Want Better Math Grades?
✅ Unlimited Solutions
✅ Step-by-Step Answers
✅ Available 24/7
➕ Free Bonuses ($1085 value!)
On this page
- Search IntMath
- Math interactives
- About (site info)
- Uses of Trignometry
- ASCIIMath input, KaTeX output
- ASCIIMath input, LaTeX and KaTeX output
- Send Math in emails
- Syntax for ASCIIMathML
- Math Display Experiments
- Scientific Notebook
Math Problem Solver
Related Sections
Math Tutoring
Need help? Chat with a tutor anytime, 24/7.
This tool combines the power of mathematical computation engine that excels at solving mathematical formulas with the power of artificial intelligence large language models to parse and generate natural language answers. This creates a math problem solver that's more accurate than ChatGPT, more flexible than a math calculator, and provides answers faster than a human tutor.
Sign up for free here .
Problem Solver Subjects
Our math problem solver that lets you input a wide variety of math math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects.
- Math Word Problems
- Pre-Algebra
- Geometry Graphing
- Trigonometry
- Precalculus
- Finite Math
- Linear Algebra
Here are example math problems within each subject that can be input into the calculator and solved. This list is constanstly growing as functionality is added to the calculator.
Basic Math Solutions
Below are examples of basic math problems that can be solved.
- Long Arithmetic
- Rational Numbers
- Operations with Fractions
- Ratios, Proportions, Percents
- Measurement, Area, and Volume
- Factors, Fractions, and Exponents
- Unit Conversions
- Data Measurement and Statistics
- Points and Line Segments
Math Word Problem Solutions
Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.
Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?
Simplified Equation: 17 - x = 8
Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?
Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)
Simplified Equation: {r = d + 12, d = b + 6, r = 2 �� b}
Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?
Simplified: 40 - 10 - 5
Pre-Algebra Solutions
Below are examples of Pre-Algebra math problems that can be solved.
- Variables, Expressions, and Integers
- Simplifying and Evaluating Expressions
- Solving Equations
- Multi-Step Equations and Inequalities
- Ratios, Proportions, and Percents
- Linear Equations and Inequalities
Algebra Solutions
Below are examples of Algebra math problems that can be solved.
- Algebra Concepts and Expressions
- Points, Lines, and Line Segments
- Simplifying Polynomials
- Factoring Polynomials
- Linear Equations
- Absolute Value Expressions and Equations
- Radical Expressions and Equations
- Systems of Equations
- Quadratic Equations
- Inequalities
- Complex Numbers and Vector Analysis
- Logarithmic Expressions and Equations
- Exponential Expressions and Equations
- Conic Sections
- Vector Spaces
- 3d Coordinate System
- Eigenvalues and Eigenvectors
- Linear Transformations
- Number Sets
- Analytic Geometry
Trigonometry Solutions
Below are examples of Trigonometry math problems that can be solved.
- Algebra Concepts and Expressions Review
- Right Triangle Trigonometry
- Radian Measure and Circular Functions
- Graphing Trigonometric Functions
- Simplifying Trigonometric Expressions
- Verifying Trigonometric Identities
- Solving Trigonometric Equations
- Complex Numbers
- Analytic Geometry in Polar Coordinates
- Exponential and Logarithmic Functions
- Vector Arithmetic
Precalculus Solutions
Below are examples of Precalculus math problems that can be solved.
- Operations on Functions
- Rational Expressions and Equations
- Polynomial and Rational Functions
- Analytic Trigonometry
- Sequences and Series
- Analytic Geometry in Rectangular Coordinates
- Limits and an Introduction to Calculus
Calculus Solutions
Below are examples of Calculus math problems that can be solved.
- Evaluating Limits
- Derivatives
- Applications of Differentiation
- Applications of Integration
- Techniques of Integration
- Parametric Equations and Polar Coordinates
- Differential Equations
Statistics Solutions
Below are examples of Statistics problems that can be solved.
- Algebra Review
- Average Descriptive Statistics
- Dispersion Statistics
- Probability
- Probability Distributions
- Frequency Distribution
- Normal Distributions
- t-Distributions
- Hypothesis Testing
- Estimation and Sample Size
- Correlation and Regression
Finite Math Solutions
Below are examples of Finite Math problems that can be solved.
- Polynomials and Expressions
- Equations and Inequalities
- Linear Functions and Points
- Systems of Linear Equations
- Mathematics of Finance
- Statistical Distributions
Linear Algebra Solutions
Below are examples of Linear Algebra math problems that can be solved.
- Introduction to Matrices
- Linear Independence and Combinations
Chemistry Solutions
Below are examples of Chemistry problems that can be solved.
- Unit Conversion
- Atomic Structure
- Molecules and Compounds
- Chemical Equations and Reactions
- Behavior of Gases
- Solutions and Concentrations
Physics Solutions
Below are examples of Physics math problems that can be solved.
- Static Equilibrium
- Dynamic Equilibrium
- Kinematics Equations
- Electricity
- Thermodymanics
Geometry Graphing Solutions
Below are examples of Geometry and graphing math problems that can be solved.
- Step By Step Graphing
- Linear Equations and Functions
- Polar Equations
Looking for the old Mathway Calculator? We've moved it to here .
Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.
Email Address Sign Up
Solving Word Questions
With LOTS of examples!
In Algebra we often have word questions like:
Example: Sam and Alex play tennis.
On the weekend Sam played 4 more games than Alex did, and together they played 12 games.
How many games did Alex play?
How do we solve them?
The trick is to break the solution into two parts:
Turn the English into Algebra.
Then use Algebra to solve.
Turning English into Algebra
To turn the English into Algebra it helps to:
- Read the whole thing first
- Do a sketch if possible
- Assign letters for the values
- Find or work out formulas
You should also write down what is actually being asked for , so you know where you are going and when you have arrived!
Also look for key words:
When you see | Think | |
---|---|---|
add, total, sum, increase, more, combined, together, plus, more than | + | |
minus, less, difference, fewer, decreased, reduced | − | |
multiplied, times, of, product, factor | × | |
divided, quotient, per, out of, ratio, percent, rate | ÷ | |
maximize or minimize | geometry formulas | |
rate, speed | distance formulas | |
how long, days, hours, minutes, seconds | time |
Thinking Clearly
Some wording can be tricky, making it hard to think "the right way around", such as:
Example: Sam has 2 dollars less than Alex. How do we write this as an equation?
- Let S = dollars Sam has
- Let A = dollars Alex has
Now ... is that: S − 2 = A
or should it be: S = A − 2
or should it be: S = 2 − A
The correct answer is S = A − 2
( S − 2 = A is a common mistake, as the question is written "Sam ... 2 less ... Alex")
Example: on our street there are twice as many dogs as cats. How do we write this as an equation?
- Let D = number of dogs
- Let C = number of cats
Now ... is that: 2D = C
or should it be: D = 2C
Think carefully now!
The correct answer is D = 2C
( 2D = C is a common mistake, as the question is written "twice ... dogs ... cats")
Let's start with a really simple example so we see how it's done:
Example: A rectangular garden is 12m by 5m, what is its area ?
Turn the English into Algebra:
- Use w for width of rectangle: w = 12m
- Use h for height of rectangle: h = 5m
Formula for Area of a Rectangle : A = w × h
We are being asked for the Area.
A = w × h = 12 × 5 = 60 m 2
The area is 60 square meters .
Now let's try the example from the top of the page:
Example: Sam and Alex play Tennis. On the weekend Sam played 4 more games than Alex did, and together they played 12 games. How many games did Alex play?
- Use S for how many games Sam played
- Use A for how many games Alex played
We know that Sam played 4 more games than Alex, so: S = A + 4
And we know that together they played 12 games: S + A = 12
We are being asked for how many games Alex played: A
Which means that Alex played 4 games of tennis.
Check: Sam played 4 more games than Alex, so Sam played 8 games. Together they played 8 + 4 = 12 games. Yes!
A slightly harder example:
Example: Alex and Sam also build tables. Together they make 10 tables in 12 days. Alex working alone can make 10 in 30 days. How long would it take Sam working alone to make 10 tables?
- Use a for Alex's work rate
- Use s for Sam's work rate
12 days of Alex and Sam is 10 tables, so: 12a + 12s = 10
30 days of Alex alone is also 10 tables: 30a = 10
We are being asked how long it would take Sam to make 10 tables.
30a = 10 , so Alex's rate (tables per day) is: a = 10/30 = 1/3
Which means that Sam's rate is half a table a day (faster than Alex!)
So 10 tables would take Sam just 20 days.
Should Sam be paid more I wonder?
And another "substitution" example:
Example: Jenna is training hard to qualify for the National Games. She has a regular weekly routine, training for five hours a day on some days and 3 hours a day on the other days. She trains altogether 27 hours in a seven day week. On how many days does she train for five hours?
- The number of "5 hour" days: d
- The number of "3 hour" days: e
We know there are seven days in the week, so: d + e = 7
And she trains 27 hours in a week, with d 5 hour days and e 3 hour days: 5d + 3e = 27
We are being asked for how many days she trains for 5 hours: d
The number of "5 hour" days is 3
Check : She trains for 5 hours on 3 days a week, so she must train for 3 hours a day on the other 4 days of the week.
3 × 5 hours = 15 hours, plus 4 × 3 hours = 12 hours gives a total of 27 hours
Some examples from Geometry:
Example: A circle has an area of 12 mm 2 , what is its radius?
- Use A for Area: A = 12 mm 2
- Use r for radius
And the formula for Area is: A = π r 2
We are being asked for the radius.
We need to rearrange the formula to find the area
Example: A cube has a volume of 125 mm 3 , what is its surface area?
Make a quick sketch:
- Use V for Volume
- Use A for Area
- Use s for side length of cube
- Volume of a cube: V = s 3
- Surface area of a cube: A = 6s 2
We are being asked for the surface area.
First work out s using the volume formula:
Now we can calculate surface area:
An example about Money:
Example: Joel works at the local pizza parlor. When he works overtime he earns 1¼ times the normal rate. One week Joel worked for 40 hours at the normal rate of pay and also worked 12 hours overtime. If Joel earned $660 altogether in that week, what is his normal rate of pay?
- Joel's normal rate of pay: $N per hour
- Joel works for 40 hours at $N per hour = $40N
- When Joel does overtime he earns 1¼ times the normal rate = $1.25N per hour
- Joel works for 12 hours at $1.25N per hour = $(12 × 1¼N) = $15N
- And together he earned $660, so:
$40N + $(12 × 1¼N) = $660
We are being asked for Joel's normal rate of pay $N.
So Joel’s normal rate of pay is $12 per hour
Joel’s normal rate of pay is $12 per hour, so his overtime rate is 1¼ × $12 per hour = $15 per hour. So his normal pay of 40 × $12 = $480, plus his overtime pay of 12 × $15 = $180 gives us a total of $660
More about Money, with these two examples involving Compound Interest
Example: Alex puts $2000 in the bank at an annual compound interest of 11%. How much will it be worth in 3 years?
This is the compound interest formula:
So we will use these letters:
- Present Value PV = $2,000
- Interest Rate (as a decimal): r = 0.11
- Number of Periods: n = 3
- Future Value (the value we want): FV
We are being asked for the Future Value: FV
Example: Roger deposited $1,000 into a savings account. The money earned interest compounded annually at the same rate. After nine years Roger's deposit has grown to $1,551.33 What was the annual rate of interest for the savings account?
The compound interest formula:
- Present Value PV = $1,000
- Interest Rate (the value we want): r
- Number of Periods: n = 9
- Future Value: FV = $1,551.33
We are being asked for the Interest Rate: r
So the annual rate of interest is 5%
Check : $1,000 × (1.05) 9 = $1,000 × 1.55133 = $1,551.33
And an example of a Ratio question:
Example: At the start of the year the ratio of boys to girls in a class is 2 : 1 But now, half a year later, four boys have left the class and there are two new girls. The ratio of boys to girls is now 4 : 3 How many students are there altogether now?
- Number of boys now: b
- Number of girls now: g
The current ratio is 4 : 3
Which can be rearranged to 3b = 4g
At the start of the year there was (b + 4) boys and (g − 2) girls, and the ratio was 2 : 1
b + 4 g − 2 = 2 1
Which can be rearranged to b + 4 = 2(g − 2)
We are being asked for how many students there are altogether now: b + g
There are 12 girls !
And 3b = 4g , so b = 4g/3 = 4 × 12 / 3 = 16 , so there are 16 boys
So there are now 12 girls and 16 boys in the class, making 28 students altogether .
There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1
And now for some Quadratic Equations :
Example: The product of two consecutive even integers is 168. What are the integers?
Consecutive means one after the other. And they are even , so they could be 2 and 4, or 4 and 6, etc.
We will call the smaller integer n , and so the larger integer must be n+2
And we are told the product (what we get after multiplying) is 168, so we know:
n(n + 2) = 168
We are being asked for the integers
That is a Quadratic Equation , and there are many ways to solve it. Using the Quadratic Equation Solver we get −14 and 12.
Check −14: −14(−14 + 2) = (−14)×(−12) = 168 YES
Check 12: 12(12 + 2) = 12×14 = 168 YES
So there are two solutions: −14 and −12 is one, 12 and 14 is the other.
Note: we could have also tried "guess and check":
- We could try, say, n=10: 10(12) = 120 NO (too small)
- Next we could try n=12: 12(14) = 168 YES
But unless we remember that multiplying two negatives make a positive we might overlook the other solution of (−14)×(−12).
Example: You are an Architect. Your client wants a room twice as long as it is wide. They also want a 3m wide veranda along the long side. Your client has 56 square meters of beautiful marble tiles to cover the whole area. What should the length of the room be?
Let's first make a sketch so we get things right!:
- the length of the room: L
- the width of the room: W
- the total Area including veranda: A
- the width of the room is half its length: W = ½L
- the total area is the (room width + 3) times the length: A = (W+3) × L = 56
We are being asked for the length of the room: L
This is a quadratic equation , there are many ways to solve it, this time let's use factoring :
And so L = 8 or −14
There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!
So the length of the room is 8 m
L = 8, so W = ½L = 4
So the area of the rectangle = (W+3) × L = 7 × 8 = 56
There we are ...
... I hope these examples will help you get the idea of how to handle word questions. Now how about some practice?
How do you solve word problems in math?
Master word problems with eight simple steps from a math tutor!
Author Amber Watkins
Published April 2024
- Key takeaways
- Students who struggle with reading, tend to struggle with understanding and solving word problems. So the best way to solve word problems in math is to become a better reader!
- Mastery of word problems relies on your child’s knowledge of keywords for word problems in math and knowing what to do with them.
- There are 8 simple steps each child can use to solve word problems- let’s go over these together.
Table of contents
- How to solve word problems
Lesson credits
As a tutor who has seen countless math worksheets in almost every grade – I’ll tell you this: every child is going to encounter word problems in math. The key to mastery lies in how you solve them! So then, how do you solve word problems in math?
In this guide, I’ll share eight steps to solving word problems in math.
How to solve word problems in math in 8 steps
Step 1: read the word problem aloud.
For a child to understand a word problem, it needs to be read with accuracy and fluency! That is why, when I tutor children with word problems, I always emphasize the importance of reading properly.
Mastering step 1 looks like this:
- Allow your child to read the word problem aloud to you.
- Don’t let your child skip over or mispronounce any words.
- If necessary, model how to read the word problem, then allow your child to read it again. Only after the word problem is read accurately, should you move on to step 2.
Step 2: Highlight the keywords in the word problem
The keywords for word problems in math indicate what math action should be taken. Teach your child to highlight or underline the keywords in every word problem.
Here are some of the most common keywords in math word problems:
- Subtraction words – less than, minus, take away
- Addition words – more than, altogether, plus, perimeter
- Multiplication words – Each, per person, per item, times, area
- Division words – divided by, into
- Total words – in all, total, altogether
Let’s practice. Read the following word problem with your child and help them highlight or underline the main keyword, then decide which math action should be taken.
Michael has ten baseball cards. James has four baseball cards less than Michael. How many total baseball cards does James have?
The words “less than” are the keywords and they tell us to use subtraction .
Step 3: Make math symbols above keywords to decode the word problem
As I help students with word problems, I write math symbols and numbers above the keywords. This helps them to understand what the word problem is asking.
Let’s practice. Observe what I write over the keywords in the following word problem and think about how you would create a math sentence using them:
Step 4: Create a math sentence to represent the word problem
Using the previous example, let’s write a math sentence. Looking at the math symbols and numbers written above the word problem, our math sentence should be: 10 – 5 = 5 !
Each time you practice a word problem with your child, highlight keywords and write the math symbols above them. Then have your child create a math sentence to solve.
Step 5: Draw a picture to help illustrate the word problem
Pictures can be very helpful for problems that are more difficult to understand. They also are extremely helpful when the word problem involves calculating time , comparing fractions , or measurements .
Step 6: Always show your work
Help your child get into the habit of always showing their work. As a tutor, I’ve found many reasons why having students show their work is helpful:
- By showing their work, they are writing the math steps repeatedly, which aids in memory
- If they make any mistakes they can track where they happened
- Their teacher can assess how much they understand by reviewing their work
- They can participate in class discussions about their work
Step 7: When solving word problems, make sure there is always a word in your answer!
If the word problem asks: How many peaches did Lisa buy? Your child’s answer should be: Lisa bought 10 peaches .
If the word problem asks: How far did Kyle run? Your child’s answer should be: Kyle ran 20 miles .
So how do you solve a word problem in math?
Together we reviewed the eight simple steps to solve word problems. These steps included identifying keywords for word problems in math, drawing pictures, and learning to explain our answers.
Is your child ready to put these new skills to the test? Check out the best math app for some fun math word problem practice.
Parents, sign up for a DoodleMath subscription and see your child become a math wizard!
Amber Watkins
Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring elementary through college level math. "Knowing that my work in math education makes such an impact leaves me with an indescribable feeling of pride and joy!"
What we offer
Quick links
All rights reserved.
Are you a parent, teacher or student?
Get started for free!
Maths information pack
We ask for your contact info so we can send our info pack directly to your inbox for your convenience, exam prep information pack, case studies information pack.
Book a chat with our team
I’m new to Doodle
My school is already using Doodle
Information pack
We ask for your contact info so that our education consultants can get in touch with you and let you know a bit more about doodle., student login, which programme would you like to use.
DoodleMaths
DoodleTables
DoodleEnglish
DoodleSpell
If you’d like to use Doodle’s browser version, please visit this page on a desktop.
To log in to Doodle on this device, you can do so through our apps. You can find out how to download them here:
- Pre-Algebra Topics
- Algebra Topics
- Algebra Calculator
- Algebra Cheat Sheet
- Algebra Practice Test
- Algebra Readiness Test
- Algebra Formulas
- Want to Build Your Own Website?
Sign In / Register
REAL WORLD PROBLEMS: How to Write Equations Based on Algebra Word Problems
I know that you often sit in class and wonder, "Why am I forced to learn about equations, Algebra and variables?"
But... trust me, there are real situations where you will use your knowledge of Algebra and solving equations to solve a problem that is not school related. And... if you can't, you're going to wish that you remembered how.
It might be a time when you are trying to figure out how much you should get paid for a job, or even more important, if you were paid enough for a job that you've done. It could also be a time when you are trying to figure out if you were over charged for a bill.
This is important stuff - when it comes time to spend YOUR money - you are going to want to make sure that you are getting paid enough and not spending more than you have to.
Ok... let's put all this newly learned knowledge to work.
Click here if you need to review how to solve equations.
There are a few rules to remember when writing Algebra equations:
Writing Equations For Word Problems
- First, you want to identify the unknown, which is your variable. What are you trying to solve for? Identify the variable: Use the statement, Let x = _____. You can replace the x with whatever variable you are using.
- Look for key words that will help you write the equation. Highlight the key words and write an equation to match the problem.
- The following key words will help you write equations for Algebra word problems:
subtraction
Multiplication.
double (2x)
triple (3x)
quadruple (4x)
divided into
Let's look at an example of an algebra word problem.
Example 1: Algebra Word Problems
Linda was selling tickets for the school play. She sold 10 more adult tickets than children tickets and she sold twice as many senior tickets as children tickets.
- Let x represent the number of children's tickets sold.
- Write an expression to represent the number of adult tickets sold.
- Write an expression to represent the number of senior tickets sold.
- Adult tickets cost $5, children's tickets cost $2, and senior tickets cost $3. Linda made $700. Write an equation to represent the total ticket sales.
- How many children's tickets were sold for the play? How many adult tickets were sold? How many senior tickets were sold?
As you can see, this problem is massive! There are 5 questions to answer with many expressions to write.
A few notes about this problem
1. In this problem, the variable was defined for you. Let x represent the number of children’s tickets sold tells what x stands for in this problem. If this had not been done for you, you might have written it like this:
Let x = the number of children’s tickets sold
2. For the first expression, I knew that 10 more adult tickets were sold. Since more means add, my expression was x +10 . Since the direction asked for an expression, I don’t need an equal sign. An equation is written with an equal sign and an expression is without an equal sign. At this point we don’t know the total number of tickets.
3. For the second expression, I knew that my key words, twice as many meant two times as many. So my expression was 2x .
4. We know that to find the total price we have to multiply the price of each ticket by the number of tickets. Take note that since x + 10 is the quantity of adult tickets, you must put it in parentheses! So, when you multiply by the price of $5 you have to distribute the 5.
5. Once I solve for x, I know the number of children’s tickets and I can take my expressions that I wrote for #1 and substitute 50 for x to figure out how many adult and senior tickets were sold.
Where Can You Find More Algebra Word Problems to Practice?
Word problems are the most difficult type of problem to solve in math. So, where can you find quality word problems WITH a detailed solution?
The Algebra Class E-course provides a lot of practice with solving word problems for every unit! The best part is.... if you have trouble with these types of problems, you can always find a step-by-step solution to guide you through the process!
Click here for more information.
The next example shows how to identify a constant within a word problem.
Example 2 - Identifying a Constant
A cell phone company charges a monthly rate of $12.95 and $0.25 a minute per call. The bill for m minutes is $21.20.
1. Write an equation that models this situation.
2. How many minutes were charged on this bill?
Notes For Example 2
- $12.95 is a monthly rate. Since this is a set fee for each month, I know that this is a constant. The rate does not change; therefore, it is not associated with a variable.
- $0.25 per minute per call requires a variable because the total amount will change based on the number of minutes. Therefore, we use the expression 0.25m
- You must solve the equation to determine the value for m, which is the number of minutes charged.
The last example is a word problem that requires an equation with variables on both sides.
Example 3 - Equations with Variables on Both Sides
You have $60 and your sister has $120. You are saving $7 per week and your sister is saving $5 per week. How long will it be before you and your sister have the same amount of money? Write an equation and solve.
Notes for Example 3
- $60 and $120 are constants because this is the amount of money that they each have to begin with. This amount does not change.
- $7 per week and $5 per week are rates. They key word "per" in this situation means to multiply.
- The key word "same" in this problem means that I am going to set my two expressions equal to each other.
- When we set the two expressions equal, we now have an equation with variables on both sides.
- After solving the equation, you find that x = 30, which means that after 30 weeks, you and your sister will have the same amount of money.
I'm hoping that these three examples will help you as you solve real world problems in Algebra!
- Solving Equations
- Algebra Word Problems
Need More Help With Your Algebra Studies?
Get access to hundreds of video examples and practice problems with your subscription!
Click here for more information on our affordable subscription options.
Not ready to subscribe? Register for our FREE Pre-Algebra Refresher course.
ALGEBRA CLASS E-COURSE MEMBERS
Click here for more information on our Algebra Class e-courses.
Need Help? Try This Online Calculator!
Affiliate Products...
On this site, I recommend only one product that I use and love and that is Mathway If you make a purchase on this site, I may receive a small commission at no cost to you.
Privacy Policy
Let Us Know How we are doing!
send us a message to give us more detail!
Facebook X |
Would you prefer to share this page with others by linking to it?
- Click on the HTML link code below.
- Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.
Copyright © 2009-2020 | Karin Hutchinson | ALL RIGHTS RESERVED.
- Get started with computers
- Learn Microsoft Office
- Apply for a job
- Improve my work skills
- Design nice-looking docs
- Getting Started
- Smartphones & Tablets
- Typing Tutorial
- Online Learning
- Basic Internet Skills
- Online Safety
- Social Media
- Zoom Basics
- Google Docs
- Google Sheets
- Career Planning
- Resume Writing
- Cover Letters
- Job Search and Networking
- Business Communication
- Entrepreneurship 101
- Careers without College
- Job Hunt for Today
- 3D Printing
- Freelancing 101
- Personal Finance
- Sharing Economy
- Decision-Making
- Graphic Design
- Photography
- Image Editing
- Learning WordPress
- Language Learning
- Critical Thinking
- For Educators
- Translations
- Staff Picks
- English expand_more expand_less
Algebra Topics - Introduction to Word Problems
Algebra topics -, introduction to word problems, algebra topics introduction to word problems.
Algebra Topics: Introduction to Word Problems
Lesson 9: introduction to word problems.
/en/algebra-topics/solving-equations/content/
What are word problems?
A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem. For instance, does this sound familiar?
Johnny has 12 apples. If he gives four to Susie, how many will he have left?
You could solve this problem by looking at the numbers and figuring out what the problem is asking you to do. In this case, you're supposed to find out how many apples Johnny has left at the end of the problem. By reading the problem, you know Johnny starts out with 12 apples. By the end, he has 4 less because he gave them away. You could write this as:
12 - 4 = 8 , so you know Johnny has 8 apples left.
Word problems in algebra
If you were able to solve this problem, you should also be able to solve algebra word problems. Yes, they involve more complicated math, but they use the same basic problem-solving skills as simpler word problems.
You can tackle any word problem by following these five steps:
- Read through the problem carefully, and figure out what it's about.
- Represent unknown numbers with variables.
- Translate the rest of the problem into a mathematical expression.
- Solve the problem.
- Check your work.
We'll work through an algebra word problem using these steps. Here's a typical problem:
The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took two days, and the van cost $360. How many miles did she drive?
It might seem complicated at first glance, but we already have all of the information we need to solve it. Let's go through it step by step.
Step 1: Read through the problem carefully.
With any problem, start by reading through the problem. As you're reading, consider:
- What question is the problem asking?
- What information do you already have?
Let's take a look at our problem again. What question is the problem asking? In other words, what are you trying to find out?
The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took 2 days, and the van cost $360. How many miles did she drive?
There's only one question here. We're trying to find out how many miles Jada drove . Now we need to locate any information that will help us answer this question.
There are a few important things we know that will help us figure out the total mileage Jada drove:
- The van cost $30 per day.
- In addition to paying a daily charge, Jada paid $0.50 per mile.
- Jada had the van for 2 days.
- The total cost was $360 .
Step 2: Represent unknown numbers with variables.
In algebra, you represent unknown numbers with letters called variables . (To learn more about variables, see our lesson on reading algebraic expressions .) You can use a variable in the place of any amount you don't know. Looking at our problem, do you see a quantity we should represent with a variable? It's often the number we're trying to find out.
Since we're trying to find the total number of miles Jada drove, we'll represent that amount with a variable—at least until we know it. We'll use the variable m for miles . Of course, we could use any variable, but m should be easy to remember.
Step 3: Translate the rest of the problem.
Let's take another look at the problem, with the facts we'll use to solve it highlighted.
The rate to rent a small moving van is $30 per day , plus $0.50 per mile . Jada rented a van to drive to her new home. It took 2 days , and the van cost $360 . How many miles did she drive?
We know the total cost of the van, and we know that it includes a fee for the number of days, plus another fee for the number of miles. It's $30 per day, and $0.50 per mile. A simpler way to say this would be:
$30 per day plus $0.50 per mile is $360.
If you look at this sentence and the original problem, you can see that they basically say the same thing: It cost Jada $30 per day and $0.50 per mile, and her total cost was $360 . The shorter version will be easier to translate into a mathematical expression.
Let's start by translating $30 per day . To calculate the cost of something that costs a certain amount per day, you'd multiply the per-day cost by the number of days—in other words, 30 per day could be written as 30 ⋅ days, or 30 times the number of days . (Not sure why you'd translate it this way? Check out our lesson on writing algebraic expressions .)
$30 per day and $.50 per mile is $360
$30 ⋅ day + $.50 ⋅ mile = $360
As you can see, there were a few other words we could translate into operators, so and $.50 became + $.50 , $.50 per mile became $.50 ⋅ mile , and is became = .
Next, we'll add in the numbers and variables we already know. We already know the number of days Jada drove, 2 , so we can replace that. We've also already said we'll use m to represent the number of miles, so we can replace that too. We should also take the dollar signs off of the money amounts to make them consistent with the other numbers.
30 ⋅ 2 + .5 ⋅ m = 360
Now we have our expression. All that's left to do is solve it.
Step 4: Solve the problem.
This problem will take a few steps to solve. (If you're not sure how to do the math in this section, you might want to review our lesson on simplifying expressions .) First, let's simplify the expression as much as possible. We can multiply 30 and 2, so let's go ahead and do that. We can also write .5 ⋅ m as 0.5 m .
60 + .5m = 360
Next, we need to do what we can to get the m alone on the left side of the equals sign. Once we do that, we'll know what m is equal to—in other words, it will let us know the number of miles in our word problem.
We can start by getting rid of the 60 on the left side by subtracting it from both sides .
60 | + .5m = | 360 |
-60 | -60 |
The only thing left to get rid of is .5 . Since it's being multiplied with m , we'll do the reverse and divide both sides of the equation with it.
.5m | = | 300 |
.5 | .5 |
.5 m / .5 is m and 300 / 0.50 is 600 , so m = 600 . In other words, the answer to our problem is 600 —we now know Jada drove 600 miles.
Step 5: Check the problem.
To make sure we solved the problem correctly, we should check our work. To do this, we can use the answer we just got— 600 —and calculate backward to find another of the quantities in our problem. In other words, if our answer for Jada's distance is correct, we should be able to use it to work backward and find another value, like the total cost. Let's take another look at the problem.
According to the problem, the van costs $30 per day and $0.50 per mile. If Jada really did drive 600 miles in 2 days, she could calculate the cost like this:
$30 per day and $0.50 per mile
30 ⋅ day + .5 ⋅ mile
30 ⋅ 2 + .5 ⋅ 600
According to our math, the van would cost $360, which is exactly what the problem says. This means our solution was correct. We're done!
While some word problems will be more complicated than others, you can use these basic steps to approach any word problem. On the next page, you can try it for yourself.
Let's practice with a couple more problems. You can solve these problems the same way we solved the first one—just follow the problem-solving steps we covered earlier. For your reference, these steps are:
If you get stuck, you might want to review the problem on page 1. You can also take a look at our lesson on writing algebraic expressions for some tips on translating written words into math.
Try completing this problem on your own. When you're done, move on to the next page to check your answer and see an explanation of the steps.
A single ticket to the fair costs $8. A family pass costs $25 more than half of that. How much does a family pass cost?
Here's another problem to do on your own. As with the last problem, you can find the answer and explanation to this one on the next page.
Flor and Mo both donated money to the same charity. Flor gave three times as much as Mo. Between the two of them, they donated $280. How much money did Mo give?
Problem 1 Answer
Here's Problem 1:
A single ticket to the fair costs $8. A family pass costs $25 more than half that. How much does a family pass cost?
Answer: $29
Let's solve this problem step by step. We'll solve it the same way we solved the problem on page 1.
Step 1: Read through the problem carefully
The first in solving any word problem is to find out what question the problem is asking you to solve and identify the information that will help you solve it . Let's look at the problem again. The question is right there in plain sight:
So is the information we'll need to answer the question:
- A single ticket costs $8 .
- The family pass costs $25 more than half the price of the single ticket.
Step 2: Represent the unknown numbers with variables
The unknown number in this problem is the cost of the family pass . We'll represent it with the variable f .
Step 3: Translate the rest of the problem
Let's look at the problem again. This time, the important facts are highlighted.
A single ticket to the fair costs $8 . A family pass costs $25 more than half that . How much does a family pass cost?
In other words, we could say that the cost of a family pass equals half of $8, plus $25 . To turn this into a problem we can solve, we'll have to translate it into math. Here's how:
- First, replace the cost of a family pass with our variable f .
f equals half of $8 plus $25
- Next, take out the dollar signs and replace words like plus and equals with operators.
f = half of 8 + 25
- Finally, translate the rest of the problem. Half of can be written as 1/2 times , or 1/2 ⋅ :
f = 1/2 ⋅ 8 + 25
Step 4: Solve the problem
Now all we have to do is solve our problem. Like with any problem, we can solve this one by following the order of operations.
- f is already alone on the left side of the equation, so all we have to do is calculate the right side.
- First, multiply 1/2 by 8 . 1/2 ⋅ 8 is 4 .
- Next, add 4 and 25. 4 + 25 equals 29 .
That's it! f is equal to 29. In other words, the cost of a family pass is $29 .
Step 5: Check your work
Finally, let's check our work by working backward from our answer. In this case, we should be able to correctly calculate the cost of a single ticket by using the cost we calculated for the family pass. Let's look at the original problem again.
We calculated that a family pass costs $29. Our problem says the pass costs $25 more than half the cost of a single ticket. In other words, half the cost of a single ticket will be $25 less than $29.
- We could translate this into this equation, with s standing for the cost of a single ticket.
1/2s = 29 - 25
- Let's work on the right side first. 29 - 25 is 4 .
- To find the value of s , we have to get it alone on the left side of the equation. This means getting rid of 1/2 . To do this, we'll multiply each side by the inverse of 1/2: 2 .
According to our math, s = 8 . In other words, if the family pass costs $29, the single ticket will cost $8. Looking at our original problem, that's correct!
So now we're sure about the answer to our problem: The cost of a family pass is $29 .
Problem 2 Answer
Here's Problem 2:
Answer: $70
Let's go through this problem one step at a time.
Start by asking what question the problem is asking you to solve and identifying the information that will help you solve it . What's the question here?
To solve the problem, you'll have to find out how much money Mo gave to charity. All the important information you need is in the problem:
- The amount Flor donated is three times as much the amount Mo donated
- Flor and Mo's donations add up to $280 total
The unknown number we're trying to identify in this problem is Mo's donation . We'll represent it with the variable m .
Here's the problem again. This time, the important facts are highlighted.
Flor and Mo both donated money to the same charity. Flor gave three times as much as Mo . Between the two of them, they donated $280 . How much money did Mo give?
The important facts of the problem could also be expressed this way:
Mo's donation plus Flor's donation equals $280
Because we know that Flor's donation is three times as much as Mo's donation, we could go even further and say:
Mo's donation plus three times Mo's donation equals $280
We can translate this into a math problem in only a few steps. Here's how:
- Because we've already said we'll represent the amount of Mo's donation with the variable m , let's start by replacing Mo's donation with m .
m plus three times m equals $280
- Next, we can put in mathematical operators in place of certain words. We'll also take out the dollar sign.
m + three times m = 280
- Finally, let's write three times mathematically. Three times m can also be written as 3 ⋅ m , or just 3 m .
m + 3m = 280
It will only take a few steps to solve this problem.
- To get the correct answer, we'll have to get m alone on one side of the equation.
- To start, let's add m and 3 m . That's 4 m .
- We can get rid of the 4 next to the m by dividing both sides by 4. 4 m / 4 is m , and 280 / 4 is 70 .
We've got our answer: m = 70 . In other words, Mo donated $70 .
The answer to our problem is $70 , but we should check just to be sure. Let's look at our problem again.
If our answer is correct, $70 and three times $70 should add up to $280 .
- We can write our new equation like this:
70 + 3 ⋅ 70 = 280
- The order of operations calls for us to multiply first. 3 ⋅ 70 is 210.
70 + 210 = 280
- The last step is to add 70 and 210. 70 plus 210 equals 280 .
280 is the combined cost of the tickets in our original problem. Our answer is correct : Mo gave $70 to charity.
/en/algebra-topics/distance-word-problems/content/
Module 10: Linear Equations
Apply a problem-solving strategy to word problems, learning outcomes.
- Approach word problems with a positive attitude
- Use a problem solving strategy for word problems
- Translate more complex word problems into algebraic expressions and equations
Approach Word Problems with a Positive Attitude
The world is full of word problems. How much money do I need to fill the car with gas? How much should I tip the server at a restaurant? How many socks should I pack for vacation? How big a turkey do I need to buy for Thanksgiving dinner, and what time do I need to put it in the oven? If my sister and I buy our mother a present, how much will each of us pay?
Now that we can solve equations, we are ready to apply our new skills to word problems. Do you know anyone who has had negative experiences in the past with word problems? Have you ever had thoughts like the student in the cartoon below?
Negative thoughts about word problems can be barriers to success.
When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. We need to calm our fears and change our negative feelings.
Start with a fresh slate and begin to think positive thoughts, like the student in the cartoon below. Read the positive thoughts and say them out loud.
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.
Think of something that you can do now but couldn’t do three years ago. Whether it’s driving a car, snowboarding, cooking a gourmet meal, or speaking a new language, you have been able to learn and master a new skill. Word problems are no different. Even if you have struggled with word problems in the past, you have acquired many new math skills that will help you succeed now!
Use a Problem-Solving Strategy for Word Problems
In earlier chapters, you translated word phrases into algebraic expressions, using some basic mathematical vocabulary and symbols. Since then, you’ve increased your math vocabulary as you learned about more algebraic procedures, and you’ve had more practice translating from words into algebra.
You have also translated word sentences into algebraic equations and solved some word problems. The word problems applied math to everyday situations. You had to restate the situation in one sentence, assign a variable, and then write an equation to solve. This method works as long as the situation is familiar to you and the math is not too complicated.
Now we’ll develop a strategy you can use to solve any word problem. This strategy will help you become successful with word problems. We’ll demonstrate the strategy as we solve the following problem.
Pete bought a shirt on sale for $[latex]18[/latex], which is one-half the original price. What was the original price of the shirt?
Solution: Step 1. Read the 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.
- In this problem, do you understand what is being discussed? Do you understand every word?
Step 2. Identify what you are looking for. It’s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!
- In this problem, the words “what was the original price of the shirt” tell you what you are looking for: the original price of the shirt.
Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.
- Let [latex]p=[/latex] the original price of the shirt
Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.
Write the equation. | [latex]18=\Large\frac{1}{2}p[/latex] |
Multiply both sides by 2. | [latex]\color{red}{2}\cdot18=\color{red}{2}\cdot\Large\frac{1}{2}\normalsize p[/latex] |
Simplify. | [latex]36=p[/latex] |
Step 6. Check the answer in the problem and make sure it makes sense.
- We found that [latex]p=36[/latex], which means the original price was [latex]\text{\$36}[/latex]. Does [latex]\text{\$36}[/latex] make sense in the problem? Yes, because [latex]18[/latex] is one-half of [latex]36[/latex], and the shirt was on sale at half the original price.
Step 7. Answer the question with a complete sentence.
- The problem asked “What was the original price of the shirt?” The answer to the question is: “The original price of the shirt was [latex]\text{\$36}[/latex].”
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. Determine the constants and variables in the problem. A constant is a number in the problem that is not going to change. A variable is a number that you don’t yet know its value.
- Name what you are looking for. Choose a letter to represent that quantity.
- Translate words into algebraic expressions and equations. Write an equation to represent the problem. 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.
Translate word problems into expressions
One of the first steps to solving word problems is converting an English sentence into a mathematical sentence. In the table below, words or phrases commonly associated with mathematical operators are categorized. Word problems often contain these or similar words, so it’s good to see what mathematical operators are associated with them.
Addition [latex]+[/latex] | Subtraction [latex]-[/latex] | Multiplication [latex]\times[/latex] | Variable ? | Equals [latex]=[/latex] |
---|---|---|---|---|
More than | Less than | Double | A number | Is |
Together | In the past | Product | Often, a value for which no information is given. | The same as |
Sum | Slower than | times | After how many hours? | |
Total | The remainder of | How much will it cost? | ||
In the future | Difference | |||
Faster than |
Some examples follow:
- “[latex]x\text{ is }5[/latex]” becomes [latex]x=5[/latex]
- “Three more than a number” becomes [latex]x+3[/latex]
- “Four less than a number” becomes [latex]x-4[/latex]
- “Double the cost” becomes [latex]2\cdot\text{ cost }[/latex]
- “Groceries and gas together for the week cost $250” means [latex]\text{ groceries }+\text{ gas }=250[/latex]
- “The difference of [latex]9[/latex] and a number” becomes [latex]9-x[/latex]. Notice how [latex]9[/latex] is first in the sentence and the expression.
Let’s practice translating a few more English phrases into algebraic expressions.
Translate the table into algebraic expressions:
some number | the sum of the number and [latex]3[/latex] | twice the sum of the number and [latex]3[/latex] |
a length | double the length | double the length, decreased by [latex]6[/latex] |
a cost | the difference of the cost and [latex]20[/latex] | [latex]2[/latex] times the difference of the cost and [latex]20[/latex] |
some quantity | the difference of [latex]5[/latex] and the quantity | the difference of [latex]5[/latex] and the quantity, divided by [latex]2[/latex] |
an amount of time | triple the amount of time | triple the amount of time, increased by [latex]5[/latex] |
a distance | the sum of [latex]-4[/latex] and the distance | the sum of [latex]-4[/latex] and the twice the distance |
[latex]a[/latex] | [latex]a+3[/latex] | [latex]2\left(a+3\right)[/latex] |
[latex]l[/latex] | [latex]2l[/latex] | [latex]2l-6[/latex] |
[latex]c[/latex] | [latex]c-20[/latex] | [latex]2\left(c-20\right)[/latex] |
[latex]q[/latex] | [latex]5-q[/latex] | [latex]\frac{5-q}{2}[/latex] |
[latex]t[/latex] | [latex]3t[/latex] | [latex]3t+5[/latex] |
[latex]d[/latex] | [latex]-4+d[/latex] | [latex]-4+2d[/latex] |
In this example video, we show how to translate more words into mathematical expressions.
For another review of how to translate algebraic statements into words, watch the following video.
The power of algebra is how it can help you model real situations in order to answer questions about them. Let’s use this approach with another example.
Yash brought apples and bananas to a picnic. The number of apples was three more than twice the number of bananas. Yash brought [latex]11[/latex] apples to the picnic. How many bananas did he bring?
Step 1. the problem. | |
Step 2. what you are looking for. | How many bananas did he bring? |
Step 3. what you are looking for.Choose a variable to represent the number of bananas. | Let [latex]b=\text{number of bananas}[/latex] |
Step 4. Restate the problem in one sentence with all the important information.Translate into an equation. | [latex]11\enspace\Rightarrow[/latex] The number of apples[latex]=\enspace\Rightarrow[/latex] was [latex]3\enspace\Rightarrow[/latex] three [latex]+\enspace\Rightarrow[/latex] more than [latex]2b\enspace\Rightarrow[/latex] twice the number of bananas |
Step 5. the equation. | [latex]11=2b+3[/latex] |
Subtract 3 from each side. | [latex]11\color{red}{-3}=2b+3\color{red}{-3}[/latex] |
Simplify. | [latex]8=2b[/latex] |
Divide each side by 2. | [latex]\Large\frac{8}{\color{red}{2}}\normalsize =\Large\frac{2b}{\color{red}{2}}[/latex] |
Simplify. | [latex]4=b[/latex] |
Step 6. First, is our answer reasonable? Yes, bringing four bananas to a picnic seems reasonable. The problem says the number of apples was three more than twice the number of bananas. If there are four bananas, does that make eleven apples? Twice 4 bananas is 8. Three more than 8 is 11. | |
Step 7. the question. | Yash brought 4 bananas to the picnic. |
https://ohm.lumenlearning.com/multiembedq.php?id=142722&theme=oea&iframe_resize_id=mom2
Twenty-eight less than five times a certain number is [latex]232[/latex]. What is the number?
Following the steps provided:
- Read and understand: we are looking for a number.
- Constants and variables: [latex]28[/latex] and [latex]232[/latex] are constants, “a certain number” is our variable, because we don’t know its value, and we are asked to find it. We will call it [latex]x[/latex].
- Translate: five times a certain number translates to [latex]5x[/latex] Twenty-eight less than five times a certain number translates to [latex]5x-28[/latex], because subtraction is built backward. “is 232” translates to “[latex]=232″[/latex] since “is” is associated with equals.
- Write an equation: [latex]5x-28=232[/latex]
[latex]\begin{array}{r}5x-28=232\\5x=260\\x=52\,\,\,\end{array}[/latex]
[latex]\begin{array}{r}5\left(52\right)-28=232\\5\left(52\right)=260\\260=260\end{array}[/latex]
In the video that follows, we show another example of how to translate a sentence into a mathematical expression using a problem solving method.
In the next example, we will apply our Problem-Solving Strategy to applications of percent.
Nga’s car insurance premium increased by [latex]\text{\$60}[/latex], which was [latex]\text{8%}[/latex] of the original cost. What was the original cost of the premium?
Step 1. the problem. Remember, if there are words you don’t understand, look them up. | |
Step 2. what you are looking for. | the original cost of the premium |
Step 3. Choose a variable to represent the original cost of premium. | Let [latex]c=\text{the original cost}[/latex] |
Step 4. Restate as one sentence. Translate into an equation. | |
Step 5. the equation. | [latex]60=0.08c[/latex] |
Divide both sides by [latex]0.08[/latex]. | [latex]\Large\frac{60}{\color{red}{0.08}}\normalsize =\Large\frac{0.08c}{\color{red}{0.08}}[/latex] |
Simplify. | [latex]c=750[/latex] |
Step 6. Is our answer reasonable? Yes, a [latex]\text{\$750}[/latex] premium on auto insurance is reasonable. Now let’s check our algebra. Is 8% of 750 equal to [latex]60[/latex]?[latex]750=c[/latex] [latex]0.08(750)=60[/latex] [latex]60=60\quad\checkmark[/latex] | |
Step 7. the question. | The original cost of Nga’s premium was [latex]\text{\$750}[/latex]. |
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]
MAKE WAVES WITH THIS FREE WEEKLONG VOCABULARY UNIT!
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
Thanks so much for stopping by!
- Read more about: Math
You might also like...
Fraction Activities Students Love – Math
Fractions can be tough! While it takes time and repeated exposure with fractions for students to have a real understanding of them, there are lots
Math Games Using Dice
Games are an important part of math class, in my opinion. Not only are kids able to practice the skills that we have been focusing
Math Games Using Dominoes
Math games have always been part of our math time. I love the fact that any time I introduce a math game, I know I’ll
Hi, I’m Jenn, CEO and owner of The Teacher Next Door!
I know that you strive to be an effective upper elementary teacher while maintaining a healthy work-life balance.
In order to do that, you need resources that are impactful, yet simple .
The problem is that most resources and curriculums out there are far from simple. The pages upon pages of daily lesson plans are just plain overwhelming .
At TTND, we believe teachers should be living their lives outside of the classroom, and not spend hours lesson planning and searching for resources.
We understand that now, more than ever, teachers need space to be themselves which is why we create and support teachers with timesaving tips and standards-aligned resources.
Want access to TTND's Free Resource Library? Sign up for our newsletter and we'll email you the exclusive password!
Trending posts.
SEARCH BY TOPIC
- Classroom Ideas
- Holidays and Seasonal
- Mentor Texts
- Reading Block
- Uncategorized
- Writing & Grammar
POPULAR RESOURCES
JOIN MY NEWSLETTER
Gain access to a library of FREE resources for upper elementary grades!
Facebook Group
Teachers Pay Teachers
Free Resource Library
💌 Contact Us
Disclosures
Privacy Policy
Refund Policy
Purchase Orders
Your Downloads
Reward Points
© The Teacher Next Door, LLC. All rights reserved.
* Please note: If your school has strong email filters, you may wish to use your personal email to ensure access.
Word Problem Calculator
Get detailed solutions to your math problems with our word problem step-by-step calculator . practice your math skills and learn step by step with our math solver. check out all of our online calculators here ., example, solved problems, difficult problems, are you struggling with math.
Access detailed step by step solutions to thousands of problems, growing every day!
Popular problems
Most popular problems solved with this calculator:
High Impact Tutoring Built By Math Experts
Personalized standards-aligned one-on-one math tutoring for schools and districts
Free ready-to-use math resources
Hundreds of free math resources created by experienced math teachers to save time, build engagement and accelerate growth
Word Problems Explained For Elementary School Teachers & Parents
Sophie Bartlett
Solving word problems in elementary school is an essential part of the math curriculum. Here are over 30 math word problems to practice with children, plus expert guidance on how to solve them.
This blog is part of our series of blogs designed for teachers, schools, and parents supporting home learning .
What is a word problem?
A word problem in math is a math question written as one sentence or more that requires children to apply their math knowledge to a ‘real-life’ scenario.
This means that children must be familiar with the vocabulary associated with the mathematical symbols they are used to, in order to make sense of the word problem.
For example:
Word Problems Grade 4 Number and Base 10
11 grade 4 number and base 10 questions to develop your students' reasoning and problem solving skills.
Isn’t brilliant arithmetic enough?
In short, no. Students need to build good reading comprehension, even in math. Overtime math problems become increasingly complex and require students to possess deep conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
As students progress through their mathematical education, they will need to be able to apply mathematical reasoning and develop mathematical arguments and proofs using math language. They will also need to be dynamic, applying their math knowledge to a variety of increasingly sophisticated problems.
To support this schools are adopting a ‘mastery’ approach to math
“Teaching for mastery”, is defined with these components:
- Math teaching for mastery rejects the idea that a large proportion of people ‘just can’t do math’.
- All students are encouraged by the belief that by working hard at math they can succeed.
- Procedural fluency and conceptual understanding are developed in tandem because each supports the development of the other.
- Significant time is spent developing deep knowledge of the key ideas that are needed to support future learning. The structure and connections within the mathematics are emphasized, so that students develop deep learning that can be sustained.
(The Essence of Maths Teaching for Mastery, 2016)
Mastery helps children to explore math in greater depth
Fluency in arithmetic is important; however, with this often lies the common misconception that once a child has learned the number skills appropriate to their grade level/age, they should be progressed to the next grade level/age of number skills.
The mastery approach encourages exploring the breadth and depth of these math concepts (once fluency is secure) through reasoning and problem solving.
How to teach children to solve word problems?
Here are two simple math strategies for problem solving that can be applied to many word problems before solving them.
- What do you already know?
- How can this problem be drawn/represented pictorially?
Let’s see how this can be applied to word problems to help achieve the answer.
Solving a simple word problem
There are 28 students in a class.
The teacher has 8 liters of orange juice.
She pours 225 milliliters of orange juice for every student.
How much orange juice is left over?
1. What do you already know?
- There are 1,000ml in 1 liter
- Pours = liquid leaving the bottle = subtraction
- For every = multiply
- Left over = requires subtraction at some point
2. How can this problem be drawn/represented pictorially?
The bar model , also known as strip diagram , is always a great way of representing problems. However, if you are not familiar with this, there are always other ways of drawing it out.
Read more: What is a bar model
For example, for this question, you could draw 28 students (or stick man x 28) with ‘225 ml’ above each one and then a half-empty bottle with ‘8 liters’ marked at the top.
Now to put the math to work. This is a 5th grade multi-step problem, so we need to use what we already know and what we’ve drawn to break down the steps.
Solving a more complex, mixed word problem
Mara is in a bookshop.
She buys one book for $6.99 and another that costs $3.40 more than the first book.
She pays using a $20 bill.
What change does Mara get? (What is the remainder?)
- More than = add
- Using decimals means I will have to line up the decimal points correctly in calculations
- Change from money = subtract
See this example of bar modelling for this question:
Now to put the math to work using what we already know and what we’ve drawn to break down the steps.
Mara is in a bookshop.
She buys one book for $6.99 and another that costs $3.40 more than the first book. 1) $6.99 + ($6.99 + $3.40) = $17.38
What change does Mara get? 2) $20 – $17.38 = $2.62
Math word problems for Kindergarten to Grade 5
The more children learn about math as they go through elementary school, the trickier the word problems they face will become.
Below you will find some information about the types of word problems your child will be coming up against on a year by year basis, and how word problems apply to each elementary grade.
Word problems in kindergarten
Throughout kindergarten a child is likely to be introduced to word problems with the help of concrete resources (manipulatives, such as pieces of physical apparatus like coins, cards, counters or number lines) to help them understand the problem.
An example of a word problem for kindergarten would be
Chris has 3 red bounce balls and 2 green bounce balls. How many bounce balls does Chris have in all?
Word problems in 1st grade
First grade is a continuation of kindergarten when it comes to word problems, with children still using concrete resources to help them understand and visualize the problems they are working on
An example of a word problem for first grade would be:
A class of 10 children each have 5 pencils in their pencil cases. How many pencils are there in total?
Word problems in 2nd grade
In second grade, children will move away from using concrete resources when solving word problems, and move towards using written methods. Teachers will begin to demonstrate the adding and subtracting within 100, adding up to 4- two-digit numbers at a time.
This is also the year in which 2-step word problems will be introduced. This is a problem which requires two individual calculations to be completed.
2nd grade word problem: geometry properties of shape
Shaun is making shapes out of plastic straws.
At the vertices where the straws meet, he uses blobs of modeling clay to fix them together
Here are some of the shapes he makes:
4 | 4 | |
3 | 3 | |
6 | 6 |
One of Sean’s shapes is a triangle. Which is it? Explain your answer.
Answer: shape B as a triangle has 3 sides (straws) and 3 vertices, or angles (clay)
2nd grade word problem: statistics
2nd grade is collecting pebbles. This pictogram shows the different numbers of pebbles each group finds.
Word problems in 3rd grade
At this stage of their elementary school career, children should feel confident using the written method for addition and subtraction. They will begin multiplying and dividing within 100.
This year children will be presented with a variety of problems, including 2-step problems and be expected to work out the appropriate method required to solve each one.
3rd grade word problem: number and place value
My number has four digits and has a 7 in the hundreds place.
The digit which has the highest value in my number is 2.
The digit which has the lowest value in my number is 6.
My number has 3 fewer tens than hundreds.
What is my number?
Answer: 2,746
Word problems in 4th grade
One and two-step word problems continue in fourth grade, but this is also the year that children will be introduced to word problems containing decimals.
4th grade word problem: fractions and decimals
Stan, Frank and John are washing their cars outside their houses.
Stan has washed 0.5 of his car.
Frank has washed 1/5 of his car.
Norm has washed 2/5 of his car.
Who has washed the most?
Explain your answer.
Answer: Stan (he has washed 0.5 whereas Frank has only washed 0.2 and Norm 0.4)
Word problems in 5th grade
In fifth grade children move on from 2-step word problems to multi-step word problems . These will include fractions and decimals.
Here are some examples of the types of math word problems in fifth grade will have to solve.
5th grade word problem: ratio and proportion
The Angel of the North is a large statue in England. It is 20 meters tall and 54 meters wide.
Ally makes a scale model of the Angel of the North. Her model is 40 centimeters tall. How wide is her model?
Answer: 108cm
5th grade word problem: algebra
Amina is making designs with two different shapes.
She gives each shape a value.
Calculate the value of each shape.
Answer: 36 (hexagon) and 25.
5th grade word problem: measurement
Answer: 1.7 liters or 1,700ml
Topic based word problems
The following examples give you an idea of the kinds of math word problems your child will encounter in elementary school
4th grade word problem: place value
This machine subtracts one hundredth each time the button is pressed. The starting number is 8.43. What number will the machine show if the button is pressed six times? Answer: 8.37
Download free number and place value word problems for grades 2, 3, 4 and 5
2nd grade word problem: addition and subtraction
Sam has 64 sweets. He gets given 12 more. He then gives 22 away. How many sweets is he left with? Answer: 54
Download free addition and subtraction word problems for for grades 2, 3, 4 and 5
2nd grade word problem: addition
Sammy thinks of a number. He subtracts 70. His new number is 12. What was the number Sammy thought of? Answer: 82
5th grade word problem: subtraction
The temperature at 7pm was 4oC. By midnight, it had dropped by 9 degrees. What was the temperature at midnight? Answer: -5oC
3rd grade word problem: multiplication
Eggs are sold in boxes of 12. The egg boxes are delivered to stores in crates. Each crate holds 9 boxes. How many eggs are in a crate? Answer: 108
Download free multiplication word problems for grades 2, 3, 4 and 5.
5th grade word problem: division
A factory produces 3,572 paint brushes every day. They are packaged into boxes of 19. How many boxes does the factory produce every day? Answer: 188
Download free division word problems for grades 2, 3, 4 and 5.
Free resource: Use these four operations word problems to practice addition, subtraction, multiplication and division all together.
4th grade word problem: fractions
At the end of every day, a chocolate factory has 1 and 2/6 boxes of chocolates left over. How many boxes of chocolates are left over by the end of a week? Answer: 9 and 2/6 or 9 and 1/3
Download free fractions and decimals word problems for grades 2, 3, 4 and 5.
2nd grade word problem: money
Lucy and Noor found some money on the playground at recess. Lucy found 2 dimes and 1 penny, and Noor found 2 quarters and a dime. How many cents did Lucy and Noor find? Answer: Lucy = $0.21, Noor = $0.60; $0.21 + $0.61 = $0.81
3rd grade word problem: area
A rectangle measures 6cm by 5cm.
What is its area? Answer: 30cm2
3rd grade word problem: perimeter
The swimming pool at the Sunshine Inn hotel is 20m long and 7m wide. Mary swims around the edge of the pool twice. How many meters has she swum? Answer: 108m
5th grade word problem: ratio (crossover with measurement)
A local council has spent the day painting double yellow lines. They use 1 pot of yellow paint for every 100m of road they paint. How many pots of paint will they need to paint a 2km stretch of road? Answer: 20 pots
5th grade word problem: PEMDAS
Draw a pair of parentheses in one of these calculations so that they make two different answers. What are the answers?
50 – 10 × 5 =
5th grade word problem: volume
This large cuboid has been made by stacking shipping containers on a boat. Each individual shipping container has a length of 6m, a width of 4m and a height of 3m. What is the volume of the large cuboid? Answer: 864m3
Remember: The word problems can change but the math won’t
It can be easy for children to get overwhelmed when they first come across word problems, but it is important that you remind them that while the context of the problem may be presented in a different way, the math behind it remains the same.
Word problems are a good way to bring math into the real world and make math more relevant for your child. So help them practice, or even ask them to turn the tables and make up some word problems for you to solve.
READ MORE :
- 1st grade math problems
- 2nd grade math problems
- 3rd grade math problems
- 4th grade math problems
- 5th grade math problems
- 6th grade Math Problems
- 7th grade math problems
- 8th grade math problems
Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?
Related articles
20 Effective Math Strategies To Approach Problem-Solving
Why Student Centered Learning Is Important: A Guide For Educators
13 Effective Learning Strategies: A Guide to Using them in your Math Classroom
Differentiated Instruction: 9 Differentiated Curriculum And Instruction Strategies For Teachers
Ultimate Guide to Metacognition [FREE]
Looking for a summary on metacognition in relation to math teaching and learning?
Check out this guide featuring practical examples, tips and strategies to successfully embed metacognition across your school to accelerate math growth.
Privacy Overview
- HW Guidelines
- Study Skills Quiz
- Find Local Tutors
- Demo MathHelp.com
- Join MathHelp.com
Select a Course Below
- ACCUPLACER Math
- Math Placement Test
- PRAXIS Math
- + more tests
- 5th Grade Math
- 6th Grade Math
- Pre-Algebra
- College Pre-Algebra
- Introductory Algebra
- Intermediate Algebra
- College Algebra
Translating Word Problems: Keywords
Keywords Examples
The hardest thing about doing word problems is using the part where you need to take the English words and translate them into mathematics. Usually, once you get the math equation, you're fine; the actual math involved is often fairly simple. But figuring out the actual equation can seem nearly impossible. What follows is a list of hints and helps. Be advised, however: To really learn "how to do" word problems, you will need to practice, practice, practice.
How do I convert word problems into math?
- Read the entire exercise.
- Work in an organized manner.
- Look for the keywords.
- Apply your knowledge of "the real world".
Content Continues Below
MathHelp.com
Algebra Word Problems
Step 1 in effectively translating and solving word problems is to read the problem entirely. Don't start trying to solve anything when you've only read half a sentence. Try first to get a feel for the whole problem; try first to see what information you have, and then figure out what you still need.
Step 2 is to work in an organized manner. Figure out what you need but don't have. Name things. Pick variables to stand for the unknows, clearly labelling these variables with what they stand for. Draw and label pictures neatly. Explain your reasoning as you go along. And make sure you know just exactly what the problem is actually asking for. You need to do this for two reasons:
- Working clearly will help you think clearly, and
- figuring out what you need will help you translate your final answer back into English.
Regarding point (a) above:
It can be really frustrating (and embarassing) to spend fifteen minutes solving a word problem on a test, only to realize at the end that you no longer have any idea what " x " stands for, so you have to do the whole problem over again. I did this on a calculus test — thank heavens it was a short test! — and, trust me, you don't want to do this to yourself. Taking fifteen seconds to label things is a better use of your time than spending fifteen minutes reworking the entire exercise!
Step 3 is to look for "key" words. Certain words indicate certain mathematica operations. Some of those words are easy. If an exercise says that one person "added" her marbles to the pile belonging to somebody else, and asks for how many marbles are now in the pile, you know that you'll be adding two numbers.
What are common keywords for word problems?
The following is a listing of most of the more-common keywords for word problems:
increased by more than combined, together total of sum, plus added to comparatives ("greater than", etc)
Subtraction:
decreased by minus, less difference between/of less than, fewer than left, left over, after save (old-fashioned term) comparatives ("smaller than", etc)
Multiplication:
of times, multiplied by product of increased/decreased by a factor of (this last type can involve both addition or subtraction and multiplication!) twice, triple, etc each ("they got three each", etc)
per, a out of ratio of, quotient of percent (divide by 100) equal pieces, split average
is, are, was, were, will be gives, yields sold for, cost
Note that "per", in "Division", means "divided by", as in "I drove 90 miles on three gallons of gas, so I got 30 miles per gallon". Also, "a" sometimes means "divided by", as in "When I tanked up, I paid $12.36 for three gallons, so the gas was $4.12 a gallon".
Warning: The "less than" construction, in "Subtraction", is backwards in the English from what it is in the math. If you need, for instance, to translate " 1.5 less than x ", the temptation is to write " 1.5 − x ". Do not do this!
You can see how this is wrong by using this construction in a "real world" situation: Consider the statement, "He makes $1.50 an hour less than me." You do not figure his wage by subtracting your wage from $1.50 . Instead, you subtract $1.50 from your wage. So remember: the "less than" construction is backwards.
(Technically, the "greater than" construction, in "Addition", is also backwards in the math from the English. But the order in addition doesn't matter, so it's okay to add backwards, because the result will be the same either way.)
Also note that order is important in the "quotient/ratio of" and "difference between/of" constructions. If a problems says "the ratio of x and y ", it means " x divided by y ", not " y divided by x ". If the problem says "the difference of x and y ", it means " x − y ", not " y − x ".
Advertisement
Some times, you'll be expected to bring your "real world" knowledge to an exercise. For instance, suppose you're told that "Shelby worked eight hours MTThF and six hours WSat". You would be expected to understand that this meant that she worked eight hours for each of the four days Monday, Tuesday, Thursday, and Friday; and six hours for each of the two days Wednesday and Saturday. Suppose you're told that Shelby earns "time and a half" for any hours she works over forty for a given week. You would be expected to know that "time and a half" means 1.5 times her base rate of pay; if her base rate is twelve dollars an hour, then she'd get 1.5 × 12 = 18 dollars for every over-time hour.
You'll be expected to know that a "dozen" is twelve; you may be expected to know that a "score" is twenty. You'll be expected to know the number of days in a year, the number of hours in a day, and other basic units of measure.
Probably the greatest source of error, though, is the use of variables without definitions. When you pick a letter to stand for something, write down explicitly what that latter is meant to stand for. Does " S " stand for "Shelby" or for "hours Shelby worked"? If the former, what does this mean, in practical terms? (And, if you can't think of any meaningful definition, then maybe you need to slow down and think a little more about what's going on in the word problem.)
In all cases, don't be shy about using your "real world" knowledge. Sometimes you'll not feel sure of your translation of the English into a mathematical expression or equation. In these cases, try plugging in numbers. For instance, if you're not sure if you should be dividing or multiplying, try the process each way with regular numbers. For instance, suppose you're not sure if "half of (the unknown amount)" should be represented by multiplying by one-half, or by dividing by one-half. If you use numbers, you can be sure. Pick an easy number, like ten. Half of ten is five, so we're looking for the operation (that is, multiplication or division) that gives us an answer of 5 . First, let's try division:
ten divided by one-half:
10/(1/2) = (10/1)×(2/1) = 20
Well, that's clearly wrong. How about going the other way?
ten multiplied by one-half:
(10)×(1/2) = 10 ÷ 2 = 5
That's more like it! You know that half of ten is five, and now you can see which mathematical operations gets you the right value. So now you'd know that the expression you're wanting is definitely " (1/2) x ".
You have experience and knowledge; don't be afraid to apply your skills to this new context!
URL: https://www.purplemath.com/modules/translat.htm
Page 1 Page 2
Standardized Test Prep
College math, homeschool math, share this page.
- Terms of Use
- About Purplemath
- About the Author
- Tutoring from PM
- Advertising
- Linking to PM
- Site licencing
Visit Our Profiles
- 1-224-725-3522
- [email protected]
Word Problems Calculators: (41) lessons
2 number word problems.
Free 2 number Word Problems Calculator - This calculator handles word problems in the format below: * Two numbers have a sum of 70 and a product of 1189 What are the numbers? * Two numbers have a sum of 70. Their difference 32
2 Unknown Word Problems
Free 2 Unknown Word Problems Calculator - Solves a word problem based on two unknown variables
Age Difference
Free Age Difference Calculator - Determines the ages for an age difference word problem.
Age Word Problems
Free Age Word Problems Calculator - Determines age in age word problems
Angle of Elevation
Free Angle of Elevation Calculator - Solves angle of elevation word problems
Free Break Even Calculator - Given a fixed cost, variable cost, and revenue function or value, this calculates the break-even point
Coin Combinations
Free Coin Combinations Calculator - Given a selection of coins and an amount, this determines the least amount of coins needed to reach that total.
Coin Total Word Problems
Free Coin Total Word Problems Calculator - This word problem lesson solves for a quantity of two coins totaling a certain value with a certain amount more or less of one coin than another
Coin Word Problems
Free Coin Word Problems Calculator - This word problem lesson solves for a quantity of two coins totaling a certain value
Collinear Points that form Unique Lines
Free Collinear Points that form Unique Lines Calculator - Solves the word problem, how many lines can be formed from (n) points no 3 of which are collinear.
Compare Raises
Free Compare Raises Calculator - Given two people with a salary and annual raise amount, this determines how long it takes for the person with the lower salary to catch the person with the higher salary.
Consecutive Integer Word Problems
Free Consecutive Integer Word Problems Calculator - Calculates the word problem for what two consecutive integers, if summed up or multiplied together, equal a number entered.
Cost Revenue Profit
Free Cost Revenue Profit Calculator - Given a total cost, variable cost, revenue amount, and profit unit measurement, this calculates profit for each profit unit
Free Decay Calculator - Determines decay based on an initial mass and decay percentage and time.
Distance Catch Up
Free Distance Catch Up Calculator - Calculates the amount of time that it takes for a person traveling at one speed to catch a person traveling at another speed when one person leaves at a later time.
Distance Rate and Time
Free Distance Rate and Time Calculator - Solves for distance, rate, or time in the equation d=rt based on 2 of the 3 variables being known.
Find two numbers word problems
Free Find two numbers word problems Calculator - Given two numbers with a sum of s where one number is n greater than another, this calculator determines both numbers.
Inclusive Number Word Problems
Free Inclusive Number Word Problems Calculator - Given an integer A and an integer B, this calculates the following inclusive word problem questions: 1) The Average of all numbers inclusive from A to B 2) The Count of all numbers inclusive from A to B 3) The Sum of all numbers inclusive from A to B
Free Map Scale Calculator - Solves map scale problems based on unit measurements
Markup Markdown
Free Markup Markdown Calculator - Given the 3 items of a markup word problem, cost, markup percentage, and sale price, this solves for any one of the three given two of the items. This works as a markup calculator, markdown calculator.
Numbers Word Problems
Free Numbers Word Problems Calculator - Solves various basic math and algebra word problems with numbers
Free Overtime Calculator - Solves overtime wage problems
Percent Off Problem
Free Percent Off Problem Calculator - Given the 3 items of a percent word problem, Reduced Price, percent off, and full price, this solves for any one of the three given two of the items.
Percentage of the Pie Word Problem
Free Percentage of the Pie Word Problem Calculator - This takes two or three fractions of ownership in some good or object, and figures out what remaining fraction is left over.
Percentage Word Problems
Free Percentage Word Problems Calculator - Solves percentage word problems
Population Doubling Time
Free Population Doubling Time Calculator - Determines population growth based on a doubling time.
Population Growth
Free Population Growth Calculator - Determines population growth based on an exponential growth model.
Product of Consecutive Numbers
Free Product of Consecutive Numbers Calculator - Finds the product of (n) consecutive integers, even or odd as well. Examples include: product of 2 consecutive integers product of 2 consecutive numbers product of 2 consecutive even integers product of 2 consecutive odd integers product of 2 consecutive even numbers product of 2 consecutive odd numbers product of two consecutive integers product of two consecutive odd integers product of two consecutive even integers product of two consecutive numbers product of two consecutive odd numbers product of two consecutive even numbers product of 3 consecutive integers product of 3 consecutive numbers product of 3 consecutive even integers product of 3 consecutive odd integers product of 3 consecutive even numbers product of 3 consecutive odd numbers product of three consecutive integers product of three consecutive odd integers product of three consecutive even integers product of three consecutive numbers product of three consecutive odd numbers product of three consecutive even numbers product of 4 consecutive integers product of 4 consecutive numbers product of 4 consecutive even integers product of 4 consecutive odd integers product of 4 consecutive even numbers product of 4 consecutive odd numbers product of four consecutive integers product of four consecutive odd integers product of four consecutive even integers product of four consecutive numbers product of four consecutive odd numbers product of four consecutive even numbers product of 5 consecutive integers product of 5 consecutive numbers product of 5 consecutive even integers product of 5 consecutive odd integers product of 5 consecutive even numbers product of 5 consecutive odd numbers product of five consecutive integers product of five consecutive odd integers product of five consecutive even integers product of five consecutive numbers product of five consecutive odd numbers product of five consecutive even numbers
Ratio Word Problems
Free Ratio Word Problems Calculator - Solves a ratio word problem using a given ratio of 2 items in proportion to a whole number.
Rebound Ratio
Free Rebound Ratio Calculator - Calculates a total downward distance traveled given an initial height of a drop and a rebound ratio percentage
Slope Word Problems
Free Slope Word Problems Calculator - Solves slope word problems
Solution Mixture
Free Solution Mixture Calculator - Determines a necessary amount of a Solution given two solution percentages and 1 solution amount.
Split Fund Interest
Free Split Fund Interest Calculator - Given an initial principal amount, interest rate on Fund 1, interest rate on Fund 2, and a total interest paid, calculates the amount invested in each fund.
Sum of Consecutive Numbers
Free Sum of Consecutive Numbers Calculator - Finds the sum of (n) consecutive integers, even or odd as well. Examples include: sum of 2 consecutive integers sum of 2 consecutive numbers sum of 2 consecutive even integers sum of 2 consecutive odd integers sum of 2 consecutive even numbers sum of 2 consecutive odd numbers sum of two consecutive integers sum of two consecutive odd integers sum of two consecutive even integers sum of two consecutive numbers sum of two consecutive odd numbers sum of two consecutive even numbers sum of 3 consecutive integers sum of 3 consecutive numbers sum of 3 consecutive even integers sum of 3 consecutive odd integers sum of 3 consecutive even numbers sum of 3 consecutive odd numbers sum of three consecutive integers sum of three consecutive odd integers sum of three consecutive even integers sum of three consecutive numbers sum of three consecutive odd numbers sum of three consecutive even numbers sum of 4 consecutive integers sum of 4 consecutive numbers sum of 4 consecutive even integers sum of 4 consecutive odd integers sum of 4 consecutive even numbers sum of 4 consecutive odd numbers sum of four consecutive integers sum of four consecutive odd integers sum of four consecutive even integers sum of four consecutive numbers sum of four consecutive odd numbers sum of four consecutive even numbers sum of 5 consecutive integers sum of 5 consecutive numbers sum of 5 consecutive even integers sum of 5 consecutive odd integers sum of 5 consecutive even numbers sum of 5 consecutive odd numbers sum of five consecutive integers sum of five consecutive odd integers sum of five consecutive even integers sum of five consecutive numbers sum of five consecutive odd numbers sum of five consecutive even numbers
Sum of Five Consecutive Integers
Free Sum of Five Consecutive Integers Calculator - Finds five consecutive integers, if applicable, who have a sum equal to a number. Sum of 5 consecutive integers
Sum of Four Consecutive Integers
Free Sum of Four Consecutive Integers Calculator - Finds four consecutive integers, if applicable, who have a sum equal to a number. Sum of 4 consecutive integers
Sum of the First (n) Numbers
Free Sum of the First (n) Numbers Calculator - Determines the sum of the first (n) * Whole Numbers * Natural Numbers * Even Numbers * Odd Numbers * Square Numbers * Cube Numbers * Fourth Power Numbers
Sum of Three Consecutive Integers
Free Sum of Three Consecutive Integers Calculator - Finds three consecutive integers, if applicable, who have a sum equal to a number. Sum of 3 consecutive integers
Free Sun Shadow Calculator - This solves for various components and scenarios of the sun shadow problem
Unit Savings
Free Unit Savings Calculator - A discount and savings word problem using 2 people and full prices versus discount prices.
Work Word Problems
Free Work Word Problems Calculator - Given Person or Object A doing a job in (r) units of time and Person or Object B doing a job in (s) units of time, this calculates how long it would take if they combined to do the job.
An Automated Online Math Tutor serving 8.1 million parents and students in 235 countries and territories.
Our Services
- All Subjects
- A.I. Training Data and Analytics
- Get Paid as an Affiliate
Top Categories
- Trigonometry
- Pre-Algebra
- Pre-Calculus
- Post a Math Problem
- Grades 6-12
- School Leaders
Have you seen our latest free teacher workshop?
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
[contextly_auto_sidebar]
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 .
You Might Also Like
350+ Amazing Online Learning Resources
There are so many ways to extend classroom learning. Continue Reading
Copyright © 2024. All rights reserved. 5335 Gate Parkway, Jacksonville, FL 32256
Word Problems Activities
Teach your child all about word problems with amazing educational resources for children. These online word problems learning resources break down the topic into smaller parts for better conceptual understanding and grasp. Get started now to make word problems practice a smooth, easy and fun process for your child!
CONTENT TYPE
- Lesson Plans
- Math (8,414)
- Number Sense (1,316)
- Number Recognition (50)
- Number Recognition Within 5 (17)
- Number Recognition Within 10 (17)
- Number Recognition Within 20 (16)
- Number Tracing (470)
- Number Tracing Within 5 (135)
- Number Tracing Within 10 (125)
- Number Tracing Within 20 (210)
- Number Sequence (83)
- Counting (273)
- Counting Objects Within 5 (105)
- Counting Objects Within 10 (106)
- Counting Objects Within 20 (17)
- Compare Numbers (147)
- Compare Objects (17)
- Compare Numbers Using Place Value (29)
- Compare 2-Digit Numbers (6)
- Compare 3-Digit Numbers (29)
- Order Numbers (37)
- Order 3-Digit Numbers (10)
- Skip Counting (79)
- Skip Count By 2 (20)
- Skip Count By 5 (19)
- Skip Count By 10 (24)
- Skip Count By 100 (14)
- Even And Odd Numbers (27)
- Place Value (143)
- Teen Numbers (15)
- Word Form (5)
- Expanded And Standard Form (14)
- Unit Form (4)
- Round Numbers (47)
- Round Numbers To The Nearest 10 (18)
- Round Numbers To The Nearest 100 (14)
- Addition (1,231)
- Add With Pictures (180)
- Addition Properties (37)
- Commutative Property Of Addition (10)
- Addition Strategies (321)
- Compose And Decompose Numbers (138)
- Number Bonds (19)
- Count All To Add (21)
- Add Using A Number Line (19)
- Count On To Add (23)
- Add With 10 (24)
- Doubles And Near Doubles Addition Strategy (37)
- Make 10 Strategy (18)
- Add Using Multiples Of 10 (18)
- Add Three Whole Numbers (73)
- 2-Digit Addition (124)
- 2-Digit Addition Without Regrouping (60)
- 2-Digit Addition With Regrouping (26)
- 3-Digit Addition (170)
- 3-Digit Addition Without Regrouping (82)
- 3-Digit Addition With Regrouping (55)
- 4-Digit Addition (60)
- 4-Digit Addition Without Regrouping (25)
- 4-Digit Addition With Regrouping (29)
- Large Numbers Addition (63)
- 5-Digit Addition (30)
- 6-Digit Addition (25)
- Subtraction (987)
- Subtract With Pictures (110)
- Subtraction Strategies (137)
- Count Back Strategy (13)
- Subtract Using A Number Line (14)
- Doubles And Near Doubles Subtraction Strategy (6)
- Subtract From 10 Strategy (10)
- Subtract Using Multiples Of 10 (17)
- 2-Digit Subtraction (174)
- 2-Digit Subtraction Without Regrouping (97)
- 2-Digit Subtraction With Regrouping (30)
- 3-Digit Subtraction (173)
- 3-Digit Subtraction Without Regrouping (87)
- 3-Digit Subtraction With Regrouping (45)
- 4-Digit Subtraction (75)
- 4-Digit Subtraction Without Regrouping (36)
- 4-Digit Subtraction With Regrouping (35)
- Large Numbers Subtraction (114)
- 5-Digit Subtraction (54)
- 6-Digit Subtraction (49)
- Multiplication (807)
- Multiplication Strategies (155)
- Multiplication With Equal Groups (41)
- Multiplication With Arrays (44)
- Multiplication Sentences (65)
- Multiplication On A Number Line (13)
- Repeated Addition To Multiply (32)
- Times Tables (265)
- Multiplication By 2 (25)
- Multiplication By 3 (26)
- Multiplication By 4 (24)
- Multiplication By 5 (28)
- Multiplication By 6 (24)
- Multiplication By 7 (22)
- Multiplication By 8 (23)
- Multiplication By 9 (23)
- Multiplication By 10 (20)
- Multiplication By 11 (22)
- Multiplication By 12 (22)
- Multiplication Properties (163)
- Commutative Property Of Multiplication (10)
- Distributive Property Of Multiplication (77)
- Multiply By Multiples Of 10 (60)
- Estimate Products (22)
- Multi-Digit Multiplication (192)
- Multiply 2-Digit By 1-Digit Numbers (44)
- Multiply 2-Digit By 2-Digit Numbers (58)
- Multiply 3-Digit By 1-Digit Numbers (20)
- Multiply 3-Digit By 2-Digit Numbers (30)
- Multiply 4-Digit By 1-Digit Numbers (18)
- Division (442)
- Divide On A Number Line (13)
- Division Facts (158)
- Division By 2 (15)
- Division By 3 (15)
- Division By 4 (15)
- Division By 5 (15)
- Division By 6 (15)
- Division By 7 (15)
- Division By 8 (15)
- Division By 9 (15)
- Division By 10 (14)
- Estimate Quotients (19)
- Long Division (125)
- Divide 2-Digit By 1-Digit Numbers (23)
- Divide 3-Digit By 1-Digit Numbers (27)
- Divide 4-Digit By 1-Digit Numbers (21)
- Divide 4-Digit By 2-Digit Numbers (7)
- Fractions (635)
- Fractions Using Models (79)
- Fractions On A Number Line (26)
- Compare Fractions (64)
- Compare Fractions Using Models (16)
- Compare Fractions Using A Number Line (10)
- Order Fractions (20)
- Order Fractions Using Models (10)
- Equivalent Fractions (70)
- Equivalent Fractions Using Models (29)
- Equivalent Fractions Using A Number Line (10)
- Improper Fractions As Mixed Numbers (12)
- Mixed Numbers As Improper Fractions (4)
- Fractions Operations (348)
- Add Fractions (58)
- Add Fractions Using Models (23)
- Add Like Fractions (26)
- Add Unlike Fractions (12)
- Estimate Fraction Sums (7)
- Subtract Fractions (47)
- Subtract Fractions Using Models (21)
- Subtract Like Fractions (18)
- Subtract Unlike Fractions (11)
- Add Mixed Numbers (51)
- Add Mixed Numbers Using Models (12)
- Add A Mixed Number To A Fraction (14)
- Subtract Mixed Numbers (54)
- Subtract Mixed Numbers Using Models (11)
- Subtract A Fraction From A Mixed Number (19)
- Multiply Fractions (65)
- Multiply Fractions Using Models (18)
- Multiply Fractions By Whole Numbers (42)
- Multiply Mixed Numbers (32)
- Multiply Mixed Numbers By Whole Numbers (10)
- Multiply Mixed Numbers By Fractions (10)
- Divide Fractions (20)
- Scaling Fractions (10)
- Decimals (1,845)
- Read And Write Decimals (113)
- Decimals Using Models (22)
- Decimals On A Number Line (18)
- Decimal Place Value (71)
- Expanded Form Of Decimals (7)
- Word Form Of Decimals (10)
- Compare Decimals (53)
- Compare Decimals Using Models (10)
- Compare Decimals Using A Number Line (11)
- Order Decimals (27)
- Round Decimals (52)
- Round Decimals To The Nearest Whole (23)
- Round Decimals To The Nearest Tenths (10)
- Round Decimals To The Nearest Hundredths (10)
- Convert Decimals To Fractions (11)
- Decimal Operations (1,587)
- Add Decimals (382)
- Subtract Decimals (387)
- Multiply Decimals (263)
- Multiply Decimals By Powers Of 10 (27)
- Multiply Decimals By Whole Numbers (75)
- Divide Decimals (170)
- Divide Decimals By Powers Of 10 (18)
- Divide Decimals By Whole Numbers (52)
- Divide Whole Numbers By Decimals (45)
- Geometry (294)
- Positional Words (15)
- Lines, Line Segments, Rays (6)
- Parallel And Perpendicular Lines (5)
- Angles (32)
- Shapes (178)
- 2D Shapes (143)
- Attributes Of 2D Shapes (45)
- Polygons (11)
- Triangles (15)
- Quadrilaterals (26)
- 3D Shapes (31)
- 3D Shapes In Real Life (10)
- Partition Into Equal Parts (29)
- Partition In Halves, Thirds, And Fourths (24)
- Coordinate Plane (27)
- Read Points On The Coordinate Plane (10)
- Plot Points On The Coordinate Plane (10)
- Data Handling (85)
- Sorting Objects (18)
- Bar Graphs (12)
- Line Plots (13)
- Picture Graphs (10)
- Measurement (248)
- Length (71)
- Measure Lengths Using The Ruler (30)
- Estimate Lengths (8)
- Comparing Lengths (27)
- Height (16)
- Comparing Heights (16)
- Weight (23)
- Comparing Weights (10)
- Capacity (22)
- Conversion Of Measurement Units (27)
- Perimeter (35)
- Volume (21)
- Am And Pm (21)
- Time In Hours (25)
- Time In Half Hours (20)
- Time In Quarter Hours (21)
- Time To The Nearest 5 Minutes (27)
- Time To The Nearest Minute (13)
- Digital Clock (19)
- Elapsed Time (5)
- Money (144)
- Identify Coins (37)
- Counting Money (40)
- Compare Money (20)
- Add And Subtract Money (31)
- Multiply And Divide Money (19)
- Algebra (163)
- Number Patterns (49)
- Expressions And Equations (48)
- Evaluate Exponents (11)
- Order Of Operations (18)
- Factors And Multiples (51)
- Prime And Composite Numbers (15)
- Word Problems (773)
- Addition Word Problems (175)
- Addition Word Problems Within 20 (82)
- 2-Digit Addition Word Problems (28)
- 3-Digit Addition Word Problems (18)
- Decimal Addition Word Problems (25)
- Subtraction Word Problems (134)
- Subtraction Word Problems Within 20 (65)
- 2-Digit Subtraction Word Problems (12)
- Decimal Subtraction Word Problems (25)
- Multiplication Word Problems (117)
- Decimal Multiplication Word Problems (28)
- Division Word Problems (83)
- Decimal Division Word Problems (11)
- Multi-Step Word Problems (81)
- Fraction Word Problems (44)
- Money Word Problems (23)
- ELA (8,687)
- Reading (5,838)
- Phonics (5,305)
- Bossy R (79)
- Words With Ar (12)
- Words With Er (8)
- Words With Ir (8)
- Words With Or (7)
- Words With Ur (8)
- Diphthongs (50)
- Words With Oi (14)
- Words With Ou (13)
- Words With Ow (11)
- Words With Oy (11)
- Consonant Blends (238)
- Ending Blends (120)
- Beginning Blends (119)
- L Blend Words (56)
- R Blend Words (50)
- Alphabet (1,007)
- Letter Recognition (1,007)
- Letter A (23)
- Letter B (27)
- Letter C (22)
- Letter D (28)
- Letter E (22)
- Letter F (23)
- Letter G (28)
- Letter H (24)
- Letter I (26)
- Letter J (26)
- Letter K (22)
- Letter L (22)
- Letter M (23)
- Letter N (25)
- Letter O (22)
- Letter P (29)
- Letter Q (27)
- Letter R (22)
- Letter S (22)
- Letter T (23)
- Letter U (22)
- Letter V (22)
- Letter W (22)
- Letter X (22)
- Letter Y (22)
- Letter Z (22)
- Lowercase Letters (187)
- Uppercase Letters (207)
- Matching Lowercase And Uppercase Letters (209)
- Alphabetical Order (65)
- Abc Song (20)
- Letter Sounds (471)
- Beginning Sounds (162)
- Ending Sounds (18)
- Vowels (454)
- Long Vowel Sounds (155)
- Long Vowel A Sound (34)
- Long Vowel E Sound (33)
- Long Vowel I Sound (32)
- Long Vowel O Sound (30)
- Long Vowel U Sound (35)
- Silent E (44)
- Short Vowel Sounds (256)
- Short Vowel A Sound (108)
- Short Vowel E Sound (53)
- Short Vowel I Sound (101)
- Short Vowel O Sound (70)
- Short Vowel U Sound (54)
- Vowel Teams (112)
- Words With Ai And Ay (8)
- Words With Ea And Ee (11)
- Words With Ie And Y (8)
- Words With Oa And Ow (9)
- Words With Oo (10)
- Words With Ue And Ui (9)
- Blending (811)
- Ccvc Words (86)
- Ccvcc Words (42)
- Cvc Words (460)
- Cvcc Words (197)
- Consonant Digraphs (43)
- Digraph Ch (15)
- Digraph Ck (3)
- Digraph Ng (3)
- Digraph Ph (9)
- Digraph Sh (16)
- Digraph Th (15)
- Digraph Wh (15)
- Double Consonants (52)
- Rhyming Words (189)
- Trigraphs (54)
- Trigraph Dge (9)
- Trigraph Igh (9)
- Trigraph Tch (9)
- Three Letter Blends (53)
- Sight Words (2,025)
- Dolch Sight Words (567)
- Fry Sight Words (444)
- Syllables (15)
- Hard And Soft Sounds Of C And G (5)
- Segmenting Phonemes (5)
- Adding Deleting And Substituting Phonemes (12)
- Silent Letter Words (6)
- Reading Comprehension (506)
- Cause And Effect (32)
- Inference (36)
- Identify The Main Idea And Key Details (49)
- Categorize Pictures Into Groups (4)
- What'S The Title? (5)
- Prediction (32)
- Sequencing (46)
- Arrange Pictures In Order (3)
- Arrange Sentences In Order (4)
- Story Elements (28)
- Authors Purpose (23)
- Compare And Contrast (32)
- Ask And Answer Questions (27)
- Central Message (13)
- Point Of View (19)
- Sensory Words (5)
- Character Traits (22)
- Text Structure (15)
- Fact Or Opinion (6)
- Reality And Fantasy (8)
- Using Illustrations (38)
- Using Text Features (25)
- Context Clues (24)
- Communication Skills (29)
- Listening Skills (5)
- Speaking Skills (13)
- Writing (2,448)
- Handwriting (2,245)
- Letter Tracing (402)
- Letter Tracing A (18)
- Letter Tracing B (19)
- Letter Tracing C (18)
- Letter Tracing D (19)
- Letter Tracing E (18)
- Letter Tracing F (20)
- Letter Tracing G (18)
- Letter Tracing H (19)
- Letter Tracing I (18)
- Letter Tracing J (18)
- Letter Tracing K (18)
- Letter Tracing L (18)
- Letter Tracing M (19)
- Letter Tracing N (18)
- Letter Tracing O (18)
- Letter Tracing P (18)
- Letter Tracing Q (18)
- Letter Tracing R (18)
- Letter Tracing S (18)
- Letter Tracing T (18)
- Letter Tracing U (18)
- Letter Tracing V (18)
- Letter Tracing W (18)
- Letter Tracing X (18)
- Letter Tracing Y (18)
- Letter Tracing Z (18)
- Word Tracing (673)
- Sentence Tracing (254)
- Cursive Writing (915)
- Cursive Alphabet (407)
- Cursive Letter A (20)
- Cursive Letter B (20)
- Cursive Letter C (20)
- Cursive Letter D (20)
- Cursive Letter E (20)
- Cursive Letter F (20)
- Cursive Letter G (20)
- Cursive Letter H (20)
- Cursive Letter I (20)
- Cursive Letter J (20)
- Cursive Letter K (20)
- Cursive Letter L (20)
- Cursive Letter M (20)
- Cursive Letter N (20)
- Cursive Letter O (20)
- Cursive Letter P (20)
- Cursive Letter Q (20)
- Cursive Letter R (20)
- Cursive Letter S (20)
- Cursive Letter T (20)
- Cursive Letter U (20)
- Cursive Letter V (20)
- Cursive Letter W (20)
- Cursive Letter X (20)
- Cursive Letter Y (20)
- Cursive Letter Z (20)
- Cursive Words (276)
- Cursive Sentences (258)
- Creative Writing (166)
- Opinion Writing (17)
- Descriptive Writing (63)
- Narrative Writing (15)
- Writing Paragraphs (109)
- Writing Sentences (32)
- Grammar (588)
- Adverbs (41)
- Adjectives (67)
- Nouns (133)
- Singular And Plural Nouns (33)
- Irregular Plural Nouns (16)
- Common And Proper Nouns (13)
- Collective Nouns (17)
- Pronouns (46)
- Parts Of Speech (22)
- Conjunctions (29)
- Prepositions (25)
- Punctuation (50)
- Types Of Sentences (19)
- Sentence Structure (31)
- Verbs (137)
- Tenses (86)
- Irregular Verbs (14)
- Determiners (2)
- Article A An The (5)
- Spelling (40)
- Common Misspellings (10)
- Unscramble (19)
- Vocabulary (605)
- Contractions (13)
- Affixes (30)
- Suffixes And Prefixes (21)
- Inflectional Endings (4)
- Commonly Confused Words (24)
- Homophones (24)
- Compound Words (12)
- Figures Of Speech (34)
- Alliteration (8)
- Synonyms And Antonyms (30)
- Word Puzzles (273)
- Word Search (234)
- Anagrams (13)
- Shades Of Meaning (9)
- Sorting Words Into Categories (25)
- Flashcards (45)
- Vocabulary Flashcards (1)
- Phonics Flashcards (42)
- Grammar Flashcards (2)
- General Knowledge (295)
- Vegetables (19)
- Fruits (24)
- Dessert (9)
- Animals (58)
- Underwater (9)
- Dinosaurs (8)
- Reptiles (9)
- Seasonal (28)
- Christmas (12)
- Halloween (8)
- Kitchen (11)
- Utensils (6)
- Musical Instruments (30)
- Transport (9)
- Vehicles (9)
- Insects (9)
- Professions (8)
- Monuments (8)
- Household Items (8)
- Flowers (8)
- Buildings (8)
- Art & Creativity (236)
- Coloring (181)
- Animals (32)
- Underwater (8)
- Reptiles (8)
- Vegetables (8)
- Transport (8)
- Vehicles (8)
- Musical Instruments (8)
- Kitchen (8)
- Utensils (5)
- Insects (8)
- Rhymes (25)
- Cooking (7)
- Stories (10)
- Logic & Thinking (16)
- Puzzles (11)
- Matching (3)
- Multiplayer (12)
- Time Based (12)
- Player Vs Player (12)
- Motor Skills (16)
- Fine Finger Movement (9)
- Aiming And Precision (6)
Addition Word Problems
Adding One by Making a Model Game
Treat yourself to an immersive learning experience with our 'Adding One by Making a Model' game.
Adding Within 5 by Making a Model Game
Add more arrows to your child’s math quiver by adding within 5 by making a model.
Add within 5: Summer Word Problems Worksheet
Engaging summer-themed worksheet with word problems to enhance addition skills within 5.
Add within 5: Halloween Word Problems Worksheet
Spooky-themed worksheet for practicing addition within 5 through Halloween word problems.
Subtraction Word Problems
Solve Subtraction Scenarios Game
Apply your knowledge to solve subtraction scenarios.
Word Problems: Subtracting One Game
Sharpen your math skills with the 'Word Problems: Subtracting One' game.
Subtract within 5: Summer Word Problems Worksheet
A fun, summer-themed worksheet designed to enhance students' subtraction skills with problems up to 5.
Subtract within 5: Halloween Word Problems Worksheet
Spooky themed worksheet to master subtraction within 5 through fun Halloween word problems!
Multiplication Word Problems
Solve the Word Problems Related to Multiplication Game
Unearth the wisdom of mathematics by learning to solve word problems related to multiplication.
Solve Word Problems on Decimal Multiplication Game
Kids must solve word problems on decimal multiplication to practice decimals.
Complete the Word Problem for Equal Groups Worksheet
Help your child revise multiplication by solving word problems for equal groups.
Complete the Word Problem for Arrays Worksheet
Learners must complete the word problems for arrays to enhance their math skills.
Division Word Problems
Word Problems on How many Tens Game
Learn to solve world problems on 'How many Tens' with this game.
Solve Word Problems on Division Game
Learn to solve math problems by solving word problems on division.
Use Multiplication to Solve Division Word Problems Worksheet
Boost your ability to use multiplication to solve division word problems by printing this worksheet.
Solving Problems on Division Worksheet
Put your skills to the test by practicing to solve problems on division.
Fraction Word Problems
Solve the Word Problems on Fraction Addition Game
Have your own math-themed party by learning how to solve the word problems on fraction addition.
Solve the Word Problems on Fraction Subtraction Game
Add more arrows to your child’s math quiver by solving word problems on fraction subtraction.
Find Numerator to Have the Same Amount Worksheet
Be on your way to become a mathematician by finding the numerator to have the same amount.
Apply Fractions to Compare Worksheet
Combine math learning with adventure by applying fractions to compare.
All Word Problems Resources
Model and Add (Within 10) Game
Unearth the wisdom of mathematics by learning how to model and add (within 10).
Word Problems: Subtracting Within 10 Game
Enjoy the marvel of math-multiverse by practicing to solve word problems on subtracting within 10.
Add within 5: Christmas Word Problems Worksheet
Engage in festive math fun with this Christmas-themed worksheet, adding numbers within 5.
Subtract within 5: Christmas Word Problems Worksheet
Engaging Christmas-themed worksheet for students to master subtraction within 5 through word problems.
Solve Word Problems using Division Game
Apply your knowledge to solve word problems using division.
Solve Word Problems on Fraction-Whole Number Multiplication Game
Apply your knowledge to solve word problems on fraction-whole number multiplication.
Interpret Multiplication Scenarios
Engage in solving multiplication scenarios with these fun worksheets about the properties of 0 and 1!
Divide 2-digit Numbers by 1-digit Numbers: Summer Word Problems Worksheet
A summer-themed worksheet for students to practice dividing 2-digit numbers by 1-digit numbers.
Solve 'Add To' Scenarios Game
Add more arrows to your child’s math quiver by solving 'Add To' scenarios.
Solve 'Take Apart' Scenarios Game
Take the pressure off by simplifying subtraction by solving 'Take Apart' scenarios.
Word Problems on Adding Fractions & Mixed Numbers Worksheet
Become a mathematician by practicing word problems on adding fractions & mixed numbers.
Add within 5: Shopping Word Problems Worksheet
Engaging worksheet with a shopping theme to help students master addition within 5 through word problems.
Solve Comparison Word Problems Game
Unearth the wisdom of mathematics by learning how to solve comparison word problems.
Word Problems on Addition of Fractions Game
Use your fraction skills to solve word problems on addition of fractions.
Subtract within 5: Shopping Word Problems Worksheet
Engaging subtraction worksheet with a shopping theme, helping students solve problems within 5.
Make a Model to Multiply Worksheet
Put your skills to the test by practicing to make a model to multiply.
Solve 'Put Together' Scenarios Game
Shine bright in the math world by learning how to solve 'Put Together' scenarios.
Subtraction Scenario Game
Take a look at subtraction scenarios with this game.
Divide 2-digit Numbers by 1-digit Numbers: Halloween Word Problems Worksheet
Halloween-themed worksheet to enhance skills in dividing 2-digit numbers by 1-digit numbers.
Adding Fractions & Mixed Numbers Word Problems Worksheet
Help your child solve word problems on adding fractions & mixed numbers.
Find the Number of Groups Game
Find the number of groups to practice division.
Word Problems on Subtraction of Fractions Game
Have your own math-themed party by learning how to solve word problems on subtraction of fractions.
Add within 5: Travel Word Problems Worksheet
This worksheet combines fun travel-themed scenarios with math problems, requiring students to add numbers within 5.
Subtract within 5: Travel Word Problems Worksheet
Travel-themed worksheet to enhance students' subtraction skills within 5 through word problems.
Solve 'Add To' Word Problems Game
Unearth the wisdom of mathematics by learning how to solve 'Add To' word problems.
Take Away Scenario Game
Use your subtraction skills to solve 'Take Away' scenarios.
Multiply by Making a Model Worksheet
Pack your math practice time with fun by multiplying by making a model.
Divide 2-digit Numbers by 1-digit Numbers: Christmas Word Problems Worksheet
Christmas-themed worksheet to practice dividing 2-digit numbers by 1-digit numbers through word problems.
Your one stop solution for all grade learning needs.
- Daily Crossword
- Word Puzzle
- Word Finder
- Word of the Day
- Synonym of the Day
- Word of the Year
- Language stories
- All featured
- Gender and sexuality
- All pop culture
- Writing hub
- Grammar essentials
- Commonly confused
- All writing tips
- Pop culture
- Writing tips
Advertisement
- problem-solving
adjective as in analytic
Strongest matches
analytical , investigative
Weak matches
inquiring , rational , sound , systematic
adjective as in analytical
analytic , cogent , detailed , diagnostic , interpretive , investigative , penetrating , rational , scientific , systematic , thorough
conclusive , discrete , dissecting , explanatory , expository , inquiring , inquisitive , judicious , logical , organized , perceptive , perspicuous , precise , questioning , ratiocinative , reasonably , searching , solid , sound , studious , subtle , testing , valid
adjective as in analytic/analytical
cogent , conclusive , detailed , diagnostic , discrete , dissecting , explanatory , expository , inquiring , inquisitive , interpretive , investigative , judicious , logical , organized , penetrating , perceptive , perspicuous , precise , questioning , ratiocinative , rational , reasonable , scientific , searching , solid , sound , studious , subtle , systematic , testing , thorough , valid , well-grounded
Example Sentences
“These are problem-solving products but that incorporate technology in a really subtle, unobtrusive way,” she says.
And it is a “problem-solving populism” that marries the twin impulses of populism and progressivism.
“We want a Republican Party that returns to problem-solving mode,” he said.
Problem-solving entails accepting realities, splitting differences, and moving forward.
It teaches female factory workers technical and life skills, such as literacy, communication and problem-solving.
Problem solving with class discussion is absolutely essential, and should occupy at least one third of the entire time.
In teaching by the problem-solving method Professor Lancelot 22 makes use of three types of problems.
Sequential Problem Solving is written for those with a whole brain thinking style.
Thus problem solving involves both the physical world and the interpersonal world.
Sequential Problem Solving begins with the mechanics of learning and the role of memorization in learning.
Related Words
Words related to problem-solving are not direct synonyms, but are associated with the word problem-solving . Browse related words to learn more about word associations.
adjective as in logical
- investigative
adjective as in examining and determining
- explanatory
- inquisitive
- interpretive
- penetrating
- perspicuous
- questioning
- ratiocinative
- well-grounded
adjective as in examining
Viewing 5 / 11 related words
From Roget's 21st Century Thesaurus, Third Edition Copyright © 2013 by the Philip Lief Group.
5 Easy Steps to Solve Any Word Problem in Math
- February 27, 2021
Picture this my teacher besties. You are solving word problems in your math class and every student, yes every student knows how to solve word problems without immediately entering a state of confusion! They know how to attack the problem head-on and have a method to solve every single problem that is presented to them.
How Do You Solve Word Problems in Math?
Ask yourself this, what do you think is the #1 phrase a student says as soon as they see a word problem?
You guessed it, my teacher friend, I don’t know how to do this! I think the most common question I get when I’m teaching my math classes, is how do I solve this?
Students see word problems and immediately enter freak-out mode! Let’s take solving word problems in the classroom and make it easier for students to SOLVE the problem!
How to Solve Word Problems Step by Step
There are so many methods that students can choose from when learning how to solve word problems. The 4 step method is the foundation for all of the methods that you will see, but what about a variation of the 4 step method that every student can do just because they get it.
Students are most likely confused about how to solve word problems because they have never used a consistent method over the years. I’m all about consistency in my classroom. Fortunately, in my school district, I get to teach most of the students year after year because of how small our class sizes are. So I’m going to give you a method based on the 4 step method, that allows all students to be successful at solving word problems.
Even the most unmotivated math student will learn how to solve word problems and not skip them!
Tips, Tricks, and Teaching Strategies to Solving Word Problems in Math
Going back to the 4 step method just in case you need a refresher. If you know me at all a little reminder of “oh yeah I remember that now” always helps me!
4 steps in solving word problems in math:
- Understand the Problem
- Plan the solution
- Solve the Problem
- Check the solution
This 4 step method is the basis of the method I’m going to tell you all about. The problem isn’t with the method itself, it is the fact that most students see word problems and just start panicking!
Why can they do an entire assignment and then see a word problem and then suddenly stop? Is there a reason why books are designed with word problems at the end?
These are questions that I constantly have asked myself over the last several years. I finally got to the point where my students needed a consistent approach to solving word problems that worked every single time.
The first thing I knew I needed to start doing was introducing students to word problems at the beginning of each lesson.
Once students first see the word problems at the beginning of the lesson, they are less likely to be scared of them when it comes time to do it by themselves!
This also will increase their confidence in the classroom. In case you missed it, I shared all about how I increase my students’ confidence in the classroom.
Wonder how increasing their confidence will help keep them motivated in the classroom?
So confident motivated students will see word problems that could be on their homework, any standardized test, and say I GOT THIS!
Steps to Solving Word Problems in Mathematics
We are ready to SOLVE any word problem our students are going to encounter in math class.
Here are my 5 easy steps to SOLVE any word problem in math:
- S – State the objective
- O – Outline your plan
- L – Look for Key Details – Information
- V – Verify and Solve
- E – Explain and check your solution
Do you want to learn how to implement this 5 steps problem-solving strategy into your classroom? I’m hosting a FREE workshop all about how to implement this strategy in your classroom!
I am so excited to be offering a workshop to increase students’ confidence in solving word problems. The workshop is held in my Facebook Group The Round Robin Math Community. It also will be sent straight to your inbox and you can watch it right now!
If you’re interested, join today and all the details will be sent to you ASAP!
I will see you there!
PS. Need the SOLVE method for your bulletin board for your students’ math journals/notebooks? Check out this bulletin board resource here:
Love, Robin
- Latest Posts
Robin Cornecki
Latest posts by robin cornecki ( see all ).
- The #1 method for finding slope without using a formula! - April 25, 2023
- Here’s a Quick Way to Convert Percents to Fractions and Decimals. - July 21, 2022
- How to use the Four-Function Calculator for the Praxis Core Math Test. - April 23, 2022
Hi, I'm Robin!
I am a secondary math teacher with over 19 years of experience! If you’re a teacher looking for help with all the tips, tricks, and strategies for passing the praxis math core test, you’re in the right place!
I also create engaging secondary math resources for grades 7-12!
Learn more about me and how I can help you here .
Let's Connect!
Get my top 7 strategies.
- Solutions Integral Calculator Derivative Calculator Algebra Calculator Matrix Calculator More...
- Graphing Line Graph Exponential Graph Quadratic Graph Sine Graph More...
- Calculators BMI Calculator Compound Interest Calculator Percentage Calculator Acceleration Calculator More...
- Geometry Pythagorean Theorem Calculator Circle Area Calculator Isosceles Triangle Calculator Triangles Calculator More...
- Tools Notebook Groups Cheat Sheets Worksheets Study Guides Practice Verify Solution
x^{\msquare} | \log_{\msquare} | \sqrt{\square} | \nthroot[\msquare]{\square} | \le | \ge | \frac{\msquare}{\msquare} | \cdot | \div | x^{\circ} | \pi | |||||||||||
\left(\square\right)^{'} | \frac{d}{dx} | \frac{\partial}{\partial x} | \int | \int_{\msquare}^{\msquare} | \lim | \sum | \infty | \theta | (f\:\circ\:g) | f(x) |
▭\:\longdivision{▭} | \times \twostack{▭}{▭} | + \twostack{▭}{▭} | - \twostack{▭}{▭} | \left( | \right) | \times | \square\frac{\square}{\square} |
- Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Expanded Form Mean, Median & Mode
- Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Prove That Logical Sets Word Problems
- Pre Calculus Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Coterminal Angle Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry
- Calculus Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform
- Functions Line Equations Functions Arithmetic & Comp. Conic Sections Transformation
- Linear Algebra Matrices Vectors
- Trigonometry Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify
- Statistics Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution
- Physics Mechanics
- Chemistry Chemical Reactions Chemical Properties
- Finance Simple Interest Compound Interest Present Value Future Value
- Economics Point of Diminishing Return
- Conversions Roman Numerals Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time Volume
- Pre Algebra
- Pre Calculus
- Linear Algebra
- Trigonometry
- Conversions
x^{\msquare} | \log_{\msquare} | \sqrt{\square} | \nthroot[\msquare]{\square} | \le | \ge | \frac{\msquare}{\msquare} | \cdot | \div | x^{\circ} | \pi | |||||||||||
\left(\square\right)^{'} | \frac{d}{dx} | \frac{\partial}{\partial x} | \int | \int_{\msquare}^{\msquare} | \lim | \sum | \infty | \theta | (f\:\circ\:g) | f(x) |
- \twostack{▭}{▭} | \lt | 7 | 8 | 9 | \div | AC |
+ \twostack{▭}{▭} | \gt | 4 | 5 | 6 | \times | \square\frac{\square}{\square} |
\times \twostack{▭}{▭} | \left( | 1 | 2 | 3 | - | x |
▭\:\longdivision{▭} | \right) | . | 0 | = | + | y |
Number Line
- x^{2}-x-6=0
- -x+3\gt 2x+1
- line\:(1,\:2),\:(3,\:1)
- prove\:\tan^2(x)-\sin^2(x)=\tan^2(x)\sin^2(x)
- \frac{d}{dx}(\frac{3x+9}{2-x})
- (\sin^2(\theta))'
- \lim _{x\to 0}(x\ln (x))
- \int e^x\cos (x)dx
- \int_{0}^{\pi}\sin(x)dx
- \sum_{n=0}^{\infty}\frac{3}{2^n}
- Is there a step by step calculator for math?
- Symbolab is the best step by step calculator for a wide range of math problems, from basic arithmetic to advanced calculus and linear algebra. It shows you the solution, graph, detailed steps and explanations for each problem.
- Is there a step by step calculator for physics?
- Symbolab is the best step by step calculator for a wide range of physics problems, including mechanics, electricity and magnetism, and thermodynamics. It shows you the steps and explanations for each problem, so you can learn as you go.
- How to solve math problems step-by-step?
- To solve math problems step-by-step start by reading the problem carefully and understand what you are being asked to find. Next, identify the relevant information, define the variables, and plan a strategy for solving the problem.
word-problems
- My Notebook, the Symbolab way Math notebooks have been around for hundreds of years. You write down problems, solutions and notes to go back...
We want your feedback
Please add a message.
Message received. Thanks for the feedback.
- Our Mission
Using Video Projects to Reinforce Learning in Math
A collaborative project can help students deeply explore math concepts, explain problem-solving strategies, and demonstrate their learning.
Problem-solving, and the creativity that generates and fuels it, lies at the heart of mathematics. Mathematics is essentially about reasoning and much less about memorization or even procedural skills, although both processes are meaningful and useful to simplify and support problem-solving. The National Council of Teachers of Mathematics (NCTM) has consistently advocated to keep problem-solving as the centerpiece of mathematics teaching, and global trends in mathematics education have increasingly emphasized problem-solving and mathematical modeling.
Problem-solving allows students to deepen their conceptual comprehension and appreciate the usefulness and relevance of mathematics. Thus, it generates and fosters interest, engagement, and a deeper understanding of the world around them. Because problem-solving is often used in the mathematics classroom, it’s particularly important to find fresh and interesting ways to attract and maintain students’ engagement.
Video Projects Support Interest in Problem-Solving
To this end, I assign video projects to my students. In groups of two or three, they solve a set of problems on a topic and then choose one to illustrate, solve, and explain their favorite problem-solving strategy in detail, along with the reasons they chose it. The student-created videos are collected and stored on a Padlet even after I have evaluated them—kept as a reference, keepsake, and support. I have a library of student-created videos that benefit current and future students when they have some difficulties with a topic and associated problems.
Some topics in mathematics are well-suited for applications and problem-solving. These are usually multistep problems that require a combination of strategies and procedural fluency. Typical examples are the motion, work, and mixture problems in algebra, the optimization problems in precalculus or calculus, and related rates problems in calculus.
This collection of student-created videos is about related rates problems (note that some links may not work, as this collection is old). Video activities based on problem-solving can be done at any level of mathematics, as problem-solving is a task in which children are engaged in math class from an early age.
Useful Recording Tools
Some examples of useful recording apps include Screencastify , ScreenPal , iMovie , and QuickTime . Each of them has pros and cons, so I suggest looking at the particular specifications of each tool in terms of the number and length of videos allowed by the free version of those apps. I let my students choose what app they want to use to create their videos—they are generally very familiar with this sort of technology and may be more at ease with one tool over another. All they have to produce is a usable link to their video that will be posted on the common Padlet.
Loom is an intuitive, user-friendly screen recording tool that can record audio, video, browser windows, or entire screens in a Chrome extension, desktop app, or mobile app. You can sign up for a free Loom for Education account; students don’t need an account to watch a teacher’s videos, but they will in order to create their own videos.
Loom’s training module is thorough and includes tutorials, special feature descriptions, and examples. Once you click the Loom icon, there’s a short countdown that precedes the recording. When you stop the recording, a link automatically saves to your clipboard and can be easily shared via email, social media, or an embed code.
The videos will also save to your personal library and can be shared to a team library to make them easily accessible to colleagues. Editing features are quite limited (trimming and changing playback speed), which means you may have to do multiple takes, but teachers can control the settings for comment and download options.
4 Problem-Solving Strategies
Mathematician George Polya outlined a four-step model in his famous book, How to Solve It . It involves understanding the problem, devising a plan, carrying it out, and finally looking back and reflecting. These are the strategies that my students must demonstrate while creating their videos.
- Understand the problem: Students reread the problem carefully, summarize and rewrite the information in mathematical notation, use keyword analysis, draw a picture or a diagram, or even act out the scenario.
- Devise a plan: Looking for patterns and solving a simpler problem are my favorite approaches, but other ideas—guess-and-check, working backward, eliminating possibilities, using a formula and solving an equation—can work well too, depending on the circumstances. Most often, for good problems, several of these strategies have to be employed at the same time and help support confidence in the solution.
- Carry out the plan: This is where “show your work” comes in with full force. Communicating their thoughts and ideas is paramount: Students should be systematic, show their thinking in a logical progression, check their work, and be flexible and persistent.
- Look back and reflect: It’s important to consider which part of the problem was the most challenging and why, which process was most effective, and other strategies that could have worked. This makes for more efficient and deeper learning.
Related rates problems can be intimidating at first, and it is useful for students to write out explicitly the steps and strategies they take to solve the first few problems.
My students come up with a model that follows the previously mentioned steps. It includes labeling the rates with their units and sign, an understanding of the rate they must find, finding at least one equation that binds the variables together, differentiating this equation with respect to time, plugging in the given information, and, finally, writing a short sentence that summarizes their conclusion (including sign and units).
Benefits of the Video Activity
My students and I have experienced several benefits of this task.
Students are encouraged to communicate mathematically. The importance of communication among learners is also heavily emphasized in the NCTM publication Principles and Standards for School Mathematics .
Student collaboration. Viewing learning as a collective endeavor , rather than an individual competition, helps students develop their social and collaborative skills. When students take joint responsibility for their learning—sharing ideas and resources—it fosters a safe environment where they perceive each other as allies rather than competitors, which increases engagement and academic achievement.
Problem-solving skills are strengthened. As reported in the Executive Summary of the NCTM Principles and Standards for School Mathematics , when solving mathematical problems, students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations that serve them well beyond the classroom.
Teachers can clearly see students’ understanding. This includes conceptual understanding, procedural precision, logical and analytical thinking, problem-solving strategies, and clarity of communication.
A sense of belonging in math class is cemented. The experience generates positive, affirmative memories—the goal of social and emotional learning—and “ encourages student focus and motivation, improves relationships between students and teachers, and increases student confidence and success .” It should be promoted, particularly in the STEM disciplines.
In other words, it’s a keeper.
45,000+ students realised their study abroad dream with us. Take the first step today
Meet top uk universities from the comfort of your home, here’s your new year gift, one app for all your, study abroad needs, start your journey, track your progress, grow with the community and so much more.
Verification Code
An OTP has been sent to your registered mobile no. Please verify
Thanks for your comment !
Our team will review it before it's shown to our readers.
- Study Material /
Solve Unitary Method Questions and Word Problems
- Updated on
- Sep 4, 2024
The Unitary Method is a fundamental mathematical technique used to solve problems by finding the value of a single unit and then using it to determine the value of multiple units. It is widely applicable in solving real-life problems, particularly in areas like ratio and proportion, percentage calculations, and unit conversions. The Unitary method is essential for understanding how to break down complex problems into simpler, more manageable parts. This approach is often used in various types of competitive exams, including those for banking , government jobs , and entrance tests , where questions related to the Unitary Method appear frequently. Key concepts include understanding ratios, proportions, and basic arithmetic operations. This guide covers the definition, types, properties, formulas, and word problems associated with the Unitary Method, providing a comprehensive overview to enhance your problem-solving skills.
Table of Contents
- 1 What is the Unitary Method?
- 2.1 1. Direct Variation (Direct Proportion)
- 2.2 2. Inverse Variation (Inverse Proportion)
- 3 Properties of Unitary Method
- 4 Formulas of Unitary Method
- 5 Types of Unitary Method Word Problems
- 6 Unitary Method Questions: Step-by-Step Solution
What is the Unitary Method?
The Unitary Method is a fundamental mathematical approach used to solve problems by first determining the value of a single unit and then using that value to find the value of multiple units. It operates on the principle that if the value of one unit is known, the value of any number of units can be calculated through multiplication or division.
Important Terms:
- Unit : A single quantity or measurement, such as one item, one kilogram, or one liter.
- Ratio : A relationship between two quantities, showing how many times one value is contained within another.
- Proportion : An equation that states that two ratios are equal.
- Multiplier : A factor by which a unit is multiplied to find the value of multiple units.
- Divisor : A number by which a total is divided to find the value of a single unit.
- Cost per Unit : The price of one unit of an item or service.
- Rate : A measure of a quantity relative to another quantity, such as speed (distance per unit of time) or density (mass per unit of volume).
- Percentage : A ratio or fraction out of 100, used to express proportions.
How It Works:
- If the value of multiple units is known, divide the total value by the number of units to find the value of one unit.
- Example: If 5 apples cost $10, the cost of one apple is $10 ÷ 5 = $2.
- If the value of one unit is known, multiply it by the number of units to find the total value.
- Example: If one apple costs $2, the cost of 8 apples is $2 × 8 = $16.
Types of Unitary Method
The Unitary Method can be categorized into two main types, based on the relationship between the quantities involved:
1. Direct Variation (Direct Proportion)
In direct variation, as one quantity increases, the other quantity also increases in the same proportion, and vice versa. The Unitary Method is applied here to find the value of one quantity when the other is known.
Example : If 5 kilograms of rice cost $20, then the cost of 1 kilogram (the unit) is $20 ÷ 5 = $4. If you want to find the cost of 8 kilograms of rice, you multiply the unit cost by 8: $4 × 8 = $32.
Application : This type of unitary method is used in problems involving prices, wages, and other quantities that increase or decrease in direct proportion to each other.
2. Inverse Variation (Inverse Proportion)
In inverse variation, as one quantity increases, the other quantity decreases proportionally, and vice versa. Here, the Unitary Method is used to find one quantity when the product of two quantities is constant.
Example : If 6 workers can complete a task in 12 days, then the work done by 1 worker (the unit) in 12 days is equivalent to the work done by 6 workers. To find out how long it will take for 3 workers to complete the task, divide the total work (6 × 12 = 72 worker-days) by the number of workers (3), resulting in 72 ÷ 3 = 24 days.
Application : This type is used in problems involving speed and time, work and workers, and other scenarios where an increase in one quantity leads to a proportional decrease in another.
Also Read: Reciprocal: Definition, Meaning and Solved Examples
Properties of Unitary Method
The Unitary Method has several key properties that make it an effective and versatile tool for solving a wide range of mathematical problems. Here are the main properties of the Unitary Method:
1. Proportionality
- Property : If one quantity changes, the other changes in a consistent ratio.
- Example : If 2 pens cost $4, then 4 pens will cost $8 (double the quantity, double the cost).
2. Linearity
- Property : Changes between quantities are linear, meaning direct or inverse proportionality.
- Example : If a car travels 60 miles in 1 hour, it will travel 120 miles in 2 hours (distance is directly proportional to time).
3. Scalability
- Property : The method can be applied to any number of units.
- Example : If 1 apple costs $2, then 50 apples will cost $2 × 50 = $100.
4. Versatility
- Property : Can be used for various types of problems (e.g., ratios, speed, cost).
- Example : If a worker can complete a task in 5 days, 2 workers can complete it in 2.5 days (work is inversely proportional to the number of workers).
5. Simplicity
- Property : Breaks down complex problems into simpler steps.
- Example : To find the cost of 7 chocolates when 1 chocolate costs $3, simply multiply: $3 × 7 = $21.
6. Consistency
- Property : Provides uniform and reliable results.
- Example : If 10 books cost $50, then 1 book costs $50 ÷ 10 = $5. For 20 books, it’s $5 × 20 = $100.
7. Applicability in Both Direct and Inverse Proportions
- Property : Works for both direct and inverse relationships.
- Example : Direct: 3 meters of cloth costs $30, so 6 meters cost $60. Inverse: 4 workers take 8 hours to complete a task; 8 workers will take 4 hours.
Formulas of Unitary Method
The Unitary Method primarily revolves around finding the value of one unit and then using that value to determine the value of multiple units. The formulas associated with the Unitary Method are straightforward and can be categorized based on direct and inverse proportion problems.
1. Direct Proportion Formula
In direct proportion, as one quantity increases, the other increases proportionally. The key formulas are:
- Finding the value of one unit:
Example : If 5 apples cost $10, then the cost of one apple is: 10/5 = 2 dollars
- Finding the value of multiple units:
Example : If one apple costs $2, then the cost of 8 apples is: 2×8 = 16 dollars
2. Inverse Proportion Formula
In inverse proportion, as one quantity increases, the other decreases proportionally. The key formulas are:
- Finding the value of one unit (work or time):
Example : If 6 workers take 12 days to complete a task, the total worker-days is: 6×12 = 72 worker-days
Example : If 3 workers are to complete the same task, the time taken would be: 72/3 = 24 days
Also Read: All Perfect Cube Numbers
Types of Unitary Method Word Problems
Here are five-word problems that can be solved using the Unitary Method:
1. Cost Calculation
Problem : If 7 notebooks cost Rs 35, what is the cost of 5 notebooks?
- Cost of 1 notebook = Rs35 ÷ 7 = Rs5
- Cost of 5 notebooks = Rs 5 × 5 = $25
2. Time and Work
Problem : If 8 workers can complete a task in 12 days, how many days will it take for 6 workers to complete the same task?
- Total work = 8 workers × 12 days = 96 worker-days
- Time taken by 6 workers = 96 worker-days ÷ 6 workers = 16 days
3. Distance and Speed
Problem : A car travels 240 kilometers in 4 hours. How far will it travel in 7 hours at the same speed?
- Distance covered in 1 hour = 240 km ÷ 4 hours = 60 km/hour
- Distance in 7 hours = 60 km/hour × 7 hours = 420 kilometers
4. Wage Calculation
Problem : If 5 workers earn Rs 400 in a day, how much will 8 workers earn in a day?
- Earnings of 1 worker = Rs 400 ÷ 5 = $80
- Earnings of 8 workers = Rs 80 × 8 = $640
5. Quantity and Cost
Problem : If 10 kilograms of sugar cost $50, how much will 15 kilograms of sugar cost?
- Cost of 1 kilogram of sugar = Rs 50 ÷ 10 kg = $5/kg
- Cost of 15 kilograms = Rs 5/kg × 15 kg = $75
Unitary Method Questions: Step-by-Step Solution
Question 1 If 15 workers can complete a construction project in 20 days, how many days will it take for 25 workers to complete the same project, assuming the work rate is consistent?
Solution: Total work = Number of workers × Number of days
Total work = 15 × 20
Total work = 300 worker-days
Days for 25 workers = Total work / Number of workers
Days for 25 workers = 300 / 25
Days for 25 workers = 12 days
Question 2:A machine can produce 1200 units in 8 hours. If the production rate is consistent, how many units can it produce in 15 hours?
Solution: Units per hour = Total units / Number of hours
Units per hour = 1200 / 8
Units per hour = 150
Units in 15 hours = Units per hour × Number of hours
Units in 15 hours = 150 × 15
Units in 15 hours = 2250
Question 3:If 30 students can complete a group project in 10 days, how many students are required to complete the same project in 6 days?
Solution: Total work = Number of students × Number of days
Total work = 30 × 10
Total work = 300 student-days
Number of students for 6 days = Total work / Number of days
Number of students for 6 days = 300 / 6
Number of students for 6 days = 50 students
Question 4:A factory produces 5000 units of a product in 12 hours. How many units will it produce in 20 hours?
Units per hour = 5000 / 12
Units per hour ≈ 416.67
Units in 20 hours = Units per hour × Number of hours
Units in 20 hours = 416.67 × 20
Units in 20 hours ≈ 8333.33
Question 5:If 9 liters of paint cover 72 square meters, how many liters are required to cover 150 square meters?
Solution: Coverage per liter = Total coverage / Number of liters
Coverage per liter = 72 / 9
Coverage per liter = 8 square meters
Liters required = Total area / Coverage per liter
Liters required = 150 / 8
Liters required = 18.75 liters
Question 6:If a car travels 360 kilometers on 40 liters of fuel, how many liters will it need to travel 540 kilometers?
Solution: Distance per liter = Total distance / Number of liters
Distance per liter = 360 / 40
Distance per liter = 9 kilometers
Liters required = Total distance / Distance per liter
Liters required = 540 / 9
Liters required = 60 liters
Question 7:If 5 workers can finish a task in 16 days, how many days will it take for 8 workers to complete the same task?
Total work = 5 × 16
Total work = 80 worker-days
Days for 8 workers = Total work / Number of workers
Days for 8 workers = 80 / 8
Days for 8 workers = 10 days
Question 8:A factory produces 2400 units of an item in 6 hours. How many hours will it take to produce 6000 units?
Solution: Production rate = Total units / Number of hours
Production rate = 2400 / 6
Production rate = 400 units per hour
Hours required = Total units / Production rate
Hours required = 6000 / 400
Hours required = 15 hours
Question 9:If 10 kg of a substance is used to prepare 25 liters of solution, how many kilograms are needed to prepare 75 liters of the same solution?
Solution: Kilograms per liter = Total kilograms / Number of liters
Kilograms per liter = 10 / 25
Kilograms per liter = 0.4 kg per liter
Kilograms required = Kilograms per liter × Number of liters
Kilograms required = 0.4 × 75
Kilograms required = 30 kg
Question 10:A contractor can paint 1500 square meters in 10 hours. If another contractor can paint at twice the speed, how many hours will it take for this second contractor to paint 1500 square meters?
Solution: First contractor’s rate = Total area / Number of hours
First contractor’s rate = 1500 / 10
First contractor’s rate = 150 square meters per hour
Second contractor’s rate = 2 × First contractor’s rate
Second contractor’s rate = 2 × 150
Second contractor’s rate = 300 square meters per hour
Hours required = Total area / Second contractor’s rate
Hours required = 1500 / 300
Hours required = 5 hours
Unitary method is a technique used to solve problems by first finding the value of a single unit, then multiplying it to find the value of the required quantity. For example, if 5 apples cost ₹20, to find the cost of 3 apples, we first find the cost of 1 apple (₹20 ÷ 5 = ₹4) and then multiply by 3 (₹4 × 3 = ₹12).
Unitary method is a technique to solve problems by first finding the value of one unit and then multiplying it by the required number of units. It’s a common method used in mathematics for calculations involving ratios, proportions, and rates.
Unitary method formula is a technique to find the value of a single unit from the value of multiple units, and then use that value to find the value of a different number of units. — Value of a single unit = Total value / Total number of units — Value of required number of units = Value of a single unit x Required number of units.
RELATED BLOGS
| |
| |
|
This was all about the “ Unitary Method ”. For more such informative blogs, check out our Study Material Section , or you can learn more about us by visiting our Indian exams page.
Mohit Rajak
Mohit Rajak, a soul entwined with the rhythm of words, finds solace in crafting verses that dance between the lines of poetry. With a pen as his wand, he weaves intricate tales and musings, breathing life into the blank canvas of pages. Through the art of blogging, Mohit embraces the world, sharing his thoughts, emotions, and unique perspective with those who venture into the realm of his written expressions. Each word, a brushstroke painting the canvas of his literary journey.
Leave a Reply Cancel reply
Save my name, email, and website in this browser for the next time I comment.
Contact no. *
Connect With Us
45,000+ students realised their study abroad dream with us. take the first step today..
Resend OTP in
Need help with?
Study abroad.
UK, Canada, US & More
IELTS, GRE, GMAT & More
Scholarship, Loans & Forex
Country Preference
New Zealand
Which English test are you planning to take?
Which academic test are you planning to take.
Not Sure yet
When are you planning to take the exam?
Already booked my exam slot
Within 2 Months
Want to learn about the test
Which Degree do you wish to pursue?
When do you want to start studying abroad.
January 2024
September 2024
What is your budget to study abroad?
How would you describe this article ?
Please rate this article
We would like to hear more.
Have something on your mind?
Make your study abroad dream a reality in January 2022 with
India's Biggest Virtual University Fair
Essex Direct Admission Day
Why attend .
Don't Miss Out
Solving Proportion Equations Worksheets
Ratio Riddles
Ratio Solver
Equation Match
Ratio Resolver
Fraction Finder
Proportion Puzzle
Fraction Quest
Ratio Challenges
Decimal Discoveries
Decimal Dynamics
Variable Voyage
Algebraic Balance
Proportional Path
Proportion Puzzles
About these 15 worksheets.
These worksheets will help students understand and apply the concept of proportions, a fundamental aspect of mathematics. These worksheets cater to students from grade 6 through high school and cover a wide range of proportion-related topics. They are designed to enhance students’ skills in solving equations that express the equality of two ratios, using methods such as cross-multiplication and inverse operations. Let’s delve into the various types of problems you might encounter on these worksheets and the mathematical skills they help develop, as well as their real-world applications.
Basic Proportion Problems
One of the foundational elements of these worksheets is solving basic proportion problems. These exercises often present students with two ratios set equal to each other, such as a/b = c/d, and require them to solve for one unknown variable. For instance, if given x/4 = 3/12, students would cross-multiply to find x = 1. This exercise teaches students the cross-multiplication method, a critical technique for solving proportions. It reinforces the understanding that in a proportion, the product of the means equals the product of the extremes.
Proportions with Fractions and Decimals
As students progress, they encounter proportions involving fractions and decimals. These problems require careful attention to detail, as students must handle fractional and decimal values accurately. For example, solving 2.5/x = 7.5/15 involves cross-multiplying and solving for x, which would result in x = 5. These exercises help students become comfortable working with different numerical forms and enhance their precision in mathematical calculations.
Algebraic Proportions
More advanced worksheets include algebraic proportions, where variables are part of the ratios. For instance, students might solve an equation like x+2/5 = 3x/10. Solving these requires students to apply their knowledge of algebraic manipulation alongside proportion-solving techniques. These problems develop students’ ability to work with algebraic expressions and understand how proportions can be applied in algebraic contexts.
Word Problems Involving Proportions
Word problems are a significant component of proportion worksheets, as they help students apply mathematical concepts to real-world scenarios. These problems might involve scenarios such as mixing ingredients in a recipe, calculating distances based on map scales, or determining the cost of items based on unit prices. For example, a problem might state that if 3 pencils cost $1.50, how much would 10 pencils cost? Students would set up the proportion 3/1.5 = 10/x and solve for x to find the total cost. These exercises enhance students’ problem-solving skills and their ability to translate real-world situations into mathematical equations.
Graphical Representation of Proportions
Some worksheets incorporate graphical elements, asking students to determine if a set of data points on a graph represents a proportional relationship. Students might be tasked with plotting points and checking if the line passes through the origin, indicating a proportional relationship. These exercises help students visualize proportions and understand their graphical representation, reinforcing the concept that proportional relationships are linear and pass through the origin.
Constant of Proportionality
Worksheets on proportions often include problems related to finding the constant of proportionality. This involves determining the constant ratio between two quantities that are directly proportional. For example, if given that y = kx, students might be asked to find the value of k given specific values of x and y. Understanding the constant of proportionality is crucial for grasping how changes in one quantity affect another in a proportional relationship.
Real-World Applications of Proportions
Proportions are not just abstract mathematical concepts; they have numerous real-world applications. In everyday life, you might use proportions when cooking, such as adjusting a recipe to serve more or fewer people. For instance, if a recipe for four people requires two cups of flour, you would use a proportion to calculate the amount needed for six people. In business, proportions help in scaling production, determining cost efficiencies, and analyzing market trends. For example, a company might use proportions to calculate the amount of raw material needed to produce a certain number of products.
In the medical field, proportions are vital for calculating correct medication dosages based on a patient’s weight. For example, if a medication dosage is prescribed at 2 mg per kilogram of body weight, a doctor would use a proportion to determine the appropriate dose for a patient weighing 70 kg. This ensures safe and effective treatment.
In construction and engineering, proportions are used to create scale models and drawings, ensuring that every part of a structure is built to the correct dimensions. For example, if a blueprint uses a scale of 1 inch to 10 feet, a builder would use proportions to convert measurements from the blueprint to actual dimensions.
IMAGES
VIDEO
COMMENTS
Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems. An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time.
Problem Solver Subjects. Our math problem solver that lets you input a wide variety of math math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects. Here are example math problems within each subject that can be input into the calculator and solved.
Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents. Solving Word Questions. With LOTS of examples! In Algebra we often have word questions like: Example: Sam and Alex play tennis.
A Guide on Steps to Solving Word Problems: 10 Strategies. 1. Understand the Problem by Paraphrasing. One of the first steps in tackling a math word problem is to make sure your students understand what the problem is asking. Encourage them to paraphrase the problem in their own words.
Step 2: Highlight the keywords in the word problem. The keywords for word problems in math indicate what math action should be taken. Teach your child to highlight or underline the keywords in every word problem. Here are some of the most common keywords in math word problems: Subtraction words- less than, minus, take away.
The key word "same" in this problem means that I am going to set my two expressions equal to each other. When we set the two expressions equal, we now have an equation with variables on both sides. After solving the equation, you find that x = 30, which means that after 30 weeks, you and your sister will have the same amount of money.
The first in solving any word problem is to find out what question the problem is asking you to solve and identify the information that will help you solve it. Let's look at the problem again. The question is right there in plain sight: A single ticket to the fair costs $8. A family pass costs $25 more than half that.
Step 5. Solve the equation using good algebra techniques. Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers. Write the equation. 18= 1 2p 18 = 1 2 p. Multiply both sides by 2. 2⋅18=2⋅ 1 2p 2 ⋅ 18 = 2 ⋅ 1 2 p. Simplify.
Solving word problems in math may require following a process that makes it easier to solve. Learn the steps used in solving word problems which include visualizing the problem, writing the ...
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 ...
Word Problem Calculator. Get detailed solutions to your math problems with our Word Problem step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here. Go! Symbolic mode. Text mode.
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. Word problems in mathematics are a powerful tool for helping students make sense of and reason with mathematical concepts. Many students, however, struggle with ...
Solving word problems in elementary school is an essential part of the math curriculum. Here are over 30 math word problems to practice with children, plus expert guidance on how to solve them. This blog is part of our series of blogs designed for teachers, schools, and parents supporting home learning.
Algebra Word Problems. Step 1 in effectively translating and solving word problems is to read the problem entirely. Don't start trying to solve anything when you've only read half a sentence. Try first to get a feel for the whole problem; try first to see what information you have, and then figure out what you still need.
Free Inclusive Number Word Problems Calculator - Given an integer A and an integer B, this calculates the following inclusive word problem questions: 1) The Average of all numbers inclusive from A to B 2) The Count of all numbers inclusive from A to B 3) The Sum of all numbers inclusive from A to B. Calculator · Watch the Video.
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.
Word Problems Activities. Teach your child all about word problems with amazing educational resources for children. These online word problems learning resources break down the topic into smaller parts for better conceptual understanding and grasp. Get started now to make word problems practice a smooth, easy and fun process for your child!
Word Problems. These word problem generators allow you to create many new word problems to practice with. Students can generate multiple word problems of each type for problem-solving practice. Teachers can use the word problem generators to create word problems for students. Once you answer a word problem the answer is shown in a proof.
Find 80 different ways to say PROBLEM-SOLVING, along with antonyms, related words, and example sentences at Thesaurus.com.
You see, true problem-solving is messy and goes way beyond solving word problems. George Polya is often called the Father of Problem-Solving. In 1945, he outlined a 4-step process for solving problems in his ground-breaking book How to Solve It. You can see the four steps pictured below. Now think about the process I went through while solving ...
Steps to Solving Word Problems in Mathematics. We are ready to SOLVE any word problem our students are going to encounter in math class. Here are my 5 easy steps to SOLVE any word problem in math: S - State the objective. O - Outline your plan. L - Look for Key Details - Information. V - Verify and Solve.
A multi-step word problem, also known as a two-step word problem or two-step equation word problem, is a math situation that involves more than one equation having to be answered in order to solve the ultimate question. This requires students to apply their problem solving skills to determine which operation or operations to use to tackle the ...
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.As most word problems involve a narrative of some sort, they are ...
To solve math problems step-by-step start by reading the problem carefully and understand what you are being asked to find. Next, identify the relevant information, define the variables, and plan a strategy for solving the problem. word-problems. en. Related Symbolab blog posts.
Understand the problem: Students reread the problem carefully, summarize and rewrite the information in mathematical notation, use keyword analysis, draw a picture or a diagram, or even act out the scenario. Devise a plan: Looking for patterns and solving a simpler problem are my favorite approaches, but other ideas—guess-and-check, working backward, eliminating possibilities, using a ...
LINEAR FUNCTION LESSON TARGETS In this lesson, you are challenge to: 1. Solve word problems involving linear function. 2. Classify the concepts use to attain the correct answer to the worded problem. 2.1 DEFINITION OF LINEAR FUNCTION A Linear function is a function of the form: f(x) = mx + b where m and b are real numbers, and m is not equal to 0. Its graph is a line with the slope m and y ...
The Unitary Method is a fundamental mathematical technique used to solve problems by finding the value of a single unit and then using it to determine the value of multiple units. ... properties, formulas, and word problems associated with the Unitary Method, providing a comprehensive overview to enhance your problem-solving skills. Table of ...
Solving these requires students to apply their knowledge of algebraic manipulation alongside proportion-solving techniques. These problems develop students' ability to work with algebraic expressions and understand how proportions can be applied in algebraic contexts. Word Problems Involving Proportions. Word problems are a significant ...
We categorized the 214 routine word problems by schema. We identified keywords within these problems and determined whether a keyword and its implied operation matched the correct problem solution. For single-step routine word problems, we determined that keywords featured within the problem led to a correct problem solution with less than a 50 ...
The workshop will introduce attendees to the "Plan, Do, Check, Act" Kata problem-solving process, which will provide participants the tools for streamlining their shops and codes. "It's a class that teaches employees how to use a system that helps give them some control of their work space," said Paul Sherman, lead instructor, Code 100TO. ...