problem solving word problems middle school

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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A Math Word Problem Framework That Fosters Conceptual Thinking

This strategy for selecting and teaching word problems guides students to develop their understanding of math concepts.

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Word problems in mathematics are a powerful tool for helping students make sense of and reason with mathematical concepts. Many students, however, struggle with word problems because of the various cognitive demands. As districtwide STEAM professional development specialists, we’ve spent a lot of time focusing on supporting our colleagues and students to ensure their success with word problems. We found that selecting the right word problems, as well as focusing on conceptual understanding rather than procedural knowledge, provides our students with real growth.

As our thinking evolved, we began to instill a routine that supports teaching students to solve with grit by putting them in the driver’s seat of the thinking. Below you’ll find the routine that we’ve found successful in helping students overcome the challenges of solving word problems.

Not all word problems are created equal

Prior to any instruction, we always consider the quality of the task for teaching and learning. In our process, we use word problems as the path to mathematics instruction. When selecting the mathematical tasks for students, we always consider the following questions:

• Does the task align with the learning goals and standards?
• Will the task engage and challenge students at an appropriate level, providing both a sense of accomplishment and further opportunities for growth?
• Is the task open or closed? Open tasks provide multiple pathways to foster a deeper understanding of mathematical concepts and skills. Closed tasks can still provide a deep understanding of mathematical concepts and skills if the task requires a high level of cognitive demand. 
• Does the task encourage critical thinking and problem-solving skills?
• Will the task allow students to see the relevance of mathematics to real-world situations?
• Does the task promote creativity and encourage students to make connections between mathematical concepts and other areas of their lives?

If we can answer yes to as many of these questions as possible, we can be assured that our tasks are rich. There are further insights for rich math tasks on NRICH and sample tasks on Illustrative Mathematics and K-5 Math Teaching Resources .

Developing conceptual understanding

Once we’ve selected the rich math tasks, developing conceptual understanding becomes our instructional focus. We present students with Numberless Word Problems and simultaneously use a word problem framework to focus on analysis of the text and to build conceptual understanding, rather than just memorization of formulas and procedures. 

• First we remove all of the numbers and have students read the problem focusing on who or what the problem is about; they visualize and connect the scenario to their lives and experiences. 
• Next we have our students rewrite the question as a statement to ensure that they understand the questions.
• Then we have our students read the problem again and have them think analytically. They ask themselves these questions: Are there parts? Is there a whole? Are things joining or separating? Is there a comparison? 
• Once that’s completed, we reveal the numbers in the problem. We have the students read the problem again to determine if they have enough information to develop a model and translate it into an equation that can be solved.
• After they’ve solved their equation, we have students compare it against their model to check their answer.  

Collaboration and workspace are key to building the thinking

To build the thinking necessary in the math classroom , we have students work in visibly random collaborative groups (random groups of three for grades 3 through 12, random groups of two for grades 1 and 2). With random groupings, we’ve found that students don’t enter their groups with predetermined roles, and all students contribute to the thinking.

For reluctant learners, we make sure these students serve as the scribe within the group documenting each member’s contribution. We also make sure to use nonpermanent vertical workspaces (whiteboards, windows [using dry-erase markers], large adhesive-backed chart paper, etc.). The vertical workspace provides accessibility for our diverse learners and promotes problem-solving because our students break down complex problems into smaller, manageable steps. The vertical workspaces also provide a visually appealing and organized way for our students to show their work.  We’ve witnessed how these workspaces help hold their attention and improve their focus on the task at hand.

Facilitate and provide feedback to move the thinking along

As students grapple with the task, the teacher floats among the collaborative groups, facilitates conversations, and gives the students feedback. Students are encouraged to look at the work of other groups or to provide a second strategy or model to support their thinking. Students take ownership and make sense of the problem, attempt solutions, and try to support their thinking with models, equations, charts, graphs, words, etc. They work through the problem collaboratively, justifying their work in their small group. In essence, they’re constructing their knowledge and preparing to share their work with the rest of the class. 

Word problems are a powerful tool for teaching math concepts to students. They offer a practical and relatable approach to problem-solving, enabling students to understand the relevance of math in real-life situations. Through word problems, students learn to apply mathematical principles and logical reasoning to solve complex problems. 

Moreover, word problems also enhance critical thinking, analytical skills, and decision-making abilities. Incorporating word problems into math lessons is an effective way to make math engaging, meaningful, and applicable to everyday life.

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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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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?

Practice math word problems with Prodigy Math

Join millions of teachers using Prodigy to make learning fun and differentiate instruction as they answer in-game questions, including math word problems from 1st to 8th grade!

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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There's no cost to you or your students and Prodigy is fully aligned with state standards for grades 1-8 math.

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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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14 Effective Ways to Help Your Students Conquer Math Word Problems

If a train leaving Minneapolis is traveling at 87 miles an hour…

Word problems can be tricky for a lot of students, but they’re incredibly important to master. After all, in the real world, most math is in the form of word problems. “If one gallon of paint covers 400 square feet, and my wall measures 34 feet by 8 feet, how many gallons do I need?” “This sweater costs $135, but it’s on sale for 35% off. So how much is that?” Here are the best teacher-tested ideas for helping kids get a handle on these problems.

1. Solve word problems regularly

This might be the most important tip of all. Word problems should be part of everyday math practice, especially for older kids. Whenever possible, use word problems every time you teach a new math skill. Even better: give students a daily word problem to solve so they’ll get comfortable with the process.

Learn more: Teaching With Jennifer Findlay

2. Teach problem-solving routines

There are a LOT of strategies out there for teaching kids how to solve word problems (keep reading to see some terrific examples). The important thing to remember is that what works for one student may not work for another. So introduce a basic routine like Plan-Solve-Check that every kid can use every time. You can expand on the Plan and Solve steps in a variety of ways, but this basic 3-step process ensures kids slow down and take their time.

Learn more: Word Problems Made Easy

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3. Visualize or model the problem

Encourage students to think of word problems as an actual story or scenario. Try acting the problem out if possible, and draw pictures, diagrams, or models. Learn more about this method and get free printable templates at the link.

Learn more: Math Geek Mama

4. Make sure they identify the actual question

Educator Robert Kaplinsky asked 32 eighth grade students to answer this nonsensical word problem. Only 25% of them realized they didn’t have the right information to answer the actual question; the other 75% gave a variety of numerical answers that involved adding, subtracting, or dividing the two numbers. That tells us kids really need to be trained to identify the actual question being asked before they proceed. 

Learn more: Robert Kaplinsky

5. Remove the numbers

It seems counterintuitive … math without numbers? But this word problem strategy really forces kids to slow down and examine the problem itself, without focusing on numbers at first. If the numbers were removed from the sheep/shepherd problem above, students would have no choice but to slow down and read more carefully, rather than plowing ahead without thinking. 

Learn more: Where the Magic Happens Teaching

6. Try the CUBES method

This is a tried-and-true method for teaching word problems, and it’s really effective for kids who are prone to working too fast and missing details. By taking the time to circle, box, and underline important information, students are more likely to find the correct answer to the question actually being asked.

Learn more: Teaching With a Mountain View

7. Show word problems the LOVE

Here’s another fun acronym for tackling word problems: LOVE. Using this method, kids Label numbers and other key info, then explain Our thinking by writing the equation as a sentence. They use Visuals or models to help plan and list any and all Equations they’ll use. 

8. Consider teaching word problem key words

This is one of those methods that some teachers love and others hate. Those who like it feel it offers kids a simple tool for making sense of words and how they relate to math. Others feel it’s outdated, and prefer to teach word problems using context and situations instead (see below). You might just consider this one more trick to keep in your toolbox for students who need it.

Learn more: Book Units Teacher

9. Determine the operation for the situation

Instead of (or in addition to) key words, have kids really analyze the situation presented to determine the right operation(s) to use. Some key words, like “total,” can be pretty vague. It’s worth taking the time to dig deeper into what the problem is really asking. Get a free printable chart and learn how to use this method at the link.

Learn more: Solving Word Problems With Jennifer Findlay

10. Differentiate word problems to build skills

Sometimes students get so distracted by numbers that look big or scary that they give up right off the bat. For those cases, try working your way up to the skill at hand. For instance, instead of jumping right to subtracting 4 digit numbers, make the numbers smaller to start. Each successive problem can be a little more difficult, but kids will see they can use the same method regardless of the numbers themselves.

Learn more: Differentiating Math 

11. Ensure they can justify their answers

One of the quickest ways to find mistakes is to look closely at your answer and ensure it makes sense. If students can explain how they came to their conclusion, they’re much more likely to get the answer right. That’s why teachers have been asking students to “show their work” for decades now.

Learn more: Madly Learning

12. Write the answer in a sentence

When you think about it, this one makes so much sense. Word problems are presented in complete sentences, so the answers should be too. This helps students make certain they’re actually answering the question being asked… part of justifying their answer.

Learn more: Multi-Step Word Problems

13. Add rigor to your word problems

A smart way to help kids conquer word problems is to, well… give them better problems to conquer. A rich math word problem is accessible and feels real to students, like something that matters. It should allow for different ways to solve it and be open for discussion. A series of problems should be varied, using different operations and situations when possible, and even include multiple steps. Visit both of the links below for excellent tips on adding rigor to your math word problems.

Learn more: The Routty Math Teacher and Alyssa Teaches

14. Use a problem-solving rounds activity.

Put all those word problem strategies and skills together with this whole-class activity. Start by reading the problem as a group and sharing important information. Then, have students work with a partner to plan how they’ll solve it. In round three, kids use those plans to solve the problem individually. Finally, they share their answer and methods with their partner and the class. Be sure to recognize and respect all problem-solving strategies that lead to the correct answer.

Learn more: Teacher Trap

Like these word problem tips and tricks? Learn more about Why It’s Important to Honor All Math Strategies .

Plus, 60+ Awesome Websites For Teaching and Learning Math .

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3 Types of Word Problems to Teach

Problem solving is a multifaceted process! While I’ve written about Math Problem Solving Strategies and How to Teach Word Problems and Problem Solving , there is still so much more to cover.

Noelle presented an amazing math training this summer on Practical Problem Solving Strategies. I was truly amazed at just how much I learned. I will be breaking down the training into 3 blog posts over the course of this month, so if you missed the training, be sure to check back here for more updates.

If you want to learn more, check out this book, Mathematize It! , that covers the topic of teaching how to solve word problems in much more detail.

Today we are going to talk about the 3 types or categories of word problems that you teach and your students may face: action, relationship, and comparison. The purpose of identifying word problem types is to force students to slow down and analyze what is happening in the word problem before jumping to computation.

You can also grab our problem solving posters freebie below!

Action Word Problems

Here is an example of an action word problem: 

How do we know that this is an action? Ask yourself:

• Did something occur?
• Was there some kind of change?

If yes, the word problem likely falls into the action category.

Relationship Word Problems

Here is an example of a relationship word problem: 

How do we know this is a relationship? Ask yourself:

• Are parts being described or referred to in relation to a whole? 
• Is a whole being described or referred to in relation to a part?

If yes, the word problem is a relationship. Here we can see the parts of the marching band relate to the total number of marching band members. 

Comparison Word Problems

And lastly, here is an example of a comparison word problem: 

How do we know this is a comparison?

Ask yourself:

• Is something in the word problem being described in comparison to something else?

In this word problem, we can see that the cost of popcorn is being described by the cost of the candy. 

Why is this helpful to know?

Why do students need to know this? Well, by observing and “making meaning” from the words and scenarios they are processing, students are less likely to rush to determine a path to the solution. 

Does this sound familiar? Students quickly perform some operations with the values given. In this first step of the problem-solving process, we want to take the focus off the values and direct students to notice what is being described in the problem.

The goal is not for them to be able to identify and put the word problem into the correct category. We simply want students to notice what is happening, and over time they will start to recognize patterns in word problems. 

Next week, I will dive deeper into how we take these word problem types and use them to help students with the first part of the problem solving process: restating the problem .

Grab our problem solving posters freebie!

In the meantime, can you identify the category these sample problems belong in?

• Ricky buys a package of chicken to use throughout the week. On Monday, he uses 28 ounces to make chicken salad for lunch. On Thursday, he grills 53 ounces of chicken for dinner. If Ricky determines he has 37 ounces of chicken remaining to cook, how many ounces of chicken did he buy at the beginning of the week?
• Gavin has two pet turtles, a red-eared slider and a map turtle. His red-eared slider weighs 2,680 grams and his map turtle weighs 670 grams. How many times bigger is the red-eared slider than the map turtle?
• Ivory created a paper chain of her school colors, blue, green, and white, as a decoration for a pep rally. The blue section measured 5.5  feet long, the green section measured 4.25  feet long, and the white section measured 3.75  feet long. What is the total length of the paper chain?
• A king-sized chocolate bar has a mass of 2.6 ounces. A regular-sized chocolate bar has a mass of 1.55 ounces. How many more ounces is the king-sized chocolate bar than the regular-sized chocolate bar?
• A nature center has a stocked pond with an automatic fish feeder. The fish feeder has 70.5 pounds of fish food and releases food into the pond twice a day. If the feeder releases 2.6 pounds of food in the morning and 1.2 pounds of food in the evening, how many pounds of food are remaining in the feeder at the end of the day? 
• The San Francisco Bay Area is hosting a triathlon, a race consisting of swimming, biking, and running. The athletes will swim for 0.75  miles and bike for 15.5  miles. If the total distance of the triathlon is 20.5  miles, how many miles is the running portion of the race?

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• Find Angles And Classify
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• Finding Sides Of Similar Triangles
• Finding Squares and Square Roots
• Identify And Make Quadrilateral
• Identify Polygon
• Identify Similar Triangles With Proofs
• Identifying Parallel, Intersecting, and Perpendicular Lines
• Naming Adjacent, Supplementary, and Vertical Angles
• Perimeter and Area
• Pythagorean Theorem Word Problems
• Similar Figures- Finding Unknown Sides
• Squares And Square Roots
• Surface Area and Volume of Triangular Solids And Cylinders
• The Pythagorean Theorem
• Transformations
• Transversals
• Volume Word Problems

Graphing and Charting Data Worksheets

• Box and Whisker Plot
• Read and Make Stem and Leaf Plots
• Reading and Making Bar Graphs
• Reading and Making Line Graphs
• Reading and Making Pie Graphs
• Reading Frequency Tables
• Tree Diagrams

Integer Worksheets

• Adding and Subtracting Integers
• Calculator Fun
• Multiplying and Dividing Integers
• Open Ended Integer Problems
• Representing Integers

Measurement Worksheets

• Adding And Subtracting Measurement With Fractions
• Adding And Subtracting Measurements
• Adding English Measurement
• Adding Units of Measurement
• Adding Units of Measurement- Mass, Length, and Volume
• Adding Units of Time and Weight
• Converting Units of Length, Mass, Capacity
• Measure length in cm, mm and meters
• Measurement Word Problems
• Multiplying English Measurement
• Scientific Notation
• Scale Factors
• Subtracting English Measurement
• Unit Conversion Time And Weight
• Writing Scientific Notation

Money Math Worksheets

• Calculating Interest with U.S. Dollars
• Calculating Interest with U.S. Dollars over 1 full year
• Interest Word Problems

Multiplication Worksheets

• 4 Digit to 4 Digit Multiplication & 3 Digit to 4 Digit Multiplication
• 4 to 5 Digit Multiplication & 5 to 5 Digit Multiplication

Percentage Worksheets

• Numbers Based on Percentages
• Percent of a Number

Probability & Statistics Worksheets

• Calculate Probability As A Decimal
• Calculate Probability As A Fraction
• Calculate Probability As A Percentage
• Mean, Median, Mode
• Probability Word Problems

Ratio and Proportions Worksheets

• Are these Proportional?
• Creating Proportions
• Equivalent Proportions
• Missing Proportion
• Ratio And Proportion Word Problems
• Ratio Tables
• Ratio Word Problems
• Ratio Word Problems (Moderate)
• Rewriting Ratios
• Solving Proportion Problems
• Word Based Proportions Easy
• Word Based Proportions Difficult

Subtraction Worksheets

• 4 Digit to 4 Digit Subtraction & 3 Digit to 4 Digit Subtraction
• 4 Digit to 5 Digit Subtraction & 5 Digit to 5 Digit Subtraction

Word Problems Worksheets

• Fractions with Number Word Problems
• Fractions As Words Word Problems
• Fraction Word Problems w/ Mixed Numbers

Math Tips For Grade 6, Grade 7, & Grade 8:

• Top 10 Grade 6, Grade 7, and Grade 8 Math Skills

What Do You Learn About Math In Grade 6 through Grade 8?

• What Do You Learn About Math in Sixth Grade?
• What Math Concepts Are Taught In Seventh Grade?
• What Math Concepts Are Taught in Eighth Grade?
• 10 Awesome Jobs that Require Great Math Skills
• A Problem a Day Makes the Bad Math Grades Go Away
• An Impossible Math Problem! What Do You Do?
• Fractions, Decimals, and Percents: How do they relate and how do they differ?
• How does math help us make predictions?
• How To Become A Strong Math Student
• Ten Tips to Become Better at Algebra
• The Math Used in Professional Auto Racing
• The Math Used in Professional Baseball: More than a Game
• The Math used in Professional Basketball
• The Math Used in Professional Football
• The Math Used In Professional Ice Hockey
• The Math used in Professional Soccer
• Why Do We Learn About Coordinate Graphs?
• Why Giving Your Child an Allowance Is an Important Learning Experience
• Why is Graphing So Important in your Life Anyway?

They learn a broad range of mathematics topics. These are the math concepts that students must understand by the end of the 8th grade. All of these mathematical concepts are used to develop a well rounded base knowledge of mathematical ideas and language as students' progress to higher levels of mathematics.

What do students in grade 6 through grade 8 learn in math? They learn a broad range of mathematics topics. These are the math concepts that students must understand by the end of the 8th grade based on the National Mathematics standards.

Numbers and Operations concepts students study include understanding numbers, number relationships, and number systems. Students need to understand fractions, decimals, and percents and the relationship of their location on a number line. This includes understanding quantitative relationships of ratios and proportions of numbers. Using factors, multiples, prime numbers, and relative prime numbers to solve math problems.

Students study the uses associative and commutative properties in addition and multiplication. This includes developing an understanding of inverse relationships in addition, subtraction, multiplication, and division. Also they learn the relationships squaring and finding the square roots of numbers. They develop and analyze algorithms for computing fractions, decimals, and integers as applied to problem solving situations.

Algebra focuses on the concepts to represent, analyze, and general a variety of patterns as they relate to symbolic rules. They interpret data on as either linear or non-linear when transferred from data tables to graphs or equations. They learn to use symbolic algebra to represent situations found in algebraic expressions and equations. They learn to use graphing calculators to analyze expressions and equations, along with traditional computational tools.

Geometry concepts focus analyzing the characteristics of two and three dimensional objects to find their angles, side lengths, perimeters, areas, and more. They use coordinate geometry to examine special objects such as polygons, and objects with parallel and perpendicular lines. They also analyze the relationships in objects as to congruence, similarity, and the Pythagorean Theorem. They also describe transformations of objects by similarity and rotation. Finally they use geometric patterns to solve problems.

Measurement concepts focus on using customary standard and non-standard units of measurement and determine the relationships between varieties of objects. This is also connected with geometry as they learn how to measure the area, volume, and mass of different geometric shapes. They learn how to measure all aspects of circles, prisms, and pyramids.

Students apply measurement applications to the conversion of U.S. customary units of measurement into the metric system. They develop a basic understanding of meter, liter, and grams; including their variables. They learn to apply estimation skills for determining the shape, volume, area, and mass of different objects.

Data Analysis and Probability concepts focus on using appropriate language to explain findings in mathematical experiments and simulations. They learn how to develop questions that help find the differences between two or more samples in a population. They develop mathematical theories for explaining events that will result in likely or unlikely outcomes. They interpret data that are represented on graphical plots to make predictions of likely outcomes.

Problem Solving for eighth grade students focuses the development of problem solving strategies to help them develop a fundamental understanding of mathematics. Students use word problems and other real world simulations in problems solving situations.

Representation concepts focus on students learning to collect and organize data, then using the data to solve problems. Answers are presented as models that are numerical, written, physical, and social. They are able to draw graphs, charts, tables, and other forms to explain how they solved a problem.

Connection concepts are designed for eighth grade students to demonstrate how to make connections to real world applications and other subject content areas. This includes making connections with other concepts in mathematics.

Communicate their mathematics ideas in the form of sentences, drawings, posters, and multimedia applications is another concept that students need to master. This is used to ascertain their level of understanding as they explain mathematical concepts to other students and teachers.

Reasoning and Proof concepts are used to explain mathematical findings and problem solving techniques. This is necessary so that they develop skills on how to present logical arguments to math situations.

All of these mathematical concepts are used to develop a well rounded base knowledge of mathematical ideas and language as students' progress to higher levels of mathematics.

Math Wheels for Note-taking?

Teaching Problem Solving in the Middle School Classroom

I love teaching problem solving to my middle schoolers! By this stage in their math journey, they’ve already laid a foundation. Now, I get to show them all the different ways they can approach a problem. It’s so rewarding to see how unique each student is, especially when one strategy works great for one and another for someone else. In the end, though, they all reach the right answer, which is what really matters. This process also sparks some amazing, authentic math conversations in the classroom. Today, I’m excited to share all the posts I’ve written to help with teaching problem solving!

Helping our students develop problem solving skills can be difficult. It takes time and lots of opportunities to practice those skills. Over the years I’ve used a variety of teaching strategies and activities when it comes to problem solving. Some worked well and some not so much. So I’ve pulled together the things that worked well to share with you here. I hope that as you read through the posts you will find some nuggets that will help you make teaching problem solving easier and more effective.

Roundup of Posts for Teaching Problem Solving

Teaching math problem solving strategies.

This post is all about helping our students develop strong problem-solving skills through a variety of strategies. I highlight different approaches that can guide our students in breaking down math problems, making them more manageable and less intimidating. It also dives into why exposing our students to multiple strategies is important. It gives them the tools to find what works best for their individual learning styles.

My Problem Solving Doodle Notes resource is a fantastic tool for teaching problem solving in a way that’s interactive and visually engaging for students. In this blog post, I share how I’ve used this resource to teach a variety of problem solving strategies that make breaking down math problems easier. The doodle notes allow my students to keep track of various strategies like guessing and checking, working backward, drawing diagrams, and making organized lists. What I love most about this resource is how it encourages students to take ownership of their learning by keeping these notes as a reference all year long. It’s a fun and effective way to reinforce different methods for teaching problem solving!

To learn more about these problem solving strategies and the doodle notes read the full article here .

How to Teach Real Life Math Problem Solving Activities

My next post is all about building strong problem-solving skills in our students using real-life math activities. My experience in the classroom has led me to the conclusion that students love math when they see its relevance. There’s nothing more relevant than real-life examples of how problem solving skills are used in the day-to-day.

In this post, I explore different strategies that help students break down complex problems. This helps to make them feel less overwhelmed and more approachable. The post also explains why it’s important to introduce a variety of methods so that our students can discover what works best for them. By providing them with options, we empower them to choose strategies that fit their learning style.

5 Ways to Practice Problem Solving in Middle School

The next post emphasizes the importance of teaching students to break down complex problems into smaller, manageable steps. This one step helps them feel more confident and less overwhelmed. I also explore how teaching problem-solving approaches, such as drawing diagrams, working backward, and using logical reasoning, gives our students the flexibility to find the best method for their unique learning style.

The post also explains why building these skills is crucial for our students’ overall math success. It acknowledges that our students will face more challenging concepts. If you’re looking for ways to make teaching problem solving engaging and effective, this post offers a range of techniques that can be easily incorporated into your lessons!

Decimal Operations Math Problem Solving

Sometimes our problem solving skills change a little when it comes to specific skills and concepts. In this post, I share tips and ideas for teaching problem solving when it comes to decimals. I focus on helping students strengthen their problem solving skills through decimal operations.

This post dives into different strategies that guide our students in working through multi-step problems involving decimals. I share how I have taught problem solving skills that make the process feel less daunting. By including a variety of methods, our students can approach decimal problems from angles that make sense to them. Some of the problem solving skills I share in this post include teaching students how to use estimation, logical reasoning, or step-by-step calculations. This post highlights the importance of practicing these skills to build confidence and accuracy when tackling decimal operations. If your students are struggling with decimals and problem solving, this post is a must read!

Help Middle School Math Students Improve Problem Solving Skills

Ready to help your students expand their repertoire of problem solving strategies? This post will help! This post dives into effective ways to help middle schoolers improve their problem-solving skills in math. It covers different approaches that can simplify the process for our students. These approaches can break problems down step by step and make them more approachable.

By introducing a variety of strategies, our students gain the tools they need to navigate more complex math problems with confidence. The post also emphasizes the importance of consistency and practice in building these skills. If you’re looking for actionable ways to support your students’ growth in math while teaching problem solving, I share some great tips in this post!

Problem Solving Math Wheels

If you’ve been a follower, then you probably already know how much I loved using math wheels in the classroom. They are one of my absolute favorite tools for students. In this post, I dive into how you can use the Problem Solving Math Wheel to teach a variety of problem solving strategies.

These wheels allow our students to visually break down problems step by step. They also help them organize their strategies and make connections between different methods. By rotating through various approaches, such as guess and check, working backward, or drawing diagrams, our students can see how each technique plays a role in finding the solution. It’s a fantastic way to make abstract concepts more concrete. When we do, we are giving our students the tools to confidently approach math problems. Whether you’re working on basic operations or more complex equations, math wheels are a creative resource for teaching problem-solving skills.

Using Collaboration to Improve Math Problem Solving

If there is one thing our middle school students love it is collaboration. Any time we can add opportunities for our students to work together we have increased engagement. In this post, I explore the benefits of using collaborative problem-solving in middle school math. It emphasizes how working together allows our students to tackle challenging problems by sharing different strategies and perspectives.

Collaborative problem solving boosts critical thinking and fosters communication and teamwork skills. The post highlights how this approach encourages our students to explain their reasoning, ask questions, and build on each other’s ideas. This makes math more engaging and interactive. The post offers great strategies to use while teaching problem solving to your students!

How to Teach Problem of the Week in Middle School Math

We all know the saying “An apple a day keeps the doctor away.” But what if we applied this concept to helping our students improve their problem solving skills? In this post, I highlight the effectiveness of using a Problem of the Week to build strong problem-solving skills in middle school math.

In this post, I dive into how implementing a Problem of the Week can boost problem-solving skills in middle school math. This approach gives our students the chance to focus on one challenging problem each week. It allows them to explore various strategies and think critically about their solutions. I outline how this method promotes deeper understanding, persistence, and encourages student discussions around their problem-solving processes. If you aim to introduce a consistent and engaging routine for teaching problem solving in your classroom, this post is a great place to start.

Metric Conversions Free Problem Solving and Matching Activity

Similar to the post above on teaching problem solving with decimals, this post shares the specific problem solving strategies I used when my students were learning about metric conversions. In this post, I explore an engaging approach to teaching metric conversions through a matching activity that helps solidify problem-solving skills.

In this post, I share an activity that challenges students to pair conversion problems with their correct answers. It encourages them to think critically and work through the process step by step. This method makes learning metric conversions more interactive. It also helps students build confidence in their problem-solving abilities. The post also includes a free problem-solving activity that offers extra practice for our students. This ensures they get hands-on experience with these essential math concepts.

Teaching Problem Solving Made Easier

Teaching problem solving is about giving our students the tools they need to tackle any math problem that comes their way. Whether it’s through collaborative activities, hands-on resources, or weekly challenges, there are many ways to make problem solving effective. By exposing our students to a variety of strategies, we empower them to find what works best for their unique learning styles. I hope these ideas help you to incorporate more creative problem solving techniques into your classroom!

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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.

Sample Worksheets

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Math Curriculum For 4th Grade, 5th Grade, and 6th Grade Print and Digital

Math Curriculum For Kindergarten 1st Grade 2nd Grade and 3rd Grade

Math Escape Room - Fun Review Activity! Grades 4 to 7, 2 difficulty levels

Amazon Shopping Spree- Digital Decimal Operations Activity

FREE Measurement Conversion Chart, Metric + Customary Reference Sheet

Word Problems Detective Task Cards FREEBIE Math Multi-Step Stories with Audio

4th Grade Equivalent Fractions Assessment, Practice Quiz, Review Math Worksheet

12 Days of Christmas Math Word Problems - FREE! - Fun No-Prep Worksheets

FREE Math Word Problem Assessments

CUBES Math Strategy Poster

Real Life Multiplication Project - Design a Restaurant

(Free) 6th Grade Ratios, Rates, Unit Price, Ratio Tables & Percent Activities

Elapsed Time FREE Activity: At the Movies! English & Spanish (3rd - 6th)

FREE Titanic Math Activity

Multi Digit Addition & Subtraction Word Problems with Regrouping, Whole Numbers

Mastering Multi-Step Word Problems Starter Kit

Adding & Subtracting Fractions with Unlike Denominators Quiz, Assessment, Test

Decimals & Money Project Based Learning CREATE FRUIT SALAD PBL Math Enrichment

Math Key Word Posters FREEBIE!

Graphing Linear Equations Word Problems

Algebraic Expression Match

Sudoku Puzzle Worksheets [100 puzzles]

Multi Step Word Problems Freebie!

Math Key Word Reference Cards

Mini-Math Mystery FREE Activity 5th Grade - Long Multiplication

Solving a Word Problem with UPS Check Anchor Chart Posters, Notes, & Foldable

Multiplying Fractions and Mixed Numbers Warm-Ups or Worksheet

Long Division Review Activity

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Word Problem Worksheets

Word problems are usually one of the more difficult types of exercises for students to get comfortable with. This is because we get our students use to structure and understanding what is expected of them. This takes them completely out of their comfort zone. Word problems lend themselves to be critical thinking exercises that rely on perception and to a lesser degree language arts skills. I find it helpful to spend a great deal of time teaching students to decode these types of problems to understand what is being asked of them. Then another good helping of having them recognize keywords within that context. Story based problems are all the rage at all grade levels. This is rightly so because this is the type of math most of these young people will do when they enter the workforce. The topics that you will find below are chock full of interesting exercises for your students. So get ready to enjoy some strange scenarios in these lesson and worksheet series.

• Absolute Value - We look at situation based problems that matter how far you range away from the origin.
• Addition (Up to 20) - We look at story-based situation that involve some form of a sum up to a total of twenty.
• Addition and Subtraction - Basic operations can be spotted in these story problems and we show you how.
• Area and Perimeter - We look at various methods to determine the outcome of these problems.
• Area of Rectangles Problems - We go through various ways to identify length and width and we find their product.
• Area of Squares - Perfect for when you are planning on tiling a floor.
• Beginner Multiplication and Division - We show you how to identify keywords that trigger operations.
• Data Table - There is a mound of data to sift through here.
• Decimals - We show you how to align these values and where to place them.
• Division of Whole Numbers By Fractions - These often give students some trouble. We show you how to tackle them quickly.
• Division of Fractions by Whole Numbers - We introduce a technique that can quickly get this done for you.
• Division (3rd Grade) - These problem hinge on simple steps and methods of operation.
• Dollars and Cents - Common problems you would come across when you are shopping.
• Elapsed Time - We look to figure out how long something takes place.
• Frontend Estimation - This will help you make quick guess as to end values.
• Generate Measurement Data - A story is in place with a data chart for you to examine and learn from.
• Graphing - These problems have use read, interpret, or make decisions based on graphs.
• Gratuities and Commissions, Fees, and Tax - Learn how to quickly calculate these values.
• Indirect Length - Find out how to find measures of length of odd objects or odd placements.
• Integers - We examine how to determine the types of operations that are needed to get the job done.
• Length - Get acquainted with the types of units that are required and how to set them up.
• Length In Units - The focus here are the types of units that are used.
• Liquid Volume and Mass - The metric system is funny with how these measures are calculated.
• Markups and Markdowns - Learn how to quickly make these adjustments on the fly.
• Measurement Distance, Time, Liquid Volume - This makes for a nice review section for most aspects of measurement.
• Measures of Length - What units are involved and how do you convert between those measures?
• Mixed Basic Operations - The goal here is to learn to spot which operations are involved in the word problems.
• Multistep Ratio and Percent - Learn how to use these by practical uses.
• Multi-step - We show you a way to keep it focused and simple for you.
• Multiplication - All of these problems require some form of product to be calculated.
• Multiply or Divide - We show you how to spot the operation required.
• One and Two Step Addition and Subtraction (Up to 100) - This is usually the first step towards more complex problems.
• Order of Operations - First you will determine the operations that need to take place, then you will need to figure out which operation should take place when.
• Percentages - We apply percentage skills to all types of different situations.
• Perimeter of Polygons - Surprisingly, this is a very useful topic.
• Probability - How like is it that something will take place?
• Products of Fractions and Mixed Numbers - I feel a little cross multiplication is headed your way here.
• Products of Fractions and Whole Numbers in - Just remember that any whole number can be made into a fraction by placing it over one.
• Proportional Relationships - You will learn how to determine the proportion and use it to your advantage.
• Pythagorean Theorem - You would not imagine how applicable this is to all different types of problems.
• Real Life Middle School Math - All of these word problems would be found in your daily walk of life.
• Recognize Area - How do you determine those missing plots of area?
• Scientific Notation - These are common problems you will come across in a science lab situation.
• Simple Algebra - This serves as an introduction to it all.
• Square Root - Contractor come across these types of problems every day.
• Simple Subtraction - What is the difference? Get it?
• Sum and Difference Fraction - We work mostly with like denominators, but not always.
• Solving Systems - You will see how these types of problems are applicable to the planning process.
• Time - All types of different ways to determine measures of time.
• Visual Sum and Difference - These are for younger students.
• Word Problems Leading to Equations - We write our own math to explain an abstract concept.
• Word Problems Leading to Inequalities - Bringing these to words can be difficult or easy, your choice.
• Word Problems That Require Equations or Inequalities - You will need to diagnose each and every situation.
• Word Problems That Use All Operations - It's all about action words in these sentences.

Tips for Approaching Math Word Problems

For many students, solving math word problems is a struggle. However, they need to understand that word problems are just a jumble of words that explains a problem. However, you can teach them how to solve word problems with just a few tips which are given below.

Compile Given Information - It is helpful to have students get in the habit of writing down the data which consists of the things that are given in the problem.

Read Thoroughly and Highlight - You must ensure that you read the problem thoroughly before you start doing them. If possible, make them reread it. Any words that stick out that may indicate a math operation have them highlight by either circling, underlining, or even using a highlighter pen.

What Is It Asking? - Determine the goal of the problem by writing down the things which are required in the problem. There are often things present in the problem that are not necessary. I tell students to cross that out. I also have them write down what the problem is looking for such as units or simply write down what it is looking for followed by a question mark.

Determine the Operations Needed - Students should be on high alert for keywords that give away what the order of calculations is required. Take a look below for further help on this. Once you determine the operation, write an equation or expression to help you solve it. Now, figure out the equation in which the problem is about and compare the given and unknown values. To learn how to solve word problems in the future, they need to remember the previous practices extensively.

Keywords and Concepts to Look for In Word Problems

When students first start working with word problems in class they are easily overwhelmed. They will often say that they were not aware that they needed to read in math class. If you show students how to digest these problems by breaking them into smaller parts, it becomes easier for them much quicker. We encourage teachers to help students first try to decipher the concepts that are in place and then look for keywords that may confirm those concepts. This leads us to understand what types of operations you will need to work through to solve the problem. The basic concepts that you will see in most story based word problems include: joining problems, separate or splitting problems, part-whole problems, and basic comparison problems. Joining problem types often ask us to either add or multiply. The keywords that are often found in these types of problems are, outside of the obvious, both, combine, increase, together, total, total, triple, and twice. Separate problems often are subtraction based problems they ask you to break apart groups to some extent. The keywords that will back you up here are the words or phrases: change, difference, fewer, how many, less, lost, reduce, remain, or take away. Part-whole problems often have you compare and individual groups against one another or total them, in this case they are the next progression from the other two. These types of problems often are accompanied by the phrase: how many. The comparison problem type is often the most abstract and give students a high level of difficulty. They require students to understand the nature of relationships between values. Students are asked to describe that relationship based on conditions that are presented to them. The more experience you get with this, the easier it will become for you.

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