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## 120 Math Word Problems To Challenge Students Grades 1 to 8

Engage and motivate your students with our adaptive, game-based learning platform!

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

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

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

Best for: 1st grade, 2nd grade

## Subtraction word problems

Best for: 1st grade, second grade

## Practice math word problems with Prodigy Math

## Multiplication word problems

Best for: 2nd grade, 3rd grade

## Division word problems

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

## Mixed operations word problems

## Ordering and number sense word problems

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

## Fractions word problems

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

## Decimals word problems

Best for: 4th grade, 5th grade

## 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?

## Time word problems

## Money word problems

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

## Physical measurement word problems

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

## Ratios and percentages word problems

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

## Probability and data relationships word problems

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

## Geometry word problems

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

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

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

## Variables word problems

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

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

- 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.

## Final thoughts about math word problems

## Math Problem Answers

Various types of Math Problem Answers are solved here.

Selling price of the first pipe = $1.20

Let’s try to find the cost price of the first pipe

Selling price of the Second pipe = $1.20

Let’s try to find the cost price of the second pipe

Therefore, total cost price of the two pipes = $1.00 + $1.50 = $2.50

And total selling price of the two pipes = $1.20 + $1.20 = $2.40

Therefore, Mr. Jones loss 10 cents.

3. A recipe calls for 2 1/2 cups and I want to make 1 1/2 recipes. How many cups do I need?

From Math Problem Answers to HOME PAGE

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## Solving Problems With Math

## Problem Solving and Estimating

## Problem Solving Process

- Identify the question you’re trying to answer.
- Work backwards, identifying the information you will need and the relationships you will use to answer that question.
- Continue working backwards, creating a solution pathway.
- If you are missing necessary information, look it up or estimate it. If you have unnecessary information, ignore it.
- Solve the problem, following your solution pathway.

How many times does your heart beat in a year?

Suppose you count 80 beats in a minute. To convert this to beats per year:

How thick is a single sheet of paper? How much does it weigh?

The first two example questions in this set are examined in more detail here.

There are several possible solution pathways to answer this question. We will explore one.

View the following video for more about the zucchini muffin problem.

You need to replace the boards on your deck. About how much will the materials cost?

This will allow us to estimate the material cost for the whole 384 ft 2 deck

This example is worked through in the following video.

Is it worth buying a Hyundai Sonata hybrid instead the regular Hyundai Sonata?

We can then find the number of gallons each car would require for the year.

If gas in your area averages about $3.50 per gallon, we can use that to find the running cost:

#1. Click here to try this problem.

#2. Click here to try this problem.

#3. Click here to try this problem.

## Example: Sales Tax

The sales tax rate in a city is 9.3%. How much sales tax will you pay on a $140 purchase? Solution:

Click here to try another version of this problem:

## Example: Property Tax

We can compute the equivalent percentage: 3200/215000 = 0.01488, or about 1.49% effective rate.

Taxes are often referred to as progressive, regressive, or flat.

- A flat tax , or proportional tax, charges a constant percentage rate.
- A progressive tax increases the percent rate as the base amount increases.
- A regressive tax decreases the percent rate as the base amount increases.

## Example: Federal Income Tax

## Earning $10,000

What was Stephen’s effective tax rate?

The effective tax rate paid is 1075/10000 = 10.75%

## Example: Gasoline Tax

Click here to try other tax problems .

## Share This Book

## Solving Word Questions

In Algebra we often have word questions like:

## Example: Sam and Alex play tennis.

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

The trick is to break the solution into two parts:

Turn the English into Algebra.

## Turning English into Algebra

To turn the English into Algebra it helps to:

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

## Thinking Clearly

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

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

The correct answer is S = A − 2

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

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

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

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

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

Turn the English into Algebra:

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

We are being asked for the Area.

The area is 60 square meters .

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

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

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

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

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

Which means that Alex played 4 games of tennis.

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

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

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

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

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

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

So 10 tables would take Sam just 20 days.

Should Sam be paid more I wonder?

And another "substitution" example:

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

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

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

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

The number of "5 hour" days is 3

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

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

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

We are being asked for the radius.

We need to rearrange the formula to find the area

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

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

We are being asked for the surface area.

First work out s using the volume formula:

Now we can calculate surface area:

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

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

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

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

More about Money, with these two examples involving Compound Interest

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

This is the compound interest formula:

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

We are being asked for the Future Value: FV

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

The compound interest formula:

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

We are being asked for the Interest Rate: r

So the annual rate of interest is 5%

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

And an example of a Ratio question:

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

Which can be rearranged to 3b = 4g

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

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

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

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

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

And now for some Quadratic Equations :

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

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

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

We are being asked for the integers

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

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

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

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

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

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

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

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

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

So the length of the room is 8 m

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

## SAT Math Problem Solving

Each test has ten questions and should take 12 minutes.

## Practice SAT Problem Solving

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## 20 Grade-School Math Questions So Hard You'll Wonder How You Graduated

## 1. Question: What is the number of the parking space covered by the car?

## Answer: 87.

## 2. Question: Replace the question mark in the above problem with the appropriate number.

This problem shouldn't be too difficult to solve if you play a lot of sudoku.

## 3. Question: Find the equivalent number.

This problem comes straight from a standardized test given in New York in 2014.

## 4. Question: How many small dogs are signed up to compete in the dog show?

This question comes directly from a second grader's math homework. Yikes.

## Answer: 42.5 dogs.

## 5. Question: Find the area of the red triangle.

## 6. Question: How tall is the table?

## Answer: 150 cm.

## 7. Question: If the cost of a bat and a baseball combined is $1.10 and the bat costs $1.00 more than the ball, how much is the ball?

This problem, mathematically speaking, is very similar to one of the other ones on this list.

## Answer: $0.05.

## 8. Question: When is Cheryl's birthday?

If you're having trouble reading that, see here:

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard doesn't not know too.

Bernard: At first I don't know when Cheryl's birthday is, but I know now.

Albert: Then I also know when Cheryl's birthday is.

So when is Cheryl's birthday?"

## Answer: July 16.

## 9. Question: Find the missing letter.

This one comes from a first grader's homework.

## Answer: The missing letter is J.

## 10. Question: Solve the equation.

This problem might look easy, but a surprising number of adults are unable to solve it correctly.

## 11. Question: Where should a line be drawn to make the below equation accurate?

## Answer: A line should be drawn on a "+" sign.

## 12. Question: Solve the unfinished equation.

Try to figure out what all of the equations have in common.

## Answer: 4 = 256.

The formula used in each equation is 4 x = Y. So, 4 1 = 4, 4 2 = 16, 4 3 = 64, and 4 4 = 256.

## 13. Question: How many triangles are in the image above?

## Answer: 18.

## 14. Question: Add 8.563 and 4.8292.

Adding two decimals together is easier than it looks.

## Answer: 13.3922.

## 15. Question: There is a patch of lily pads on a lake. Every day, the patch doubles in size…

## Answer: 47 days.

## 16. Question: How many feet are in a mile?

## Answer: 5,280.

This was one of the questions featured on the popular show Are You Smarter Than a 5th Grader?

## 17. Question: What value of "x" makes the equation below true?

## Answer: -3.

## 18. Question: What is 1.92 divided by 3?

You might need to ask your kids for help on this one.

## Answer: 0.64.

## 19. Question: Solve the math equation above.

## 20. Question: How many zombies are there?

Finding the answer to this final question will require using fractions.

## Answer: 34.

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The first stores close on March 9.

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The home of mathematics education in New Zealand.

## Problem Solving

## 📬 Sign Up for Our Amazing Newsletter!

## How to Work Through Hard Math Problems

## The Case for Doing Hard Things

## Strategies for Difficult Math Problems — and Beyond

Here are a few strategies for dealing with hard problems, and the frustration that comes with them:

## Subscribe for news, tips and advice from AoPS

## Aops programs

## People also looked at

- 1 Department of Education, Uppsala University, Uppsala, Sweden
- 2 Department of Education, Culture and Communication, Malardalen University, Vasteras, Sweden
- 3 School of Natural Sciences, Technology and Environmental Studies, Sodertorn University, Huddinge, Sweden
- 4 Faculty of Education, Gothenburg University, Gothenburg, Sweden

## Introduction

## The Present Study

a) What is the effect of CL approach on students’ problem-solving in mathematics?

## Participants

FIGURE 1 . Flow chart for participants included in data collection and data analysis.

TABLE 1 . Background characteristics of classes and teachers in intervention and control groups.

## Intervention

## Implementation of the Intervention

## Control Group

## Tests of Mathematical Problem-Solving

## Measures of Peer Acceptance and Friendships

## Statistical Analyses

## What Is the Effect of the CL Approach on Students’ Problem-Solving in Mathematics?

## Is Social Acceptance and Friendships Associated With the Effect of CL on Students’ Problem-Solving in Mathematics?

## Limitations

## Implications

## Data Availability Statement

## Ethics Statement

## Author Contributions

The project was funded by the Swedish Research Council under Grant 2016-04,679.

## Conflict of Interest

## Publisher’s Note

## Acknowledgments

We would like to express our gratitude to teachers who participated in the project.

## Supplementary Material

CrossRef Full Text | Google Scholar

PubMed Abstract | CrossRef Full Text | Google Scholar

Received: 15 May 2021; Accepted: 09 August 2021; Published: 24 August 2021.

*Correspondence: Nina Klang, [email protected]

## Appendix A: Applications

Apply a problem-solving strategy to basic word problems, learning outcomes.

- Practice mindfulness with your attitude about word problems
- Apply a general problem-solving strategy to solve word problems

## Approach Word Problems with a Positive Attitude

Negative thoughts about word problems can be barriers to success.

When it comes to word problems, a positive attitude is a big step toward success.

If we take control and believe we can be successful, we will be able to master word problems.

## Use a Problem-Solving Strategy for Word Problems

Step 6. Check the answer in the problem and make sure it makes sense.

Step 7. Answer the question with a complete sentence.

If this were a homework exercise, our work might look like this:

https://ohm.lumenlearning.com/multiembedq.php?id=142694&theme=oea&iframe_resize_id=mom1

We list the steps we took to solve the previous example.

## Problem-Solving Strategy

- Read the word problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the internet.
- Identify what you are looking for.
- Name what you are looking for. Choose a variable to represent that quantity.
- Translate into an equation. It may be helpful to first restate the problem in one sentence before translating.
- Solve the equation using good algebra techniques.
- Check the answer in the problem. Make sure it makes sense.
- Answer the question with a complete sentence.

For a review of how to translate algebraic statements into words, watch the following video.

Let’s use this approach with another example.

https://ohm.lumenlearning.com/multiembedq.php?id=142722&theme=oea&iframe_resize_id=mom2

In the next example, we will apply our Problem-Solving Strategy to applications of percent.

https://ohm.lumenlearning.com/multiembedq.php?id=142735&theme=oea&iframe_resize_id=mom3

https://ohm.lumenlearning.com/multiembedq.php?id=142761&theme=oea&iframe_resize_id=mom4

- Write Algebraic Expressions from Statements: Form ax+b and a(x+b). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/Hub7ku7UHT4 . License : CC BY: Attribution
- Question ID 142694, 142722, 142735, 142761. Authored by : Lumen Learning. License : CC BY: Attribution . License Terms : IMathAS Community License, CC-BY + GPL
- Prealgebra. Provided by : OpenStax. License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

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## VIDEO

## COMMENTS

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