grade 4 problem solving examples

Grade 4 Word Problem Worksheets

Free printable fourth grade math worksheets to help your students improve their ability to solve word problems! Applying mathematical concepts to solve word problems can be challenging. These free worksheets are great repetition for your students! Click on the images below to download the word problem worksheets. They’re perfect for daily math warm ups! Don’t forget to check out the word problem task cards. Print them off, laminate them and use them for early finishers during maths!

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Unit 1: Place value

Unit 2: addition, subtraction, and estimation, unit 3: multiply by 1-digit numbers, unit 4: multiply by 2-digit numbers, unit 5: division, unit 6: factors, multiples and patterns, unit 7: equivalent fractions and comparing fractions, unit 8: add and subtract fractions, unit 9: multiply fractions, unit 10: understand decimals, unit 11: plane figures, unit 12: measuring angles, unit 13: area and perimeter, unit 14: units of measurement.

4th Grade Word Problems

Related Pages More Word Problems More Grade 4 Math Topics Singapore Math Common Core Math

The following are some examples of 4th Grade Math Word Problems that use mixed operations (addition, subtraction, multiplication and division). These problems are solved with the help of block diagrams or bar models (Singapore Math) or tape diagrams (Common Core).

Example: There were 42 mangoes in each crate. 12 such crates of mangoes were delivered to a factory. 4 mangoes were rotten and had to be thrown away. The remaining mangoes were packed into boxes of 10 mangoes each. How many boxes of mangoes were there?

Solution: Step 1: Find the total number of mangoes delivered.

12 × 42 = 504

The total number of mangoes delivered was 504.

Step 2: Find the number of remaining mangoes.

504 – 4 = 500

Step 3: Find the number of boxes of mangoes.

500 ÷ 10 = 50

There were 50 boxes of mangoes.

Example: There were 9500 spectators at a football match. 6375 of them were men. Of the remaining spectators, there were 4 times as many children as women. How many children were there?

Solution: Step 1: Find the number of women and children.

9500 – 6375 = 3125

There were 3125 women and children.

Step 2: Find the number of women.

3125 ÷ 5 = 625

There were 625 women.

Step 3: Find the number of children.

625 × 4 = 2500

There were 2500 children.

4th Grade Word Problems and Bar Models Example: Dad bought two hammers. One cost $18 and the other costs $28 more. What was his total bill?

Grade 4 Common Core Math Example: Kyle is making 9 birdhouses. He uses 8 nails for each birdhouse. If Kyle has a box of 100 nails, how many nails will he have left after making the birdhouses?

Model Drawing for 4th Grade Examples: Multiplication

• A ribbon that’s 1,530 inches long is cut into two pieces. The length of one piece is 2 times the length of the other. What is the length of the longer piece?
• A piece of fabric that’s 1,640 feet long is cut into two pieces. The length of one piece is 3 times the length of the other. What is the length of the longer piece?

Part-Whole Division 3. A man divided his fortune of $92,000 into 8 equal parts. He gave 4 portions to his wife, 1 portion to his son, and divided the rest equally among three charities. How much more money did the wife receive than the son? 4. A woman divide her collection of 1,200 books into 10 equal parts. She gave 3 portions to her husband, 4 portions to her daughter, and the rest equally to three nieces. How many books did her daughter receive?

Rate Problems 5. Andrew can type 55 words per minute. How many words can he type in 8 minutes? 6. Eddie can write 15 short poems an hour. How many poems can he write in 3 hours?

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Problem Solving Study Guide

Problem solving is an essential skill in mathematics that involves the ability to understand a problem, develop a plan to solve it, carry out the plan, and evaluate the solution for accuracy. Here are some key steps and strategies to help you become a better problem solver:

• Understand the Problem: Read the problem carefully and make sure you understand what is being asked. Identify the known and unknown quantities, and determine the relationships between them.
• Devise a Plan: Consider different strategies for solving the problem, such as drawing a diagram, making a table, using logical reasoning, working backwards, or using a similar problem as a model.
• Carry Out the Plan: Once you have a strategy in mind, start solving the problem step by step, making sure to show all your work and calculations.
• Evaluate the Solution: After finding a solution, check to see if it makes sense and satisfies all the conditions given in the problem. Also, consider if there are alternative ways to solve the problem or if the answer could be expressed differently.

Here are some common strategies for problem solving:

• Draw a Diagram: When dealing with geometric or spatial problems, drawing a diagram can help you visualize the situation and identify the key elements.
• Make a Table or Chart: Organizing information in a table or chart can help you identify patterns , relationships, or trends that can lead to a solution.
• Work Backwards: Start with the end goal and work backwards to determine the steps needed to reach that goal.
• Use Logical Reasoning: Apply logic and reasoning to make educated guesses and eliminate unlikely possibilities.
• Look for a Pattern: Sometimes problems can be solved by identifying a pattern or sequence in the given information.

By practicing these problem-solving strategies and approaches, you can become more confident and proficient in tackling mathematical problems of varying complexity.

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Maths Problems With Answers - Grade 4

A set of Maths problems with answers for grade 4 are presented. Also Solutions and explanations are included.

• Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?
• There are 123 boxes of sweets in a store. There are 25 sweets in each box. How many sweets are in the store?
• There are 365 days in one year, and 100 years in one century. How many days are in one century?
• Billy read 2 books. He read the first one in one week with 25 pages everyday. He read the second book in 12 days with 23 pages everyday. What is the total number of pages that Billy read?
• 123 school girls are to be transported in small vans. Each van can carry 8 girls only. What is the smallest possible number of vans that are needed to transport all 123 school girls?
• John had $100 to buy drinks and sandwiches for his birhtday party. He bought 5 small boxes of drinks at $4 each box and 8 boxes of sandwiches at $6 each box. How much money was left after the shopping?
• A factory produces 5500 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
• Tom, Julia, Mike and Fran have 175 cards to use in a certain game. They decided to share them equally. How many cards should each one take and how many cards are left?
• Sam, Carla and Sarah spent on afternoon collecting sea shells. Sam collected 11. If we add the number of sea shells collected by Sam and Carla, the total would be 24. If we add the number of sea shells collected by Carla and Sarah, the total would be 25 shells. How many shells did each one collect?
• Mr Joshua runs 6 kilometers everyday from Monday to Friday. He also runs 12 kilometers a day on Saturday and Sunday. How many kilometers does Joshua run in a week?
• Tom and Bob are brothers and they each had the same amount of money which they put together to buy a toy. The cost of the toy was $22. If the cashier gave them a change of 6$, how much money did each have?
• John has 5 boxes of sweets. One group of boxes has 5 sweets in each box. The second group of boxes has 4 sweets in each box. John has a total of 22 sweets. How many boxes of each type John has?(Hint: use table)
• There is a total of 16 chickens and rabbits in a farm. The total number of legs (chickens and rabbits) is equal to 50. How many chickens and how many rabbits are there?(Hint:use a table)
• There are 4 more chickens than rabbits in a farm. The total number of legs (chickens and rabbits) is equal to 44. How many chickens and how many rabbits are there?(Hint:use a table)

Answers to the Above Questions

• a) UK b) Russia c) 7,500,148 d) 49,839,760 e) Russia, Canada, USA, China, India, Uk.
• 3075 sweets
• 36,500 days in one century
• 16 vans (no decimal values)
• 1375 toys per day
• 43 each and 3 left
• 80 cm squared
• Sam: 11, Carla: 13 and Sarah: 12
• 54 kilometers
• 2 boxes with 5 sweets each and 3 boxes with 4 sweets each
• 7 chickens and 9 rabbits
• 10 chickens and 6 rabbits

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4 Operations: Mixed word problems

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How to Teach Long Division to Kids in 6 Easy Steps

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Step 1: Start with Division Vocabulary

Step 2: introduce long division layout, step 3: demonstrate with an examples, step 4: practice without bringing down zeros, step 5: teach bringing down zeros, step 6: explain problems with remainders.

Long division can be challenging for kids because it involves many steps and new vocabulary, making it easy to lose track of the process. This complexity often confuses students, especially when bringing down digits or handling remainders. Teaching long division step by step helps kids understand it better. This guide on “ how to teach long division to kids ” will provide clear steps to simplify learning for kids, making it less overwhelming.

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What Should My Child Know Before Learning Long Division?

Before diving into teaching long division, children must have a solid foundation in several key areas. These pre-requisites ensure that they are prepared for the complexities of long division:

• Understanding Multiplication: Kids should be comfortable with multiplication facts up to 12. This knowledge is fundamental because long division requires frequent multiplication to check and subtract products during the division steps.

Here are some fun activities to brush up your child’s understanding of multiplication facts:

• Basic Division Concepts: Ensure children understand the concept of division as sharing or grouping equally. They should be able to perform simple division tasks without remainders, using numbers that are easy to handle.

Here are some fun activities to brush up your child’s understanding of division facts:

• Familiarity with Subtraction: Subtraction is a significant part of the long division process, used to find the difference after multiplying the divisor. Children should be confident in subtracting large numbers, as they will need to do this repeatedly in each step of long division.

Assess how well your kids are versed with subtraction with these fun subtraction games :

• Number Sense: Good number sense , or an understanding of how numbers work and relate to each other, helps children anticipate the results of multiplication and division, making the process of long division smoother and more intuitive.

Ensuring kids are proficient in these areas makes teaching long division more effective, setting them up for success.

How to Teach Long Division in 6 Steps

Before learning the steps of long division, kids need to understand the key terms used throughout the process. Knowing these will help them follow long division strategies more easily.

• Dividend: This is the number being divided in the problem. In the long division layout, the dividend is written inside the long division bracket (often called the “house”).
• Divisor: The number dividing the dividend is called the divisor . The divisor is placed outside the long division bracket.
• Quotient: The quotient is the answer or the result of the division problem. This is written above the bracket, aligned with the digits of the dividend being divided.
• Remainder: If the division isn’t exact, there’s an amount left over called the remainder . The remainder is written as “R” followed by the remaining value after the division process.

Setting up a long division problem correctly is an essential skill for kids to learn. Here’s how to structure it visually:

• Write the Dividend Inside: Start by placing the dividend (the number being divided) inside the long division bracket, often called the “house.” This makes it clear that this number is the one being split into smaller groups.
• Place the Divisor Outside: Write the divisor (the number doing the dividing) outside, to the left of the bracket. This shows which number will be used repeatedly to divide the dividend into smaller groups.
• Draw Lines for the Quotient: The space above the bracket is where the quotient (the result of the division) will be written. Each digit of the quotient will align above the digit or digits of the dividend that are being divided.

1: Set Up the Problem

Write 1564 under the division bar and 27 outside the division bar.

• Look at the first two digits of the dividend (15). Since 15 is less than 27, we need to include the next digit, making it 156.
• Now, determine how many times 27 can fit into 156. 27 goes into 156 a total of 5 times because 27 multiplied by 6 (the next higher number) would exceed 156.

3. Multiply

• Multiply the quotient digit found (5) by the divisor (27), which equals 135.
• Write 135 under 156.

4. Subtract

• Subtract 135 from 156, which equals 21.
• Write 21 below 135.

5. Bring Down

Bring down the next digit of the dividend (the 4 in 1564), making the new number 214.

6. Repeat the Process

• Determine how many times 27 can fit into 214. It fits 7 times (since 27 multiplied by 8 exceeds 214).
• Multiply 27 by 7 (the next quotient digit) to get 189.
• Write 189 under 214, and subtract to find the difference: 214 – 189 = 25.

7. Remainder

• Since there are no more digits to bring down, 25 is the remainder.
• The complete quotient is 57 with a remainder of 25.

After understanding the layout, kids can apply what they’ve learned by playing these games in, each focusing on different levels of difficulty: 

• Dividing 2-Digit Numbers by 1-Digit

• Dividing 3-Digit Numbers by 1-Digit

• Dividing 4-Digit Numbers by 1-Digit

• Divide 4-Digit By 2-Digit Numbers

To build a strong foundation in long division, it’s crucial for children to practice problems where they bring down each digit consecutively without the complication of zeros . This helps them focus on mastering the basic steps of division:

Sequential Bringing Down: Start with simpler numbers where each digit in the dividend needs to be brought down one at a time. This practice solidifies their understanding of the division process step by step.

Example Problems:

• 21 ÷ 3: Begin by dividing the first digit. Since 2 divided by 3 doesn’t work, we use 21. 21 divided by 3 equals 7, so 7 is written above the division bar.
• 154 ÷ 7: Start with the first digit. 1 divided by 7 is not possible, so consider the first two digits, 15. 15 divided by 7 equals 2. Write 2 above the division bar, multiply 2 by 7 (which is 14), subtract 14 from 15 to get 1, then bring down the next digit to make it 14. Continue this way.

Handling zeros can be tricky, but it’s one of the key ways to teach long division. Here’s how to approach problems involving zeros:

Example: 120 ÷ 4

• Divide: Start by dividing the first non-zero digit. Since 1 is smaller than 4, look at the first two digits, 12. Divide 12 by 4 to get 3.
• Write the Quotient: Write 3 above the long division bracket.
• Multiply and Subtract: Multiply 3 by 4 (giving 12) and subtract this from 12, leaving 0.
• Bring Down Zeros: Bring down the next digit, which is 0, making it 0. Divide this 0 by 4 to get 0. Write 0 next to the 3 in the quotient.
• Multiply and Subtract: Multiply 0 by 4 to get 0 and subtract, leaving no remainder.

In some cases, division doesn’t result in an even quotient. This means there’s an amount leftover, called a remainder. Here’s how to handle it:

Example: 29 ÷ 4

• Divide: Start by dividing the first digit, 2, by 4. Since 2 is smaller than 4, consider the first two digits, 29.
• Find the Quotient: Divide 29 by 4 to get 7. Write 7 above the long division bracket.
• Multiply and Subtract: Multiply 7 by 4, which gives 28. Subtract 28 from 29, leaving 1.
• Write the Remainder: Since there’s nothing left to bring down, write “R1” (remainder of 1) next to the 7.

Knowing how to recognize and handle remainders is one of the essential long division tricks that help kids understand why not all division problems divide evenly. 

5 Fun Ways to Teach Long Division

Practicing long division is crucial for reinforcing the steps and strategies. Here are five effective ways to help kids master this skill:

• Online Long Division Games 

Use interactive online games that challenge students to solve division problems step-by-step. These games make learning fun while providing instant feedback to help them understand mistakes.

• Long Division Worksheets

Provide worksheets that start with simpler problems and progressively increase in complexity. Use colorful designs and real-world scenarios to keep kids engaged.

Create or find flashcards that present division problems on one side and answers on the other. This simple tool is a quick way to reinforce division facts and promote speedy calculations.

• Real-Life Problems

Apply division concepts to real-world situations, like dividing treats among friends or organizing items into equal groups. This practical approach makes long division relatable.

• Group Activities

Collaborative exercises where kids work together to solve division problems encourage discussion and peer learning. This can help clarify challenging steps and foster teamwork.

Learning long division can be challenging, but kids can grasp the concept effectively with clear steps, consistent practice, and engaging resources like games and worksheets. With these strategies on how to teach long division, children will build confidence and become proficient problem-solvers at their own pace.

Frequently Asked Questions (FAQs)

What is an easy way to learn division.

An easy way to learn division is by starting with simple problems and using visual aids like counters or drawings to illustrate the process. Gradually move to more complex problems as confidence builds.

What are some tips for teaching long division to struggling students?

Break down the steps into smaller, manageable parts, and offer lots of practice with engaging resources like games and worksheets. Provide positive reinforcement to encourage their progress and address specific challenges with patience.

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Division Worksheets Grade 4 Solving Division Problems

Welcome to our Division Worksheets Grade 4 page. Here you will find a wide range of free 4th Grade Division Worksheets, which will help your child learn to solve division problems across a range of different contexts.

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Division Worksheets Grade 4

Solving division problems.

The worksheets on this page have been designed to support your child on their division journey from the start of 4th grade to the end.

The first two sets of sheets involve working out division problems where there is no remainder.

The second two sets involve working out harder division problems with remainders.

In order to solve the second sets of word problems, the remainder needs to be rounded up or down, depending on the context.

Each set of division word problems has been subdivided into 3 worksheets:

• Sheet A - an easier worksheet;
• Sheet B - a medium worksheet;
• Sheet C - a harder worksheet.

Division Worksheets Grade 4 - Worksheets

Set 1 - solving division problems with no remainder..

• Division Problems 4.1 Sheet A
• PDF version
• Division Problems 4.1 Sheet B
• Division Problems 4.1 Sheet C

Set 2 - solving division problems with no remainder.

• Division Problems 4.2 Sheet A
• Division Problems 4.2 Sheet B
• Division Problems 4.2 Sheet C

Set 3 with remainders

This set involves solving division problems with a remainder. The answer needs to be rounded up or down, depending on the context.

• Division Problems 4.3 Sheet A
• Division Problems 4.3 Sheet B
• Division Problems 4.3 Sheet C

Set 4 with remainders

• Division Problems 4.4 Sheet A
• Division Problems 4.4 Sheet B
• Division Problems 4.4 Sheet C

Looking for some easier Division worksheets

Our 3rd grade division worksheets are similar to those on this page but at an easier level.

The link below will take you to our division worksheets for 3rd grade.

• Division Worksheets Grade 3 Word Problems
• Division Facts to 10x10 Worksheets
• Long Division Worksheets 3rd Grade

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More Division Worksheets

• Divide a multi-digit number by a single digit;
• Use remainders when dividing;
• Calculate division facts related to multiplication facts.
• Divding by Multiples of 10 and 100 Worksheets
• 4th Grade Long Division Worksheets
• Division Facts Worksheets (randomly generated)

More Fourth Grade Math Problems

Here is our set of 4th grade math problems to help your child with their problem solving skills.

Each problem sheet comes complete with answers, and is available in both standard and metric units where applicable.

Many of the problems are based around 'real-life' problems and data such as the world's heaviest animals.

Using these sheets will help your child to:

• apply their addition, subtraction and problem solving skills;
• apply their knowledge of rounding and place value;
• solve a range of 'real life' problems;
• attempt more challenging longer problems.

Using the problems in this section will help your child develop their problem solving and reasoning skills.

These sheets involve solving one or two more challenging longer problems.

• 4th Grade Math Problems

These sheets involve solving many 'real-life' problems involving data.

• 4th Grade Math Word Problems

These sheets involve solving a range of multiplciation problems.

• Multiplication Word Problems 4th Grade

Fourth Grade Math Games

Here you will find a range of free printable 4th Grade Math games. All children like to play Math games, and you will find a good range of Grade 4 Math Games here for your child to play and enjoy.

The following games involve different 4th Grade Math activities which you and your child can enjoy together.

All the free 4th Grade Math Worksheets in this section support the Elementary Math Benchmarks for Fourth Grade.

• Math Games 4th Grade
• 4th Grade Math Puzzles

Here you will find a range of printable 4th grade math puzzles for your child to enjoy.

The puzzles will help your child practice and apply their addition, subtraction, multiplication and division facts as well as developing their thinking and reasoning skills in a fun and engaging way.

Using these puzzles will help your child to:

• learn and practice their addition facts;
• practice adding both positive and negative numbers;
• practice their subtraction facts;
• practice multiplication and division facts;
• develop problem solving skills and reasoning.

All the puzzles support elementary math benchmarks for 4th grade.

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