word problems on problem solving

120 Math Word Problems To Challenge Students Grades 1 to 8

Written by Marcus Guido

• Teaching Tools

• Subtraction
• Multiplication
• Mixed operations
• Ordering and number sense
• Comparing and sequencing
• Physical measurement
• Ratios and percentages
• Probability and data relationships

You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.

A jolt of creativity would help. But it doesn’t come.

Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.

This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes . ( See our entire list of back to school resources for teachers here .)

There are 120 examples in total.

The list of examples is supplemented by tips to create engaging and challenging math word problems.

120 Math word problems, categorized by skill

Addition word problems.

Best for: 1st grade, 2nd grade

1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total?

2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now?

3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total?

5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies?

6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?

7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now?

8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total?

Subtraction word problems

Best for: 1st grade, second grade

9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left?

10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing?

11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

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12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half?

13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now?

14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month?

15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left?

16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left?

Multiplication word problems

Best for: 2nd grade, 3rd grade

17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have?

18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total?

19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?

20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total?

21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn?

Division word problems

Best for: 3rd grade, 4th grade, 5th grade

22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag?

23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on?

24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total?

25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost?

26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible?

Mixed operations word problems

27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now?

28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?

29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have?

30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag?

Ordering and number sense word problems

31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?

32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?

33. Composing Numbers: What number is 6 tens and 10 ones?

34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I?

35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points?

Fractions word problems

Best for: 3rd grade, 4th grade, 5th grade, 6th grade

36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar?

37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait?

38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total?

39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink?

40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total?

41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left?

42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete?

43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use?

44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction.

45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make?

46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number.

Decimals word problems

Best for: 4th grade, 5th grade

47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total?

48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left?

49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked?

50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower?

51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo?

52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week?

Comparing and sequencing word problems

Best for: Kindergarten, 1st grade, 2nd grade

53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?

54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?

55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs?

56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers?

57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20?

58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36?

59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April?

Time word problems

66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her?

69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school?

70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for?

71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home?

Money word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade

60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total?

61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left?

62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times?

63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost?

64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total?

65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left?

67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional.

68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year?

Physical measurement word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade

72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler?

73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres?

74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years?

75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year?

76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink?

77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get?

78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy?

79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total?

80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres?

81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction?

Ratios and percentages word problems

Best for: 4th grade, 5th grade, 6th grade

82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have?

83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers?

84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players?

85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport?

86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population?

87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there?

88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?

Probability and data relationships word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade

89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased?

90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1?

91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction.

92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni?

93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test?

94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal?

95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y .

Geometry word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade

96. Introducing Perimeter:  The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter?

97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total?

98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume?

99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw?

100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter?

101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area?

102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw?

103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm?

104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy?

105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle?

106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it?

107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it?

108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it?

109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides?

110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units?

111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side?

112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter?

113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield?

114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius?

Variables word problems

Best for: 6th grade, 7th grade, 8th grade

115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent?

116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored.

117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast.

118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored.

119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.

120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours?

How to easily make your own math word problems & word problems worksheets

Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do:

• Link to Student Interests:  By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
• Make Questions Topical:  Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
• Include Student Names:  Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
• Be Explicit:  Repeating keywords distills the question, helping students focus on the core problem.
• Test Reading Comprehension:  Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
• Focus on Similar Interests:  Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
• Feature Red Herrings:  Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.

A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones.

Final thoughts about math word problems

You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students.

Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments.

The result?

A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach.

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Math Word Problems and Solutions - Distance, Speed, Time

Problem 1 A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon? Click to see solution Solution: Let $x$ be the number of kilograms he sold in the morning.Then in the afternoon he sold $2x$ kilograms. So, the total is $x + 2x = 3x$. This must be equal to 360. $3x = 360$ $x = \frac{360}{3}$ $x = 120$ Therefore, the salesman sold 120 kg in the morning and $2\cdot 120 = 240$ kg in the afternoon.

Problem 2 Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did each of them pick? Click to see solution Solution: Let $x$ be the amount Peter picked. Then Mary and Lucy picked $2x$ and $x+2$, respectively. So $x+2x+x+2=26$ $4x=24$ $x=6$ Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.

Problem 3 Sophia finished $\frac{2}{3}$ of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book? Click to see solution Solution: Let $x$ be the total number of pages in the book, then she finished $\frac{2}{3}\cdot x$ pages. Then she has $x-\frac{2}{3}\cdot x=\frac{1}{3}\cdot x$ pages left. $\frac{2}{3}\cdot x-\frac{1}{3}\cdot x=90$ $\frac{1}{3}\cdot x=90$ $x=270$ So the book is 270 pages long.

Problem 4 A farming field can be ploughed by 6 tractors in 4 days. When 6 tractors work together, each of them ploughs 120 hectares a day. If two of the tractors were moved to another field, then the remaining 4 tractors could plough the same field in 5 days. How many hectares a day would one tractor plough then? Click to see solution Solution: If each of $6$ tractors ploughed $120$ hectares a day and they finished the work in $4$ days, then the whole field is: $120\cdot 6 \cdot 4 = 720 \cdot 4 = 2880$ hectares. Let's suppose that each of the four tractors ploughed $x$ hectares a day. Therefore in 5 days they ploughed $5 \cdot 4 \cdot x = 20 \cdot x$ hectares, which equals the area of the whole field, 2880 hectares. So, we get $20x = 2880$ $ x = \frac{2880}{20} = 144$. Hence, each of the four tractors would plough 144 hectares a day.

Problem 5 A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose? Click to see solution Solution: Let $x$ be the number he chose, then $2\cdot x - 138 = 102$ $2x = 240$ $x = 120$

Problem 6 I chose a number and divide it by 5. Then I subtracted 154 from the result and got 6. What was the number I chose? Click to see solution Solution: Let $x$ be the number I chose, then $\frac{x}{5}-154=6$ $\frac{x}{5}=160$ $x=800$

Problem 8 One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 18 cm 2 . Find the lengths of all sides. Click to see solution Solution: Let $x$ be the length of the longer side $x \gt 3$, then the other side's length is $x-3$ cm. Then the area is S 1 = x(x - 3) cm 2 . After we increase the lengths of the sides they will become $(x +1)$ and $(x - 3 + 1) = (x - 2)$ cm long. Hence the area of the new rectangle will be $A_2 = (x + 1)\cdot(x - 2)$ cm 2 , which is 18 cm 2 more than the first area. Therefore $A_1 +18 = A_2$ $x(x - 3) + 18 = (x + 1)(x - 2)$ $x^2 - 3x + 18 = x^2 + x - 2x - 2$ $2x = 20$ $x = 10$. So, the sides of the rectangle are $10$ cm and $(10 - 3) = 7$ cm long.

Problem 9 The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from each cow each year? Click to see solution Solution: Let x be the amount of milk the first cow produced during the first year. Then the second cow produced $(8100 - x)$ litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of $15\%$ or $10\%$. So $8100 + \frac{15}{100}\cdot x + \frac{10}{100} \cdot (8100 - x) = 9100$ Therefore $8100 + \frac{3}{20}x + \frac{1}{10}(8100 - x) = 9100$ $\frac{1}{20}x = 190$ $x = 3800$ Therefore, the cows produced 3800 and 4300 litres of milk the first year, and $4370$ and $4730$ litres of milk the second year, respectively.

Problem 10 The distance between stations A and B is 148 km. An express train left station A towards station B with the speed of 80 km/hr. At the same time, a freight train left station B towards station A with the speed of 36 km/hr. They met at station C at 12 pm, and by that time the express train stopped at at intermediate station for 10 min and the freight train stopped for 5 min. Find: a) The distance between stations C and B. b) The time when the freight train left station B. Click to see solution Solution a) Let x be the distance between stations B and C. Then the distance from station C to station A is $(148 - x)$ km. By the time of the meeting at station C, the express train travelled for $\frac{148-x}{80}+\frac{10}{60}$ hours and the freight train travelled for $\frac{x}{36}+\frac{5}{60}$ hours. The trains left at the same time, so: $\frac{148 - x}{80} + \frac{1}{6} = \frac{x}{36} + \frac{1}{12}$. The common denominator for 6, 12, 36, 80 is 720. Then $9(148 - x) +120 = 20x +60$ $1332 - 9x + 120 = 20x + 60$ $29x = 1392$ $x = 48$. Therefore the distance between stations B and C is 48 km. b) By the time of the meeting at station C the freight train rode for $\frac{48}{36} + \frac{5}{60}$ hours, i.e. $1$ hour and $25$ min. Therefore it left station B at $12 - (1 + \frac{25}{60}) = 10 + \frac{35}{60}$ hours, i.e. at 10:35 am.

Problem 11 Susan drives from city A to city B. After two hours of driving she noticed that she covered 80 km and calculated that, if she continued driving at the same speed, she would end up been 15 minutes late. So she increased her speed by 10 km/hr and she arrived at city B 36 minutes earlier than she planned. Find the distance between cities A and B. Click to see solution Solution: Let $x$ be the distance between A and B. Since Susan covered 80 km in 2 hours, her speed was $V = \frac{80}{2} = 40$ km/hr. If she continued at the same speed she would be $15$ minutes late, i.e. the planned time on the road is $\frac{x}{40} - \frac{15}{60}$ hr. The rest of the distance is $(x - 80)$ km. $V = 40 + 10 = 50$ km/hr. So, she covered the distance between A and B in $2 +\frac{x - 80}{50}$ hr, and it was 36 min less than planned. Therefore, the planned time was $2 + \frac{x -80}{50} + \frac{36}{60}$. When we equalize the expressions for the scheduled time, we get the equation: $\frac{x}{40} - \frac{15}{60} = 2 + \frac{x -80}{50} + \frac{36}{60}$ $\frac{x - 10}{40} = \frac{100 + x - 80 + 30}{50}$ $\frac{x - 10}{4} = \frac{x +50}{5}$ $5x - 50 = 4x + 200$ $x = 250$ So, the distance between cities A and B is 250 km.

Problem 12 To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took. Click to see solution Solution: Let $x$ be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made: $3\cdot 25 + (x - 3)\cdot 30 = 75 + 30(x - 3)$ Therefore: $25 x = 75 + 30(x -3) - 100$ $25x = 75 +30x -90 - 100$ $190 -75 = 30x -25$ $115 = 5x$ $x = 23$ So the company worked 23 days and they made $23\cdot 25+100 = 675$ pieces.

Problem 13 There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3 roses, every three boys planted 1 birch. By the end of the day they planted $24$ plants. How many birches and roses were planted? Click to see solution Solution: Let $x$ be the number of roses. Then the number of birches is $24 - x$, and the number of boys is $3\times (24-x)$. If each girl planted 3 roses, there are $\frac{x}{3}$ girls in the class. We know that there are 24 students in the class. Therefore $\frac{x}{3} + 3(24 - x) = 24$ $x + 9(24 - x) = 3\cdot 24$ $x +216 - 9x = 72$ $216 - 72 = 8x$ $\frac{144}{8} = x$ $x = 18$ So, students planted 18 roses and 24 - x = 24 - 18 = 6 birches.

Problem 14 A car left town A towards town B driving at a speed of V = 32 km/hr. After 3 hours on the road the driver stopped for 15 min in town C. Because of a closed road he had to change his route, making the trip 28 km longer. He increased his speed to V = 40 km/hr but still he was 30 min late. Find: a) The distance the car has covered. b) The time that took it to get from C to B. Click to see solution Solution: From the statement of the problem we don't know if the 15 min stop in town C was planned or it was unexpected. So we have to consider both cases. A The stop was planned. Let us consider only the trip from C to B, and let $x$ be the number of hours the driver spent on this trip. Then the distance from C to B is $S = 40\cdot x$ km. If the driver could use the initial route, it would take him $x - \frac{30}{60} = x - \frac{1}{2}$ hours to drive from C to B. The distance from C to B according to the initially itinerary was $(x - \frac{1}{2})\cdot 32$ km, and this distance is $28$ km shorter than $40\cdot x$ km. Then we have the equation $(x - 1/2)\cdot 32 + 28 = 40x$ $32x -16 +28 = 40x$ $-8x = -12$ $8x = 12$ $x = \frac{12}{8}$ $x = 1 \frac{4}{8} = 1 \frac{1}{2} = 1 \frac{30}{60} =$ 1 hr 30 min. So, the car covered the distance between C and B in 1 hour and 30 min. The distance from A to B is $3\cdot 32 + \frac{12}{8}\cdot 40 = 96 + 60 = 156$ km. B Suppose it took $x$ hours for him to get from C to B. Then the distance is $S = 40\cdot x$ km. The driver did not plan the stop at C. Let we accept that he stopped because he had to change the route. It took $x - \frac{30}{60} + \frac{15}{60} = x - \frac{15}{60} = x - \frac{1}{4}$ h to drive from C to B. The distance from C to B is $32(x - \frac{1}{4})$ km, which is $28$ km shorter than $40\cdot x$, i.e. $32(x - \frac{1}{4}) + 28 = 40x$ $32x - 8 +28 = 40x$ $20= 8x$ $x = \frac{20}{8} = \frac{5}{2} = 2 \text{hr } 30 \text{min}.$ The distance covered equals $ 40 \times 2.5 = 100 km$.

Problem 15 If a farmer wants to plough a farm field on time, he must plough 120 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially? Click to see solution Solution: Let $x$ be the number of days in the initial plan. Therefore, the whole field is $120\cdot x$ hectares. The farmer had to work for $x + 2$ days, and he ploughed $85(x + 2)$ hectares, leaving $40$ hectares unploughed. Then we have the equation: $120x = 85(x + 2) + 40$ $35x = 210$ $x = 6$ So the farmer planned to have the work done in 6 days, and the area of the farm field is $120\cdot 6 = 720$ hectares.

Problem 16 A woodworker normally makes a certain number of parts in 24 days. But he was able to increase his productivity by 5 parts per day, and so he not only finished the job in only 22 days but also he made 80 extra parts. How many parts does the woodworker normally makes per day and how many pieces does he make in 24 days? Click to see solution Solution: Let $x$ be the number of parts the woodworker normally makes daily. In 24 days he makes $24\cdot x$ pieces. His new daily production rate is $x + 5$ pieces and in $22$ days he made $22 \cdot (x + 5)$ parts. This is 80 more than $24\cdot x$. Therefore the equation is: $24\cdot x + 80 = 22(x +5)$ $30 = 2x$ $x = 15$ Normally he makes 15 parts a day and in 24 days he makes $15 \cdot 24 = 360$ parts.

Problem 17 A biker covered half the distance between two towns in 2 hr 30 min. After that he increased his speed by 2 km/hr. He covered the second half of the distance in 2 hr 20 min. Find the distance between the two towns and the initial speed of the biker. Click to see solution Solution: Let x km/hr be the initial speed of the biker, then his speed during the second part of the trip is x + 2 km/hr. Half the distance between two cities equals $2\frac{30}{60} \cdot x$ km and $2\frac{20}{60} \cdot (x + 2)$ km. From the equation: $2\frac{30}{60} \cdot x = 2\frac{20}{60} \cdot (x+2)$ we get $x = 28$ km/hr. The intial speed of the biker is 28 km/h. Half the distance between the two towns is $2 h 30 min \times 28 = 2.5 \times 28 = 70$. So the distance is $2 \times 70 = 140$ km.

Problem 18 A train covered half of the distance between stations A and B at the speed of 48 km/hr, but then it had to stop for 15 min. To make up for the delay, it increased its speed by $\frac{5}{3}$ m/sec and it arrived to station B on time. Find the distance between the two stations and the speed of the train after the stop. Click to see solution Solution: First let us determine the speed of the train after the stop. The speed was increased by $\frac{5}{3}$ m/sec $= \frac{5\cdot 60\cdot 60}{\frac{3}{1000}}$ km/hr = $6$ km/hr. Therefore, the new speed is $48 + 6 = 54$ km/hr. If it took $x$ hours to cover the first half of the distance, then it took $x - \frac{15}{60} = x - 0.25$ hr to cover the second part. So the equation is: $48 \cdot x = 54 \cdot (x - 0.25)$ $48 \cdot x = 54 \cdot x - 54\cdot 0.25$ $48 \cdot x - 54 \cdot x = - 13.5$ $-6x = - 13.5$ $x = 2.25$ h. The whole distance is $2 \times 48 \times 2.25 = 216$ km.

Problem 19 Elizabeth can get a certain job done in 15 days, and Tony can finish only 75% of that job within the same time. Tony worked alone for several days and then Elizabeth joined him, so they finished the rest of the job in 6 days, working together. For how many days have each of them worked and what percentage of the job have each of them completed? Click to see solution Solution: First we will find the daily productivity of every worker. If we consider the whole job as unit (1), Elizabeth does $\frac{1}{15}$ of the job per day and Tony does $75\%$ of $\frac{1}{15}$, i.e. $\frac{75}{100}\cdot \frac{1}{15} = \frac{1}{20}$. Suppose that Tony worked alone for $x$ days. Then he finished $\frac{x}{20}$ of the total job alone. Working together for 6 days, the two workers finished $6\cdot (\frac{1}{15}+\frac{1}{20}) = 6\cdot \frac{7}{60} = \frac{7}{10}$ of the job. The sum of $\frac{x}{20}$ and $\frac{7}{10}$ gives us the whole job, i.e. $1$. So we get the equation: $\frac{x}{20}+\frac{7}{10}=1$ $\frac{x}{20} = \frac{3}{10}$ $x = 6$. Tony worked for 6 + 6 = 12 days and Elizabeth worked for $6$ days. The part of job done is $12\cdot \frac{1}{20} = \frac{60}{100} = 60\%$ for Tony, and $6\cdot \frac{1}{15} = \frac{40}{100} = 40\%$ for Elizabeth.

Problem 20 A farmer planned to plough a field by doing 120 hectares a day. After two days of work he increased his daily productivity by 25% and he finished the job two days ahead of schedule. a) What is the area of the field? b) In how many days did the farmer get the job done? c) In how many days did the farmer plan to get the job done? Click to see solution Solution: First of all we will find the new daily productivity of the farmer in hectares per day: 25% of 120 hectares is $\frac{25}{100} \cdot 120 = 30$ hectares, therefore $120 + 30 = 150$ hectares is the new daily productivity. Lets x be the planned number of days allotted for the job. Then the farm is $120\cdot x$ hectares. On the other hand, we get the same area if we add $120 \cdot 2$ hectares to $150(x -4)$ hectares. Then we get the equation $120x = 120\cdot 2 + 150(x -4)$ $x = 12$ So, the job was initially supposed to take 12 days, but actually the field was ploughed in 12 - 2 =10 days. The field's area is $120 \cdot 12 = 1440$ hectares.

Problem 21 To mow a grass field a team of mowers planned to cover 15 hectares a day. After 4 working days they increased the daily productivity by $33 \times \frac{1}{3}\%$, and finished the work 1 day earlier than it was planned. A) What is the area of the grass field? B) How many days did it take to mow the whole field? C) How many days were scheduled initially for this job? Hint : See problem 20 and solve by yourself. Answer: A) 120 hectares; B) 7 days; C) 8 days.

Problem 22 A train travels from station A to station B. If the train leaves station A and makes 75 km/hr, it arrives at station B 48 minutes ahead of scheduled. If it made 50 km/hr, then by the scheduled time of arrival it would still have 40 km more to go to station B. Find: A) The distance between the two stations; B) The time it takes the train to travel from A to B according to the schedule; C) The speed of the train when it's on schedule. Click to see solution Solution: Let $x$ be the scheduled time for the trip from A to B. Then the distance between A and B can be found in two ways. On one hand, this distance equals $75(x - \frac{48}{60})$ km. On the other hand, it is $50x + 40$ km. So we get the equation: $75(x - \frac{48}{60}) = 50x + 40$ $x = 4$ hr is the scheduled travel time. The distance between the two stations is $50\cdot 4 +40 = 240$ km. Then the speed the train must keep to be on schedule is $\frac{240}{4} = 60$ km/hr.

Problem 23 The distance between towns A and B is 300 km. One train departs from town A and another train departs from town B, both leaving at the same moment of time and heading towards each other. We know that one of them is 10 km/hr faster than the other. Find the speeds of both trains if 2 hours after their departure the distance between them is 40 km. Click to see solution Solution: Let the speed of the slower train be $x$ km/hr. Then the speed of the faster train is $(x + 10)$ km/hr. In 2 hours they cover $2x$ km and $2(x +10)$km, respectively. Therefore if they didn't meet yet, the whole distance from A to B is $2x + 2(x +10) +40 = 4x +60$ km. However, if they already met and continued to move, the distance would be $2x + 2(x + 10) - 40 = 4x - 20$km. So we get the following equations: $4x + 60 = 300$ $4x = 240$ $x = 60$ or $4x - 20 = 300$ $4x = 320$ $x = 80$ Hence the speed of the slower train is $60$ km/hr or $80$ km/hr and the speed of the faster train is $70$ km/hr or $90$ km/hr.

Problem 24 A bus travels from town A to town B. If the bus's speed is 50 km/hr, it will arrive in town B 42 min later than scheduled. If the bus increases its speed by $\frac{50}{9}$ m/sec, it will arrive in town B 30 min earlier than scheduled. Find: A) The distance between the two towns; B) The bus's scheduled time of arrival in B; C) The speed of the bus when it's on schedule. Click to see solution Solution: First we will determine the speed of the bus following its increase. The speed is increased by $\frac{50}{9}$ m/sec $= \frac{50\cdot60\cdot60}{\frac{9}{1000}}$ km/hr $= 20$ km/hr. Therefore, the new speed is $V = 50 + 20 = 70$ km/hr. If $x$ is the number of hours according to the schedule, then at the speed of 50 km/hr the bus travels from A to B within $(x +\frac{42}{60})$ hr. When the speed of the bus is $V = 70$ km/hr, the travel time is $x - \frac{30}{60}$ hr. Then $50(x +\frac{42}{60}) = 70(x-\frac{30}{60})$ $5(x+\frac{7}{10}) = 7(x-\frac{1}{2})$ $\frac{7}{2} + \frac{7}{2} = 7x -5x$ $2x = 7$ $x = \frac{7}{2}$ hr. So, the bus is scheduled to make the trip in $3$ hr $30$ min. The distance between the two towns is $70(\frac{7}{2} - \frac{1}{2}) = 70\cdot 3 = 210$ km and the scheduled speed is $\frac{210}{\frac{7}{2}} = 60$ km/hr.

Math Word Problems

Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a particular question. For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8.

There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:

• Question : Understand what the question is asking. What operation or operations do you need to use to solve this question? Ask for help to understand the question if you can't do it on your own.
• Estimate : Use an estimation strategy, so you can check your answer for reasonableness in the evaluate step. Try underestimating and overestimating, so you know what range the answer is supposed to be in. Be flexible in rounding numbers if it will make your estimate easier.
• Strategize : Choose a strategy to solve the problem. Will you use mental math, manipulatives, or pencil and paper? Use a strategy that works for you. Save the calculator until the evaluate stage.
• Calculate : Use your strategy to solve the problem.
• Evaluate : Compare your answer to your estimate. If you under and overestimated, is the answer in the correct range. If you rounded up or down, does the answer make sense (e.g. is it a little less or a little more than the estimate). Also check with a calculator.

Most Popular Math Word Problems this Week

Arithmetic Word Problems

• Addition Word Problems One-Step Addition Word Problems Using Single-Digit Numbers One-Step Addition Word Problems Using Two-Digit Numbers
• Subtraction Word Problems Subtraction Facts Word Problems With Differences from 5 to 12
• Multiplication Word Problems One-Step Multiplication Word Problems up to 10 × 10
• Division Word Problems Division Facts Word Problems with Quotients from 5 to 12
• Multi-Step Word Problems Easy Multi-Step Word Problems

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Word problems are one of the first ways we see applied math, and also one of the most anxiety producing math challenges many grade school kids face. This page has a great collection of word problems that provide a gentle introduction to word problems for all four basic math operations. You'll find addition word problems, subtraction word problems, multiplication word problems and division word problems, all starting with simple easy-to-solve questions that build up to more complex skills necessary for many standardized tests. As they progress, you'll also find a mix of operations that require students to figure out which type of story problem they need to solve. And if you need help, check out word problem tricks at the bottom of this page!

Addition Word Problems

20 word problems worksheets.

These introductory word problems for addition are perfect for first grade or second grade applied math.

Subtraction Word Problems

These worksheets include simple word problems for subtraction with smaller quantities. Watch for words like difference and remaining.

Mixed Addition and Subtraction Word Problems

8 word problems worksheets.

This set of worksheets includes a mix of addition and subtraction word problems. Students are required to figured out which operation to apply given the problem context.

Multiplication Word Problems

This is the first set of word problem worksheets the introduces multiplication. These worksheets include only multiplication story problems; see worksheets in the following sections for mixed operations.

Division Word Problems

These division story problems deal with only whole divisions (quotients without remainders.) This is a great first step to recognizing the keywords that signal you are solving a division word problem.

Girl Scout Cookie Division

If you've been working as Troop Cookie Mom (or Dad!) you'll know what kind of math we've been practicing... These worksheets are primarily division word problems that introduce remainders. Pull your tagalongs or your thin mints out of the box and figure out how many remainders you'll be allowed to eat!

Division With Remainders Word Problems

24 word problems worksheets.

The worksheets in this section are made up of story problems using division and involving remainders. These are similar to the Girl Scout problems in the prior section, but with different units.

Mixed Multiplication and Division Word Problems

This worksheets combine basic multiplication and division word problems. The division problems do not include remainders. These worksheets require the students to differentiate between the phrasing of a story problem that requires multiplication versus one that requires division to reach the answer.

Mixed Operation Word Problems

The whole enchilada! These workshes mix addition, subtraction, multiplication and division word problems. These worksheets will test a students ability to choose the correct operation based on the story problem text.

Extra Facts Addition Word Problems

One way to make a word problem slightly more complex is to include extra (but unused) information in the problem text. These worksheets have addition word problems with extra unused facts in the problem.

Extra Facts Subtraction Word Problems

Word problem worksheets for subtraction with extra unused facts in each problem. The worksheets start out with subtraction problems with smaller values and progress through more difficult problems.

Extra Facts Addition and Subtraction Word Problems

Mixed operation addition and subtraction word problem worksheets with extra unused facts in the problems.

Extra Facts Multiplication Word Problems

Word problems for multiplication with extra unused facts in the problem. The worksheets in this set start out with multiplication problems with smaller values and progress through more difficult problems.

Extra Facts Division Word Problems

The worksheets in this section include math word problems for division with extra unused facts in the problem. The quotients in these division problems do not include remainders.

Extra Facts Multiplication and Division Word Problems

16 word problems worksheets.

This is a collection of worksheets with mixed multiplication and division word problems and extra unused facts in the problem. The quotients in these division problems do not include remainders.

Travel Time Word Problems (Customary)

28 word problems worksheets.

These story problems deal with travel time, including determining the travel distance, travel time and speed using miles (customary units). This is a very common class of word problem and specific practice with these worksheets will prepare students when they encounter similar problems on standardized tests.

Travel Time Word Problems (Metric)

Wondering when the train arrives? These story problems deal with travel time, including determining the travel distance, travel time and speed using kilometers (metric units).

Tricks for Solving Word Problems

The math worksheets on this section of the site deal with simple word problems appropriate for primary grades. The simple addition word problems can be introduced very early, in first or second grade depending on student aptitude. Follow those worksheets up with the subtraction word problems once subtraction concept are covered, and then proceed with multiplication and division word problems in the same fashion.

Word problems are often a source of anxiety for students because we tend to introduce math operations in the abstract. Students struggle to apply even elementary operations to word problems unless they have been taught consistently to think about math operations in their day to day routines. Talking with kids regularly about 'how many more do you need' or 'how many do you have left over' or other seemingly simple questions when asked regularly can build that basic number sense that helps enormously when word problems and applied math start to show up.

There are many tricks for solving word problems that can bridge the gap, and they can be helpful tools if students are either struggling with where to start with a problem or just need a way to check their thinking on a particular problem.

Make sure your student reads the entire problem first. It is very easy to start reading a word problem and think after the first sentence or two that 'I know what they're asking for...' and then have the problem take an entirely different turn. Overcoming this early solution bias can be difficult, and it is much better to develop the habit of making a complete pass over the problem before deciding on a path to the solution.

There are particular words that seem to show up in word problems for different operations that can tip you off to what might be the correct operation to apply. These key words aren't a sure-fire way to know what to do with a problem, but they can be a useful starting point.

For example, phrases like 'combined,' 'total,' 'together' or 'sum' are very often signals that the problem is going to involve addition.

Subtraction word problems very often use words such as 'difference,' 'less,' or 'decrease' in their wording. Word problems for younger kids will also use verbs like 'gave' or 'shared' as a stand-in for subtraction.

The key phrases to watch out for multiplication word problems include obvious ones like 'times' and 'product,' but also be on the look out for 'for each' and 'every.'

Learning when to apply division in a word problem can be tricky, especially for younger kids who haven't fully developed a concept of what division can be used for... But that's exactly why division word problems can be so useful! If you see words like 'per' or 'among' in the word problem text, your division radar should be sounding off loud and clear. Pay attention to 'shared among' and make sure students don't confuse this phrasing with a subtraction word problem. That's a clear example of when paying attention to the language is very important.

Draw a Picture!

One key bit of advice, especially for basic word problems, is to encourage students to draw a picture. Most early grade school word problems are basic counting exercises, where you're dealing with quantities or sets that are fairly small. If students can draw a picture of the problem (even using simple representations like squares or circles for the units discussed in the problem), then it can help them visualize exactly what's occurring.

Another useful visualization strategy is to use manipulatives. Paper clips, checkers or other handy objects can stand in place of the problem's subject, and this provides an opportunity to work up other simple examples with different numbers.

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Math Word Problem Worksheets

Read, explore, and solve over 1000 math word problems based on addition, subtraction, multiplication, division, fraction, decimal, ratio and more. These word problems help children hone their reading and analytical skills; understand the real-life application of math operations and other math topics. Print our exclusive colorful theme-based worksheets for a fun-filled teaching experience! Use the answer key provided below each worksheet to assist children in verifying their solutions.

List of Word Problem Worksheets

Explore the word problem worksheets in detail.

Addition Word Problems

Have 'total' fun by adding up a wide range of addends displayed in these worksheets! Simple real-life scenarios form the basis of these addition word problem worksheets.

Subtraction Word Problems

Learning can be a huge 'take away'! Find the difference between the numbers provided in each subtraction word problem. Large number subtraction up to six-digits can also be found here.

Addition and Subtraction Word Problems

Bring on 'A' game with our addition and subtraction word problems! Read, analyze, and solve real-life scenarios based on adding and subtracting numbers as required.

Multiplication Word Problems

Get 'product'ive with over 100 highly engaging multiplication word problems! Find the product and use the answer key to verify your solution. Free worksheets are also available.

Division Word Problems

"Divide and conquer" this huge collection of division word problems. Exclusive worksheets are available for the division problem leaving no remainder and with the remainder.

Fraction Word Problems

Perform various mathematical operations to solve the umpteen number of word problems based on like and unlike fractions, proper and improper fractions, and mixed numbers.

Decimal Word Problems

Let's get to the 'point'! Add, subtract, multiply, and divide to solve these decimal word problems. A wide selection of printable worksheets is available in this section. Use the answer key to verify your answers.

Ratio Word problems

Double up your success ratio with these sets of word problems, which cover a multitude of topics like express in the ratio, reducing the ratio, part-to-part ratio, part-to-whole ratio and more.

Venn Diagram Word Problems - Two Sets

Help your children improve their data analysis skills with these well-researched Venn diagram word problem worksheets. Find the union, intersection, complement and difference of two sets.

Venn Diagram Word Problems - Three Sets

These Venn diagram word problems provide ample practice in real-life application of Venn diagram involving three sets. The worksheets containing the universal set are also included.

Equation Word Problems

The printable worksheets here feature exercises consisting of one-step, two-step and multi-step equation word problems involving fractions, decimals and integers. MCQs to test the knowledge acquired have also been included.

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Math Word Problems

Word problems (or story problems) allow kids to apply what they've learned in math class to real-world situations.  Word problems build higher-order thinking, critical problem-solving, and reasoning skills.

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Addition and Subtraction Mixed

Multiplication.

Word problems where students use reasoning and critical thinking skill to solve each problem.

Mixed word problems (stories) for skills working on subtraction,addition, fractions and more.

A full index of all math worksheets on this site.

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1st Grade Math Word Problems Worksheets

Grade 1 word problems.

These grade 1 word problem worksheets relate first grade math concepts to the real world. The word problems cover addition, subtraction, time, money, fractions and lengths.

We encourage students to think about the problems carefully by:

• providing a number of mixed word problem worksheets;
• sometimes including irrelevant data within word problems.

Addition word problems

Single digit addition

Addition with sums 50 or less

3 or more numbers added together

Subtraction word problems

Subtracting single digit numbers

Subtracting numbers under 50

Mixed addition and subtraction word problems

Add / subtract word problems with mostly single digit numbers

Add / subtract word problems with numbers under 50

Time word problems

Time and elapsed time problems (whole hours)

Money word problems

Counting money (coins only)

Measurement word problems

Combining and comparing lengths (inches)

Combining and comparing lengths (cm)

Fraction word problems

Write the fraction from the story (parts of whole, parts of group)

Mixed word problems

Addition, subtraction, money, time, fractions and length word problems mixed  

Sample Grade 1 Word Problem Worksheet

More word problem worksheets

Explore all of our math word problem worksheets , from kindergarten through grade 5.

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Solving Word Questions

With LOTS of examples!

In Algebra we often have word questions like:

Example: Sam and Alex play tennis.

On the weekend Sam played 4 more games than Alex did, and together they played 12 games.

How many games did Alex play?

How do we solve them?

The trick is to break the solution into two parts:

Turn the English into Algebra.

Then use Algebra to solve.

Turning English into Algebra

To turn the English into Algebra it helps to:

• Read the whole thing first
• Do a sketch if possible
• Assign letters for the values
• Find or work out formulas

You should also write down what is actually being asked for , so you know where you are going and when you have arrived!

Also look for key words:

Thinking Clearly

Some wording can be tricky, making it hard to think "the right way around", such as:

Example: Sam has 2 dollars less than Alex. How do we write this as an equation?

• Let S = dollars Sam has
• Let A = dollars Alex has

Now ... is that: S − 2 = A

or should it be: S = A − 2

or should it be: S = 2 − A

The correct answer is S = A − 2

( S − 2 = A is a common mistake, as the question is written "Sam ... 2 less ... Alex")

Example: on our street there are twice as many dogs as cats. How do we write this as an equation?

• Let D = number of dogs
• Let C = number of cats

Now ... is that: 2D = C

or should it be: D = 2C

Think carefully now!

The correct answer is D = 2C

( 2D = C is a common mistake, as the question is written "twice ... dogs ... cats")

Let's start with a really simple example so we see how it's done:

Example: A rectangular garden is 12m by 5m, what is its area ?

Turn the English into Algebra:

• Use w for width of rectangle: w = 12m
• Use h for height of rectangle: h = 5m

Formula for Area of a Rectangle : A = w × h

We are being asked for the Area.

A = w × h = 12 × 5 = 60 m 2

The area is 60 square meters .

Now let's try the example from the top of the page:

Example: Sam and Alex play Tennis. On the weekend Sam played 4 more games than Alex did, and together they played 12 games. How many games did Alex play?

• Use S for how many games Sam played
• Use A for how many games Alex played

We know that Sam played 4 more games than Alex, so: S = A + 4

And we know that together they played 12 games: S + A = 12

We are being asked for how many games Alex played: A

Which means that Alex played 4 games of tennis.

Check: Sam played 4 more games than Alex, so Sam played 8 games. Together they played 8 + 4 = 12 games. Yes!

A slightly harder example:

Example: Alex and Sam also build tables. Together they make 10 tables in 12 days. Alex working alone can make 10 in 30 days. How long would it take Sam working alone to make 10 tables?

• Use a for Alex's work rate
• Use s for Sam's work rate

12 days of Alex and Sam is 10 tables, so: 12a + 12s = 10

30 days of Alex alone is also 10 tables: 30a = 10

We are being asked how long it would take Sam to make 10 tables.

30a = 10 , so Alex's rate (tables per day) is: a = 10/30 = 1/3

Which means that Sam's rate is half a table a day (faster than Alex!)

So 10 tables would take Sam just 20 days.

Should Sam be paid more I wonder?

And another "substitution" example:

Example: Jenna is training hard to qualify for the National Games. She has a regular weekly routine, training for five hours a day on some days and 3 hours a day on the other days. She trains altogether 27 hours in a seven day week. On how many days does she train for five hours?

• The number of "5 hour" days: d
• The number of "3 hour" days: e

We know there are seven days in the week, so: d + e = 7

And she trains 27 hours in a week, with d 5 hour days and e 3 hour days: 5d + 3e = 27

We are being asked for how many days she trains for 5 hours: d

The number of "5 hour" days is 3

Check : She trains for 5 hours on 3 days a week, so she must train for 3 hours a day on the other 4 days of the week.

3 × 5 hours = 15 hours, plus 4 × 3 hours = 12 hours gives a total of 27 hours

Some examples from Geometry:

Example: A circle has an area of 12 mm 2 , what is its radius?

• Use A for Area: A = 12 mm 2
• Use r for radius

And the formula for Area is: A = π r 2

We are being asked for the radius.

We need to rearrange the formula to find the area

Example: A cube has a volume of 125 mm 3 , what is its surface area?

Make a quick sketch:

• Use V for Volume
• Use A for Area
• Use s for side length of cube
• Volume of a cube: V = s 3
• Surface area of a cube: A = 6s 2

We are being asked for the surface area.

First work out s using the volume formula:

Now we can calculate surface area:

An example about Money:

Example: Joel works at the local pizza parlor. When he works overtime he earns 1¼ times the normal rate. One week Joel worked for 40 hours at the normal rate of pay and also worked 12 hours overtime. If Joel earned $660 altogether in that week, what is his normal rate of pay?

• Joel's normal rate of pay: $N per hour
• Joel works for 40 hours at $N per hour = $40N
• When Joel does overtime he earns 1¼ times the normal rate = $1.25N per hour
• Joel works for 12 hours at $1.25N per hour = $(12 × 1¼N) = $15N
• And together he earned $660, so:

$40N + $(12 × 1¼N) = $660

We are being asked for Joel's normal rate of pay $N.

So Joel’s normal rate of pay is $12 per hour

Joel’s normal rate of pay is $12 per hour, so his overtime rate is 1¼ × $12 per hour = $15 per hour. So his normal pay of 40 × $12 = $480, plus his overtime pay of 12 × $15 = $180 gives us a total of $660

More about Money, with these two examples involving Compound Interest

Example: Alex puts $2000 in the bank at an annual compound interest of 11%. How much will it be worth in 3 years?

This is the compound interest formula:

So we will use these letters:

• Present Value PV = $2,000
• Interest Rate (as a decimal): r = 0.11
• Number of Periods: n = 3
• Future Value (the value we want): FV

We are being asked for the Future Value: FV

Example: Roger deposited $1,000 into a savings account. The money earned interest compounded annually at the same rate. After nine years Roger's deposit has grown to $1,551.33 What was the annual rate of interest for the savings account?

The compound interest formula:

• Present Value PV = $1,000
• Interest Rate (the value we want): r
• Number of Periods: n = 9
• Future Value: FV = $1,551.33

We are being asked for the Interest Rate: r

So the annual rate of interest is 5%

Check : $1,000 × (1.05) 9 = $1,000 × 1.55133 = $1,551.33

And an example of a Ratio question:

Example: At the start of the year the ratio of boys to girls in a class is 2 : 1 But now, half a year later, four boys have left the class and there are two new girls. The ratio of boys to girls is now 4 : 3 How many students are there altogether now?

• Number of boys now: b
• Number of girls now: g

The current ratio is 4 : 3

Which can be rearranged to 3b = 4g

At the start of the year there was (b + 4) boys and (g − 2) girls, and the ratio was 2 : 1

b + 4 g − 2 = 2 1

Which can be rearranged to b + 4 = 2(g − 2)

We are being asked for how many students there are altogether now: b + g

There are 12 girls !

And 3b = 4g , so b = 4g/3 = 4 × 12 / 3 = 16 , so there are 16 boys

So there are now 12 girls and 16 boys in the class, making 28 students altogether .

There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1

And now for some Quadratic Equations :

Example: The product of two consecutive even integers is 168. What are the integers?

Consecutive means one after the other. And they are even , so they could be 2 and 4, or 4 and 6, etc.

We will call the smaller integer n , and so the larger integer must be n+2

And we are told the product (what we get after multiplying) is 168, so we know:

n(n + 2) = 168

We are being asked for the integers

That is a Quadratic Equation , and there are many ways to solve it. Using the Quadratic Equation Solver we get −14 and 12.

Check −14: −14(−14 + 2) = (−14)×(−12) = 168 YES

Check 12: 12(12 + 2) = 12×14 = 168 YES

So there are two solutions: −14 and −12 is one, 12 and 14 is the other.

Note: we could have also tried "guess and check":

• We could try, say, n=10: 10(12) = 120 NO (too small)
• Next we could try n=12: 12(14) = 168 YES

But unless we remember that multiplying two negatives make a positive we might overlook the other solution of (−14)×(−12).

Example: You are an Architect. Your client wants a room twice as long as it is wide. They also want a 3m wide veranda along the long side. Your client has 56 square meters of beautiful marble tiles to cover the whole area. What should the length of the room be?

Let's first make a sketch so we get things right!:

• the length of the room: L
• the width of the room: W
• the total Area including veranda: A
• the width of the room is half its length: W = ½L
• the total area is the (room width + 3) times the length: A = (W+3) × L = 56

We are being asked for the length of the room: L

This is a quadratic equation , there are many ways to solve it, this time let's use factoring :

And so L = 8 or −14

There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!

So the length of the room is 8 m

L = 8, so W = ½L = 4

So the area of the rectangle = (W+3) × L = 7 × 8 = 56

There we are ...

... I hope these examples will help you get the idea of how to handle word questions. Now how about some practice?

Word Problems Activities

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

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Addition Word Problems

Adding One by Making a Model Game

Treat yourself to an immersive learning experience with our 'Adding One by Making a Model' game.

Adding Within 5 by Making a Model Game

Add more arrows to your child’s math quiver by adding within 5 by making a model.

Add within 5: Summer Word Problems Worksheet

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

Add within 5: Halloween Word Problems Worksheet

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

Subtraction Word Problems

Solve Subtraction Scenarios Game

Apply your knowledge to solve subtraction scenarios.

Word Problems: Subtracting One Game

Sharpen your math skills with the 'Word Problems: Subtracting One' game.

Subtract within 5: Summer Word Problems Worksheet

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

Subtract within 5: Halloween Word Problems Worksheet

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

Multiplication Word Problems

Solve the Word Problems Related to Multiplication Game

Unearth the wisdom of mathematics by learning to solve word problems related to multiplication.

Solve Word Problems on Decimal Multiplication Game

Kids must solve word problems on decimal multiplication to practice decimals.

Complete the Word Problem for Equal Groups Worksheet

Help your child revise multiplication by solving word problems for equal groups.

Complete the Word Problem for Arrays Worksheet

Learners must complete the word problems for arrays to enhance their math skills.

Division Word Problems

Word Problems on How many Tens Game

Learn to solve world problems on 'How many Tens' with this game.

Solve Word Problems on Division Game

Learn to solve math problems by solving word problems on division.

Use Multiplication to Solve Division Word Problems Worksheet

Boost your ability to use multiplication to solve division word problems by printing this worksheet.

Solving Problems on Division Worksheet

Put your skills to the test by practicing to solve problems on division.

Fraction Word Problems

Solve the Word Problems on Fraction Addition Game

Have your own math-themed party by learning how to solve the word problems on fraction addition.

Solve the Word Problems on Fraction Subtraction Game

Add more arrows to your child’s math quiver by solving word problems on fraction subtraction.

Find Numerator to Have the Same Amount Worksheet

Be on your way to become a mathematician by finding the numerator to have the same amount.

Apply Fractions to Compare Worksheet

Combine math learning with adventure by applying fractions to compare.

All Word Problems Resources

Model and Add (Within 10) Game

Unearth the wisdom of mathematics by learning how to model and add (within 10).

Word Problems: Subtracting Within 10 Game

Enjoy the marvel of math-multiverse by practicing to solve word problems on subtracting within 10.

Add within 5: Christmas Word Problems Worksheet

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

Subtract within 5: Christmas Word Problems Worksheet

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

Solve Word Problems using Division Game

Apply your knowledge to solve word problems using division.

Solve Word Problems on Fraction-Whole Number Multiplication Game

Apply your knowledge to solve word problems on fraction-whole number multiplication.

Interpret Multiplication Scenarios

Engage in solving multiplication scenarios with these fun worksheets about the properties of 0 and 1!

Divide 2-digit Numbers by 1-digit Numbers: Summer Word Problems Worksheet

A summer-themed worksheet for students to practice dividing 2-digit numbers by 1-digit numbers.

Solve 'Add To' Scenarios Game

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

Solve 'Take Apart' Scenarios Game

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

Word Problems on Adding Fractions & Mixed Numbers Worksheet

Become a mathematician by practicing word problems on adding fractions & mixed numbers.

Add within 5: Shopping Word Problems Worksheet

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

Solve Comparison Word Problems Game

Unearth the wisdom of mathematics by learning how to solve comparison word problems.

Word Problems on Addition of Fractions Game

Use your fraction skills to solve word problems on addition of fractions.

Subtract within 5: Shopping Word Problems Worksheet

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

Make a Model to Multiply Worksheet

Put your skills to the test by practicing to make a model to multiply.

Solve 'Put Together' Scenarios Game

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

Subtraction Scenario Game

Take a look at subtraction scenarios with this game.

Divide 2-digit Numbers by 1-digit Numbers: Halloween Word Problems Worksheet

Halloween-themed worksheet to enhance skills in dividing 2-digit numbers by 1-digit numbers.

Adding Fractions & Mixed Numbers Word Problems Worksheet

Help your child solve word problems on adding fractions & mixed numbers.

Find the Number of Groups Game

Find the number of groups to practice division.

Word Problems on Subtraction of Fractions Game

Have your own math-themed party by learning how to solve word problems on subtraction of fractions.

Add within 5: Travel Word Problems Worksheet

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

Subtract within 5: Travel Word Problems Worksheet

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

Solve 'Add To' Word Problems Game

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

Take Away Scenario Game

Use your subtraction skills to solve 'Take Away' scenarios.

Multiply by Making a Model Worksheet

Pack your math practice time with fun by multiplying by making a model.

Divide 2-digit Numbers by 1-digit Numbers: Christmas Word Problems Worksheet

Christmas-themed worksheet to practice dividing 2-digit numbers by 1-digit numbers through word problems.

Your one stop solution for all grade learning needs.

• Inspiration

Word problems

Here is a list of all of the skills that cover word problems! These skills are organized by grade, and you can move your mouse over any skill name to preview the skill. To start practicing, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as you improve!

Here is a list of all of the skills that cover word problems! To start practicing, just click on any link.

Pre-K skills

• V.8 Addition word problems with pictures - sums up to 5
• W.8 Addition word problems with pictures - sums up to 10
• X.7 Subtraction word problems with pictures - numbers up to 5
• Y.7 Subtraction word problems with pictures - numbers up to 10

Kindergarten skills

• Q.1 Build cube trains to solve addition word problems - sums up to 5
• Q.2 Addition word problems with pictures - sums up to 5
• Q.3 Write addition sentences for word problems with pictures - sums up to 5
• Q.4 Addition word problems - sums up to 5
• Q.5 Model and write addition sentences for word problems - sums up to 5
• U.1 Build cube trains to solve addition word problems - sums up to 10
• U.2 Addition word problems with pictures - sums up to 10
• U.3 Write addition sentences for word problems with pictures - sums up to 10
• U.4 Addition word problems - sums up to 10
• U.5 Model and write addition sentences for word problems - sums up to 10
• V.4 Subtraction sentences up to 5 - what does the cube train show?
• X.1 Subtraction word problems with pictures - numbers up to 5
• X.2 Write subtraction sentences for word problems with pictures - up to 5
• X.3 Use cube trains to solve subtraction word problems - up to 5
• X.4 Subtraction word problems - numbers up to 5
• X.5 Model and write subtraction sentences for word problems - up to 5
• Y.4 Subtraction sentences up to 10 - what does the cube train show?
• AA.1 Subtraction word problems with pictures - numbers up to 10
• AA.2 Write subtraction sentences for word problems with pictures - up to 10
• AA.3 Use cube trains to solve subtraction word problems - up to 10
• AA.4 Subtraction word problems - numbers up to 10
• AA.5 Model and write subtraction sentences for word problems - up to 10
• CC.1 Addition and subtraction word problems with pictures
• CC.2 Use cube trains to solve addition and subtraction word problems - up to 10
• CC.3 Addition and subtraction word problems
• CC.4 Model and write addition and subtraction sentences for word problems

First-grade skills

• C.6 Skip-counting patterns - with tables
• H.1 Addition word problems with pictures - sums up to 10
• H.2 Write addition sentences for word problems with pictures - sums up to 10
• H.3 Build cube trains to solve addition word problems - sums up to 10
• H.4 Addition word problems - sums up to 10
• H.5 Model and write addition sentences for word problems - sums up to 10
• H.6 Addition sentences for word problems - sums up to 10
• I.5 Subtraction sentences up to 10: what does the cube train show?
• L.1 Subtraction word problems with pictures - up to 10
• L.2 Write subtraction sentences for word problems with pictures - up to 10
• L.3 Use cube trains to solve subtraction word problems - up to 10
• L.4 Subtraction word problems - up to 10
• L.5 Model and write subtraction sentences for word problems - up to 10
• L.6 Subtraction sentences for "take apart" word problems - up to 10
• L.7 Subtraction sentences for word problems - up to 10
• N.1 Comparison word problems up to 10: how many more?
• N.2 Subtraction sentences for comparison word problems up to 10: how many more?
• N.3 Comparison word problems up to 10: how many fewer?
• N.4 Subtraction sentences for comparison word problems up to 10: how many fewer?
• N.5 Comparison word problems up to 10: how many more or fewer?
• N.6 Subtraction sentences for comparison word problems up to 10: how many more or fewer?
• N.7 Comparison word problems up to 10: what is the larger amount?
• N.8 Comparison word problems up to 10: what is the smaller amount?
• N.9 Comparison word problems up to 10
• O.1 Addition and subtraction word problems with pictures - up to 10
• O.2 Use cube trains to solve addition and subtraction word problems - up to 10
• O.3 Word problems with unknown sums and differences - up to 10
• O.4 Addition and subtraction sentences for word problems - up to 10
• O.5 Word problems with change unknown - up to 10
• O.6 Word problems with start unknown - up to 10
• O.7 Word problems with one addend unknown - up to 10
• O.8 Word problems with both addends unknown - up to 10
• O.9 Word problems involving addition and subtraction - up to 10
• O.10 Match word problems to addition and subtraction sentences - up to 10
• R.1 Addition word problems with models - sums up to 20
• R.2 Addition word problems - sums up to 20
• R.3 Addition sentences for word problems - sums up to 20
• R.4 Add three numbers - word problems
• U. New! Subtraction word problems with models - up to 20
• U.1 Subtraction word problems - up to 20
• U.2 Subtraction sentences for word problems - up to 20
• W.1 Comparison word problems up to 20: how many more or fewer?
• W.2 Comparison word problems up to 20: what is the larger amount?
• W.3 Comparison word problems up to 20: what is the smaller amount?
• W.4 Comparison word problems up to 20: part 1
• W.5 Comparison word problems up to 20: part 2
• X. New! Word problems with sum or difference unknown - up to 20
• X. New! Word problems with change unknown - up to 20
• X. New! Word problems with start unknown - up to 20
• X.1 Word problems with one addend unknown - up to 20
• X.2 Word problems with both addends unknown - up to 20
• X.3 Use models to solve word problems involving addition and subtraction - up to 20
• X.4 Word problems involving addition and subtraction without comparisons - up to 20
• X. New! Word problems involving addition and subtraction - up to 20
• X.5 Addition and subtraction sentences for word problems - up to 20
• X.6 Match word problems to addition and subtraction sentences - up to 20
• BB.4 Compare numbers up to 100: word problems
• DD.13 Addition word problems - one-digit plus two-digit numbers
• DD.14 Addition sentences for word problems - one-digit plus two-digit numbers
• EE.11 Customary units of length: word problems
• EE.13 Metric units of length: word problems
• FF.7 Time and clocks: word problems
• HH.8 Money - word problems

Second-grade skills

• B.5 Greatest and least - word problems - up to 100
• B.6 Greatest and least - word problems - up to 1,000
• C.6 Skip-counting stories
• C.10 Skip-counting puzzles
• G.4 Addition word problems - sums to 20
• G.5 Addition sentences for word problems - sums to 20
• G.10 Addition word problems - three one-digit numbers
• G.12 Addition word problems - four or more one-digit numbers
• I.3 Subtraction word problems - up to 20
• I.4 Subtraction sentences for word problems - up to 20
• K.1 Comparison word problems - up to 20
• K.2 Use models to solve addition and subtraction word problems - up to 20
• K.3 Addition and subtraction word problems - up to 20
• K.4 Match word problems to addition and subtraction sentences - up to 20
• K.5 Two-step addition and subtraction word problems - up to 20
• K.6 Solve word problems using guess-and-check - up to 20
• L.16 Guess the number
• N.8 Addition word problems - up to two digits
• N.16 Addition word problems - three numbers up to two digits each
• N.19 Addition word problems - four numbers up to two digits each
• P.10 Subtraction word problems - up to two digits
• R. New! Use models to solve addition and subtraction word problems - up to 100
• R.1 Addition and subtraction word problems - up to 100
• R.2 Two-step addition and subtraction word problems - up to 100
• T.5 Addition word problems - up to three digits
• V.6 Subtraction word problems - up to three digits
• W.4 Addition and subtraction word problems - up to 1,000
• X.6 Solve word problems using repeated addition - sums to 25
• AA.14 Making change
• BB.2 Add money up to $1: word problems
• BB.4 Subtract money up to $1: word problems
• BB.6 Add and subtract money up to $1: word problems
• GG.6 Compare lengths: customary units
• GG.7 Customary units of length: word problems
• HH.4 Compare lengths: metric units
• HH.5 Metric units of length: word problems

Third-grade skills

• A.6 Place value word problems
• A.7 Guess the number
• B.5 Ordering puzzles
• D.3 Estimate sums by rounding: word problems
• E.3 Estimate differences by rounding: word problems
• F.3 Estimate sums and differences: word problems
• G.7 Add two numbers up to three digits: word problems
• G.12 Add three numbers up to three digits each: word problems
• H.7 Subtract numbers up to three digits: word problems
• I.3 Add two numbers up to four digits: word problems
• I.7 Add three numbers up to four digits each: word problems
• J.3 Subtract two numbers up to four digits: word problems
• K.6 Addition and subtraction word problems
• K.7 Age puzzles
• K.8 Find two numbers based on sum and difference
• M.3 Skip-counting puzzles
• S.1 Use equal groups and arrays to solve multiplication word problems
• S.2 Multiplication word problems with factors up to 5
• S.3 Use strip models to solve multiplication word problems
• S.4 Multiplication word problems with factors up to 10
• S.5 Multiplication word problems with factors up to 5: find the missing number
• S.6 Multiplication word problems with factors up to 10: find the missing number
• S.7 Compare numbers using multiplication: word problems
• T.7 Multiply one-digit numbers by two-digit numbers: word problems
• T.9 Multiply three numbers: word problems
• Y.1 Use equal groups to solve division word problems
• Y.2 Use arrays to solve division word problems
• Y.3 Use equal groups and arrays to solve division word problems
• Y.4 Division word problems
• Z.6 Multiplication and division word problems
• AA.4 Addition, subtraction, multiplication, and division word problems
• AA.5 Find two numbers based on sum, difference, product, and quotient
• BB.1 Two-step addition and subtraction word problems
• BB.2 Two-step multiplication and division word problems
• BB.3 Two-step mixed operation word problems
• BB.4 Two-step word problems: identify reasonable answers
• CC.5 Write equations with unknown numbers to represent word problems: multiplication and division only
• CC.6 Write equations with unknown numbers to represent word problems
• FF.1 Unit fractions: modeling word problems
• FF.2 Unit fractions: word problems
• FF.3 Fractions of a whole: modeling word problems
• FF.4 Fractions of a whole: word problems
• FF.5 Fractions of a group: word problems
• KK.5 Compare fractions in recipes
• MM.12 Find the area of rectangles: word problems
• MM.13 Find the missing side length of a rectangle: word problems
• NN.6 Perimeter: word problems
• OO.1 Find the area, perimeter, or side length: word problems
• SS.3 Find the end time: word problems
• SS.4 Find the elapsed time: word problems
• SS.5 Find start and end times: two-step word problems
• UU.6 Measurement word problems
• WW.6 Making change
• WW.10 Add money amounts - word problems

Fourth-grade skills

• A.9 Place value word problems
• B.5 Find the order
• C.5 Rounding puzzles
• D.2 Estimate sums: word problems
• D.4 Add two multi-digit numbers: word problems
• E.2 Estimate differences: word problems
• E.4 Subtract two multi-digit numbers: word problems
• F.8 Compare numbers using multiplication: word problems
• F.9 Comparison word problems: addition or multiplication?
• G.2 Divisibility rules: word problems
• H.4 Estimate products word problems: identify reasonable answers
• H.10 Multiply 1-digit numbers by 2-digit numbers: word problems
• H.11 Multiply 1-digit numbers by 2-digit numbers: multi-step word problems
• H.17 Multiply 1-digit numbers by 3-digit or 4-digit numbers: word problems
• H.18 Multiply 1-digit numbers by 3-digit or 4-digit numbers: multi-step word problems
• I.3 Multiply two multiples of ten: word problems
• I.5 Estimate products: word problems
• I.11 Multiply a 2-digit number by a 2-digit number: word problems
• I.12 Multiply a 2-digit number by a 2-digit number: multi-step word problems
• J.2 Division facts to 10: word problems
• J.4 Division facts to 12: word problems
• L.1 Divide numbers ending in zeros by 1-digit numbers: word problems
• L.2 Divide 2-digit numbers by 1-digit numbers: interpret remainders
• L.3 Divide 2-digit numbers by 1-digit numbers: word problems
• L.4 Divide larger numbers by 1-digit numbers: interpret remainders
• L.5 Divide larger numbers by 1-digit numbers: word problems
• M.2 Estimate sums, differences, products, and quotients: word problems
• M.5 Addition, subtraction, multiplication, and division word problems
• M.7 Find two numbers based on sum and difference
• M.9 Find two numbers based on sum, difference, product, and quotient
• M.11 Write equations to represent word problems
• M.13 Use equations to solve addition and subtraction word problems
• N.1 Multi-step addition and subtraction word problems
• N.2 Multi-step word problems with strip diagrams
• N.3 Use strip diagrams to represent and solve multi-step word problems
• N.4 Multi-step word problems
• N.5 Multi-step word problems involving remainders
• N.6 Multi-step word problems: identify reasonable answers
• N.7 Word problems with extra or missing information
• N.8 Solve word problems using guess-and-check
• O.7 Number patterns: word problems
• P.1 Fractions of a whole: word problems
• P.2 Fractions of a group: word problems
• T.4 Add and subtract fractions with like denominators: word problems
• T.5 Add and subtract fractions with like denominators in recipes
• T.12 Add and subtract mixed numbers with like denominators in recipes
• T.13 Add and subtract mixed numbers with like denominators: word problems
• U.7 Add and subtract fractions with unlike denominators: word problems
• V.6 Multiply unit fractions by whole numbers: word problems
• W.7 Multiply fractions by whole numbers: word problems
• W.10 Multiply fractions and mixed numbers by whole numbers in recipes
• W.13 Fractions of a number: word problems
• Z.7 Add and subtract decimals: word problems
• Z.10 Add 3 or more decimals: word problems
• Z.13 Solve decimal problems using diagrams
• AA.5 Find the change, price, or amount paid
• AA.8 Multi-step word problems with money: addition and subtraction only
• AA.9 Multi-step word problems with money
• CC.5 Elapsed time: word problems
• CC.6 Find start and end times: multi-step word problems
• FF.1 Measurement word problems
• FF.2 Measurement word problems with fractions
• HH.8 Relationship between area and perimeter
• HH.9 Area and perimeter: word problems
• HH.10 Rectangles: relationship between perimeter and area word problems

Fifth-grade skills

• B.2 Estimate sums and differences: word problems
• B.4 Add and subtract whole numbers: word problems
• D.3 Multiply numbers ending in zeros: word problems
• D.6 Estimate products: word problems
• D.8 Multiply by 1-digit numbers: word problems
• D.13 Multiply by 2-digit numbers: word problems
• E.3 Divide numbers ending in zeros: word problems
• E.7 Divide by 1-digit numbers: interpret remainders
• E.8 Divide multi-digit numbers by 1-digit numbers: word problems
• E.12 Divide 2-digit and 3-digit numbers by 2-digit numbers: word problems
• E.14 Divide 4-digit numbers by 2-digit numbers: word problems
• F.5 Divisibility rules: word problems
• G.2 Add, subtract, multiply, and divide whole numbers: word problems
• I.1 Write numerical expressions for word problems
• I.2 Multi-step word problems
• I.3 Multi-step word problems involving remainders
• I.4 Multi-step word problems: identify reasonable answers
• L.7 Add and subtract fractions with unlike denominators: word problems
• L.9 Add 3 or more fractions: word problems
• M.6 Add and subtract mixed numbers: word problems
• M.7 Add and subtract fractions and mixed numbers in recipes
• O.3 Multiply fractions by whole numbers: word problems
• O.6 Fractions of a number: word problems
• P.2 Multiply two fractions: word problems
• R.7 Multiplication with mixed numbers: word problems
• R.8 Multiply fractions and mixed numbers in recipes
• V.2 Add, subtract, multiply, and divide fractions and mixed numbers: word problems
• X.6 Compare, order, and round decimals: word problems
• AA.6 Add and subtract decimals: word problems
• CC.8 Multiply decimals and whole numbers: word problems
• FF.7 Division with decimal quotients: word problems
• GG.2 Add, subtract, multiply, and divide decimals: word problems
• HH.2 Add and subtract money: word problems
• HH.3 Add and subtract money: multi-step word problems
• HH.5 Multiply money amounts: word problems
• HH.6 Multiply money amounts: multi-step word problems
• HH.8 Divide money amounts: word problems
• HH.11 Find the number of each type of coin
• II.10 Multi-step problems with customary unit conversions
• JJ.8 Multi-step problems with metric unit conversions
• JJ.9 Multi-step problems with customary or metric unit conversions
• KK.5 Number patterns: word problems
• MM.2 Write variable expressions: word problems
• MM.4 Write variable equations: word problems
• TT.7 Area and perimeter: word problems
• UU.4 Volume of rectangular prisms made of unit cubes: word problems
• UU.6 Volume of cubes and rectangular prisms: word problems
• UU.7 Compare volumes and dimensions of rectangular prisms: word problems
• VV.1 Income and payroll taxes: understanding pay stubs
• VV.2 Income and payroll taxes: word problems
• VV.3 Sales and property taxes: word problems
• VV.9 Reading financial records
• VV.10 Keeping financial records

Sixth-grade skills

• A.2 Add and subtract whole numbers: word problems
• B.2 Multiply whole numbers: word problems
• B.4 Multiply numbers ending in zeros: word problems
• C.3 Divide numbers ending in zeros: word problems
• E.2 Add, subtract, multiply, or divide two whole numbers: word problems
• E.3 Estimate to solve word problems
• E.4 Multi-step word problems
• E.5 Multi-step word problems: identify reasonable answers
• F.10 GCF and LCM: word problems
• H.2 Add and subtract decimals: word problems
• H.3 Add and subtract money amounts: word problems
• I.6 Divide decimals by whole numbers: word problems
• I.11 Multiply and divide decimals: word problems
• J.2 Add, subtract, multiply, or divide two decimals: word problems
• K.2 Add and subtract fractions with like denominators: word problems
• K.4 Add and subtract fractions with unlike denominators: word problems
• K.7 Add and subtract mixed numbers: word problems
• L.3 Multiply fractions by whole numbers: word problems
• L.7 Multiply fractions: word problems
• L.14 Multiply mixed numbers: word problems
• M.5 Divide fractions by whole numbers in recipes
• M.12 Divide fractions and mixed numbers: word problems
• N.2 Add, subtract, multiply, or divide two fractions: word problems
• O.10 Absolute value and integers: word problems
• P.8 Add and subtract integers: word problems
• Q.6 Compare and order rational numbers: word problems
• S.3 Write a ratio: word problems
• S.8 Equivalent ratios: word problems
• S.11 Calculate speed, distance, or time: word problems
• S.12 Ratios and rates: complete a table and make a graph
• S.13 Use tape diagrams to solve ratio word problems
• S.14 Compare ratios: word problems
• S.15 Compare rates: word problems
• S.16 Ratios and rates: word problems
• S.19 Scale drawings: word problems
• T.3 Identify proportional relationships by graphing
• T.4 Interpret graphs of proportional relationships
• U.5 Convert between percents, fractions, and decimals: word problems
• U.7 Compare percents and fractions: word problems
• V.5 Percents of numbers: word problems
• V.8 Find what percent one number is of another: word problems
• V.11 Solve percent word problems
• W.10 Compare temperatures above and below zero
• X.7 Percents - calculate tax, tip, mark-up, and more
• Y.3 Write variable expressions: word problems
• Y.7 Evaluate variable expressions: word problems
• AA.13 Solve one-step addition and subtraction equations: word problems
• AA.14 Solve one-step multiplication and division equations: word problems
• AA.15 Write a one-step equation: word problems
• AA.16 Solve one-step equations: word problems
• AA.17 Which word problem matches the one-step equation?
• BB.4 Write and graph inequalities: word problems
• CC.2 Identify independent and dependent variables in tables and graphs
• CC.4 Identify independent and dependent variables: word problems
• CC.6 Find a value using two-variable equations: word problems
• CC.7 Solve word problems by finding two-variable equations
• CC.13 Graph a two-variable equation
• CC.14 Interpret a graph: word problems
• GG.17 Area of quadrilaterals and triangles: word problems
• HH.3 Volume of cubes and rectangular prisms: word problems
• JJ.10 Interpret measures of center and variability
• KK.1 Counting principle
• LL.1 Compare checking accounts

Seventh-grade skills

• A.6 Quantities that combine to zero: word problems
• B.14 Add and subtract integers: word problems
• D.2 Add and subtract decimals: word problems
• D.4 Multiply decimals and whole numbers: word problems
• D.6 Divide decimals by whole numbers: word problems
• D.9 Add, subtract, multiply, and divide decimals: word problems
• E.4 GCF and LCM: word problems
• F.1 Understanding fractions: word problems
• F.4 Fractions: word problems with graphs and tables
• F.7 Compare fractions: word problems
• G.2 Add and subtract fractions: word problems
• G.4 Add and subtract mixed numbers: word problems
• G.10 Multiply fractions and mixed numbers: word problems
• G.14 Divide fractions and mixed numbers: word problems
• G.16 Add, subtract, multiply, and divide fractions and mixed numbers: word problems
• I.6 Identify quotients of rational numbers: word problems
• I.11 Multi-step word problems with positive rational numbers
• L.4 Equivalent ratios: word problems
• L.7 Compare ratios: word problems
• L.8 Compare rates: word problems
• L.10 Do the ratios form a proportion: word problems
• L.12 Solve proportions: word problems
• L.13 Estimate population size using proportions
• N.1 Find the constant of proportionality from a table
• N.2 Write equations for proportional relationships from tables
• N.3 Identify proportional relationships by graphing
• N.4 Find the constant of proportionality from a graph
• N.5 Write equations for proportional relationships from graphs
• N.10 Interpret graphs of proportional relationships
• N.11 Write and solve equations for proportional relationships
• O.7 Percents of numbers: word problems
• O.9 Solve percent equations: word problems
• O.11 Percent of change: word problems
• O.12 Percent of change: find the original amount word problems
• O.13 Percent error: word problems
• P.1 Add, subtract, multiply, and divide money amounts: word problems
• P.8 Find the percent: tax, discount, and more
• P.10 Multi-step problems with percents
• R.3 Write variable expressions: word problems
• S.14 Identify equivalent linear expressions: word problems
• T.11 Choose two-step equations: word problems
• T.12 Solve two-step equations: word problems
• U.6 One-step inequalities: word problems
• V.5 Sequences: word problems
• X.1 Identify independent and dependent variables
• X.8 Interpret a graph: word problems
• BB.4 Area and perimeter: word problems
• BB.7 Circles: word problems
• CC.6 Volume of cubes and rectangular prisms: word problems
• DD.2 Scale drawings: word problems
• DD.3 Scale drawings: scale factor word problems
• HH. New! Populations and samples
• HH.9 Make inferences from multiple samples
• HH.10 Compare populations using measures of center and spread
• II.4 Experimental probability
• II.10 Find the number of outcomes: word problems

Eighth-grade skills

• A.6 Add and subtract integers: word problems
• B.7 Add and subtract rational numbers: word problems
• B.10 Multiply and divide rational numbers: word problems
• B.14 Multi-step word problems
• G.2 Solve proportions: word problems
• G.3 Estimate population size using proportions
• G.4 Scale drawings: word problems
• G.5 Scale drawings: scale factor word problems
• H.4 Find what percent one number is of another: word problems
• H.7 Percents of numbers: word problems
• H.11 Percent of change: word problems
• H.12 Percent of change: find the original amount word problems
• I.6 Find the percent: tax, discount, and more
• I.8 Multi-step problems with percents
• K.4 Write variable expressions: word problems
• L.9 Identify equivalent linear expressions: word problems
• M.10 Solve one-step and two-step equations: word problems
• M.14 Solve equations with variables on both sides: word problems
• T.5 Pythagorean theorem: word problems
• V.3 Area and perimeter: word problems
• V.5 Circles: word problems
• X.1 Find the constant of proportionality from a table
• X.2 Write equations for proportional relationships from tables
• X.3 Identify proportional relationships by graphing
• X.4 Find the constant of proportionality from a graph
• X.5 Write equations for proportional relationships from graphs
• X.8 Identify proportional relationships: word problems
• X.9 Graph proportional relationships and find the slope
• X.10 Interpret graphs of proportional relationships
• X.11 Write and solve equations for proportional relationships
• X.12 Compare proportional relationships represented in different ways
• BB.3 Identify independent and dependent variables
• CC.4 Interpret points on the graph of a linear function
• CC.6 Interpret the slope and y-intercept of a linear function
• CC.10 Write linear functions: word problems
• FF.5 Sequences: word problems
• GG.3 Solve a system of equations by graphing: word problems
• GG.9 Solve a system of equations using substitution: word problems
• GG.11 Solve a system of equations using elimination: word problems
• GG.13 Solve a system of equations using any method: word problems
• II.10 Interpret lines of best fit: word problems
• JJ.3 Experimental probability
• JJ.10 Counting principle

Algebra 1 skills

• C.9 Solve one-step and two-step linear equations: word problems
• C.11 Consecutive integer problems
• C.16 Solve linear equations with variables on both sides: word problems
• D.1 Area and perimeter: word problems
• E.1 Scale drawings: word problems
• E.5 Multi-step problems with unit conversions
• E.6 Rate of travel: word problems
• E.7 Weighted averages: word problems
• M.3 Identify independent and dependent variables
• N.4 Evaluate a linear function from its graph: word problems
• N.5 Interpret the slope and y-intercept of a linear function
• N.8 Domain and range of linear functions: word problems
• O.3 Solve a system of equations by graphing: word problems
• O.9 Solve a system of equations using substitution: word problems
• O.11 Solve a system of equations using elimination: word problems
• O.13 Solve a system of equations using augmented matrices: word problems
• O.15 Solve a system of equations using any method: word problems
• P.5 Write two-variable inequalities: word problems
• V.7 Write exponential functions: word problems
• V.8 Exponential growth and decay: word problems
• Z.7 Solve quadratic equations: word problems
• AA.5 Write linear and exponential functions: word problems
• JJ.6 Interpret lines of best fit: word problems
• JJ.8 Interpret regression lines
• JJ.9 Analyze a regression line of a data set
• KK.6 Identify independent and dependent events
• KK.8 Counting principle
• KK.9 Permutations

Geometry skills

• A.1 Identify hypotheses and conclusions
• A.2 Counterexamples
• P.1 Pythagorean theorem
• V.9 Calculate density, mass, and volume
• AA.5 Counting principle
• AA.6 Permutations
• AA.15 Find probabilities using the addition rule

Algebra 2 skills

• B.3 Solve linear equations: word problems
• E.3 Solve a system of equations by graphing: word problems
• E.7 Solve a system of equations using substitution: word problems
• E.9 Solve a system of equations using elimination: word problems
• E.11 Solve a system of equations using any method: word problems
• F.1 Write two-variable linear inequalities: word problems
• O.7 Solve quadratic equations: word problems
• Z.3 Write exponential functions: word problems
• Z.9 Exponential growth and decay: word problems
• CC.4 Compound interest: word problems
• CC.5 Continuously compounded interest: word problems
• OO.2 Counting principle
• OO.4 Find probabilities using combinations and permutations
• OO.5 Find probabilities using two-way frequency tables
• OO.10 Find conditional probabilities using two-way frequency tables
• OO.11 Find probabilities using the addition rule
• PP.8 Write the probability distribution for a game of chance
• PP.9 Expected values for a game of chance
• PP.10 Choose the better bet
• QQ.1 Find probabilities using the binomial distribution
• RR.5 Find confidence intervals for population means
• RR.6 Find confidence intervals for population proportions
• RR.7 Interpret confidence intervals for population means
• RR.8 Experiment design
• RR.9 Analyze the results of an experiment using simulations
• SS.5 Interpret regression lines
• SS.6 Analyze a regression line of a data set
• TT.19 Solve a system of equations using augmented matrices: word problems

Precalculus skills

• D.9 Solve quadratic equations: word problems
• K.5 Exponential growth and decay: word problems
• K.6 Compound interest: word problems
• N.2 Solve a system of equations by graphing: word problems
• N.5 Solve a system of equations using substitution: word problems
• N.7 Solve a system of equations using elimination: word problems
• N.9 Solve a system of equations using augmented matrices: word problems
• CC.3 Find probabilities using combinations and permutations
• CC.4 Find probabilities using two-way frequency tables
• CC.8 Find conditional probabilities using two-way frequency tables
• CC.9 Find probabilities using the addition rule
• DD.8 Write the probability distribution for a game of chance
• DD.9 Expected values for a game of chance
• DD.10 Choose the better bet
• EE.1 Find probabilities using the binomial distribution
• EE.2 Mean, variance, and standard deviation of binomial distributions
• EE.9 Use normal distributions to approximate binomial distributions
• FF.5 Find confidence intervals for population means
• FF.6 Find confidence intervals for population proportions
• FF.7 Interpret confidence intervals for population means
• FF.8 Experiment design
• FF.9 Analyze the results of an experiment using simulations
• GG.5 Interpret regression lines
• GG.6 Analyze a regression line of a data set
• GG.7 Analyze a regression line using statistics of a data set

How do you solve word problems in math?

Master word problems with eight simple steps from a math tutor!

Author Amber Watkins

Published April 2024

• Key takeaways
• Students who struggle with reading, tend to struggle with understanding and solving word problems. So the best way to solve word problems in math is to become a better reader!
• Mastery of word problems relies on your child’s knowledge of keywords for word problems in math and knowing what to do with them.
• There are 8 simple steps each child can use to solve word problems- let’s go over these together.

Table of contents

• How to solve word problems

Lesson credits

As a tutor who has seen countless math worksheets in almost every grade – I’ll tell you this: every child is going to encounter word problems in math. The key to mastery lies in how you solve them! So then, how do you solve word problems in math?

In this guide, I’ll share eight steps to solving word problems in math.

How to solve word problems in math in 8 steps

Step 1: read the word problem aloud.

For a child to understand a word problem, it needs to be read with accuracy and fluency! That is why, when I tutor children with word problems, I always emphasize the importance of reading properly.

Mastering step 1 looks like this:

• Allow your child to read the word problem aloud to you. 
• Don’t let your child skip over or mispronounce any words. 
• If necessary, model how to read the word problem, then allow your child to read it again. Only after the word problem is read accurately, should you move on to step 2.

Step 2: Highlight the keywords in the word problem

The keywords for word problems in math indicate what math action should be taken. Teach your child to highlight or underline the keywords in every word problem. 

Here are some of the most common keywords in math word problems: 

• Subtraction words – less than, minus, take away
• Addition words – more than, altogether, plus, perimeter
• Multiplication words – Each, per person, per item, times, area 
• Division words – divided by, into
• Total words – in all, total, altogether

Let’s practice. Read the following word problem with your child and help them highlight or underline the main keyword, then decide which math action should be taken.

Michael has ten baseball cards. James has four baseball cards less than Michael. How many total baseball cards does James have? 

The words “less than” are the keywords and they tell us to use subtraction .

Step 3: Make math symbols above keywords to decode the word problem

As I help students with word problems, I write math symbols and numbers above the keywords. This helps them to understand what the word problem is asking.

Let’s practice. Observe what I write over the keywords in the following word problem and think about how you would create a math sentence using them:

Step 4: Create a math sentence to represent the word problem

Using the previous example, let’s write a math sentence. Looking at the math symbols and numbers written above the word problem, our math sentence should be: 10 – 5 = 5 ! 

Each time you practice a word problem with your child, highlight keywords and write the math symbols above them. Then have your child create a math sentence to solve. 

Step 5: Draw a picture to help illustrate the word problem

Pictures can be very helpful for problems that are more difficult to understand. They also are extremely helpful when the word problem involves calculating time , comparing fractions , or measurements . 

Step 6: Always show your work

Help your child get into the habit of always showing their work. As a tutor, I’ve found many reasons why having students show their work is helpful:

• By showing their work, they are writing the math steps repeatedly, which aids in memory
• If they make any mistakes they can track where they happened
• Their teacher can assess how much they understand by reviewing their work
• They can participate in class discussions about their work

Step 7: When solving word problems, make sure there is always a word in your answer!

If the word problem asks: How many peaches did Lisa buy? Your child’s answer should be: Lisa bought 10 peaches .

If the word problem asks: How far did Kyle run? Your child’s answer should be: Kyle ran 20 miles .

So how do you solve a word problem in math?

Together we reviewed the eight simple steps to solve word problems. These steps included identifying keywords for word problems in math, drawing pictures, and learning to explain our answers. 

Is your child ready to put these new skills to the test? Check out the best math app for some fun math word problem practice.

Parents, sign up for a DoodleMath subscription and see your child become a math wizard!

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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Teaching Math Word Problem Key Words (Free Cheat Sheet)

Published: November 20, 2023

Contributor: Jeannette Tuionetoa

Disclosure: This post may contain affiliate links, meaning if you decide to make a purchase via my links, I may earn a commission at no additional cost to you. See my disclosure for more info.

Tackling word problems in math can be challenging for kids to learn. We called them story problems when I was in school. If your kids are learning math key words so they can solve word problems, they you’ll find these free cheat sheets and worksheets for word problem key words helpful. 

Math Word Problem Key Words

There is no doubt that mathematical operations using words are difficult for kids. They go from counting numbers to doing math equations with numbers.

Then all of a sudden… there are words, just words . All of a sudden algebraic expressions and mathematical operations are POOF – words.

The lack of numbers and shift in mindset can completely throw off a lot of students. If kids have difficulty with reading, then that is yet another struggle for kids as they try to learn basic problems in math.

Teaching students about challenging math keywords just got easier!

We have a FREE download of the Math Word Problems Keywords Cheat Sheet available for you at the bottom of this post. Keep scrolling to get your copy today!

Why do some kids struggle with word problems?

A key proponent in different operations in math is learning the key words that prompt kids to understand which operation skill they need to use to solve the problem.

This means that they should master regular math problems first and be able to read with comprehension. You will shortly find that if these two skills aren’t somewhat mastered first, then word problems will become an issue.

Many times math is a subject best taught in sequential order. If one step is missed, then the future steps falter. This is much like how it is when teaching word problems.

The best thing for your children is for them to first:

• Be able to read well.
• Understand math concepts and phrases.
• Know to not rush, but focus on math key words, identify relevant information, and understand the text.
• Get to know the keywords for math word problems

What are keywords for math word problems?

Key words in mathematical word operations are the words or phrases that will signal or show a student which type of math operation to choose in order to solve the math word problem.

The keywords for math word problems used in operations are a strategy that helps the math problem make sense and draw connections to how it can be answered.

Basically, when using key words, students must decipher whether they need to solve the math equation via addition, subtraction, multiplication, or division.

What are the common keywords for math word problems?

Thankfully, there are math key words that our children can learn that help them work through their word problems. They are prompts that point them in the right direction.

Just like a different language needs words translated for comprehension, students translate the words… into math .

Keywords for Math Word Problems

Learning these math keywords will help with problem solving:

Addition Math Key Words:

• increased by
• larger than
• in addition to
• how much in all

Subtraction Math Key Words:

• how many more
• how many less
• shorter than
• smaller than

Key Words for Multiplication Word Problems:

• multiplied by
• double/twice

Key Words used for Division Word Problems:

• equal group
• how many in each

You can print off a free math key words cheat sheet that has the above math key words for word problems and add it to your homeschool binder . Find the download link at the bottom of this post. 

How can we help kids learn keywords for solving numberless word problems?

Teach kids steps for solving word problems until it becomes a habit or they get comfortable with the steps. First, they can look for the important information and write those down. (Read the problem carefully). Next, kids need to define or find the variables in the math equation.

From the keywords, kids can now determine what math operation to use. Translate the words to math. Then, kids can solve the math equation. This is where the skills of solving numbered equations are important.

Finally, students have to put their answers in the form of a word sentence. NOTE: Many times kids think after solving the equation they are done. However, the key to making sure they understand that word problems need word answers.

Different Strategies to Familiarize Keywords in Word Operations

You can use some of these keywords for math word problems as vocabulary words in your homeschool.

Students can display subtraction, addition, multiplication, and multiplication handy reference posters on a bulletin board in your homeschool area. Students can also just list them on dry erase boards . These are perfect visual reminders for what keywords go with what math word problems.

Your students can also keep their keywords for math word problems with them as they study. They can place the list of keywords in a math folder or in an anchor chart – and then in their math folder.

Kids can keep the keyword poster sets in their math notebooks or keep them in a word problem journal .

Their strategy for learning word problem keywords all depends on how they best absorb information.

Students may do well using a combination of these methods. Either way, all of these different strategies can be used to get them comfortable in identifying the route to solve math word equations.

Math Word Problem Keywords Cheat Sheets & Teaching Aids:

We created a free pdf download Word Problem Key Words Cheat Sheet that you can find at the bottom of this post. It’s great to use as a reference for math word problems.

Word Problem Clue Words

Get a Clue Free Download – Check out these word problem clue word handouts and posters to help your students with word problems. There 5 pages in all that will be handy for your kids in trying to find the correct answer while using the correct operation.

Addition and Subtraction Word Problem Keywords

Subtraction Keywords/Addition Keywords – Until your kids memorize keywords and what they mean, this freebie can help. Grab these simple black and white printable signs. They will help kids look for keywords like larger numbers for subtraction word problems or addition keywords like in addition to . 

Story Problem Key Words

Words to Math – Keywords in math problems are essentially turning words into math. This graphic organizer printable is a quick reference for your students to use with numberless math word problems. Place them in a notebook chart or your homeschool classroom wall as a visual reminder.

Word Problem Key Words Poster

Key Word Posters for Math Problems – Grab these word problem keyword handy reference posters for subtraction, addition, division, and multiplication. Each poster has its specific theme and specific words to solve all problem types. Kids will enjoy having practiced with these math key words posters.

Word Problem Key Words Worksheets

Fun Key Word Sorting Activity – Your kids have now studied some keywords for math word problems helpful for problem solving in mathematical operations. Use this word problem sorting activity to test their knowledge in a fun engaging way. Add this fun activity to your test prep materials.

World Problems Worksheets with Key Words – These word problems worksheets use key phrases to help your students identify the phrases that will help them determine which math operation to use.

Word Problem Key Words for Math

Math word problems are probably the first opportunity students get to understand how math relates to real world situations. The applications can be relevant in their real life experiences like going to the market.

However, the benefit to word problems doesn’t stop there…

With word problems, students develop their higher-order thinking and critical thinking skills.

Different types of word problems guide your students to applying math various math concepts at the same time. They have to know basic number sense, basic algebra skills, and even geometry when they attempt multiplication word problems.

If we do it the right way, kids won’t see word problems as a dreadful experience in math. Understanding word problems is a learning curve and doesn’t come easily to kids.

Identify Learning Gaps

Another important aspect of word problems is that they tell a parent/teacher if a child needs help in areas like reading comprehension or math number operations skills. This type of word math is a great evaluation of your student’s thinking processes.

We can, however, help make it a better experience for them by teaching it the right way.

Free Math Key Words Cheat Sheet Instant Download

You won’t want to miss our free Word Problem Key Words Cheat Sheet PDF download for different ways kids see keywords in various types of problems in mathematics. This math tool is everything your student needs and the perfect resource to reference keywords in math operations.

Includes the keywords that will help your children solve and recognize word problems for:

• Subtraction
• Multiplication

FREE Instant Download

Math Word Problems Keywords Cheat Sheet

Jeannette Tuionetoa

Jeannette is a wife, mother and homeschooling mom. She has been mightily, saved by grace and is grateful for God’s sovereignty throughout her life’s journey. She has a Bachelor in English Education and her MBA. Jeannette is bi-lingual and currently lives in the Tongan Islands of the South Pacific. She posts daily freebies for homeschoolers!

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Our math problem solver that lets you input a wide variety of math math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects.

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Math Word Problem Solutions

Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.

Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 �� b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

Pre-Algebra Solutions

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• Variables, Expressions, and Integers
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• Solving Equations
• Multi-Step Equations and Inequalities
• Ratios, Proportions, and Percents
• Linear Equations and Inequalities

Algebra Solutions

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• Algebra Concepts and Expressions
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• Algebra Concepts and Expressions Review
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Precalculus Solutions

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• Operations on Functions
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• Evaluating Limits
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• Polynomials and Expressions
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Linear Algebra Solutions

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• Introduction to Matrices
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Strategies for Solving Word Problems – Math

It’s one thing to solve a math equation when all of the numbers are given to you but with word problems, when you start adding reading to the mix, that’s when it gets especially tricky.

The simple addition of those words ramps up the difficulty (and sometimes the math anxiety) by about 100!

How can you help your students become confident word problem solvers? By teaching your students to solve word problems in a step by step, organized way, you will give them the tools they need to solve word problems in a much more effective way.

Here are the seven strategies I use to help students solve word problems.

1. read the entire word problem.

Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too.

2. Think About the Word Problem

Students need to ask themselves three questions every time they are faced with a word problem. These questions will help them to set up a plan for solving the problem.

Here are the questions:

A. what exactly is the question.

What is the problem asking? Often times, curriculum writers include extra information in the problem for seemingly no good reason, except maybe to train kids to ignore that extraneous information (grrrr!). Students need to be able to stay focused, ignore those extra details, and find out what the real question is in a particular problem.

B. What do I need in order to find the answer?

Students need to narrow it down, even more, to figure out what is needed to solve the problem, whether it’s adding, subtracting, multiplying, dividing, or some combination of those. They’ll need a general idea of which information will be used (or not used) and what they’ll be doing.

This is where key words become very helpful. When students learn to recognize that certain words mean to add (like in all, altogether, combined ), while others mean to subtract, multiply, or to divide, it helps them decide how to proceed a little better

Here’s a Key Words Chart I like to use for teaching word problems. The handout could be copied at a smaller size and glued into interactive math notebooks. It could be placed in math folders or in binders under the math section if your students use binders.

One year I made huge math signs (addition, subtraction, multiplication, and divide symbols) and wrote the keywords around the symbols. These served as a permanent reminder of keywords for word problems in the classroom.

If you’d like to download this FREE Key Words handout, click here:

C. What information do I already have?

This is where students will focus in on the numbers which will be used to solve the problem.

3. Write on the Word Problem

This step reinforces the thinking which took place in step number two. Students use a pencil or colored pencils to notate information on worksheets (not books of course, unless they’re consumable). There are lots of ways to do this, but here’s what I like to do:

• Circle any numbers you’ll use.
• Lightly cross out any information you don’t need.
• Underline the phrase or sentence which tells exactly what you’ll need to find.

4. Draw a Simple Picture and Label It

Drawing pictures using simple shapes like squares, circles, and rectangles help students visualize problems. Adding numbers or names as labels help too.

For example, if the word problem says that there were five boxes and each box had 4 apples in it, kids can draw five squares with the number four in each square. Instantly, kids can see the answer so much more easily!

5. Estimate the Answer Before Solving

Having a general idea of a ballpark answer for the problem lets students know if their actual answer is reasonable or not. This quick, rough estimate is a good math habit to get into. It helps students really think about their answer’s accuracy when the problem is finally solved.

6. Check Your Work When Done

This strategy goes along with the fifth strategy. One of the phrases I constantly use during math time is, Is your answer reasonable ? I want students to do more than to be number crunchers but to really think about what those numbers mean.

Also, when students get into the habit of checking work, they are more apt to catch careless mistakes, which are often the root of incorrect answers.

7. Practice Word Problems Often

Just like it takes practice to learn to play the clarinet, to dribble a ball in soccer, and to draw realistically, it takes practice to become a master word problem solver.

When students practice word problems, often several things happen. Word problems become less scary (no, really).

They start to notice similarities in types of problems and are able to more quickly understand how to solve them. They will gain confidence even when dealing with new types of word problems, knowing that they have successfully solved many word problems in the past.

If you’re looking for some word problem task cards, I have quite a few of them for 3rd – 5th graders.

This 3rd grade math task cards bundle has word problems in almost every one of its 30 task card sets..

There are also specific sets that are dedicated to word problems and two-step word problems too. I love these because there’s a task card set for every standard.

CLICK HERE to take a look at 3rd grade:

This 4th Grade Math Task Cards Bundle also has lots of word problems in almost every single of its 30 task card sets. These cards are perfect for centers, whole class, and for one on one.

CLICK HERE to see 4th grade:

This 5th Grade Math Task Cards Bundle is also loaded with word problems to give your students focused practice.

CLICK HERE to take a look at 5th grade:

Want to try a FREE set of math task cards to see what you think?

3rd Grade: Rounding Whole Numbers Task Cards

4th Grade: Convert Fractions and Decimals Task Cards

5th Grade: Read, Write, and Compare Decimals Task Cards

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Problem Solving and Mathematical Discovery Courseware

This Courseware aims to develop students’ mathematical problem-solving abilities. Students will work through 160 problems from a wide spectrum of mathematical topics. 

Course information 

Students will learn several general problem-solving techniques and then explicitly examine problem solving as it relates to some specific mathematics topics.

The following units are covered in this course.

• Equations, Algebra, and Functions
• Number Theory
• Problem Solving Wrap-Up

The problems presented in this course use material that extend no further than the material covered in the Advanced Functions and Pre-Calculus Courseware. Most of the problems discussed would be accessible to strong and motivated students in Grades 10 and 11. 

Typical lesson structure

In each lesson, a short narration introduces the theme, which is a strategy or topic area. Then, individual problems are presented using narrated slideshows. Each lesson also contains a written solution to one of the problems without narration, to illustrate how written solutions might differ in context and layout.  

An Alternative Format has also been provided within each lesson. This page is a text version of the narrated slideshows. 

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PERCENT WORD PROBLEMS * Task Cards * for Middle School Math

Subject: Mathematics

Age range: 10 - 12

Resource type: Worksheet/Activity

Last updated

21 August 2024

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Dive into the world of percents with these exciting Percent Word Problem Task Cards! Designed for 5th and 6th graders, these versatile cards liven up math stations, in-class games, activities, and more. Whether used for homework, early finisher challenges, morning warm-ups, or quick assessments, these cards keep practice engaging. Each card presents a real-life scenario involving percents, prompting students to apply their understanding of finding a part, a whole, or the percent itself. Answer sheets allow students to show their work, while answer keys for teachers ensure quick assessment. Make percent practice meaningful and fun with these interactive task cards!

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I’ve spent a year using AI and it’s solving all of the wrong problems

“I want AI to do my laundry and dishes so that I can do art and writing, not for AI to do my art and writing so that I can do my laundry and dishes.” — Joanna Maciejewska

I’m old enough to remember when AI was an 80’s Sci-Fi trope. That’s not to brag, but it does afford me some small mental vestibule to hide in as I escape the overwhelming onslaught of actualized AI we face on a day-to-day basis.

From your word processors to your web browsers and even the digital assistants on your favorite devices, AI is taking over. There are no AI orphanages because almost every company is falling over itself to adopt some sort of generative tool or chatbot into its products and services at an alarming rate.

I should know, I’ve spent the last year and change knee-deep in most of it. I’ve encountered everything from image generators and artificial girlfriends to voice clones and LLMs that mimic lost loved ones . Needless to say, I’m no stranger to this super-software, and nor am I some tin-foil-hat-wearing luddite who’s claiming it’ll all end in tears. Just that much of it is… Bleh. Well, a lot of it is anyway.

Once you’ve gotten that new car scent out of certain services, it’s hard not to feel like this rich in potential tech is going to waste on all the wrong applications. In fact, I’d go as far as to say that most of the things we’re offered as consumers are counterintuitive at best, and pointless at worst.

It’s not all bad 

We’re living in the age of AI, and we should be embracing this new technology at every opportunity. It’s here to simplify our lives, make work easier, and revolutionize the human-computer interface forevermore.

And to be fair, none of that is out of the question. I use generative AI daily, be it through interacting with Meta AI through my Ray-Ban Meta Smart Glasses or linking up with ChatGPT for recipe ideas, watchlist suggestions, and the random answering of any of those previous “I should Google that” questions I have throughout the day.

Virtual assistants have been handed their most invaluable update ever by generative AI — being catapulted to Hollywood levels of performance in a matter of a few short years. It’s also poised to change everything about how we interact with our devices, even if the full realization of that is yet to come.

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We tend to think of computers as boxes with screens attached. Sometimes they're small enough to fit in a pocket or on a wrist, but they all mostly follow the same visual format. However, with the progression of virtual assistants through AI, we could be looking at a seismic shift in how we view and use our devices at a scale not seen since the invention of the mouse.

That's pretty exciting to me, and I'd want it to be for others too. However, after spending more than my fair share of time with various AI models, tools, and services, I think I’m done with AI. Because a lot of everything else attached to it is total bunk.

But there’s plenty of bad 

The upgrade to virtual assistants is only a fraction of the wider generative AI pool — and one of the least divisive elements of it at that. As the AI toolset expands it begins to cover all sorts of creative works that result in highly divisive outcomes.

Thanks to generative AI you can create just about anything. And that’s kind of a problem, creating things is a very human characteristic, and it’s not one we should so freely give up. Especially as concern over disinformation, defamation, and the use of deepfake tech to harass others grows.

Can you trust that an article wasn’t written by ChatGPT ? That an incriminating image you saw online was real? Or that the recording of a familiar and prominent voice wasn’t AI-generated? As models become increasingly sophisticated, you’d be hard-pressed to know for sure.

Even the best can struggle to spot a fake, and even those who know it's a fake can't deny some of the results. The Sony World Photography Awards judges were so impressed with one AI-generated entry that they were willing to grant it an award in the Creative category .

When AI isn’t busy being used to confuse and confound our confidence in reality, it’s crowbarring you away from all manner of human connections. I’m not entirely sure who comes up with the ideas behind what a company’s AI will offer, but who thought “We’ll let the AI handle talking to other humans for us” was a good idea?

From summarizing emails and articles so you don’t have to engage with human ideas directly to replying to texts from loved ones on your behalf, there’s nothing more bleak and depressing than realizing a large portion of generative AI exists as a roadblock between actually engaging with the world around you.

If you want a brief glimpse into the generative AI dystopia, look no further than Google’s recent “Dear Sydney” ad , in which a father harps on about his daughter’s love of running and her idol, American track and field star Sydney McLaughlin-Levrone.

She wants to write a letter to Sydney, telling her how inspiring she is. Instead, potentially because she’s not actually all that inspired, she outsources that task to her dad. Who then seemingly can’t spare ten minutes to sit with his daughter and work it out, and instead outsources it to Google Gemini, which only knows inspiration through its dictionary definition. 

That was meant to be an uplifting commercial. Aspirational even. If that doesn’t highlight the glaring disconnect between the people making these features and the audience they’re trying to pedal them to, I don’t know what will.

We never got to see Sydney receive her AI-generated email. But in a perfect world, it ended up in the spam folder, along with the dozens of other AI-generated spam emails sent to inboxes like mine daily.

I recently saw a post to X by Joanna Maciejewska that hits the nail squarely on the head: “I want AI to do my laundry and dishes so that I can do art and writing, not for AI to do my art and writing so that I can do my laundry and dishes.” 

You know what the biggest problem with pushing all-things-AI is? Wrong direction.I want AI to do my laundry and dishes so that I can do art and writing, not for AI to do my art and writing so that I can do my laundry and dishes. March 29, 2024

We’re building AI tools for everyone to use. Just don’t use them.

Making matters even more confusing is the fact that the people developing these tools don’t seem committed to their use either. Simultaneously tempting users to use them for generating writing, images, video, or music, only to develop other tools that can detect when you’ve used them and scold you for taking them up on their initial offer.

A recent analysis by The Washington Post of a 200K-strong dataset of English-language conversations captured from two ChatGPT-like AI chatbots saw homework help and creative writing at the top of the list of use cases. No wonder OpenAI is hesitant to release its own AI identifier for text . That could cause quite a bit of trouble for ChatGPT subscribers.

These companies know all too well that creating text or media that would be deemed cheating or plagiarism is one of the key selling points of their large language models. There’s a reason you can’t ask ChatGPT to write anything saucy, but it’ll have no issue writing an entire dissertation on the breeding habits of the Red-eyed tree frog.

Beyond a few exceptions, I just do not see the net benefit of generative AI (at least in how it’s presently marketed to us as consumers) as I once did. While it can make our virtual personal assistants more personal, it’s equally impressive at making actual people’s communications and contributions impersonal.

As it stands, we could all do with a little less generative AI in our devices, systems, and platforms. I’ll keep hold of the digital assistants if you don’t mind me imbibing in my share of hypocrisy, but you can take back the rest.

On the one hand, we’re supposed to fully embrace everything arriving with this new wave of generative AI tools. On the other, we’re almost forbidden from using them. The purveyors of AI are speaking to us from both sides of their mouths as we’re told about the benefits of this tech while being scolded for their application — getting ChatGPT to help with your homework? Plagiarism. Creating AI-generated images? Welcome to the wonderful world of fabricating and facilitating disinformation.

At this point, the only thing I truly know for certain is that with every passing month, I’m left looking at my ChatGPT subscription and wondering if this is really the foundation for the next big thing in tech or just a house of cards. 

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Rael Hornby, potentially influenced by far too many LucasArts titles at an early age, once thought he’d grow up to be a mighty pirate. However, after several interventions with close friends and family members, you’re now much more likely to see his name attached to the bylines of tech articles. While not maintaining a double life as an aspiring writer by day and indie game dev by night, you’ll find him sat in a corner somewhere muttering to himself about microtransactions or hunting down promising indie games on Twitter.

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Sail the Seven C’s Voyage Logbook by Robert Bear Instructs Teams on Creative Problem Solving Amid Organizational Storms

Today’s business environment is incredibly fast-moving and complicated, with problems arising left and right, like waves in a storm battering a ship. This can lead to organizations and team members feeling overwhelmed and helpless because they don’t know where and how to start dealing with these problems. Drawing on his more than four decades of experience in teaching, business, art, and the military, Robert E. Bear has authored Sail the Seven Cs Voyage Logbook , a workbook that guides members of corporate teams and other organizations on how to creatively solve problems while supporting each other. 

Written from the standpoint of a sailor, Sail the Seven Cs uses various maritime terminologies and metaphors to drive its points. According to Bear, the book and its forms function as a tool for a team, committee, task force, or a group to work together in a systematic, organized approach that can solve problems of any size. The eBook, which will soon be available on Amazon, also has a section that can help individuals and organizations secure funding for their projects by teaching them how to write grant requests. 

As outlined by the book, the seven Cs are: 

• Conviction , or a problem that one is passionate about solving. This could be an unfair practice at work, increasing productivity, taking care of employees’ interests, or filling a market niche. 
• Courage is the fortitude to step forth and become involved. Courage is the fortress of character that will sustain you through to the success of a positive change. 
• Counsel may involve more than just seeking advice from friends or peers. This also includes advice and services from professionals, such as attorneys or accountants, as well as gathering as much pertinent data as possible within the business. 
• Creativity involves crafting a map of solutions to the problem to pass through the doldrums of apathy and indifference, as well as strategies to overcome the hurricanes of skepticisms and tsunamis of intolerance. 
• Cooperation integrates as many individuals, organizations, and businesses as possible, each having a stake in the outcome of the resolved problem. It also involves leaders being able to properly allocate tasks and responsibilities. 
• Communication must be a multi-directional, fluid process throughout your network, Bear says. Teams must be able to effectively disseminate objectives, articulate ideas, impart information, and share feelings and feedback. 
• Commitment , the final C, maybe the hardest C to navigate. It may entail a return to one or more of the previous Cs for continued buoyancy and not sinking from the onslaught of the monsters of doubt and new problems that have surfaced. 

According to Bear, each team member should have their own copy of Sail the Seven C’s , to ensure that everyone is on the same page. The team should also confirm a time when they can regularly assemble and work on and review each other's efforts and logbooks.  

In addition to the exercises provided by Sail the Seven C’s , Bear also holds half-day and full-day corporate creative problem-solving workshops that reinforce these lessons and provide an even more potent start to an organization’s journey toward positive change. 

Bear recommends teams hold free word association exercises to develop their creative problem-solving skills. This encourages members to not be afraid of voicing ideas that may sound silly at first, because there may be something in there that actually works. As different people have different skills and different knowledge sets, encouraging each member to speak up when they believe they have something to contribute is vital to organizational success. 

Every Problem, Every Step, All in Focus: Learning to Solve Vision-Language Problems With Integrated Attention

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