4th grade problem solving

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4th Grade Math Word Problems Real-Life Problems

Welcome to our 4th Grade Math Word Problems page. Here you will find our range of Fourth Grade Math Problem Worksheets which will help your child apply and practice their Math skills to solve a range of challenges and 'real life' problems.

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4th Grade Math Word Problems

Here you will find a range of problem solving worksheets.

The sheets involve using a range of math skills and knowledge to solve problems.

Each problem sheet is available in both standard and metric units (where appropriate), and come complete with an answer sheet.

There is a mixture of longer math challenges and shorter word problems to solve. Some of the data comes from the real world, such as the Heaviest Terrestrial Animals sheet, some of the word problems are made up.

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.

Travelling Salamanders Problem Solving

Travelling Salamanders involve the math skills of rounding, ordering, adding and subtracting.

This sheet is available in standard and metric units.

• Travelling Salamanders metric
• PDF version
• Travelling Salamanders standard

Heaviest Terrestrial Animals Problems

Heaviest Terrestrial Animals are a sheet of 4th grade math problems which involve solving a range of problems involving decimals with mainly 1 decimal place. Rounding, adding, subtracting and multiplying by 1000 are covered in these sheets.

• Heaviest Terrestrial Animals metric
• Heaviest Terrestrial Animals standard

Great Winged Wonders Problems

These word problems are all about the wingspans of birds. The math skills include rounding, ordering, adding and subtracting decimals with up to 1 or 2 decimal places, depending on whether you choose the standard or metric version.

• Great Winged Wonders metric
• Great WInged Wonders standard

Temperatures Around the World

These word problems are all about different temperature around the world. The main focus on these worksheets is the ordering and working out differences of positive and negative whole numbers.

• Temperatures around the world 2

Looking for some easier Real-Life word problems?

If these word problems are not at the right level for you, try some of our simpler 3rd grade math problems.

The problems in this section involve integers only and are at a more basic level than the problems on this page.

• 3rd Grade Real Life Math Word Problems

Looking for some more challenging word problems?

If these word problems look too easy, then why not try our 5th grade math problems?

The problem on this page involve larger numbers and more complex problem solving. They also involve decimals with more decimal places.

There are also some sinple ratio problems to introduce your child to ratio and proportion.

• 5th Grade Math Problems Real Life
• Ratio Word Problems (5th grade)

More Recommended Math Worksheets

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

More 4th Grade Math Problems

Here is some more of our 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 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 a range of multiplciation problems.

• Multiplication Word Problems 4th Grade

These sheets involve solving a range of division problems.

• Division Worksheets Grade 4 Word Problems
• Math Games 4th Grade

Using games is a great way to learn Math facts and develop mental calculation skills in a fun and easy way.

The following games involve different 4th Grade Math activities which your child will enjoy playing.

Games include using negative numbers, decimal addition and subtraction, rounding, multiplying by 10s.

• 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.

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4th Grade Math Problems

This comprehensive review of math problems for 4th graders is just the boost your child needs to succeed in math this year.

Author Amber Watkins

Published October 19, 2023

Published Oct 19, 2023

• Key takeaways
• In fourth-grade math, it is important to master multi-digit multiplication, fractions, and decimals.
• A variety of math problems for 4th graders can be solved using a number line.
• To supplement your child’s fourth-grade math skills, consider using our math app .

Table of contents

• Multiplication

If you are on the hunt for 4th grade math practice, look no further. In this guide, we offer a cumulative review of important fourth-grade math topics.

Fourth-grade math standards put a strong emphasis on multiplication , division , and fractions .

As we cover a variety of fourth-grade math problems together, pay attention to the methods we use, including breaking down fractions and using number lines to solve real-world 4th grade word problems. 

26 Math Problems for 4th Graders

Multiplication word problems.

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Answer: Sam bought 144 bottles of water. There are 12 bottles in a dozen. 12 x 12 = 144.

Answer: Mr. Rodger bought 1,600 juice boxes. 100 x 16 = 1,600.

Answer: They bought 80 total binders. 6 x 5 = 30. 10 x 5 =50. 50 + 30 = 80.

Answer: Crystal has saved a total of 350 cents. Each dime is worth 10 cents. 35 x 10 =350.

Answer: Jason will have 720 new baseball cards after two years. There are 12 months in every year, so in two years there are 24 months (12 x 2 = 24). 24 x 30 =720.

Division Word Problems

Answer: Jack should plant 14 seeds in each row. 98 / 7 = 14.

Answer: Kim should fill Polly’s dog bowl 8 times a day.  480 / 60 = 8

Answer: The sunflower has been growing for 12 weeks. There are 12 inches in a foot, so there are 24 inches in two feet (12 x 2 =24). 24 inches divided by 2 is equal to 12.

Answer: Cait will have to walk her dog 50 times to save $500. 500 / 10 = 50

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• Kindergarten

Measurement and data

Sample questions, fraction word problems.

Answer: ⅛ + ⅛ + ⅛ + ⅛ + ⅛ + ⅛ + ⅛ + ⅛ = 6/8, so 8 people could have eaten ⅛ of a pie each or  ⅜ + ⅜ = 6/8, so 2 people could have eaten ⅜ of the pie each.

Answer: 1/9 + 1/9 + 1/9 + 1/9 + 1/9  or  3/9 + 6/9 = 5/9

Answer: Yes, they ran the same distance.

Answer: Yes they completed the same portion of their homework.

Answer: The baker will need 6/8 cups of oil. ¾ x 2 = 6/8

Answer: She will need 1 ½ feet of space in her garden. 6 x 3/12 = 18/12 = 1 6/12 or 1 ½.

Rounding & Place Value

Answer: 900

Answer: 6,000

Answer: 360

Answer: 500

Answer: 2,000

Decimal Word Problems

Answer: Jake’s grass will grow .7 millimetres in one week. .1 x 7 = .7

Answer: Jason has a total of 60 cents (.60). A nickel is worth 5 cents or .05. 

.05 x 12 is .60.

Answer: Reese spent a total of $19.50 at the movie theater. 

$4.50 x 3 = $13.50. $3.00 x 2 = $6.00. $13.50 + $6.00 = $19.50 

Answer: Steve has $6.50 left over in his budget. $11.00 + $12.50 + $20.00 = $43.50. $50.00 – $43.50 = $6.50

Answer: Yes, he will have enough money for a $200 deposit. $52.12, $69.40, $42.80, and $35.75 added together equal $200.07.

Our math help app provides math help for fourth graders in a way that keeps children engaged, rewards their effort, and scaffolds their learning. Plus, the app gives parents access to a dashboard that shows their child’s progress on math topics they struggle with. Take learning into your own hands, and check out our math app today!

Lesson credits

Amber Watkins

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

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Unit 5: Division

About this unit.

Do you like breaking things apart? Then you're going to love learning about division! We'll use place value, area models, and estimation techniques to make dividing by 1-digit numbers a breeze. In this unit, you will even get the inside scoop on what to do when there's a pesky remainder left over.

• Division: FAQ (Opens a modal)
• Estimating division that results in non-whole numbers (Opens a modal)
• Understanding remainders (Opens a modal)
• Introduction to remainders (Opens a modal)
• Interpreting remainders (Opens a modal)
• Estimate to divide by 1-digit numbers Get 3 of 4 questions to level up!
• Interpret remainders Get 3 of 4 questions to level up!
• Divide with remainders (2-digit by 1-digit) Get 3 of 4 questions to level up!

Divide multiples of 10, 100, and 1,000 by 1-digit numbers

• Quotients that are multiples of 10 (Opens a modal)
• Divide multiples of 10, 100, and 1,000 by 1-digit numbers Get 5 of 7 questions to level up!

Division with place value

• Division using place value (Opens a modal)
• Divide using place value Get 3 of 4 questions to level up!

Division with area models

• Division with area models (Opens a modal)
• Create division equations with area models Get 3 of 4 questions to level up!
• Divide by 1-digit numbers with area models Get 3 of 4 questions to level up!

Estimate quotients

• Estimating quotients (Opens a modal)
• Estimate quotients (3- and 4-digit divided by 1-digit) Get 3 of 4 questions to level up!

Multi-digit division with partial quotients

• Introduction to division with partial quotients (no remainder) (Opens a modal)
• Division with partial quotients (remainder) (Opens a modal)
• Intro to long division (no remainders) (Opens a modal)
• Divide multi-digit numbers by 2, 3, 4, and 5 (remainders) Get 5 of 7 questions to level up!
• Divide multi-digit numbers by 6, 7, 8, and 9 (remainders) Get 3 of 4 questions to level up!

Multiplication, division word problems

• Division word problem: field goals (Opens a modal)
• Multiplication word problem: pizza (Opens a modal)
• Multiplication and division word problems Get 5 of 7 questions to level up!

Multi-step word problems

• 2-step estimation word problem (Opens a modal)
• 2-step estimation word problems Get 3 of 4 questions to level up!
• Represent multi-step word problems using equations Get 3 of 4 questions to level up!
• Multi-step word problems with whole numbers Get 3 of 4 questions to level up!

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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◂ Math Worksheets and Study Guides Fourth Grade. Problem Solving

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Check Out These 50 Fourth Grade Math Word Problems of the Day

Mr. Smith’s class collected coins in a big jar for 6 months.

Opening your daily math lesson with a Fourth Grade Math Word Problem of the Day is an excellent way to set the stage for learning! Incorporate them at the start of your math block to build confidence, critical thinking skills, and a learning community. Students will get used to reading for meaning, while also identifying key information. Encourage students to write out equations and draw pictures to explain their thinking, since this helps them see the light when they are stuck!

Topics in these fourth grade math word problems cover patterns & place value, addition/subtraction, multiplication, division, fractions, decimals, measurement, and comparisons. If you’d like even more math word problems, we publish them daily on our kid-friendly site: the Daily Classroom Hub . Make sure to bookmark the link!

Want this entire set of word problems in one easy document? Get your free PowerPoint bundle by submitting your email here . All you need to do is post one of the problems on your whiteboard or projector screen. Then let kids take it from there.

50 Fourth Grade Math Word Problems

1. jill wrote the number 730,918. she challenged jane to rearrange the digits to create the highest possible number. what number did jane make.

2. Marcus was given this puzzling pattern and asked to complete it. Which two numbers should he should write next? 4, 7, 11, 14, 18, 21, 25, ___, ___

3. Mr. Mathematica gave his class these digits: 1, 5, 7, 9, 2, 8, and 5. He asked them to make the smallest number possible using every digit once. What would that number be?

4. The detectives found this number pattern as part of the code on a keypad to unlock a vault. 27, 26, 24, 23, 21, __, __. What are the last two numbers they should punch in?

5. Tom’s bicycle cost $50 more than Bob’s bicycle. Bob’s bicycle cost $180. How much did Tom’s bicycle cost?

6. Randy bought 2 baseball hats for $5.25 each. He also bought 2 wrist bands for $2.50 each. How much money did he spend?

7. Lots of birds were spotted at the new bird feeder. There were 12 sparrows, 15 crows, 8 orioles, 3 squirrels, and 9 cardinals. How many birds were there in all?

8. There were lots of visitors to the town history museum this past winter. There were 75 in December, 98 in January, and 69 in February. How many visitors did the museum have this past winter in total?

9. Luis was setting up his new office. He bought a new computer for $350. He also bought a printer for $99 and two ink cartridges for $37 each. How much did he spend?

10. There was a big sale at the Super Duper Shoe Store for 3 days. They sold 87 pairs of shoes on Friday, 95 pairs of shoes on Saturday, and 83 pairs of shoes on Sunday. How many pairs of shoes were sold all together?

11. Pia had a huge sticker collection. She had 280 stickers. Her friend, Jen, had 155 stickers in her collection. How many more stickers did Pia have than Jen?

12. Robyn scored a total of 155 points in basketball this season for the Tarrytown Tigers. She had 30 rebounds as well. Last season she scored 106 points. How many more points did she score this season than last season?

13. John went to lunch at the Cool Cat Cafe. He spent $1.25 on a juice drink and $5.50 on a sandwich. He also bought a brownie for 99 cents. He gave the cashier a $20 bill. How much change did he get?

14. Race Car Ralph drove 1,000 miles in the big cross-country auto race. 775 of those miles were with his dog, Speedy, in the car. The rest of the way, he drove alone. How many miles did Ralph drive without Speedy?

15. Best Baked Bakery baked 10,250 holiday cookies. They sold almost all of them. Only 56 were left. How many holiday cookies did they sell?

16. There were 3 cats and 4 geese in the barnyard. How many total legs were there?

17. Donna picks 5 apples every minute in the orchard. How many apples does she pick in 20 minutes?

18. Morris the magician pulled 2 doves out of his hat, twice as many rabbits as doves, and 4 times as many mice as rabbits. How many animals did he pull out of his hat?

19. Tina is making pizzas for 15 guests. If each person (including Tina) is expected to eat 2 slices, how many 8-slice pizzas should Tina make?

20. Chef Charlie is decorating a birthday cake with a circle of berries. He has 6 strawberries and would like to put 5 blueberries between each strawberry. How many blueberries does he need?

22. To make a winter stew, Jamal needs 3 pounds of sweet potatoes. If they cost $1.29 per pound, what will it cost to buy enough sweet potatoes?

22. The Hotel Swanky has 10 floors. Each floor has 16 guest rooms. There is also a ballroom, two meeting rooms, and a restaurant. How many guest rooms are in the hotel?

23. Mrs. Mason got a new bookcase for the library and filled it with books. There were 6 shelves. The top two shelves had 50 books on each shelf. The bottom four shelves had 75 books on each shelf. How many books were there in the new bookcase?

24. The cafeteria ordered 6 packs of jumbo chocolate chip cookies and 3 packs of brownies. Each pack of cookies had 12 cookies in it. They sold 45 cookies and 30 brownies. How many cookies are left?

25. The new elementary school has 30 desks in each classroom. There are four classrooms for each grade. There are 5 grades in the school. How many desks are there in the school?

26. Gina planted six rows of carrots in her garden. Each row had 30 carrots. Rabbits ate half of her carrots. How many carrots did she have left?

27. Jack planted a magic bean. The bean plant that grew was 1 foot tall on the first day. Then it doubled in height each day. How tall was the plant on the fifth day?

28. Big Brain University bought 15 new supercomputers and 50 printers. Each supercomputer cost $5,300. A printer cost $100. How much did the university spend buying new computers?

29. The new golf course had 3 tournaments every month this year. The course is open 12 months a year. Each tournament was limited to 101 golfers and was full. How many golfers played in the tournaments all together this year?

30. The school office printer can print 200 pages every 10 minutes. If the printer runs for an hour straight, how many pages can it print?

31. Lucia makes beaded bracelets. Each bracelet has 12 beads on it. She made 55 bracelets for each of the school fairs. The school had 3 fairs. How many bracelets did Lucia make?

32. Sammy Speedball is a pitcher for the Boogaloo Bearcats. He practiced his pitching on Saturday for an hour in the morning and an hour after dinner. He threw 20 pitches every 30 minutes. How many practice pitches did Sammy throw on Saturday?

33. Serena had 35 cherries. She gave 8 to each of her sisters. She still has 3 left over. How many sisters does Serena have?

34. The new teacher was giving out pencils to her class for the year. She wanted to give them out evenly. She had 15 packs of pencils with 10 pencils in each pack. She had 20 students. How many pencils should each student get? How many pencils would be left over?

35. 150 kids signed up for the summer soccer league. There are going to be ten teams, and the Dragons are one of the teams. Each team has 3 coaches and they want an equal number of players on each team. How many players should be on the Dragons?

36. the wonderful widget company produces 480 widgets every day. they have 6 widget making machines running every day, with each machine making equal amounts of widgets. the company runs six days a week. how many widgets does each machine make.

37. Farmer Fran has 35 hens. Each hen lays a dozen eggs a day. Fran packs the eggs into packs of ten. How many packs of eggs does she pack per day?

38. ReadOn Publishers gives free books to schools every year on the last day of the year. They have 900 books for this year’s giveaway. 18 schools have applied for the free books. How many should each school get if they are evenly distributed?

39. Coach Cindy is meeting with each player for practice individually. Each player will get 15 minutes with the coach. Coach Cindy has 2 hours for this on Saturday. How many players can she meet with?

40. Dr. Bea Well has 120 patients. ¼ of them wear glasses. How many of her patients don’t wear glasses?

41. Lucy has 24 stuffed animals. She loves elephants, and one-third of her stuffed animals are elephants. Half of the elephants are gray. How many elephants does she have?

42. Annie collects seashells. She has 120 shells in her collection. They are from both the Atlantic Ocean and the Pacific Ocean. ¾ of the shells are from the Atlantic Ocean. How many shells are from the Pacific Ocean?

43. Bill has 7/8 of his homework done. Andy has 9/10 of his homework done. They have the same amount of homework. Who has more homework done?

44. Jose was offered 2/5 of a jumbo chocolate bar or 3/6 of the same bar. He loves chocolate. Which should he choose if he wants the most chocolate?

45. Janelle has 6 notebooks for school. Donnie has 1/3 more than Janelle. How many notebooks do Janelle and Donnie have all together?

46. Tonya found two small interesting stones. The black one weighs 0.3 of an ounce. The red one weighs 0.09 of an ounce. Which stone weighs more?

47. Leah has a baseball bat that is 2 and a half feet long. Bryson has a bat that is 28 inches long and another one that is 2 feet and 5 inches long. Who has the longest bat?

48. Mr. Smith’s class collected coins in a big jar for 6 months. Their coins weighed 2 pounds and 8 ounces. Ms. Smith’s class did the same thing. Their coins weighed 2 ½ pounds. Whose coins weighed more?

49. The track team was practicing for the big meet. Tim ran for 25 minutes every day for 5 days. Tom ran an hour every day for 3 days. Who spent the most time running?

50. The Jones family left for the airport at 10:00 a.m. for vacation. Their flight leaves at 12:30 p.m. They stopped twice for 10 minutes each time. They got to the airport at 11:30 p.m. How much time did they spend driving?

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Check Out These 50 Fifth Grade Math Word Problems of the Day

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Free Printable Multi-Step Word Problems Worksheets for 4th Grade

Multi-Step Word Problems: Discover an extensive collection of free printable worksheets for Grade 4 Math students, crafted by Quizizz to enhance problem-solving skills and boost mathematical understanding.

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Explore printable Multi-Step Word Problems worksheets for 4th Grade

Multi-Step Word Problems worksheets for Grade 4 are an essential tool for teachers to help their students develop strong problem-solving skills in math. These worksheets provide a variety of challenging math word problems that require students to use multiple steps and operations to find the solution. By incorporating these worksheets into their lesson plans, teachers can ensure that their Grade 4 students are exposed to a diverse range of mathematical concepts, such as addition, subtraction, multiplication, and division. Furthermore, these worksheets can be easily adapted to suit individual student needs, allowing teachers to differentiate instruction and cater to various learning styles. With Multi-Step Word Problems worksheets for Grade 4, teachers can effectively engage their students in the exciting world of math and help them build a strong foundation for future success.

Quizizz is an excellent platform for teachers to access a wide variety of educational resources, including Multi-Step Word Problems worksheets for Grade 4. This interactive platform offers a vast collection of math word problems and other engaging activities, allowing teachers to create customized quizzes and assignments for their students. In addition to worksheets, Quizizz also offers features such as real-time feedback, gamification, and progress tracking, making it an ideal tool for enhancing student learning and motivation. By incorporating Quizizz into their teaching strategies, teachers can not only provide their Grade 4 students with valuable practice in solving multi-step word problems but also foster a fun and interactive learning environment that promotes student success in math.

Fun Math Problem Solving Activities for the Fourth Grade Classroom

Math is an important subject that students need to master in order to do well in their future studies. But it can be difficult to make math fun for students, especially at the fourth grade level. That’s why I’ve put together this list of my favorite problem solving activities that my fourth grade students love! Let’s take a look.

Problem Solving Ideas

Math Games – One of my favorite activities is to have the students play math games such as “24 Challenge” or “Math Baseball”. In these games, students are given a set of math facts or equations and they must solve them before their opponents can. This helps them practice their problem-solving skills while having fun. It also encourages them to work together as a team, which is great for building teamwork skills.

Word Problems – Another great activity is having the students work on word problems together. I like to have them write out the equations and then discuss how they solved each one. This helps them understand how to break down complex problems and identify key words or phrases that will help them figure out the answer more quickly. It also gets them thinking critically about how they approach solving each problem, which can be very beneficial in later grades when they have more challenging material to tackle!

Group Work – Group work can be a great way for the students to practice problem solving skills with their peers. I like to assign groups of four or five and give each group a set of math problems that they need to solve together as a team. This helps reinforce collaboration and cooperation among the students, as well as fostering an environment where everyone is comfortable voicing their ideas without fear of judgment from their peers or teacher.

Math doesn’t have to be boring! Problem solving activities are a great way for fourth grade teachers to engage their students in learning while still making sure they understand key concepts from the curriculum. From math games and word problems, to group work, there are plenty of activities you can use in your classroom that your fourth graders will love! And who knows—you might even find yourself having fun too !

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Essential Math Problems for 4th Graders

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55 Word Problems For 4th Graders: Questions And Riddles About Operations, Money, And Time

October 22, 2023 //  by  Seda Unlucay

Why not add some colorful manipulatives to make 4th grade learning more concrete, review the core numeracy skills with worksheets, or incorporate them into a daily math lesson to build problem-solving fluency?

These multi-step word problems incorporate addition , subtraction , multiplication , and division as well as time , money, and fractions . Since they involve more than one step, students should be encouraged to express their thinking with pictures and words to help plan, solve and check each problem.

1. Angel had $55. She spent $17 on a new book and $32 on a video game. How much money does she have left?

2. nine times a number plus 3 more is 75. what is the number, 3. sandy found 28 seashells on the beach. ava found 42 and alex found 38. if they share them equally, how many will each get, 4. tim scored 345 points on a video game. his score was 59 points more than stan's score. stan's score was 18 points less than arnold's score. what was arnold's score, 5. if the product of two numbers is 45 and their difference is 4, what are the two numbers, 6. adrian spent $120 on prizes for the school fair. each prize cost $12. he also bought 60 cupcakes to donate. how many items did he take to the fair , 7. anthony paid $35 for a keyboard and $18 for a mouse. he paid $90 in cash. how much change will he get back, 8. the sum of a dividend and a divisor is 39. the quotient is 12. what is the divisor , 9. the school is collecting empty cans to recycle. they would like to collect 200 cans. andy brings 8 packs of 6 and mary brings 4 packs of 12. how many cans do they still need, 10. steven had 356 fuzzy stickers, 432 scented stickers, and 225 shiny stickers in his collection. how many stickers does he have rounded to the nearest ten, 11. mandy made necklaces for three of her friends. she used 567 beads on one, 165 on another, and 587 on the third one. there were 1600 beads in the bag when she started. how many beads are left , 12. sam was running at a rate of 28 miles per hour for the first 4 hours. during the fifth hour, he ran 18 miles per hour. how many miles did sam run during the entire 5 hours, 13. angela ate 94 pieces of candy per day for one whole week. during the second week, she ate 242 pieces of candy in all. how many total pieces of candy did she eat over the course of two weeks, 14. jennifer spent $45 buying gifts for each of her 6 siblings. she also spent $74 on a gift for her father. how much money did she spend in all, 15. pamela has $1645. sandy has four times as much money. how much money do pamela and sandy have in all, 16. jane is throwing a party for 16 people. soda comes in 6-packs and costs $2.25 per pack. if each person at the party has one soda, how much money will she need to spend on drinks, 17. there are 5 chickens on a farm. each chicken lays 6 eggs a day. how many eggs will there be after 20 days , 18. samantha cut 6 pieces of ribbon. the pieces were 4.5m, 3.2m, 7.7m, and 8.2m. she put them all together to form one long piece of ribbon. how long was the ribbon , 19. paul ordered 8 pizzas for his school party. each pizza had 6 slices. there were 14 guests at the party. how many slices did each person get, 20. a toy car company made 12 cars a week for 2 weeks. they tripled this amount over the next 2 weeks. how many cars did they make after the 4 weeks , 21. stanley bakes 13 cakes a day for 6 days and then 12 more cakes a day for the next 9 days. how many cakes does he bake in total , 22. jenny's fence is 64 m long. she wants to divide it into 8 even parts. how many meters does each part have to be , 23. tania built a gigantic sandcastle with five levels. if each level is 35 cm high, how high is the sandcastle in total, 24. pamela drives 8 km to school and 8 km home. how many km does she drive after 6 weeks if she doesn't drive on the weekends, 25. jane grows potatoes. she grew 112 potatoes. she sold each potato for $3 but had to pay her employees $1 per potato. how much money did she make , 26. alexandra and her 3 friends caught 350 fish. they sold each fish for $2 and then split the money. how much money did they each make , 27. michelle is a tutor. she charged her students $40 per hour. she has 7 students and she tutors each one for 2 hours each. how much money does she earn in total, 28. cassandra had 90 pieces of candy. she ate ⅕ of her candy and gave her friend ⅖. how many pieces of candy does she still have , 29. roger has 29 classmates in his class and 100 books to share. how many could he give each classmate and how many would be leftover , 30. mary's school is going on a field trip. there are 9 school buses and each bus can hold 45 children. how many children can they fit on all 9 buses, 31. patrick collects pokemon cards. he had 28 cards and gave ¼ of them away to his friend. how many cards does he have left, 32. sam weighs 52kg. his uncle weighs twice as much as him and his sister weighs 14kg more than his uncle. how much does his uncle weigh , 33. it takes sandy 24 minutes to walk to work each day from monday to friday. how much time does she spend walking to work in one week , 34. sarah’s dollhouse cost $450 and janet's cost $235. how much more does janet's dollhouse cost compared to janet's, 35. cassandra arrived 35 minutes late for her appointment. if her appointment was at 9:45, what time did she arrive , 36. molly has a square fence around her house. what is the perimeter of the fence if each side measures 7.5 m, 37. sam had 84 chocolate bars. he shared them equally with his classmates and each student got 3. how many students are in sam's class, 38. andy owns 2 cars. he sold one for $155,000 and the other one for $160,000. how much money did he earn from selling both cars, 39. chris made $150 from working 2 days. he gave ⅓ of his earnings to his sister. how much did he give his sister, 40. jane starts school at 9 am and finishes at 4:30 pm. how much time does she spend at school, 41. there are 24 students in brenda's class. ⅓ of them are boys and the rest are girls. how many girls are in brenda's class, 42. 8 classes are going to the amusement park. there are 27 students in each class. how many students are going to the amusement park, 43. lisa can run 200m in 45 seconds. how long will it take her to run 1km, 44. tommy sold lemonade for $3 a cup. he sold 75 cups in one weekend. how much money did he earn in all, 45. you can buy a single chocolate bar for $4 or a pack of 6 for $18. how much money do you save if you buy the pack of 6, 46. andrew had 35 friends but ⅖ of them moved away in the summer. how many friends did not move, 47. jane ran 7km from monday to friday and another 32 km on the weekend. how many kilometers did she run in all, 48. ben earned $450 in september. he earned twice that much in october, and in november earned another $650. how much did he earn in all, 49. cameron runs 13km every day, except on the weekends.  how far would does he run after 5 weeks, 50. a family of two adults and three kids went to the movies. an adult ticket costs $12 and a child ticket costs ⅓ of that price. how much does it cost for all 5 tickets, 51. miranda got 16/20 on her science test. what was her score as a percentage , 52. jeremy planted five rows of peas in a garden. each row had 40 peas. ¼ of the peas did not grow. how many peas did grow, 53. sam's family has 5 cats and 7 dogs. how many legs are there in all, 54. cassandra has 360 stamps in her collection. ⅓ of them are from asia and the rest from europe. how many of her stamps are from europe, 55. samantha has 24 candies. dan has ¼ more than her. how many candies do they have altogether .

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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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