Word problems for school

Word problems for Year 5 are a great way to assess pupils’ number fluency. By the time primary school children reach Upper Key Stage 2, they will be building on their knowledge and understanding of the number system and place value, working with larger integers. An increased understanding of the connections between the different maths concepts is crucial, as children will be expected to tackle more complex, multi-step problems.

It is important children are regularly provided with the opportunity to solve a range of word problems and Year 5 maths worksheets with reasoning and problem solving incorporated alongside fluency, into all lessons.

To help you with this, we have put together a collection of 18 word problems aimed at Year 5 maths pupils.

Year 5 maths word problems in the national curriculum

The National Curriculum states that by Year 5, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. Children also begin to use the language of algebra for solving a range of problems.

By Year 5, pupils should be starting to gain confidence in solving more complex two-step and multi-step word problems, covering topics across the Year 5 curriculum.

Place value 

Solve number and practical problems involving ordering and comparing numbers to at least 1,00,000; counting forwards or backwards in steps of powers of 10; interpreting negative numbers in context and rounding to the nearest 10,100, 1000, 10,000 and 100,000.

Addition and subtraction 

Solve addition and subtraction word problems and a combination of these, including understanding the meaning of the equals sign.

Multiplication and division 

Solve problems involving multiplication and division, including using knowledge of factors, multiples, squares and cubes and scaling by simple fractions.

Fractions, decimals and percentages

Solve problems involving numbers up to 3 decimal places and problems which require knowing percentage and decimal equivalents.

Measurement 

Solve time word problems and those involving converting between units of time and problems involving measure (for example, length, mass, volume and money word problems) using decimal notation and scaling.

Statistics

Solve comparison, sum and difference problems, using information presented in a line graph.

Why are word problems important in Year 5 maths?

Word problems are an important element of the Year 5 curriculum. By this stage, children need to be building confidence in approaching a range of one, two and multi-step word problems. They require children to be creative and apply the skills they have learnt to a range of real-life situations. 

How to teach problem solving in Year 5

Children need to be taught the skills for successfully approaching and tackling word problems. Reading the question carefully and identifying the key information needed to tackle the problem, is the first step, followed by identifying which calculations are required for solving it and deciding whether it will be helpful to draw a picture/ visual representation to understand and answer the question. 

Using mental maths skills to round and estimate an answer is also very helpful for children to establish whether their final answer is realistic. Children need to also be able to calculate the inverse, to be able to check their answer, once the problem has been completed.

See also: Mental maths year 5

Here is an example:

A transport museum has 1243 visitors on Monday morning and another 1387 visitors in the afternoon. On Tuesday 736 fewer visitors go to the museum than who visited on Monday.

How many visitors were there altogether on Tuesday?

How to solve:

What do you already know?

How can this be drawn/represented pictorially?

We can draw a bar model to represent this problem:

• To calculate the total number of visitors on Monday, we need to add 1243 and 1387 together. 1243 + 1387 = 2630
• The number of fewer visitors on Tuesday needs to be subtracted from Monday’s total: 2630 – 736 = 1894.
• The total number of visitors on Tuesday was 1894.

Addition word problems for Year 5

In Year 5, addition word problems can involve whole numbers with over 4 digits and decimal numbers. Children should be able to round number to check the accuracy and begin to solve two step number problems 

Subtraction word problems for Year 5

Subtraction word problems in Year 5 require pupils to be confident subtracting numbers over 4 digits and problems involving decimal numbers. Pupils need to be able to round numbers to check accuracy and to use subtraction when solving mixed word problems. 

 Multiplication word problems for year 5

In year 5, multiplication word problems include problems involving times tables and multiplying whole numbers up to 4-digits by 1 or 2-digit numbers. Pupils also need to be able to combine multiplication with other operations, in order to solve two-step word problems. 

Third Space Learning often ties word problems into our online one-to-one tutoring. Each lesson is personalised to the needs of the individual student, growing maths knowledge and problem solving skills.

Division word problems for year 5

In Year 5, division word problems can involve whole numbers up to 4 digits being divided by 1-digit numbers. Pupils need to understand how to answer word problems, when the answer involves a remainder.

Fraction and decimal word problems in Year 5

In Year 5, fractions word problems and decimals can include questions involving ordering, addition and subtraction of fractions. They can also involve converting between fractions and decimals. 

Mixed four operation word problems

Problems with mixed operations, or ‘multi-step’ word problems, require two or more operations to solve them. A range of concepts can be covered within mixed problems, including the four operations, fractions, decimals and measures. These are worth more marks than some of the more straightforward, one-step problems.

Word problem resources

Third Space Learning offers a wide array of maths and word problems resources for other year groups such as word problems for year 6, word problems for year 3 and word problems for year 4. Our word problem collection covers all four operations and other specific maths topics such as ratio word problems and percentage word problems.

This article is for parents who think about how to help with math and support their children. The math word problems below provide a gentle introduction to common math operations for schoolers of different grades.

What are math word problems?

During long-time education, kids face various hurdles that turn into real challenges. Parents shouldn’t leave their youngsters with their problems. They need an adult’s possible help, but what if the parents themselves aren’t good at mathematics? All’s not lost. You can provide your kid with different types of support. Not let a kid burn the midnight oil! Help him/ her to get over the challenges thanks to these captivating math word examples.

Math word problems are short math questions formulated into one or several sentences. They help schoolers to apply their knowledge to real-life scenarios. Besides, this kind of task helps kids to understand this subject better.

Addition for the first and second grades

These math examples are perfect for kids that just stepped into primary school. Here you find six easy math problems with answers:

1. Peter has eight apples. Dennis gives Peter three more. How many apples does Peter have in all?

2. Ann has seven candies. Lack gives her seven candies more. How many candies does Ann have in all?

3. Walter has two books. Matt has nine books. If Matt gives all his books to Walter, how many books will Walter have?

4. There are three crayons on the table. Albert puts five more crayons on the table. How many crayons are on the table?

5. Bill has nine oranges. His friend has one orange. If his friend gives his orange to Bill, how many oranges will Bill have?

6. Jassie has four leaves. Ben has two leaves. Ben gives her all his leaves. How many leaves does Jessie have in all?

Subtraction for the first and second grades

1. There were three books in total at the book shop. A customer bought one book. How many books are left?

2. There are five pizzas in total at the pizza shop. Andy bought one pizza. How many pizzas are left?

3. Liza had eleven stickers. She gave one of her stickers to Sarah. How many stickers does Liza have?

4. Adrianna had ten stones. But then she left two stones. How many stones does Adrianna have?

5. Mary bought a big bag of candy to share with her friends. There were 20 candies in the bag. Mary gave three candies to Marissa. She also gave three candies to Kayla. How many candies were left?

6. Betty had a pack of 25 pencil crayons. She gave five to her friend Theresa. She gave three to her friend Mary. How many pencil crayons does Betty have left?

Multiplication for the 2nd grade and 3rd grade

See the simple multiplication word problems. Make sure that the kid has a concrete understanding of the meaning of multiplication before.

Bill is having his friends over for the game night. He decided to prepare snacks and games.

1. He makes mini sandwiches. If he has five friends coming over and he made three sandwiches for each of them, how many sandwiches did he make?

2. He also decided to get some juice from fresh oranges. If he used two oranges per glass of juice and made six glasses of juice, how many oranges did he use?

3. Then Bill prepared the games for his five friends. If each game takes 7 minutes to prepare and he prepared a total of four games, how many minutes did it take for Bill to prepare all the games?

4. Bill decided to have takeout food as well. If each friend and Bill eat three slices of pizza, how many slices of pizza do they have in total?

Mike is having a party at his house to celebrate his birthday. He invited some friends and family.

1. He and his mother prepared cupcakes for dessert. Each box had 8 cupcakes, and they prepared four boxes. How many cupcakes have they prepared in the total?

2. They also baked some cookies. If they baked 6 pans of cookies, and there were 7 cookies per pan, how many cookies did they bake?

3. Mike planned to serve some cold drinks as well. If they make 7 pitchers of drinks and each pitcher can fill 5 glasses, how many glasses of drinks are they preparing?

4. At the end of the party, Mike wants to give away some souvenirs to his 6 closest friends. If he gives 2 souvenir items for each friend, how many souvenirs does Mike prepare?

Division: best for 3rd and 4th grades

1. If you have 10 books split evenly into 2 bags, how many books are in each bag?

2. You have 40 tickets for the fair. Each ride costs 2 tickets. How many rides can you go on?

3. The school has $20,000 to buy new equipment. If each piece of equipment costs $100, how many pieces can the school buy in total?

4. Melissa has 2 packs of tennis balls for $10 in total. How much does 1 pack of tennis balls cost?

5. Jack has 25 books. He has a bookshelf with 5 shelves on it. If Jack puts the same number of books on each shelf, how many books will be on each shelf?

6. Matt is having a picnic for his family. He has 36 cookies. There are 6 people in his family. If each person gets the same number of cookies, how many cookies will each person get?

Division with remainders for fourth and fifth grades

1. Sarah sold 35 boxes of cookies. How many cases of ten boxes, plus extra boxes does Sarah need to deliver?

2. Candies come in packages of 16. Mat ate 46 candies. How many whole packages of candies did he eat, and how many candies did he leave? 46 candies divided by 16 candies = 2 packages and 2 candies left over.

3. Mary sold 24 boxes of chocolate biscuits. How many cases of ten boxes, plus extra boxes does she need to deliver?

4. Gummy bears come in packages of 25. Suzie and Tom ate 30 gummy bears. How many whole packages did they eat? How many gummy bears did they leave?

5. Darel sold 55 ice-creams. How many cases of ten boxes, plus extra boxes does he need to deliver?

6. Crackers come in packages of 8. Mat ate 20 crackers. How many whole packages of crackers did he eat, and how many crackers did he leave?

Mixed operations for the fifth grade

These math word problems involve four basic operations: addition, multiplication, subtraction, and division. They suit best for the fifth-grade schoolers.

200 planes are taking off from the airport daily. During the Christmas holidays, the airport is busier — 240 planes are taking off every day from the airport.

1. During the Christmas holidays, how many planes take off from the airport in each hour if the airport opens 12 hours daily?

2. Each plane takes 220 passengers. How many passengers depart from the airport every hour during the Christmas holidays? 20 x 220 = 4400.

3. Compared with a normal day, how many more passengers are departing from the airport in a day during the Christmas holidays?

4. During normal days on average 650 passengers are late for their plane daily. During the Christmas holidays, 1300 passengers are late for their plane. That’s why 14 planes couldn’t take off and are delayed. How many more passengers are late for their planes during Christmas week?

5. According to the administration’s study, an additional 5 minutes of delay in the overall operation of the airport is caused for every 27 passengers that are late for their flights. What is the delay in the overall operation if there are 732 passengers late for their flights?

Extra info math problems for the fifth grade

1. Ann has 7 pairs of red socks and 8 pairs of pink socks. Her sister has 12 pairs of white socks. How many pairs of socks does Ann have?

2. Kurt spent 17 minutes doing home tasks. He took a 3-minute snack break. Then he studied for 10 more minutes. How long did Kurt study altogether?

3. There were 15 spelling words on the test. The first schooler spelled 9 words correctly. Miguel spelled 8 words correctly. How many words did Miguel spell incorrectly?

4. In the morning, Jack gave his friend 2 gummies. His friend ate 1 of them. Later Jack gave his friend 7 more gummies. How many gummies did Jack give his friend in all?

5. Peter wants to buy 2 candy bars. They cost 8 cents, and the gum costs 5 cents. How much will Peter pay?

Finding averages for 5th grade

We need to find averages in many situations in everyday life.

1. The dog slept 8 hours on Monday, 10 hours on Tuesday, and 900 minutes on Wednesday. What was the
average number of hours the dog slept per day?

2. Jakarta can get a lot of rain in the rainy season. The rainfall during 6 days was 90 mm, 74 mm, 112 mm, 30 mm, 100 mm, and 44 mm. What was the average daily rainfall during this period?

3. Mary bought 4 books. The prices of the first 3 books were $30, $15, and $18. The average price she paid for the 4 books was $25 per books. How much did she pay for the 4th books?

Ordering and number sense for the 5th grade

1. There are 135 pencils, 200 pens, 167 crayons, and 555 books in the bookshop. How would you write these numbers in ascending order?

2. There are five carrots, one cabbage, eleven eggs, and 15 apples in the fridge. How would you write these numbers in descending order?

3. Peter has completed exercises on pages 279, 256, 264, 259, and 192. How would you write these numbers in ascending order?

4. Mary picked 32 pants, 15 dresses, 26 pairs of socks, 10 purses. Put all these numbers in order.

5. The family bought 12 cans of tuna, 23 potatoes, 11 onions, and 33 pears. Put all these numbers in order.

Fractions for the 6th-8th grades

1. Jannet cooked 12 lemon biscuits for her daughter, Jill. She ate up 4 biscuits. What fraction of lemon biscuits did Jill eat?

2. Guinet travels a distance of 7 miles to reach her school. The bus covers only 5 miles. Then she has to walk 2 miles to reach the school. What fraction of the distance does Guinet travel by bus?

3. Bob has 24 pencils in a box. Eighteen pencils have #2 marked on them, and the 6 are marked #3. What fraction of pencils are marked #3?

4. My mother places 15 tulips in a glass vase. It holds 6 yellow tulips and 9 red tulips. What fraction of tulips are red?

5. Bill owns 14 pairs of socks, of which 7 pairs are white, and the rest are brown. What fraction of pairs of socks are brown?

6. Bred spotted a total of 39 birds in an aviary at the Zoo. He counted 18 macaws and 21 cockatoos. What fraction of macaws did Bred spot at the aviary?

Decimals for the 6th grade

Write in words the following decimals:

• 0,004
• 0,07
• 2,1
• 0,725
• 46,36
• 2000,19

Comparing and sequencing for the 6th grade

1. The older brother picked 42 apples at the orchard. The younger brother picked only 22 apples. How many more apples did the older brother pick?

2. There were 16 oranges in a basket and 66 oranges in a barrel. How many fewer oranges were in the basket than were in the barrel?

3. There were 40 parrots in the flock. Some of them flew away. Then there were 25 parrots in the flock. How many parrots flew away?

4. One hundred fifty is how much greater than fifty-three?

5. On Monday, the temperature was 13°C. The next day, the temperature dropped by 8 degrees. What was the temperature on Tuesday?

6. Zoie picked 15 dandelions. Her sister picked 22 ones. How many more dandelions did her sister pick than Zoie?

Time for the 4th grade

1. The bus was scheduled to arrive at 7:10 p.m. However, it was delayed for 45 minutes. What time was it when the bus arrived?

2. My mother starts her 7-hour work at 9:15 a.m. What time does she get off from work?

3. Jack’s walk started at 6:45 p.m. and ended at 7:25 p.m. How long did his walk last?

4. The school closes at 9:00 p.m. Today, the school’s principal left 15 minutes after the office closed, and his secretary left the office 25 minutes after he left. When did the secretary leave work?

5. Suzie arrives at school at 8:20 a.m. How much time does she need to wait before the school opens? The school opens at 8:35 a.m.

6. The class starts at 9:15 a.m.. The first bell will ring 20 minutes before the class starts. When will the first bell ring?

Money word problems for the fourth grade

1. James had $20. He bought a chocolate bar for $2.30 and a coffee cup for $5.50. How much money did he have left?

2. Coffee mugs cost $1.50 each. How much do 7 coffee mugs cost?

3. The father gives $32 to his four children to share equally. How much will each of his children get?

4. Each donut costs $1.20. How much do 6 donuts cost?

5. Bill and Bob went out for takeout food. They bought 4 hamburgers for $10. Fries cost $2 each. How much does one hamburger with fries cost?

6. A bottle of juice costs $2.80, and a can is $1.50. What would it cost to buy two cans of soft drinks and a bottle of juice?

Measurement word problems for the 6th grade

The task is to convert the given measures to new units. It best suits the sixth-grade schoolers.

• 55 yd = ____ in.
• 43 ft = ____ yd.
• 31 in = ____ ft.
• 29 ft = ____ in.
• 72 in = ____ ft.
• 13 ft = ____ yd.
• 54 lb = ____ t.
• 26 t = ____ lb.
• 77 t = ____ lb.
• 98 lb = ____ t.
• 25 lb = ____ t.
• 30 t = ____ lb.

Ratios and percentages for the 6th-8th grades

It is another area that children can find quite difficult. Let’s look at simple examples of how to find percentages and ratios.

1. A chess club has 25 members, of which 13 are males, and the rest are females. What is the ratio of males to all club members?

2. A group has 8 boys and 24 girls. What is the ratio of girls to all children?

3. A pattern has 4 red triangles for every 12 yellow triangles. What is the ratio of red triangles to all triangles?

4. An English club has 21 members, of which 13 are males, and the rest are females. What is the ratio of females to all club members?

5. Dan drew 1 heart, 1 star, and 26 circles. What is the ratio of circles to hearts?

6. Percentages of whole numbers:

• 50% of 60 = …
• 100% of 70 = …
• 90% of 70 = …
• 20% of 30 = …
• 40% of 10 = …
• 70% of 60 = …
• 100% of 20 = …
• 80% of 90 = …

Probability and data relationships for the 8th grade

1. John ‘s probability of winning the game is 60%. What is the probability of John not winning the game?

2. The probability that it will rain is 70%. What is the probability that it won’t rain?

3. There is a pack of 13 cards with numbers from 1 to 13. What is the probability of picking a number 9 from the pack?

4. A bag had 4 red toy cars, 6 white cars, and 7 blue cars. When a car is picked from this bag, what is the probability of it being red or blue?

5. In a class, 22 students like orange juice, and 18 students like milk. What is the probability that a schooler likes juice?

Geometry for the 7th grade

The following task is to write out equations and find the angles. Complementary angles are two angles that sum up to 90 degrees, and supplementary angles are two angles that sum up to 180 degrees.

1. The complement of a 32° angle = …

2. The supplement of a 10° angle = …

3. The complement of a 12° angle = …

4. The supplement of a 104° angle = …

Variables/ equation word problems for the 5th grades

1. The park is 𝑥 miles away from Jack’s home. Jack had to drive to and from the beach with a total distance of 36 miles. How many miles is Jack’s home away from the park?

2. Larry bought some biscuits which cost $24. He paid $x and got back $6 of change. Find x.

3. Mike played with his children on the beach for 90 minutes. After they played for x minutes, he had to remind them that they would be leaving in 15 minutes. Find x.

4. At 8 a.m., there were x people at the orchard. Later at noon, 27 of the people left the orchard, and there were 30 people left in the orchard. Find x.

Travel time word problems for the 5th-7th grades

1. Tony sprinted 22 miles at 4 miles per hour. How long did Tony sprint?

2. Danny walked 15 miles at 3 miles per hour. How long did Danny walk?

3. Roy sprinted 30 miles at 6 miles per hour. How long did Roy sprint?

4. Harry wandered 5 hours to get Pam’s house. It is 20 miles from his house to hers. How fast did Harry go?

Choose your grade level and you’ll jump to a page with hundreds of practice word problems, one for each day of the school year. (These pages are in-progress. We’ll keep adding more until we have 30 weeks/150 worksheets per grade level.)

Kindergarten (Level K)

In Kindergarten, daily math word problem series will allow children to practice counting numbers to 20, comparing numbers (using more, most, fewest, etc.), adding and subtracting within 10, and identifying basic shapes.

Grade 1 (Level A)

Daily word problem worksheets for 1st grade students. Most problems require basic addition or subtraction. There are also occasional problems related to counting money and skip counting.

Grade 2 (Level B)

This page has 2nd grade daily math word problems. At this level, we have both single-step and multi-step problems. Single, double, and triple-digit addition and subtraction are frequently featured. Other skills include elapsed time, counting money, and repeated addition (multiplication).

Grade 3 (Level C)

In third grade, students will be presented with 2, 3, and 4-digit addition and subtraction problems, as well as questions involving basic multiplication, basic division, place value, counting money, tables & charts, and fractions.

Grade 4 (Level D)

In 4th grade, the daily word problems will consist of more multi-step math, covering operations with whole numbers, fractions, and decimals. There will also be questions related to place value, angles, graphs, and measurement conversions.

Grade 5 (Level E)

These 5th grade daily math worksheets continue to build on elementary math skills. Multi-step problems cover operations with whole numbers, as well as fractions and decimals. Understanding place value, calculating measurements, and reading charts and graphs are among the other skills covered in these worksheets.

Math Buzz

This is a different set of daily review worksheets, featuring a variety of math skills. Each day, students have 5 math questions to answer. Not all problems are word problems in this set.

We explain what a word problem is and give examples of the types of word problems your child might be challenged with in each primary-school maths year group, from Year 1 to Year 6.