both sides. }}}\end{array}\nonumber \]

Since the left- and right-hand sides of the last line are equal, this shows that when 3 is substituted for x in the equation a true statement results. Therefore, 3 is a solution of the equation.

Show that 27 is a solution of the equation x − 12 = 15

Is 23 a solution of the equation 4 = y − 11?

Substitute 23 for y in the given equation and simplify.

\[ \begin{array}{ll}{4=y-11} & {\textcolor{red}{ \text { The given equation. }}} \\ {4=23-11} & {\textcolor{red}{ \text { Substitute } 23 \text { for } y}} \\ {4=12} & {\textcolor{red} {\text { Simplify both sides. }}}\end{array}\nonumber \]

Since the left- and right-hand sides of the last line are not equal, this shows that when 23 is substituted for y in the equation a false statement results. Therefore, 23 is not a solution of the equation.

Is 8 a solution of 5 = 12 − y ?

Equivalent Equations

We start with the definition of equivalent equations.

Two equations are equivalent if they have the same solution set.

Are the equations x + 2 = 9 and x = 7 equivalent?

The number 7 is the only solution of the equation x + 2 = 9. Similarly, 7 is the only solution of the equation x = 7. Therefore x + 2 = 9 and Answer: No. x = 7 have the same solution sets and are equivalent.

Are the equations x = 4 and x + 8 = 3 equivalent?

Are the equations x 2 = x and x = 1 equivalent?

By inspection, the equation x 2 = x has two solutions, 0 and 1. On the other hand, the equation x = 1 has a single solution, namely 1. Hence, the equations x 2 = x and x = 1 do not have the same solution sets and are not equivalent.

Are the equations x = 2 and x 2 = 2 x equivalent?

Operations that Produce Equivalent Equations

There are many operations that will produce equivalent operations. In this section we look at two: addition and subtraction.

Adding the Same Quantity to Both Sides of an Equation

Adding the same quantity to both sides of an equation does not change the solution set. That is, if

\[a = b,\nonumber \]

then adding c to both sides of the equation produces the equivalent equation

\[a + c = b + c.\nonumber \]

Let’s see if this works as advertised. Consider the equation x − 4=3. By inspection, 7 is the only solution of the equation. Now, let’s add 4 to both sides of the equation to see if the resulting equation is equivalent to x − 4 = 3.

\[ \begin{array}{rlrl}{x-4} & {=3} & {} & {\textcolor{red}{ \text{The given equation. }}} \\ {x-4+4} & {=3+4} & {} & {\textcolor{red}{ \text{Add 4 to both sides of the equation.} }} \\ {x} & {=7} & {} & {\textcolor{red}{ \text{Simplify both sides of the equation. }}}\end{array}\nonumber \]

The number 7 is the only solution of the equation x = 7. Thus, the equation x = 7 is equivalent to the original equation x − 4 = 3 (they have the same solutions).

Important Point

Adding the same amount to both sides of an equation does not change its solutions.

It is also a fact that subtracting the same quantity from both sides of an equation produces an equivalent equation.

Subtracting the Same Quantity from Both Sides of an Equation

Subtracting the same quantity from both sides of an equation does not change the solution set. That is, if

then subtracting c from both sides of the equation produces the equivalent equation

\[a − c = b − c.\nonumber \]

Let’s also see if this works as advertised. Consider the equation

\[ x + 4 = 9.\nonumber \]

By inspection, 5 is the only solution of the equation. Now, let’s subtract 4 from both sides of the equation to see if the resulting equation is equivalent to x + 4 = 9.

\[ \begin{array}{rlrl}{x+4} & {=9} & {} & {\textcolor{red}{ \text { The given equation. }}} \\ {x+4-4} & {=9-4} & {} & {\textcolor{red}{ \text { Subtract 4 from both sides of the equation. }}} \\ {x} & {=5} & {} & {\textcolor{red}{ \text { Simplify both sides of the equation. }}}\end{array}\nonumber \]

The number 5 is the only solution of the equation \(x = 5\). Thus, the equation \(x = 5\) is equivalent to the original equation \(x + 4 = 9\) (they have the same solutions).

Subtracting the same amount from both sides of an equation does not change its solutions.

Writing Mathematics

When solving equations, observe the following rules to neatly arrange your work:

1. One equation per line . This means that you should not arrange your work like this:

\[ x+3=7 \quad x+3-3=7-3 \quad x=4\nonumber \]

That’s three equations on a line. Rather, arrange your work one equation per line like this:

\[ \begin{aligned} x+3 &=7 \\ x+3-3 &=7-3 \\ x &=4 \end{aligned}\nonumber \]

2. Add and subtract inline. Don’t do this:

\[ \begin{array}{r} x -7 & = & 12 \\ +7 & & + 7 \\ \hline x & = & 19 \end{array}\nonumber \]

Instead, add 7 to both sides of the equation “inline.”

\[ \begin{aligned} x-7 &=12 \\ x-7+7 &=12+7 \\ x &=19 \end{aligned}\nonumber \]

Wrap and Unwrap

Suppose that you are wrapping a gift for your cousin. You perform the following steps in order.

• Put the gift paper on.
• Put the tape on.
• Put the decorative bow on.

When we give the wrapped gift to our cousin, he politely unwraps the present, “undoing” each of our three steps in inverse order.

• Take off the decorative bow.
• Take off the tape.
• Take off the gift paper.

This seemingly frivolous wrapping and unwrapping of a gift contains some deeply powerful mathematical ideas. Consider the mathematical expression \(x+ 4\). To evaluate this expression at a particular value of x , we would start with the given value of x , then

Suppose we started with the number 7. If we add 4, we arrive at the following result: 11.

Now, how would we “unwrap” this result to return to our original number? We would start with our result, then

• Subtract 4.

That is, we would take our result from above, 11, then subtract 4, which returns us to our original number, namely 7.

Addition and Subtraction as Inverse Operations

Two extremely important observations:

The inverse of addition is subtraction. If we start with a number x and add a number a , then subtracting a from the result will return us to the original number x . In symbols,

\[x + a − a = x.\nonumber \]

The inverse of subtraction is addition. If we start with a number x and subtract a number a , then adding a to the result will return us to the original number x . In symbols,

\[x − a + a = x.\nonumber \]

Solve \(x − 8 = 10\) for x .

To undo the effects of subtracting 8, we add 8 to both sides of the equation.

\[ \begin{aligned} x-8=10 & \textcolor{red}{\text { Original equation. }} \\ x-8+8=10+8 & \textcolor{red}{ \text { Add 8 to both sides of the equation. }} \\ x=18 & \textcolor{red}{ \text { On the left, adding "undoes" the effect }} \\ & \textcolor{red}{ \text { of subtracting 8 and returns } x . \text { On the right, }} \\ & \textcolor{red}{10+8=18.} \end{aligned}\nonumber \]

Therefore, the solution of the equation is 18.

To check, substitute the solution 18 into the original equation.

\[ \begin{aligned} x - 8 = 10 & \textcolor{red}{ \text{ Original equation. }} \\ 18 - 8 = 10 & \textcolor{red}{ \text{ Substitute 18 for} x. } \\ 10 = 10 & \textcolor{red}{ \text{ Simplify both sides. }} \end{aligned}\nonumber \]

The fact that the last line of our check is a true statement guarantees that 18 is a solution of x − 8 = 10.

Solve \(x + 5 = 12\) for x .

Solve \(11 = y + 5\) for y.

To undo the effects of adding 5, we subtract 5 from both sides of the equation.

\[ \begin{aligned} 11 = y + 5 & \textcolor{red}{ \text{ Original equation. }} \\ 1 - 5 = y + 5 - 5 & \textcolor{red}{ \text{ Subtract 5 from both sides of the equation. }} \\ 6 = y & \textcolor{red}{ \text{ On the right, subtracting "undoes" the effect }} \\ & \textcolor{red}{ \text{ of adding 5 and returns } y. \text{ On the left, }} \\ & \textcolor{red}{ 11 - 5 = 6. } \end{aligned}\nonumber \]

Therefore, the solution of the equation is 6.

\[ \begin{aligned} 11 = y + 5 & \textcolor{red}{ \text{ Original equation. }} \\ 11 = 6 + 5 & \textcolor{red}{ \text{ Substitute 6 for } y.} \\ 11 = 11 & \textcolor{red}{ \text{ Simplify both sides. }} \end{aligned}\nonumber \]

The fact that the last line of our check is a true statement guarantees that 6 is a solution of 11 = y + 5.

Solve \(y - 8 = 11\) for y .

\(y = 19.\)

Word Problems

The solution of a word problem must incorporate each of the following steps.

Requirements for Word Problem Solutions

• Statements such as “Let P represent the perimeter of the rectangle.”
• Labeling unknown values with variables in a table.
• Labeling unknown quantities in a sketch or diagram.
• Set up an Equation . Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
• Solve the Equation . You must always solve the equation set up in the previous step.
• Answer the Question . This step is easily overlooked. For example, the problem might ask for Jane’s age, but your equation’s solution gives the age of Jane’s sister Liz. Make sure you answer the original question asked in the problem. Your solution should be written in a sentence with appropriate units.
• Look Back . It is important to note that this step does not imply that you should simply check your solution in your equation. After all, it’s possible that your equation incorrectly models the problem’s situation, so you could have a valid solution to an incorrect equation. The important question is: “Does your answer make sense based on the words in the original problem statement.”

Let's give these requirements a test drive.

Four more than a certain number is 12. Find the number.

In our solution, we will carefully address each step of the Requirements for Word Problem Solutions.

1. Set up a Variable Dictionary . We can satisfy this requirement by simply stating “Let x represent a certain number.”

2. Set up an Equation . “Four more than a certain number is 12” becomes

\[ \begin{aligned} \colorbox{cyan}{4} & \text{ more than } & \colorbox{cyan}{a certain number} & \text{ is } & \colorbox{cyan}{12} \\ 4 & + & x & = & 12 \end{aligned}\nonumber \]

3. Solve the Equation . To “undo” the addition, subtract 4 from both sides of the equation.

\[ \begin{aligned} 4 + x = 12 & \textcolor{red}{ \text{ Original equation.}} \\ 4 + x - 4 = 12 - 4 & \textcolor{red}{ \text{Subtract 4 from both sides of the equation. }} \\ x = 8 & \textcolor{red}{ \text{ On the left, subtracting 4 "undoes" the effect}} \\ & \textcolor{red}{ \text{ of adding 4 and returns } x. \text{ On the right, }} \\ & \textcolor{red}{12 - 4 = 8.} \end{aligned}\nonumber \]

4. Answer the Question . The number is 8.

5. Look Back . Does the solution 8 satisfy the words in the original problem? We were told that “four more than a certain number is 12.” Well, four more than 8 is 12, so our solution is correct.

12 more than a certain number is 19. Find the number.

Amelie withdraws $125 from her savings account. Because of the withdrawal, the current balance in her account is now $1,200. What was the original balance in the account before the withdrawal?

In our solution, we will carefully address each step of the Requirements for Word Problem Solutions .

1. Set up a Variable Dictionary. We can satisfy this requirement by simply stating “Let B represent the original balance in Amelie’s account.”

2. Set up an Equation . We can describe the situation in words and symbols.

\[ \begin{aligned} \colorbox{cyan}{Original Balance} & \text{ minus } & \colorbox{ Amelie's Withdrawal } & \text{ is } & \colorbox{cyan}{ Current Balance } \\ B & - & 125 & = & 1200 \end{aligned}\nonumber \]

3. Solve the Equation . To “undo” the subtraction, add 125 to both sides of the equation.

\[ \begin{aligned} B - 125 = 1200 & \textcolor{red}{ \text{ Original equation. }} \\ B - 125 + 125 = 1200 + 125 & \textcolor{red}{ \text{Add 125 to both sides of the equation. }} \\ B = 1325 & \textcolor{red}{ \text{ On the left, adding 125 "undoes" the effect}} \\ & \textcolor{red}{ \text{ of subtracting 125 and returns } B. \text{ On the right, }} \\ & \textcolor{red}{ 1200 + 125 = 1325.} \end{aligned}\nonumber \]

4. Answer the Question . The original balance was $1,325.

5. Look Back . Does the solution $1,325 satisfy the words in the original problem? Note that if Amelie withdraws $125 from this balance, the new balance will be $1,200. Hence, the solution is correct.

Fred withdraws $230 from his account, lowering his balance to $3,500. What was his original balance?

The perimeter of a triangle is 114 feet. Two sides of the triangle measure 30 feet and 40 feet, respectively. Find the measure of the third side of the triangle.

1. Set up a Variable Dictionary. When geometry is involved, we can create our variable dictionary by labeling a carefully constructed diagram. With this thought in mind, we draw a triangle, then label its known and unknown sides and its perimeter.

The figure makes it clear that x represents the length of the unknown side of the triangle. The figure also summarizes information needed for the solution. 2. Set up an equation. We know that the perimeter of a triangle is found by finding the sum of its three sides; in words and symbols,

\[ \begin{aligned} \colorbox{cyan}{ Perimeter } & \text{ is } & \colorbox{cyan}{ First Side } & \text{ plus } & \colorbox{cyan}{ Second Side } & \text{ plus } & \colorbox{cyan}{ Third Side } \\ 114 & = & x & + & 30 & + & 40 \end{aligned}\nonumber \]

Simplify the right-hand side by adding 30 and 40; i.e., \(30 + 40 = 70\).

\[ 114 = x + 70\nonumber \]

3. Solve the Equation. To “undo” adding 70, subtract 70 from both sides of the equation.

\[ \begin{aligned} 114 = x + 70 & \textcolor{red}{ \text{ Our equation. }} \\ 114 - 70 = x + 70 - 70 & \textcolor{red}{ \text{ Subtract 70 from both sides. }} \\ 44 = x & \textcolor{red}{ \text{ On the right, subtracting 70 "undoes" the effect}} \\ & \textcolor{red}{ \text{of adding 70 and returns to } x. \text{ On the left,}} \\ & \textcolor{red}{ 114 - 70 = 44.} \end{aligned}\nonumber \]

4. Answer the Question . The unknown side of the triangle is 44 feet.

5. Look Back . Does the solution 44 feet satisfy the words of the original problem? We were told that the perimeter is 114 feet and two of the sides have length 30 feet and 40 feet respectively. We found that the third side has length 44 feet. Now, adding the three sides, 30+ 40+ 44 = 114, which equals the given perimeter of 114 feet. The answer works!

The perimeter of a quadrilateral is 200 meters. If three of the sides measure 20, 40, and 60 meters, what is the length of the fourth side.

In Exercises 1-12, which of the numbers following the given equation are solutions of the given equation? Support your response with work similar to that shown in Examples 1 and 2.

1. x − 4 = 6; 10, 17, 13, 11

2. x − 9 = 7; 17, 23, 19, 16

3. x + 2 = 6; 5, 11, 7, 4

4. x + 3 = 9; 6, 9, 7, 13

5. x + 2 = 3; 8, 1, 4, 2

6. x + 2 = 5; 10, 3, 6, 4

7. x − 4 = 7; 12, 11, 18, 14

8. x − 6 = 7; 13, 16, 20, 14

9. x + 3 = 4; 8, 4, 2, 1

10. x + 5 = 9; 5, 11, 7, 4

11. x − 6 = 8; 17, 21, 14, 15

12. x − 2 = 9; 11, 14, 12, 18

In Exercises 13-52, solve the given equation for x .

14. x + 6 = 19

16. 10 = 8 + x

17. 13 + x = 17

18. 7+ x = 15

19. 9+ x = 10

20. 14 + x = 17

21. 19 = x − 3

22. 2= x − 11

23. x − 18 = 1

24. x − 20 = 8

25. x − 3 = 11

26. x − 17 = 18

27. 2+ x = 4

28. 1+ x = 16

29. x − 14 = 12

30. x − 1 = 17

32. x + 11 = 14

33. 11 + x = 17

34. 11 + x = 18

35. x + 13 = 17

36. x + 1 = 16

37. 20 = 3 + x

39. 20 = 8 + x

40. 10 = 3 + x

41. 3= x − 20

42. 13 = x − 15

43. x + 16 = 17

44. x + 6 = 12

45. 5= x − 6

46. 10 = x − 7

47. 18 = x − 6

48. 14 = x − 4

49. 18 = 13 + x

50. 17 = 5 + x

51. x − 9 = 15

52. x − 11 = 17

53. 12 less than a certain number is 19. Find the number.

54. 19 less than a certain number is 1. Find the number.

55. A triangle has a perimeter of 65 feet. It also has two sides measuring 19 feet and 17 feet, respectively. Find the length of the third side of the triangle.

56. A triangle has a perimeter of 55 feet. It also has two sides measuring 14 feet and 13 feet, respectively. Find the length of the third side of the triangle.

57. Burt makes a deposit to an account having a balance of $1900. After the deposit, the new balance in the account is $8050. Find the amount of the deposit.

58. Dave makes a deposit to an account having a balance of $3500. After the deposit, the new balance in the account is $4600. Find the amount of the deposit.

59. 8 more than a certain number is 18. Find the number.

60. 3 more than a certain number is 19. Find the number.

61. Michelle withdraws a $120 from her bank account. As a result, the new account balance is $1000. Find the account balance before the withdrawal.

62. Mercy withdraws a $430 from her bank account. As a result, the new account balance is $1200. Find the account balance before the withdrawal.

63. Foreclosures . Between January and March last year, 650,000 homes received a foreclosure notice. Between the first three months of this year, there were 804,000 foreclosure notices. What was the increase in home foreclosure notices? Associated Press Times-Standard 4/22/09

64. Home Price . According to the Humboldt State University Economics Department’s Humboldt Economic Index, the median home price in the US fell $1500 over the last month to $265,000. What was the median home price before the price drop?

65. Unmanned Areal Vehicle . Northrup Grumman’s Global Hawk unmanned drone can fly at 65,000 feet, 40,000 feet higher than NASA’s Ikhana unmanned aircraft. How high can the Ikhana fly?

66. Tribal Land . The Yurok Tribe has the option to purchase 47,000 acres in order to increase its ancestral territory. The first phase would include 22,500 acres in the Cappel and Pecman watersheds. The second phase plans for acreage in the Blue Creek area. How many acres could be purchased in the second phase? Times-Standard 4/15/09

63. 154,000

65. 25,000 feet

Problem Solving - Addition and Subtraction

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Problems Involving Addition and Subtraction Facts & Worksheets

In mathematics, we often encounter word problems ranging from basic problems asking for the total to complex word problems wherein we need to solve for a supplementary equation or problem first, before we get to solve for the main problem.

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Table of Contents

See the fact file below for more information on the problems involving addition and subtraction or alternatively, you can download our 30-page Problems Involving Addition and Subtraction worksheet pack to utilise within the classroom or home environment.

Key Facts & Information

Know what is being asked.

• For young learners, the best way to understand a word problem is to read the word problem aloud.
• Anna has 10 apples. Her friend, Tamiya, gave her 11 oranges. How many fruits does Anna have in all?
• Throughout the discussion, we will use the word problem above.
• Now, read the sample word problem aloud. Then, identify the question or what is being asked in the problem.
• In the sample word problem, what we want to answer is the question “How many fruits does Anna have in all?”
• To know what is being asked, we have to look for some keywords.
• Some common keywords for addition and subtraction word problems are listed above.
• Notice that the keyword “in all” can be seen in the word problem.
• Therefore, we need to use addition.

BREAK DOWN THE WORD PROBLEM

• Now that we know what is being asked, we have to break down the word problem into segments or parts for us to have a better grasp and understanding of the problem.

WRITE THE EQUATION

• Now that we know what is being asked and the given phrases, we can translate the phrases that we have into a mathematical equation.
• First, we have the phrase that Anna currently has 10 apples.
• Then, we also know that we have to do addition based on the question being asked in the problem.
• We also know that Anna’s friend, Tamiya, gave her 11 oranges.
• Then, using addition we have to find the total number of fruits that Anna has.

SOLVE THE EQUATION

• Now that we have the mathematical equation, we can now proceed with the usual mathematical way of solving the problem.

TWO-STEP WORD PROBLEMS

• For two-step word problems, we can treat them as normal word problems. The only difference is that we have to solve for something first before we get to solve for the actual problem.
• Erin has 10 more apples than Anna. Anna has 13 apples. How many apples do they have in total?
• We know that the question being asked is the total number of apples that Erin and Anna both have.
• But as of the moment, we have no idea how many apples Erin has.
• We only know that the quantity of apples that Erin has is 10 more than the quantity of apples that Anna has.
• From the word problem presented, we know that Anna has 13 apples.
• Now, we know that Erin has 23 apples.
• Since we already know the quantity of apples Erin has, we can now proceed into solving the main question.
• How many apples do they have in total?
• They have 36 apples in total.

Problems Involving Addition and Subtraction Worksheets

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Home / United States / Math Classes / 4th Grade Math / Two-step Addition and Subtraction

Two-step Addition and Subtraction

Some real-life problems related to math cannot be solved in a single step. In such cases, we break down the questions us ing different strategies and find out the solution. Learn how to solve such real-life math problems related to addition and subtraction. ...Read More Read Less

Table of Contents

Solving Word problems

Solved examples.

• Frequently Asked Questions

Solving problems related to addition and subtraction is made easier by observing aspects of a problem. For this, you need to consider the following questions .

What is given?

       First, we need to identify the data that has been provided.

What to find out?

       Then, we need to figure out what we need to calculate.

• How do we find out?

       Finally, we need to analyze which method of operation has to be carried out with the given values so that we can arrive at the required answer.

For example:

Liam has 1000 books in his library. If he bought 500 more and gave away 300 books, how many books does he have in his library now?

Understand the problem

• Liam has 1000 books.
• He bought 500 more.
• He gave away 300 books.
• How many books does Liam have now?

How will you solve it?

• Add 1000 and 500 to find out how many books Liam has.
• Then subtract 300 from the sum to find out how many books Liam has now.

Let k be the initial number of books.

k = 1000 + 500  

Step 2 : Let n be the unknown difference after Liam gave away 300 books.

\( n-k=300 \)

\(\Rightarrow n~=~1500-300 \)

\(\therefore n~=~1200 \)

So, Liam has a total of 1200 books in his library.

Harry has 10 pencils. He bought 5 more pencils.

If he has used 2 pencils, how many pencils are left with him?

Initially, Liam had 10 pencils, and later he bought 5 more.

Liam has 10 + 5 = 15 pencils.

Since Liam has used 2 pencils.

The number of pencils he still has is, 

= 15 – 2  

Leah and Jay decide to play a game. They need to fill a huge container each with as many items as possible so that one container weighs more than the other. The container that weighs the most wins. It is known that Leah’s container weighs 542 pounds, and both containers weigh 1276 pounds together. By what difference does the winner win?

Let the weight of Jay’s container be x pounds.

Since both containers weigh 1276 pounds, the weight of Jay’s container can be given as,

\(x=1276-542\)  

\(x~=~734 \)

734 > 542. 

734 – 542  

Hence, Jay wins the contest by 192 pounds.

A construction company uses 200 fewer rods in constructing building A than building B. There were 624 rods used in building B and 721 rods were used in constructing C. How many rods does the company use to construct building A? Also, find the total number of rods that were used for all three buildings.

Step 1 : How many rods are used in building A ?

Let \(x\) be the number of rods used in building A

\(x~=~624-200\)

\(x~=~424\)

Step 2: Find the total number of rods used in all three buildings.

Let \(y\) be the total number of rods used in the three buildings.

\(y~=~x+624+721\)

\(y~=~424+624+721\)

\(\therefore y~=~1769\)

So, the total number of rods used in all three buildings is 1769.

What is two-step addition or subtraction?

As the name suggests, two-step addition or subtraction involves two steps. In each step, one equation is solved. After the second step, we arrive at the final answer. 

How do addition and subtraction of the same number undo each other?

Let us understand this with the help of an example. Say you have 10 balloons, to which you add 3 more. Now you have 10 + 3, which is 13 balloons. If you burst 3 of them, you will be left with 13 – 3 = 10 balloons, which is the number of balloons we started off with. Hence, the addition and subtraction of the same numbers keeps the initial number the same. 

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Addition and subtraction word problems

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Last updated

11 April 2017

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Useful word problems.

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80 Educational Children's Math Picture Books

R eady for the biggest list of math picture books ? Because I’ve found SO MANY amazing math books, I can’t wait to tell you about them!

Use these at home, in the classroom, or with your homeschool. You’ll discover books about counting , addition, subtraction, number sense, the 100th day, sorting, fractions, division, geometry, problem-solving, money, telling time, multiplication , and algebra.

Three cheers for math!

Table of Contents

Counting math books, the 100th day books, number sense books, telling time books, addition and subtraction books, sorting and pattern books, measurement books, multiplication books, division and fraction books, geometry books, money books, algebra books, math problem-solving books, best math books.

One Big Pair of Underwear

HAHA — this is the silliest “counting” picture book you’ll read! It’s counting, subtracting, and patterns silliness that your kids will adore.

Count your way from one to ten as this family gets ready for dinner including shopping and cooking the food.

You’ll love the clever creations Medina makes with vegetables — 1 avocado deer and 2 radish mice, just to name a few.

Anno’s Counting Book by Mitsumasa Anno

Bold graphic images help children find the black dots from one to ten in different images. Fun!

What’s more relatable than candy? And brightly colored illustrations? This tasty book about large numbers is pitch-perfect.

How Many Bugs in a Box

We love this engaging book. Lift the flaps and see what pops out!

Rhyme and count with these naughty monkeys.

The snake wants to count the mice — for his dinner. Count up and count down.

Monkey counts to ten and back as she bravely faces the crocodile-infested waters in order to get to a banana tree.

Alice needs to find 100 things to bring for the 100th day — but she’s having lots of trouble deciding what.

What is he going to bring for the 100th day of school? You’ll love this delightful rhyming book.

It’s not only the kids that get to bring 100 things to school, Miss Bindergarten is getting together 100 things, too.

Learn about counting by tens as the queens plan a special birthday surprise for the king.

Grapes of Math

Fun and rhyming riddles to help kids learn problem-solving strategies.

Learn about odd and even numbers with this silly story about a boy who discovers that everything in his life is ODD! (Also read: My Even Day and My Half Day .)

Hungry for Math: Poems to Munch On

Just like numbers, ideas are infinite. This is fun story of making the challenging concept of infinity more understandable.

Even Steven is all about, you guessed it, even-numbered things. Then one day, his cousin Odd Todd comes to visit. Which terrifies Even Steven. Because even Odd Todd knocks in odd numbers. . .

Learn about a boy who loved numbers and was known as The Magician from Budapest in this playful mathematical biography.

Go Figure!: A Totally Cool Book About Numbers

Learn more about the numbers in our everyday life, their purpose, and history. Then try some of the fun number magic tricks, puzzles, and activities.

365 Penguins

Penguins are arriving every single day at their doorstep. What are they doing to do?!

How Much Is a Million?

David M. Schwartz, illustrated by  Steven Kellogg

Marvelosissimo the mathematical magician will teach you about really BIG numbers.

Skip count and estimate with pumpkins.

This is a fun book that offers 100 math riddles, each with adaptations for young kids and bigger kids.

Telling Time with Big Mama Cat by Dan Harper

Follow along with the daily schedule and use the movable hands to practice telling time.

Learn about the different measurements of time (seconds, minutes), go through a day and take mini-quizzes to figure out how much you’re learning.

This funny book is all about Mr. Crocodile’s schedule which includes finding and catching some pesky monkeys.

Pigeon Math

Hilarious! Addition and subtraction never felt so fun!!  An increasingly exasperated narrator is TRYING to tell the story about ten pigeons but it’s not going well. Visual support, goofy humor, and plenty of kid-appeal make this a 100% must-own, must-read STEM picture book.

Add the baby animals with the grown-ups to see how many all together.

Jen Arena   (Author),  Stephen Gilpin

A winter addition adventure of snowmen that will get you to 100 total.

A loving family shares a favorite cultural sweet treat and practices counting and subtracting in this beautifully written, Indian-flavored math story! Mama makes 10 gulab jamuns for guests. But, one child eats three. Now there are only 7 for the guests. And another child eats 3 more. Now there are only 4 left. Mamma wonders how she will have time to make more treats for her guests. The kids will help her make them! 

The Chicken Problem

This is a Peg and Cat picture book story their perfect picnic that goes totally crazy with runaway chickens.  Peg is “ totally freaking out ” and needs to get the one hundred chickens back in the coop. Peg and Cat must solve the chicken problem fast. I love the illustrations, the problem-solving characters, and the silly story.

Comic Book Math ~ Fun-Schooling Journal: Adding, Writing & Subtracting Games

by Sarah Janisse Brown

Use your imagination and practice math skills in a fun way. 

Subtract your way through this goofy story about an elevator going down.

Animal stories help kids learn the basics of putting numbers in groups and taking numbers away.

Count and add the animals on the back of the trucks.

Go on a butterfly addition hunt and see who will win.

When the music stops, someone is out. Subtract to see how many are left.

The O’Malleys pass the time on a long car trip by counting up different color cars using tally marks. The winner is the one who tallies the most.

Arithmechicks Take Away: A Math Story

This gives kids photographs from which they can make decisions about sorting. Use with actual physical objects to make the lessons more concrete.

Blockhead: The Life of Fibonacci

Fibonacci sees patterns in nature and develops the Fibonacci Sequence.

Learn about all the spirals in nature.

What groups can you sort out of Packy the Packrat’s stuff?

Fannie in the Kitchen: The Whole Story from Soup to Nuts of How Fannie Farmer Invented Recipes with Precise Measurements  

Kitchen measurements equal delicious foods.

Measuring Penny by Loreen Leedy

Lisa loves measurement, so she starts measuring her dog, Penny.

How Big is a Foot by Rolf Myller

The king needs to figure out how big of a bed to make for his queen. This introduces standardizing measurements.

An inchworm shows the bird why he shouldn’t be eaten — because he can measure anything!

Amanda learns that multiplication is the fastest way to count.

Kings Chessboard

Multiplying Menace: The Revenge of Rumpelstiltskin

by Pam Calvert and Wayne Geehan

This is a fun multiplication story about mischievous Rumplestiltskin and his multiplication stick.

Gorgeous illustrations illustrate this fable about a smart girl who outsmarts a king.

This is an introduction to multiplication and factorals.

Spaghetti And Meatballs For All!  

by Marilyn Burns and Debbie Tilley

Yummy! It’s time for spaghetti. But how much does everyone get to eat?

Equal Shmequal

, illustrated by  Philomena O’Neill

Mouse helps her friends how to equally divide up teams for a game of tug of war.

Elinor J Pinczes , illustrated by  Bonnie MacKain

If 100 ants are marching to a picnic, how should they sort themselves into a line? 1 line of 100? 2 lines of 50? 

The Doorbell Rang

Pat Hutchins

More and more friends arrive to share Ma’s cookies. How many cookies should each person get?

The Lion’s Share

The shared meal keeps getting divided in half leaving only a crumb for the ant. So she and the other guests bake cakes for the king. Which they have to divide.

Using the illustrations, readers get to answer division and fraction questions. What fraction of the cow is blue? Fun farm math!

Fractions in Disguise

by Edward Einhorn and David Clark

This is a mystery story about finding a missing fraction — clever!

by  Dayle Ann Dodds , illustrated by  Abby Carter

The Strawberry Inn is filled with five visitors who all want a piece of one cake. How will Miss Blue solve this problem?

Learn the basic shapes with this cute introductory book.

Lia and Luis Puzzled by Ana Crespo, illustrated by Giovana Medeiros

Grandma gives the twins a puzzle they must complete to discover what the surprise is. What will it be? First, the twins will have to collaborate and use geometry and sorting to put the puzzle together. Lia and Luis are Brazilian American and the story includes words in Portuguese like the word for Grandma and yay.

by Cindy Neuschwander and Bryan Langdo

To get to the pharaoh’s burial tomb, the kids must decode the geometric hieroglyphics.

Sir Cumference and the First Round Table by

Cindy Neuschwander and Wayne Geehan

The king needs a place for his your knights to sit and discuss battle and peace plans. Luckily Sir Cumference, Lady Di of Ameter, and their son Radius can help.

by Cindy Neuschwander and Wayne Geehan

Radius must use his wits and math skills to rescue the missing king.

When a Line Bends . . . A Shape Begins

Learn about shapes in this brightly illustrated beginning circus story.

The name says it all — learn about perimeter, area, and volume with this crew of monsters.

What’s Your Angle, Pythagoras?

Pythagoras discovered through experimentation that there are mathematical principles that always stay the same — like with right triangles.

The Greedy Triangle

Marilyn Burns , illustrated by  Gordon Silveria

This triangle doesn’t just want to have three angles, he is greedy for more angles which changes his shape completely. 

To successfully journey back to earth, Captain Invincible must use his knowledge of 3D shapes.

Grandfather Tang’s Story by Ann Tonpert, illustrated by Robert Andrew Parker

Moving the tangram shapes, help narrate the story of two fox fairies.

In this Three Little Pigs math story, the pigs must learn geometric shapes and tangrams.

Alexander trades his one dollar for many coins because he misses the point of how much things are worth, placing importance on the number of monies he has more than the value. Hilarious.

Count five pennies, count two nickels, and add them up.

Grandma’s birthday is coming. Watch as Max and Ruby learn about how much things cost and what the best presents really are.

From the history of bartering things to the creation of different types of money, this is a great informational math book about money.

Little Critter needs to earn money so that he can buy a skateboard.

Interesting information about collecting coins, plus a place to start collecting.

Pigs Will Be Pigs: Fun with Math and Money by Amy Axelrod, illustrated by Sharon McGinley-Nally

David A. Adler ,  Edward Miller

Find the unknown number of creepy things by using addition, subtraction, multiplication, and division.

The Deductive Detective

This entertaining math picture book incorporates math with the mystery genre. Detective Duck needs to use his deductive reasoning to figure out which of the twelve animal bakers stole the cake from the cake contest.  He follows the clues, subtracting each suspect as he rules them out.  Until only one animal is left! Can you use your thinking skills to figure out the culprit before Detective Duck?

Frank adopts Lucky from a shelter. Together, they have fun, educational adventures around the neighborhood. For example, Frank learns about math and puzzles, thinking about how much hair Lucky sheds and dividing up and sharing the bed with Lucky. The author makes the duo’s learning fun and embedded throughout the day, whether it’s geography, science, or math. Love it.

One Minute Mysteries: 65 Short Mysteries You Solve With Math!

by Eric Yoder and Natalie Yoder

Real-world math brainteasers. 

by Jon Scieszka and Lane Smith

If you’ve ever been a victim of a MATH CURSE, you know how horrible it can be. Because you can break the curse. FUN and funny!

by Greg Tang and Greg Paprocki

Using real artwork, this is a math picture book where kids solve math problems and appreciate famous art.

The Book of Perfectly Perilous Math: 24 Death-Defying Challenges for Young Mathematicians

Math for All Seasons

Put on your thinking caps. Look closely at the illustrations to solve the math problems.

Find books about place value , too!

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