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20 Effective Math Strategies To Approach Problem-Solving
Katie Keeton
Math strategies for problem-solving help students use a range of approaches to solve many different types of problems. It involves identifying the problem and carrying out a plan of action to find the answer to mathematical problems.
Problem-solving skills are essential to math in the general classroom and real-life. They require logical reasoning and critical thinking skills. Students must be equipped with strategies to help them find solutions to problems.
This article explores mathematical problem solving strategies, logical reasoning and critical thinking skills to help learners with solving math word problems independently in real-life situations.
What are problem-solving strategies?
Problem-solving strategies in math are methods students can use to figure out solutions to math problems. Some problem-solving strategies:
- Draw a model
- Use different approaches
- Check the inverse to make sure the answer is correct
Students need to have a toolkit of math problem-solving strategies at their disposal to provide different ways to approach math problems. This makes it easier to find solutions and understand math better.
Strategies can help guide students to the solution when it is difficult ot know when to start.
The ultimate guide to problem solving techniques
Download these ready-to-go problem solving techniques that every student should know. Includes printable tasks for students including challenges, short explanations for teachers with questioning prompts.
20 Math Strategies For Problem-Solving
Different problem-solving math strategies are required for different parts of the problem. It is unlikely that students will use the same strategy to understand and solve the problem.
Here are 20 strategies to help students develop their problem-solving skills.
Strategies to understand the problem
Strategies that help students understand the problem before solving it helps ensure they understand:
- The context
- What the key information is
- How to form a plan to solve it
Following these steps leads students to the correct solution and makes the math word problem easier .
Here are five strategies to help students understand the content of the problem and identify key information.
1. Read the problem aloud
Read a word problem aloud to help understand it. Hearing the words engages auditory processing. This can make it easier to process and comprehend the context of the situation.
2. Highlight keywords
When keywords are highlighted in a word problem, it helps the student focus on the essential information needed to solve it. Some important keywords help determine which operation is needed. For example, if the word problem asks how many are left, the problem likely requires subtraction. Ensure students highlight the keywords carefully and do not highlight every number or keyword. There is likely irrelevant information in the word problem.
3. Summarize the information
Read the problem aloud, highlight the key information and then summarize the information. Students can do this in their heads or write down a quick summary. Summaries should include only the important information and be in simple terms that help contextualize the problem.
4. Determine the unknown
A common problem that students have when solving a word problem is misunderstanding what they are solving. Determine what the unknown information is before finding the answer. Often, a word problem contains a question where you can find the unknown information you need to solve. For example, in the question ‘How many apples are left?’ students need to find the number of apples left over.
5. Make a plan
Once students understand the context of the word problem, have dentified the important information and determined the unknown, they can make a plan to solve it. The plan will depend on the type of problem. Some problems involve more than one step to solve them as some require more than one answer. Encourage students to make a list of each step they need to take to solve the problem before getting started.
Strategies for solving the problem
1. draw a model or diagram.
Students may find it useful to draw a model, picture, diagram, or other visual aid to help with the problem solving process. It can help to visualize the problem to understand the relationships between the numbers in the problem. In turn, this helps students see the solution.
Similarly, you could draw a model to represent the objects in the problem:
2. Act it out
This particular strategy is applicable at any grade level but is especially helpful in math investigation in elementary school . It involves a physical demonstration or students acting out the problem using movements, concrete resources and math manipulatives . When students act out a problem, they can visualize and contectualize the word problem in another way and secure an understanding of the math concepts. The examples below show how 1st-grade students could “act out” an addition and subtraction problem:
3. Work backwards
Working backwards is a popular problem-solving strategy. It involves starting with a possible solution and deciding what steps to take to arrive at that solution. This strategy can be particularly helpful when students solve math word problems involving multiple steps. They can start at the end and think carefully about each step taken as opposed to jumping to the end of the problem and missing steps in between.
For example,
To solve this problem working backwards, start with the final condition, which is Sam’s grandmother’s age (71) and work backwards to find Sam’s age. Subtract 20 from the grandmother’s age, which is 71. Then, divide the result by 3 to get Sam’s age. 71 – 20 = 51 51 ÷ 3 = 17 Sam is 17 years old.
4. Write a number sentence
When faced with a word problem, encourage students to write a number sentence based on the information. This helps translate the information in the word problem into a math equation or expression, which is more easily solved. It is important to fully understand the context of the word problem and what students need to solve before writing an equation to represent it.
5. Use a formula
Specific formulas help solve many math problems. For example, if a problem asks students to find the area of a rug, they would use the area formula (area = length × width) to solve. Make sure students know the important mathematical formulas they will need in tests and real-life. It can help to display these around the classroom or, for those who need more support, on students’ desks.
Strategies for checking the solution
Once the problem is solved using an appropriate strategy, it is equally important to check the solution to ensure it is correct and makes sense.
There are many strategies to check the solution. The strategy for a specific problem is dependent on the problem type and math content involved.
Here are five strategies to help students check their solutions.
1. Use the Inverse Operation
For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7. As good practice, encourage students to use the inverse operation routinely to check their work.
2. Estimate to check for reasonableness
Once students reach an answer, they can use estimation or rounding to see if the answer is reasonable. Round each number in the equation to a number that’s close and easy to work with, usually a multiple of ten. For example, if the question was 216 ÷ 18 and the quotient was 12, students might round 216 to 200 and round 18 to 20. Then use mental math to solve 200 ÷ 20, which is 10. When the estimate is clear the two numbers are close. This means your answer is reasonable.
3. Plug-In Method
This method is particularly useful for algebraic equations. Specifically when working with variables. To use the plug-in method, students solve the problem as asked and arrive at an answer. They can then plug the answer into the original equation to see if it works. If it does, the answer is correct.
If students use the equation 20m+80=300 to solve this problem and find that m = 11, they can plug that value back into the equation to see if it is correct. 20m + 80 = 300 20 (11) + 80 = 300 220 + 80 = 300 300 = 300 ✓
4. Peer Review
Peer review is a great tool to use at any grade level as it promotes critical thinking and collaboration between students. The reviewers can look at the problem from a different view as they check to see if the problem was solved correctly. Problem solvers receive immediate feedback and the opportunity to discuss their thinking with their peers. This strategy is effective with mixed-ability partners or similar-ability partners. In mixed-ability groups, the partner with stronger skills provides guidance and support to the partner with weaker skills, while reinforcing their own understanding of the content and communication skills. If partners have comparable ability levels and problem-solving skills, they may find that they approach problems differently or have unique insights to offer each other about the problem-solving process.
5. Use a Calculator
A calculator can be introduced at any grade level but may be best for older students who already have a foundational understanding of basic math operations. Provide students with a calculator to allow them to check their solutions independently, accurately, and quickly. Since calculators are so readily available on smartphones and tablets, they allow students to develop practical skills that apply to real-world situations.
Step-by-step problem-solving processes for your classroom
In his book, How to Solve It , published in 1945, mathematician George Polya introduced a 4-step process to solve problems.
Polya’s 4 steps include:
- Understand the problem
- Devise a plan
- Carry out the plan
Today, in the style of George Polya, many problem-solving strategies use various acronyms and steps to help students recall.
Many teachers create posters and anchor charts of their chosen process to display in their classrooms. They can be implemented in any elementary, middle school or high school classroom.
Here are 5 problem-solving strategies to introduce to students and use in the classroom.
How Third Space Learning improves problem-solving
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Former teachers and math experts write all of Third Space Learning’s tutoring lessons. Expertly designed lessons follow a “my turn, follow me, your turn” pedagogy to help students move from guided instruction and problem-solving to independent practice.
Throughout each lesson, tutors ask higher-level thinking questions to promote critical thinking and ensure students are developing a deep understanding of the content and problem-solving skills.
Problem-solving
Educators can use many different strategies to teach problem-solving and help students develop and carry out a plan when solving math problems. Incorporate these math strategies into any math program and use them with a variety of math concepts, from whole numbers and fractions to algebra.
Teaching students how to choose and implement problem-solving strategies helps them develop mathematical reasoning skills and critical thinking they can apply to real-life problem-solving.
READ MORE :
- 8 Common Core math examples
- Tier 3 Interventions: A School Leaders Guide
- Tier 2 Interventions: A School Leaders Guide
- Tier 1 Interventions: A School Leaders Guide
There are many different strategies for problem-solving; Here are 5 problem-solving strategies: • draw a model • act it out • work backwards • write a number sentence • use a formula
Here are 10 strategies for problem-solving: • Read the problem aloud • Highlight keywords • Summarize the information • Determine the unknown • Make a plan • Draw a model • Act it out • Work backwards • Write a number sentence • Use a formula
1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back
Some strategies you can use to solve challenging math problems are: breaking the problem into smaller parts, using diagrams or models, applying logical reasoning, and trying different approaches.
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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?
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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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- Green’s, Stokes’, and the divergence theorems
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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
Copyright © 2005-2024 Math-Drills.com You may use the math worksheets on this website according to our Terms of Use to help students learn math.
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You are on the roof of the physics building, 46.0 m above the ground. Your...
A block is on a frictionless table, on earth. The block accelerates at5.3ms2when a 10...
A 0.450 kg ice puck, moving east with a speed of3.00mshas a head in collision...
A uniform plank of length 2.00 m and mass 30.0 kg is supported by three...
An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope...
A ski tow operates on a 15.0 degrees slope of lenth 300m. The rope moves...
Two blocks with masses 4.00 kg and 8.00 kg are connected by string and slide...
From her bedroom window a girl drops a water-filled balloon to the ground 6.0 m...
A 730-N man stands in the middle of a frozen pond of radius 5.0 m....
A 5.00 kg package slides 1.50 m down a long ramp that is inclined at12.0∘below...
Ropes 3m and 5m in length are fastened to a holiday decoration that is suspended...
A skier of mass 70 kg is pulled up a slope by a motor driven...
A 1.0 kg ball and a 2.0 kg ball are connected by a 1.0-m-long rigid,...
A sled with rider having a combined mass of 120 kg travels over the perfectly...
A 7.00- kg bowling ball moves at 3.00 m/s. How fast must a 2.45- g...
Two point chargesq1=+2.40nC andq2=−6.50nC are 0.100 m apart. Point A is midway between them and...
A block of mass m slides on a horizontal frictionless table with an initial speed...
A space traveler weights 540 N on earth. what will the traveler weigh on another...
A block of mass m=2.20 kg slides down a 30 degree incline which is 3.60...
A weatherman carried an aneroid barometer from the groundfloor to his office atop a tower....
If a negative charge is initially at rest in an electric field, will it move...
A coin with a diameter of 2.40cm is dropped on edge on to a horizontal...
An atomic nucleus initially moving at 420 m/s emits an alpha particle in the direction...
An 80.0-kg skydiver jumps out of a balloon at an altitude of1000 m and opens...
A 0.145 kg baseball pitched at 39.0 m/s is hit on a horizontal line drive...
A 1000 kg safe is 2.0 m above a heavy-duty spring when the rope holding...
A 500 g ball swings in a vertical circle at the end of a1.5-m-long string....
A rifle with a weight of 30 N fires a 5.0 g bullet with a...
The tires of a car make 65 revolutions as the car reduces its speed uniformly...
A 2.0- kg piece of wood slides on the surface. The curved sides are perfectly...
A 292 kg motorcycle is accelerating up along a ramp that is inclined 30.0° above...
A projectile is shot from the edge of a cliff 125 m above ground level...
A lunch tray is being held in one hand, as the drawing illustrates. The mass...
The initial velocity of a car, vi, is 45 km/h in the positivex direction. The...
An Alaskan rescue plane drops a package of emergency rations to a stranded party of...
Raindrops make an angle theta with the vertical when viewed through a moving train window....
A 0.50 kg ball that is tied to the end of a 1.1 m light...
If the coefficient of static friction between your coffeecup and the horizontal dashboard of your...
A car is initially going 50 ft/sec brakes at a constant rate (constant negative acceleration),...
A swimmer is capable of swimming 0.45m/s in still water (a) If sheaim her body...
A block is hung by a string from inside the roof of avan. When the...
A race driver has made a pit stop to refuel. Afterrefueling, he leaves the pit...
A relief airplane is delivering a food package to a group of people stranded on...
The eye of a hurricane passes over Grand Bahama Island. It is moving in a...
An extreme skier, starting from rest, coasts down a mountainthat makes an angle25.0∘with the horizontal....
Four point charges form a square with sides of length d, as shown in the...
In a scene in an action movie, a stuntman jumps from the top of one...
The spring in the figure (a) is compressed by length delta x . It launches...
An airplane propeller is 2.08 m in length (from tip to tip) and has a...
A helicopter carrying dr. evil takes off with a constant upward acceleration of5.0ms2. Secret agent...
A 15.0 kg block is dragged over a rough, horizontal surface by a70.0 N force...
A box is sliding with a speed of 4.50 m/s on a horizontal surface when,...
3.19 Win the Prize. In a carnival booth, you can win a stuffed giraffe if...
A car is stopped at a traffic light. It then travels along a straight road...
a. When the displacement of a mass on a spring is12A, what fraction of the...
At a certain location, wind is blowing steadily at 10 m/s. Determine the mechanical energy...
A jet plane lands with a speed of 100 m/s and can accelerate at a...
In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints...
An antelope moving with constant acceleration covers the distance between two points 70.0 m apart...
A bicycle with 0.80-m-diameter tires is coasting on a level road at 5.6 m/s. A...
The rope and pulley have negligible mass, and the pulley is frictionless. The coefficient of...
A proton with an initial speed of 800,000 m/s is brought to rest by an...
The volume of a cube is increasing at the rate of 1200 cm supmin at...
An airplane starting from airport A flies 300 km east, then 350 km at 30...
To prove: In the following figure, triangles ABC and ADC are congruent. Given: Figure is...
Conduct a formal proof to prove that the diagonals of an isosceles trapezoid are congruent....
The distance between the centers of two circles C1 and C2 is equal to 10...
Segment BC is Tangent to Circle A at Point B. What is the length of...
Find an equation for the surface obtained by rotating the parabola y=x2 about the y-axis.
Find the area of the parallelogram with vertices A(-3, 0), B(-1 , 3), C(5, 2),...
If the atomic radius of lead is 0.175 nm, find the volume of its unit...
At one point in a pipeline the water’s speed is 3.00 m/s and the gauge...
Find the volume of the solid in the first octant bounded by the coordinate planes,...
A paper cup has the shape of a cone with height 10 cm and radius...
A light wave has a 670 nm wavelength in air. Its wavelength in a transparent...
An airplane pilot wishes to fly due west. A wind of 80.0 km/h (about 50...
Find the equation of the sphere centered at (-9, 3, 9) with radius 5. Give...
Determine whether the congruence is true or false. 5≡8 mod 3
Find all whole number solutions of the congruence equation. (2x+1)≡5 mod 4
Determine whether the congruence is true or false. 100≡20 mod 8
I want example of an undefined term and a defined term in geometry and explaining...
Two fair dice are rolled. Let X equal the product of the 2dice. Compute P{X=i}...
Suppose that two defective refrigerators have been included in a shipment of six refrigerators. The...
Based on the Normal model N(100, 16) describing IQ scores, what percent of peoples
The probability density function of the net weight in pounds of a packaged chemical herbicide...
Let X represent the difference between the number of heads and the number of tails...
An urn contains 3 red and 7 black balls. Players A and B withdraw balls...
80% A poll is given, showing are in favor of a new building project. 8...
The probability that the San Jose Sharks will win any given game is 0.3694 based...
Find the value of P(X=7) if X is a binomial random variable with n=8 and...
Find the value of P(X=8) if X is a binomial random variable with n=12 and...
On a 8 question multiple-choice test, where each question has 2 answers, what would be...
If you toss a fair coin 11 times, what is the probability of getting all...
A coffee connoisseur claims that he can distinguish between a cup of instant coffee and...
Two firms V and W consider bidding on a road-building job, which may or may...
Two cards are drawn without replacement from an ordinary deck, find the probability that the...
In August 2012, tropical storm Isaac formed in the Caribbean and was headed for the...
A local bank reviewed its credit card policy with the intention of recalling some of...
The accompanying table gives information on the type of coffee selected by someone purchasing a...
A batch of 500 containers for frozen orange juice contains 5 that are defective. Two...
The probability that an automobile being filled with gasoline also needs an oil change is...
Let the random variable X follow a normal distribution with μ=80 and σ2=100. a. Find...
A card is drawn randomly from a standard 52-card deck. Find the probability of the...
The next number in the series 38, 36, 30, 28, 22 is ?
What is the coefficient of x8y9 in the expansion of (3x+2y)17?
A boat on the ocean is 4 mi from the nearest point on a straight...
How many different ways can you make change for a quarter? (Different arrangements of the...
Seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and...
Approximately 80,000 marriages took place in the state of New York last year. Estimate the...
The probability that a student passes the Probability and Statistics exam is 0.7. (i)Find the...
Customers at a gas station pay with a credit card (A), debit card (B), or...
It is conjectured that an impurity exists in 30% of all drinking wells in a...
Assume that the duration of human pregnancies can be described by a Normal model with...
According to a renowned expert, heavy smokers make up 70% of lung cancer patients. If...
Two cards are drawn successively and without replacement from an ordinary deck of playing cards...
Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L),...
A bag contains 6 red, 4 blue and 8 green marbles. How many marbles of...
A normal distribution has a mean of 50 and a standard deviation of 4. Please...
Seven women and nine men are on the faculty in the mathematics department at a...
An automatic machine in a manufacturing process is operating properly if the lengths of an...
Three cards are drawn without replacement from the 12 face cards (jacks, queens, and kings)...
Among 157 African-American men, the mean systolic blood pressure was 146 mm Hg with a...
A TIRE MANUFACTURER WANTS TO DETERMINE THE INNER DIAMETER OF A CERTAIN GRADE OF TIRE....
Differentiate the three measures of central tendency: ungrouped data.
Find the mean of the following data: 12,10,15,10,16,12,10,15,15,13
A wallet containing four P100 bills, two P200 bills, three P500 bills, and one P1,000...
The number of hours per week that the television is turned on is determined for...
Data was collected for 259 randomly selected 10 minute intervals. For each ten-minute interval, the...
Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in...
A normal distribution has a mean of 80 and a standard deviation of 14. Determine...
True or false: a. All normal distributions are symmetrical b. All normal distributions have a...
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Annual sales, in millions of dollars, for 21 pharmaceutical companies follow. 8408 1374 1872 8879...
The velocity function (in meters per second) is given for a particle moving along a...
Find the area of the parallelogram with vertices A(-3,0) , B(-1,6) , C(8,5) and D(6,-1)
What is the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4),...
The integral represents the volume of a solid. Describe the solid. π∫01(y4−y8)dy a) The integral...
Two components of a minicomputer have the following joint pdf for their useful lifetimes X...
Use the table of values of f(x,y) to estimate the values of fx(3,2), fx(3,2.2), and...
Calculate net price factor and net price. Dollars list price −435.20$ Trade discount rate −26%,15%,5%.
Represent the line segment from P to Q by a vector-valued function and by a...
(x2+2xy−4y2)dx−(x2−8xy−4y2)dy=0
If f is continuous and integral 0 to 9 f(x)dx=4, find integral 0 to 3...
Find the parametric equation of the line through a parallel to ba=[3−4],b=[−78]
Find the velocity and position vectors of a particle that has the given acceleration and...
If we know that the f is continuous and integral 0 to 4f(x)dx=10, compute the...
Integration of (y⋅tanxy)
For the matrix A below, find a nonzero vector in the null space of A...
Find a nonzero vector orthogonal to the plane through the points P, Q, and R....
Suppose that the augmented matrix for a system of linear equations has been reduced by...
Find two unit vectors orthogonal to both (3 , 2, 1) and (- 1, 1,...
What is the area of the parallelogram whose vertices are listed? (0,0), (5,2), (6,4), (11,6)
Using T defined by T(x)=Ax, find a vector x whose image under T is b,...
Use the definition of Ax to write the matrix equation as a vector equation, or...
We need to find the volume of the parallelepiped with only one vertex at the...
List five vectors in Span {v1,v2}. For each vector, show the weights on v1 and...
(1) find the projection of u onto v and (2) find the vector component of...
Find the area of the parallelogram determined by the given vectors u and v. u...
(a) Find the point at which the given lines intersect. r = 2,...
(a) find the transition matrix from B toB′,(b) find the transition matrix fromB′to B,(c) verify...
A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If...
Given the following vector X, find anon zero square marix A such that AX=0; You...
Construct a matrix whose column space contains (1, 1, 5) and (0, 3.1) and whose...
At what point on the paraboloid y=x2+z2 is the tangent plane parallel to the plane...
Label the following statements as being true or false. (a) If V is a vector...
Find the Euclidean distance between u and v and the cosine of the angle between...
Write an equation of the line that passes through (3, 1) and (0, 10)
There are 100 two-bedroom apartments in the apartment building Lynbrook West.. The montly profit (in...
State and prove the linearity property of the Laplace transform by using the definition of...
The analysis of shafts for a compressor is summarized by conformance to specifications. Suppose that...
The Munchies Cereal Company combines a number of components to create a cereal. Oats and...
Movement of a Pendulum A pendulum swings through an angle of 20∘ each second. If...
If sinx+siny=aandcosx+cosy=b then find tan(x−y2)
Find the values of x such that the angle between the vectors (2, 1, -1),...
Find the dimensions of the isosceles triangle of largest area that can be inscribed in...
Suppose that you are headed toward a plateau 50 meters high. If the angle of...
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport....
Find an equation of the plane. The plane through the points (2, 1, 2), (3,...
Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following...
two small spheres spaced 20.0cm apart have equal charges. How many extra electrons must be...
The base of a pyramid covers an area of 13.0 acres (1 acre =43,560 ft2)...
Find out these functions' domain and range. To find the domain in each scenario, identify...
Your bank account pays an interest rate of 8 percent. You are considering buying a...
Whether f is a function from Z to R ifa)f(n)=±n.b)f(n)=n2+1.c)f(n)=1n2−4.
The probability density function of X, the lifetime of a certain type of electronic device...
A sandbag is released by a balloon that is rising vertically at a speed of...
A proton is located in a uniform electric field of2.75×103NCFind:a) the magnitude of the electric...
A rectangular plot of farmland are finite on one facet by a watercourse and on...
A solenoid is designed to produce a magnetic field of 0.0270 T at its center....
I want to find the volume of the solid enclosed by the paraboloidz=2+x2+(y−2)2and the planesz=1,x=−1y=0,andy=4
Let W be the subspace spanned by the u’s, and write y as the sum...
Can u find the point on the planex+2y+3z=13that is closest to the point (1,1,1). You...
A spring of negligible mass stretches 3.00 cm from its relaxed length when a force...
A force of 250 Newtons is applied to a hydraulic jack piston that is 0.01...
Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface...
A credit card contains 16 digits between 0 and 9. However, only 100 million numbers...
Every real number is also a complex number? True of false?
Let F be a fixed 3x2 matrix, and let H be the set of all...
Find a vector a with representation given by the directed line segment AB. Draw AB...
Find A such that the given set is Col A. {[2s+3tr+s−2t4r+s3r−s−t]:r,s,t real}
Find the vector that has the same direction as (6, 2, -3) but is four...
For the matrices (a) find k such that Nul A is a subspace of Rk,...
How many subsets with an odd number of elements does a set with 10 elements...
In how many ways can a set of five letters be selected from the English...
Suppose that f(x) = x/8 for 3 < x < 5. Determine the following probabilities:...
Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to...
Find two vectors parallel to v of the given length. v=PQ→ with P(1,7,1) and Q(0,2,5);...
A dog in an open field runs 12.0 m east and then 28.0 m in...
Can two events with nonzero probabilities be both independent and mutually exclusive? Explain your reasoning.
Use the Intermediate Value Theorem to show that there is a root of the given...
In a fuel economy study, each of 3 race cars is tested using 5 different...
A company has 34 salespeople. A board member at the company asks for a list...
A dresser drawer contains one pair of socks with each of the following colors: blue,...
A restaurant offers a $12 dinner special with seven appetizer options, 12 choices for an...
A professor writes 40 discrete mathematics true/false questions. Of the statements in these questions, 17...
Suppose E(X)=5 and E[X(X–1)]=27.5, find ∈(x2) and the variance.
A Major League baseball diamond has four bases forming a square whose sides measure 90...
Express f(x)=4x3+6x2+7x+2 in term of Legendre Polynomials.
Find a basis for the space of 2×2 diagonal matrices. Basis ={[],[]}
Which of the following expressions are meaningful? Which are meaningless? Explain. a) (a⋅b)⋅c (a⋅b)⋅c has...
Vectors V1 and V2 are different vectors with lengths V1 and V2 respectively. Find the...
Find an equation for the plane containing the two (parallel) lines v1=(0,1,−2)+t(2,3,−1) and v2=(2,−1,0)+t(2,3,−1).
Find, correct to the nearest degree, the three angles of the triangle with the given...
Find the vector, not with determinants, but by using properties of cross products. (i+j)×(i−j)
Find the curve’s unit tangent vector. Also, find the length of the indicated portion of...
Construct a 4×3 matrix with rank 1
Find x such that the matrix is equal to its inverse.A=[7x−8−7]
Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3...
Write in words how to read each of the following out loud.a.{x∈R′∣0<x<1}b.{x∈R∣x≤0orx⇒1}c.{n∈Z∣nisafactorof6}d.{n∈Z⋅∣nisafactorof6}
Pets Plus and Pet Planet are having a sale on the same aquarium. At Pets...
Find the average value of F(x, y, z) over the given region. F(x,y,z)=x2+9 over the...
Find the trace of the plane in the given coordinate plane. 3x−9y+4z=5,yz
Determine the level of measurement of the variable. Favorite color Choose the correct level of...
How wide is the chasm between what men and women earn in the workplace? According...
Write an algebraic expression for: 6 more than a number c.
Please, can u convert 3.16 (6 repeating) to a fraction.
Evaluate the expression. P(8, 3)
In a poker hand consisting of 5 cards, find the probability of holding 3 aces.
Give an expression that generates all angles coterminal with each angle. Let n represent any...
An ideal Otto cycle has a compression ratio of 10.5, takes in air at 90...
A piece of wire 10 m long is cut into two pieces. One piece is...
Put the following equation of a line into slope intercept form, simplifying all fractions 3x+3y=24
Find the point on the hyperbola xy = 8 that is closest to the point...
Water is pumped from a lower reservoir to a higher reservoir by a pump that...
A piston–cylinder device initially contains 0.07m3 of nitrogen gas at 130 kPa and 180∘. The...
Write an algebraic expression for each word phrase. 4 more than p
A club has 25 members. a) How many ways are there to choose four members...
For each of the sets below, determine whether {2} is an element of that set....
Which expression has both 8 and n as factors?
If repetitions are not permitted (a) how many 3 digit number can be formed from...
To determine the sum of all multiples of 3 between 1 and 1000
On average, there are 3 accidents per month at one intersection. We need to find...
One number is 2 more than 3 times another. Their sum is 22. Find the...
The PMF for a flash drive with X (GB) of memory that was purchased is...
An airplane needs to reach a velocity of 203.0 km/h to takeoff. On a 2000...
A racquetball strikes a wall with a speed of 30 m/s and rebounds with a...
Assuming that the random variable x has a cumulative distribution function,F(x)={0,x<00.25x,0≤x<51,5≤xDetermine the following:a)p(x<2.8)b)p(x>1.5)c)p(x<−z)d)p(x>b)
At t = 0 a grinding wheel has an angular velocity of 24.0 rad/s. It...
How many 3/4's are in 1?
You’re driving down the highway late one night at 20 m/s when a deer steps...
Table salt contains 39.33 g of sodium per 100 g of salt. The U.S. Food...
The constant-pressure heat capacity of a sample of a perfect gas was found to vary...
Coffee is draining from a conical filter into a cylindrical coffepot at the rate of...
Cart is driven by a large propeller or fan, which can accelerate or decelerate the...
A vending machine dispenses coffee into an eight-ounce cup. The amounts of coffee dispensed into...
On an essentially frictionless, horizontal ice rink, a skater moving at 3.0 m/s encounters a...
The gage pressure in a liquid at a depth of 3 m is read to...
Consider a cylindrical specimen of a steel alloy 8.5 mm (0.33 in.) in diameter and...
Calculate the total kinetic energy, in Btu, of an object with a mass of 10...
A 0.500-kg mass on a spring has velocity as a function of time given by...
An Australian emu is running due north in a straight line at a speed of...
Another pitfall cited is expecting to improve the overall performance of a computer by improving...
You throw a glob of putty straight up toward the ceiling, which is 3.60 m...
A 0.150-kg frame, when suspended from a coil spring, stretches the spring 0.070 m. A...
A batch of 140 semiconductor chips is inspected by choosing a sample of 5 chips....
A rock climber stands on top of a 50-m-high cliff overhanging a pool of water....
A tank whose bottom is a mirror is filled with water to a depth of...
Two sites are being considered for wind power generation. In the first site, the wind...
0.250 kilogram of water at75.0∘Care contained in a tiny, inert beaker. How much ice, at...
Two boats start together and race across a 60-km-wide lake and back. Boat A goes...
A roller coaster moves 200 ft horizontally and the rises 135 ft at an angle...
A tow truck drags a stalled car along a road. The chain makes an angle...
Consider the curve created by2x2+3y2–4xy=36(a) Show thatdydx=2y−2x3y−2x(b) Calculate the slope of the line perpendicular to...
The current entering the positive terminal of a device is i(t)=6e−2t mA and the voltage...
The fastest measured pitched baseball left the pitcher’s hand at a speed of 45.0 m/s....
Calculate the total potential energy, in Btu, of an object that is 20 ft below...
A chemist in an imaginary universe, where electrons have a different charge than they do...
When jumping, a flea reaches a takeoff speed of 1.0 m/s over a distance of...
Determine the energy required to accelerate a 1300-kg car from 10 to 60 km/h on...
The deepest point in the ocean is 11 km below sea level, deeper than MT....
A golfer imparts a speed of 30.3 m/s to a ball, and it travels the...
Calculate the frequency of each of the following wavelengths of electromagnetic radiation. A) 632.8 nm...
Prove that there is a positive integer that equals the sum of the positive integers...
A hurricane wind blows across a 6.00 m×15.0 m flat roof at a speed of...
If an electron and a proton are expelled at the same time,2.0×10−10mapart (a typical atomic...
The speed of sound in air at 20 C is 344 m/s. (a) What is...
Which of the following functions f has a removable discontinuity at a? If the discontinuity...
A uniform steel bar swings from a pivot at one end with a period of...
A wind farm generator uses a two-bladed propellermounted on a pylon at a height of...
A copper calorimeter can with mass 0.100 kg contains 0.160 kgof water and 0.018 kg...
Jones figures that the total number of thousands of miles that a used auto can...
Assign a binary code in some orderly manner to the 52 playingcards. Use the minimum...
A copper pot with mass 0.500 kg contains 0.170 kg of water ata temperature of...
Ea for a certain biological reaction is 50 kJ/mol, by what factor ( how many...
When a person stands on tiptoe (a strenuous position), the position of the foot is...
A solution was prepared by dissolving 1210 mg of K3Fe(CN)6 (329.2 g/mol) in sufficient waterto...
A 58-kg skier is going down a slope oriented 35 degree abovethe horizontal. The area...
The mechanics at lincoln automotive are reboring a 6-in deepcylinder to fit a new piston....
A 0.48 kg piece of wood floats in water but is found to sinkin alcohol...
A 50-g ice cube at 0oC is heated until 45-g hasbecome water at 100oC and...
A solution containing 6.23 ppm of KMnO4 had a transmittance of 0.195 in a 1.00-cm...
A black body at 7500K consists of an opening of diameter 0.0500mm, looking into an...
A new absolute temperature scale is proposed. On thisscale the ice point of water is...
A 65.0 mm focal length converging lens is 78.0 mm away from a sharp image....
A crate of fruit with mass 35.0 kg and specific heat capacity 3650 J/Kg ....
A freezer has a thermal efficiency of 2.40. Thefreezer is to convert 1.80 kg of...
A horizontal force of 210N is exerted on a 2.0 kg discus as it rotates...
Lead has a specific heat of 0.030 cal/gC. In an insulated container, 300 grams of...
A parachutist relies on air resistance mainly on her parachute to decrease her downward velocity....
The distance between a carbon atom (m=12 u) and an oxygen atom (m + 16...
A car heading north collides at an intersection with a truckheading east. If they lock...
Water stands at a depth H in a large, open tank whose sidewalls are vertical....
The heaviest invertebrate is the giant squid, which is estimated to have a weight of...
Which of the following is a correct comment? */ Comments */ ** Comment ** /*...
The concentrated sulfuric acid we use in the laboratory is 98% H2SO4 by mass. Calculate...
Consider the reaction N2(g)+3H2(g)→2NH3(g) suppose that a particular moment during the reaction molecular hydrogen on...
use Green’s Theorem to find the counterclockwise circulation and outward flux for the field F...
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- The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
- The calculus section will carry out differentiation as well as definite and indefinite integration.
- The matrices section contains commands for the arithmetic manipulation of matrices.
- The graphs section contains commands for plotting equations and inequalities.
- The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.
Math Topics
More solvers.
- Add Fractions
- Simplify Fractions
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A collection of mathematics problems with an answer and solution to each problem. ... Math Practice Problems for 1st Grade. Counting One-digit addition One-digit subtraction. Problems for 2nd Grade. Number line Comparing whole numbers.
Math strategies for problem-solving help students use a range of approaches to solve many different types of problems. It involves identifying the problem and carrying out a plan of action to find the answer to mathematical problems. Problem-solving skills are essential to math in the general classroom and real-life.
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
Looking for free math worksheets? You've found something even better! That's because Khan Academy has over 100,000 free practice questions. And they're even better than traditional math worksheets - more instantaneous, more interactive, and more fun! Just choose your grade level or topic to get access to 100% free practice questions: Early math Kindergarten 1st […]
Online practice problems with answers for students and teachers. Pick a topic and start practicing, or print a worksheet for study sessions or quizzes.
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 ...
A professor writes 40 discrete mathematics true/false questions. Of the statements in these questions, 17... Suppose E(X)=5 and E[X(X-1)]=27.5, find ∈(x2) and the variance. ... Plainmath is a platform aimed to help users to understand how to solve math problems by providing accumulated knowledge on different topics and accessible examples.
Online practice problems for math, including arithmetic, algebra, calculus, linear algebra, number theory, and statistics. Get help from hints and Step-by-step solutions. Generate printable worksheets.
Even simple math problems become easier to solve when broken down into steps. From basic additions to calculus, the process of problem solving usually takes a lot of practice before answers could come easily. As problems become more complex, it becomes even more important to understand the step-by-step process by which we solve them.
QuickMath allows students to get instant solutions to all kinds of math problems, from algebra and equation solving right through to calculus and matrices. QuickMath Solve equations and inequalities; Simplify expressions ... QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and ...