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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
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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

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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.

## Step-by-Step Calculator

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## Maths Problem-solving Examples With Solutions

What are some examples of problem-solving strategies used in mathematics?

See also : How To Solve Maths Problems Quickly

- Use or create a visual
- Observe a pattern
- Construct a number of sentences.
- Use procedures (operations) like addition, subtraction, multiplication, and division
- Create or utilize a table
- Use or create a list.
- Tto solve a simpler issue

## Mathematical Questions and Answers

x is the number of kilograms he sold in the morning.

Then in the afternoon, he sold

2x kilograms. So, the total is

x+2x=3x. This must be equal to 360.

Therefore, the salesman sold 120 kg in the morning and

In the afternoon, he sold 2 X 120 = 240kg.

Let x be the amount Peter picked.

Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.

Against the wind: D = 8(x – y), with the wind: D = 7(x + y).

8x – 8y = 7x + 7y, hence x / y = 15.

Rewrite equations of circles in standard form. Hence equation

x 2 + y 2 -2x + 4y + 1 = 0 may be written as

(x – 1) 2 + (y + 2) 2 = 4 = 2 2

x 2 + y 2 -2x + 4y – 11 = 0 as

(x – 1) 2 + (y + 2) 2 = 16 = 4 2

Knowing the radii, the area of the ring is π (4) 2 – π (2) 2 = 12

D = (-m) 2 – 4(2)(m) = m 2 – 8 m

We nos solve the inequality m 2 – 8 m < 0

The solution set of the above inequality is: (0 , 8)

6. The sum of an integer N and its reciprocal is equal to 78/15. What is the value of N?

This equation should be written in N.

Multiply all terms by N, obtain a quadratic equation, and solve to obtain N = 5.

7. M and N are integers, so that 4 m / 125 = 5 n / 64. Find values for m and n.

Cross multiply: 64 (4)m = 125 (5n)

Note that 64 = 4(3) and 125 = 5 (3)

The above equation may be written as: 4m + 3 = 5n + 3.

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## Frequently Asked Questions about Khan Academy and Math Worksheets

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## Praxis Core Math

- Algebraic properties | Lesson
- Algebraic properties | Worked example
- Solution procedures | Lesson
- Solution procedures | Worked example
- Equivalent expressions | Lesson
- Equivalent expressions | Worked example
- Creating expressions and equations | Lesson
- Creating expressions and equations | Worked example

## Algebraic word problems | Lesson

- Algebraic word problems | Worked example
- Linear equations | Lesson
- Linear equations | Worked example
- Quadratic equations | Lesson
- Quadratic equations | Worked example

## What are algebraic word problems?

- Translating sentences to equations
- Solving linear equations with one variable
- Evaluating algebraic expressions
- Solving problems using Venn diagrams

## How do we solve algebraic word problems?

- Define a variable.
- Write an equation using the variable.
- Solve the equation.
- If the variable is not the answer to the word problem, use the variable to calculate the answer.

## What's a Venn diagram?

- Your answer should be
- an integer, like 6 6 6 6
- a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5
- a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4
- a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4
- an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75
- a multiple of pi, like 12 pi 12\ \text{pi} 1 2 pi 12, space, start text, p, i, end text or 2 / 3 pi 2/3\ \text{pi} 2 / 3 pi 2, slash, 3, space, start text, p, i, end text
- (Choice A) $ 4 \$4 $ 4 dollar sign, 4 A $ 4 \$4 $ 4 dollar sign, 4
- (Choice B) $ 5 \$5 $ 5 dollar sign, 5 B $ 5 \$5 $ 5 dollar sign, 5
- (Choice C) $ 9 \$9 $ 9 dollar sign, 9 C $ 9 \$9 $ 9 dollar sign, 9
- (Choice D) $ 14 \$14 $ 1 4 dollar sign, 14 D $ 14 \$14 $ 1 4 dollar sign, 14
- (Choice E) $ 20 \$20 $ 2 0 dollar sign, 20 E $ 20 \$20 $ 2 0 dollar sign, 20
- (Choice A) 10 10 1 0 10 A 10 10 1 0 10
- (Choice B) 12 12 1 2 12 B 12 12 1 2 12
- (Choice C) 24 24 2 4 24 C 24 24 2 4 24
- (Choice D) 30 30 3 0 30 D 30 30 3 0 30
- (Choice E) 32 32 3 2 32 E 32 32 3 2 32
- (Choice A) 4 4 4 4 A 4 4 4 4
- (Choice B) 10 10 1 0 10 B 10 10 1 0 10
- (Choice C) 14 14 1 4 14 C 14 14 1 4 14
- (Choice D) 18 18 1 8 18 D 18 18 1 8 18
- (Choice E) 22 22 2 2 22 E 22 22 2 2 22

## Things to remember

Want to join the conversation.

## Problem Solving in Mathematics

## Use Established Procedures

## Look for Clue Words

Common clue words for addition problems:

Common clue words for subtraction problems:

Common clue words for multiplication problems:

Common clue words for division problems:

## Read the Problem Carefully

- Ask yourself if you've seen a problem similar to this one. If so, what is similar about it?
- What did you need to do in that instance?
- What facts are you given about this problem?
- What facts do you still need to find out about this problem?

## Develop a Plan and Review Your Work

- Define your problem-solving strategy or strategies. This might mean identifying patterns, using known formulas, using sketches, and even guessing and checking.
- If your strategy doesn't work, it may lead you to an ah-ha moment and to a strategy that does work.

If it seems like you’ve solved the problem, ask yourself the following:

- Does your solution seem probable?
- Does it answer the initial question?
- Did you answer using the language in the question?
- Did you answer using the same units?

If you feel confident that the answer is “yes” to all questions, consider your problem solved.

## Tips and Hints

Some key questions to consider as you approach the problem may be:

- What are the keywords in the problem?
- Do I need a data visual, such as a diagram, list, table, chart, or graph?
- Is there a formula or equation that I'll need? If so, which one?
- Will I need to use a calculator? Is there a pattern I can use or follow?

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## 6.1.1: Practice Problems- Solution Concentration

Explain what changes and what stays the same when 1.00 L of a solution of NaCl is diluted to 1.80 L.

The number of moles always stays the same in a dilution.

The concentration and the volumes change in a dilution.

Determine the molarity for each of the following solutions:

- 0.444 mol of CoCl 2 in 0.654 L of solution
- 98.0 g of phosphoric acid, H 3 PO 4 , in 1.00 L of solution
- 0.2074 g of calcium hydroxide, Ca(OH) 2 , in 40.00 mL of solution
- 10.5 kg of Na 2 SO 4 ·10H 2 O in 18.60 L of solution
- 7.0 × 10 −3 mol of I 2 in 100.0 mL of solution
- 1.8 × 10 4 mg of HCl in 0.075 L of solution

Determine the molarity of each of the following solutions:

- 1.457 mol KCl in 1.500 L of solution
- 0.515 g of H 2 SO 4 in 1.00 L of solution
- 20.54 g of Al(NO 3 ) 3 in 1575 mL of solution
- 2.76 kg of CuSO 4 ·5H 2 O in 1.45 L of solution
- 0.005653 mol of Br 2 in 10.00 mL of solution
- 0.000889 g of glycine, C 2 H 5 NO 2 , in 1.05 mL of solution

Calculate the number of moles and the mass of the solute in each of the following solutions:

Calculate the molarity of each of the following solutions:

There is about 1.0 g of calcium, as Ca 2+ , in 1.0 L of milk. What is the molarity of Ca 2+ in milk?

- 1.00 L of a 0.250- M solution of Fe(NO 3 ) 3 is diluted to a final volume of 2.00 L
- 0.5000 L of a 0.1222- M solution of C 3 H 7 OH is diluted to a final volume of 1.250 L
- 2.35 L of a 0.350- M solution of H 3 PO 4 is diluted to a final volume of 4.00 L
- 22.50 mL of a 0.025- M solution of C 12 H 22 O 11 is diluted to 100.0 mL

What volume of a 0.20- M K 2 SO 4 solution contains 57 g of K 2 SO 4 ?

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## Section 2.1 : Solutions and Solution Sets

- Is \(x = 6\) a solution to \(2x - 5 = 3\left( {1 - x} \right) + 22\)? Solution
- Is \(t = 7\) a solution to \({t^2} + 3t - 10 = 4 + 8t\)? Solution
- Is \(t = - 3\) a solution to \({t^2} + 3t - 10 = 4 + 8t\)? Solution
- Is \(w = - 2\) a solution to \(\displaystyle \frac{{{w^2} + 8w + 12}}{{w + 2}} = 0\)? Solution
- Is \(z = 4\) a solution to \(6z - {z^2} \ge {z^2} + 3\)? Solution
- Is \(y = 0\) a solution to \(2\left( {y + 7} \right) - 1 Solution
- Is \(x = 1\) a solution to \({\left( {x + 1} \right)^2} > 3x + 1\)? Solution

Unlimited AI-generated practice problems and answers

With Wolfram Problem Generator, each question is generated instantly, just for you.

## The most amazing part of Wolfram Problem Generator is something you can't even see.

## Practice for all ages

## Work with Step-by-step Solutions!

## Math Problem Solving Strategies

## Problem Solving Strategies

The strategies used in solving word problems:

## Solving Word Problems

## Problem Solving Strategy: Guess And Check

Using the guess and check problem solving strategy to help solve math word problems.

## Problem Solving : Make A Table And Look For A Pattern

- Identify - What is the question?
- Plan - What strategy will I use to solve the problem?
- Solve - Carry out your plan.
- Verify - Does my answer make sense?

## Find A Pattern Model (Intermediate)

a) The number of dots required for 7 rectangles is 52.

b) If the figure has 73 dots, there would be 10 rectangles.

The number of dots for 7 layers of triangles is 36.

Example: The following figures were formed using matchsticks.

a) Based on the above series of figures, complete the table below.

b) How many triangles are there if the figure in the series has 9 squares?

c) How many matchsticks would be used in the figure in the series with 11 squares?

Total = 6 + 5 + 4 + 3 + 2 + 1 = 21 handshakes.

## The following are some other examples of problem solving strategies.

Finding A Pattern (Basic) Finding A Pattern (Intermediate) Finding A Pattern (Advanced)

## Tips and Motivation to Master Problem Solving

## Never jump to solution quickly, practice patience and use your time wisely

## Problem solving is just like driving a Vehicle!

- Note every relevant detail (or step) and backtrack to the point of deviation. This approach is similar to steering a vehicle and returning to the correct track. By retracing your steps, you can identify where you went wrong and get back on track.
- Another idea is to learn from such failures while practicing problem-solving. By doing so, you can create a roadmap of similar situations and make smarter decisions in the future.

## Learn from failures and never give up!

## Follow quality over quantity!

## Always prepare your note to revise later

## Trust yourself and never underestimate yourself!

## Overcoming fear is a key step in achieving success

We mostly encounter two situations of fear in problem-solving:

## Think like a sport person to continue practice

## Practice universal principles of problem solving

- Trial and Error: Continue trying different solutions until the problem is solved.
- Algorithmic problem solving: Step-by-step instruction used to achieve the desired outcome.
- Problem solving using heuristic: A mental shortcuts that are used to solve problems — a “rule of thumb” is a good example.
- Working backward: A helpful idea to begin solving the problem by focusing on the end result.
- Breaking problem into a series of smaller steps: We often use this method to complete a large research project or solve complex problem.

## Track and monitor progress

- How do you explain your progress in the last six days and six months?
- What is your plan for the coming six days and six months?

## Practice focus and collaboration

- A person with good focus and good collaboration learns quickly.
- A person with good focus and poor collaboration learns at an average speed.
- A person with poor focus and poor collaboration learns slowly or struggles to learn it in a lifetime.

## Final conclusion and motivation!

- Understand and visualize the problem clearly.
- Use experiences, hypotheses, heuristics, and patterns.
- Do in-depth research about concepts.
- Try to break the problem into smaller problems or develop a step-by-step process to solve it efficiently.
- Think of solutions using multiple approaches!
- Take care of various edge cases and boundary conditions.
- Reach out to an expert or mentor if you get stuck.
- Note down critical steps that are working as a barrier towards the solution on a personal note.
- Refresh your perspective and try again later.
- Practice flexibility and avoid rigidity!
- Try to understand the reason; never memorize!
- Errors and mistakes are a part of continuous learning!
- Collaborate, exchange ideas, and keep ego aside!

Enjoy learning, Enjoy coding, enjoy problem solving :)

## Share feedback

Don’t fill this out if you’re human:

## More blogs to explore

© 2022 Code Algorithms Pvt. Ltd.

## Venn Diagram Examples, Problems and Solutions

- What is Venn diagram? Definition and meaning.
- Venn diagram formula with an explanation.
- Examples of 2 and 3 sets Venn diagrams: practice problems with solutions, questions, and answers.
- Simple 4 circles Venn diagram with word problems.
- Compare and contrast Venn diagram example.

Commonly, Venn diagrams show how given items are similar and different.

n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

From the above Venn diagram, it is quite clear that

n(A) = x + z n(B) = y + z n(A ∩ B) = z n(A ∪ B) = x +y+ z.

Now, let’s move forward and think about Venn Diagrams with 3 circles.

Following the same logic, we can write the formula for 3 circles Venn diagram :

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(C ∩ A) + n(A ∩ B ∩ C)

Venn Diagram Examples (Problems with Solutions)

2 Circle Venn Diagram Examples (word problems):

Here are some important questions we will find the answers:

- How many people go to work by car only?
- How many people go to work by bicycle only?
- How many people go by neither car nor bicycle?
- How many people use at least one of both transportation types?
- How many people use only one of car or bicycle?

The following Venn diagram represents the data above:

Now, we are going to answer our questions:

- Number of people who go to work by car only = 280
- Number of people who go to work by bicycle only = 220
- Number of people who go by neither car nor bicycle = 160
- Number of people who use at least one of both transportation types = n(only car) + n(only bicycle) + n(both car and bicycle) = 280 + 220 + 140 = 640
- Number of people who use only one of car or bicycle = 280 + 220 = 500

We will deep further with a more complicated triple Venn diagram example.

3 Circle Venn Diagram Examples:

Here are our questions we should find the answer:

- How many women like watching all the three movie genres?
- Find the number of women who like watching only one of the three genres.
- Find the number of women who like watching at least two of the given genres.

Let’s represent the data above in a more digestible way using the Venn diagram formula elements:

- n(C) = percentage of women who like watching comedy = 52%
- n(F ) = percentage of women who like watching fantasy = 45%
- n(R) = percentage of women who like watching romantic movies= 60%
- n(C∩F) = 25%; n(F∩R) = 28%; n(C∩R) = 30%
- Since 6% like watching none of the given genres so, n (C ∪ F ∪ R) = 94%.

Now, we are going to apply the Venn diagram formula for 3 circles.

94% = 52% + 45% + 60% – 25% – 28% – 30% + n (C ∩ F ∩ R)

Solving this simple math equation, lead us to:

It is a great time to make our Venn diagram related to the above situation (problem):

See, the Venn diagram makes our situation much more clear!

From the Venn diagram example, we can answer our questions with ease.

- The number of women who like watching all the three genres = 20% of 1000 = 200.
- Number of women who like watching only one of the three genres = (17% + 12% + 22%) of 1000 = 510
- The number of women who like watching at least two of the given genres = (number of women who like watching only two of the genres) +(number of women who like watching all the three genres) = (10 + 5 + 8 + 20)% i.e. 43% of 1000 = 430.

4 Circles Venn Diagram Example:

A set of students were asked to tell which sports they played in school.

The options are: Football, Hockey, Basketball, and Netball.

Here is the list of the results:

The next step is to draw a Venn diagram to show the data sets we have.

Compare and Contrast Venn Diagram Example:

The following compare and contrast example of Venn diagram compares the features of birds and bats:

Tools for creating Venn diagrams

You can use Microsoft products such as:

## About The Author

## Silvia Valcheva

## One Response

Well explained I hope more on this one

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## Solving Equations

An equation says that two things are equal. It will have an equals sign "=" like this:

what is on the left (x − 2) equals what is on the right (4)

So an equation is like a statement " this equals that "

## What is a Solution?

A Solution is a value we can put in place of a variable (such as x ) that makes the equation true .

## Example: x − 2 = 4

When we put 6 in place of x we get:

How about other values for x ?

- For x=5 we get "5−2=4" which is not true , so x=5 is not a solution .
- For x=9 we get "9−2=4" which is not true , so x=9 is not a solution .

In this case x = 6 is the only solution.

You might like to practice solving some animated equations .

## More Than One Solution

There can be more than one solution.

## Example: (x−3)(x−2) = 0

When we gather all solutions together it is called a Solution Set

The above solution set is: {2, 3}

## Solutions Everywhere!

Some equations are true for all allowed values and are then called Identities

## Example: sin(−θ) = −sin(θ) is one of the Trigonometric Identities

So it is also true for θ = 90°

Is it true for all values of θ ? Try some values for yourself!

## How to Solve an Equation

There is no "one perfect way" to solve all equations.

## A Useful Goal

But we often get success when our goal is to end up with:

## Example: Solve 3x−6 = 9

and a short calculation reveals that x = 5

## Like a Puzzle

Here are some things we can do:

- Add or Subtract the same value from both sides
- Clear out any fractions by Multiplying every term by the bottom parts
- Divide every term by the same nonzero value
- Combine Like Terms
- Expanding (the opposite of factoring) may also help
- Recognizing a pattern, such as the difference of squares
- Sometimes we can apply a function to both sides (e.g. square both sides)

## Example: Solve √(x/2) = 3

And the more "tricks" and techniques you learn the better you will get.

## Special Equations

There are special ways of solving some types of equations. Learn how to ...

## Check Your Solutions

You should always check that your "solution" really is a solution.

## How To Check

Take the solution(s) and put them in the original equation to see if they really work.

## Example: solve for x:

We have said x≠3 to avoid a division by zero.

Let's multiply through by (x − 3) :

Which can be solved by having x=3

Let us check x=3 using the original question:

Hang On: 3 − 3 = 0 That means dividing by Zero!

And anyway, we said at the top that x≠3 , so ...

x = 3 does not actually work, and so:

"Solving" only gives us possible solutions, they need to be checked!

- Note down where an expression is not defined (due to a division by zero, the square root of a negative number, or some other reason)
- Show all the steps , so it can be checked later (by you or someone else)

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Problems for 5th Grade. Multi-digit multiplication. Dividing completely. Writing expressions. Rounding whole numbers. Inequalities on a number line. Linear equation and inequality word problems. Linear equation word problems. Linear equation word problems.

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What is a Solution? A Solution is a value we can put in place of a variable (such as x) that makes the equation true. Example: x − 2 = 4. ... You might like to practice solving some animated equations. More Than One Solution. There can be more than one solution. Example: (x−3)(x−2) = 0. When x is 3 we get:

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