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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?

Solving Word Problems in Mathematics

     Learn what word problems are and how to solve them in 7 easy steps.

     Real life math problems don’t usually look as simple as 3 + 5 = ?. Instead, things are a bit more complex. To show this, sometimes, math curriculum creators use word problems to help students see what happens in the real world. Word problems often show math happening in a more natural way in real life circumstances. 
     As a teacher, you can share some tips with your students to show that in everyday life they actually solve such problems all the time, and it’s not as scary as it may seem. 

     As you know, word problems can involve just about any operation: from addition to subtraction and division, or even multiple operations simultaneously.

If you’re a teacher, you may sometimes wonder how to teach students to solve word problems. It may be helpful to introduce some basic steps of working through a word problem in order to guide students’ experience. So, what steps do students need for solving a word problem in math?

Steps of Solving a Word Problem

     To work through any word problem, students should do the following:

     1. Read the problem: first, students should read through the problem once.
     2. Highlight facts: then, students should read through the problem again and highlight or underline important facts such as numbers or words that indicate an operation.
     3. Visualize the problem: drawing a picture or creating a diagram can be helpful. 

     Drawing the picture can be a big help in figuring this out. However, they can also look for the clues in the words such as:

          – Addition: add, more, total, altogether, and, plus, combine, in all;

          – Subtraction: fewer, than, take away, subtract, left, difference;

          – Multiplication: times, twice, triple, in all, total, groups;

     These key words may be very helpful when learning how to determine the operation students need to perform, but we should still pay attention to the fact that in the end it all depends on the context of the wording. The same word can have different meanings in different word problems. 

     Here they should learn to identify the steps they need to perform first to solve the problem, whether it’s a simple or a complex sentence. 
     6. Solve the problem: then, students can solve the number sentence and determine the solution. For example, 3 + 8 = 11.
     7. Check the answer: finally, students should check their work to make sure that the answer is correct.

     These 7 steps will help students get closer to mastering the skill of solving word problems. Of course, they still need plenty of practice. So, make sure to create enough opportunities for that! 

     At Happy Numbers, we gradually include word problems throughout the curriculum to ensure math flexibility and application of skills. Check out how easy it is to learn how to solve word problems with our visual exercises! 

     Word problems can be introduced in Kindergarten and be used through all grades as an important part of an educational process connecting mathematics to real life experience. 

     Happy Numbers introduces young students to the first math symbols by first building conceptual understanding of the operation through simple yet engaging visuals and key words. Once they understand the connection between these keywords and the actions they represent, they begin to substitute them with math symbols and translate word problems into number sentences. In this way, students gradually advance to the more abstract representations of these concepts.

     From the beginning, visualization helps the youngest students to understand the concepts of addition, subtraction, and even more complex operations. Even if they don’t draw the representations by themselves yet, students learn the connection between operations they need to perform in the problem and the real-world process this problem describes. 

     Next, students organize data from the word problem and pictures into a number sentence. To diversify the activity, you can ask students to match a word problem with the number sentence it represents.  

     Solving measurement problems is also a good way of mastering practical math skills. This is an example where students can see that math problems are closely related to real-world situations. Happy Numbers applies this by introducing more complicated forms of word problems as we help students advance to the next skill. By solving measurement word problems, students upgrade their vocabulary, learning such new terms as “difference” and “sum,” and continue mastering the connection between math operations and their word problem representations. 

     Later, students move to the next step, in which they learn how to create drawings and diagrams by themselves. They start by distributing light bulbs equally into boxes, which helps them to understand basic properties of division and multiplication. Eventually, with the help of Dino, they master tape diagrams! 

To see the full exercise, follow this link.

     The importance of working with diagrams and models becomes even more apparent when students move to more complex word problems. Pictorial representations help students master conceptual understanding by representing a challenging multi-step word problem in a visually simple and logical form. The ability to interact with a model helps students better understand logical patterns and motivates them to complete the task. 

     Having mentioned complex word problems, we have to show some of the examples that Happy Numbers uses in its curriculum. As the last step of mastering word problems, it is not the least important part of the journey. It’s crucial for students to learn how to solve the most challenging math problems without being intimidated by them. This only happens when their logical and algorithmic thinking skills are mastered perfectly, so they easily start talking in “math” language. 

Grab your binoculars to take an expedition in this Number Sentences song, where Edwin learns that Number Sentences are equations — or mathematical sentences — that show statements using numbers and math symbols.

His Number Sentences journey takes him from the jungles of Borneo to the ice shelves off the coast of Greenland on his ship, the SS Mathematica. The only thing Edwin loves as much as the wildlife he encounters along the way is his newfound ability to communicate what he has seen to his friends using Number Sentences.

Number Sentences Song Lyrics

Verse One
I’m exploring under the canopy.
I see monkeys and count twenty-three.
Some climb a tree, now I count twenty;
this number sentence describes what I see. (23 — _____ = 20)

How many monkeys climbed? I’ll find out,
because that’s the unknown I want to know about:
I try a three, and that’s when I see,
how many monkeys climbed up a tree. (THREE!)

Chorus
Read what the question is asking about;
write down what we need to find out,
with a statement that makes sense
of the problem as a number sentence.

Verse Two
I went exploring in Antarctica
and saw through my binoculars….
thirty-two penguins on an iceberg.
Eighteen more appeared from the ice water.

To find out how many there were,
I wrote a number sentence, so I’d be sure.
Now I can see the solution is: fifty penguins
resting on top of the deep blue ocean.

Learn More

If you’d like to expand upon this video with other online resources that nicely compliment this video, we recommend following the link to hcpss.instructure.com, which lays out the basic rules and methods that will aid in understanding the concept through more traditional means.

This song targets an important Common Core learning standard for 2nd Grade. Look into the relevant standard to understand the requirements unique to this standard. To look at the specific standard follow this link to learn more about common core standard 2.OA.1.

Or continue browsing Numberock’s math video content library to discover more engaging math songs. To gain access to Numberock’s growing library of premium content, click here.

Presentation on theme: «Writing Number Sentences Created by Mr. Hemmert. ARMT 9 Write number sentences for word problems that involve multiplication or division.»— Presentation transcript:

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Writing Number Sentences Created by Mr. Hemmert

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ARMT 9 Write number sentences for word problems that involve multiplication or division.

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Getting the Idea You can often write a number sentence to solve a word problem. A number sentence uses numbers, operation symbols ( +, -, ×, ÷), and an equal sign (=) to represent a mathematical situation.

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Example 1 Mrs. Sheppard bought 16 books. Each book cost $5. Which number sentence could be used to find the total cost of the books? a.$16 + 5 = b.$16 – 5 = c.$16 × 5 = d.$16 ÷ 5 = e.Answer: C

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Example 1 Explained Mrs. Sheppard bought 16 books. Each book cost $5. Which number sentence could be used to find the total cost of the books? Choose the Correct Operation: –Step 1: Look for key words in the problem. The key word “total” means you should either add or multiply. –Step 2: Decide if you should add or multiply. Think: 16 books that cost $5. That’s like 16 groups of $5 bills. The easiest way to solve the problem is to multiply $16 × 5

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Example 2 Steve read that 128 players entered the basketball tournament in his town. The organizers split the players into 16 teams, with an equal number of players on each team. What number sentence can be used to determine P, the number of players on each team?

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Example 2 Explained Steve read that 128 players entered the basketball tournament in his town. The organizers split the players into 16 teams, with an equal number of players on each team. What number sentence can be used to determine P, the number of players on each team? Strategy –Step 1: Look for key words in the problem. The key words “split” and “equal numbers of players on each team” mean you should divide. –Step 2: What numbers do you divide? Think: 128 players split into 16 equal teams. You need to divide 128 by 16. –Step 3: Write the number sentence The problem says to use the variable P to represent the number of players on each team. –168 ÷ 16 = P

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Example 3 Kyle has 350 paperclips. He will put the same number of paperclips into 5 boxes. Which number sentence could be used to determine the number of paperclips Kyle will put in each box? a.350 × 5 = b.350 ÷ 5 = c.350 + 5 = d.350 – 5 =

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