• Skip to main content
  • Skip to primary sidebar
  • Skip to footer

Additional menu

Khan Academy Blog

Free Math Worksheets — Over 100k free practice problems on Khan Academy

Looking for free math worksheets.

You’ve found something even better!

That’s because Khan Academy has over 100,000 free practice questions. And they’re even better than traditional math worksheets – more instantaneous, more interactive, and more fun!

Just choose your grade level or topic to get access to 100% free practice questions:

Kindergarten, basic geometry, pre-algebra, algebra basics, high school geometry.

  • Trigonometry

Statistics and probability

High school statistics, ap®︎/college statistics, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra.

  • Addition and subtraction
  • Place value (tens and hundreds)
  • Addition and subtraction within 20
  • Addition and subtraction within 100
  • Addition and subtraction within 1000
  • Measurement and data
  • Counting and place value
  • Measurement and geometry
  • Place value
  • Measurement, data, and geometry
  • Add and subtract within 20
  • Add and subtract within 100
  • Add and subtract within 1,000
  • Money and time
  • Measurement
  • Intro to multiplication
  • 1-digit multiplication
  • Addition, subtraction, and estimation
  • Intro to division
  • Understand fractions
  • Equivalent fractions and comparing fractions
  • More with multiplication and division
  • Arithmetic patterns and problem solving
  • Quadrilaterals
  • Represent and interpret data
  • Multiply by 1-digit numbers
  • Multiply by 2-digit numbers
  • Factors, multiples and patterns
  • Add and subtract fractions
  • Multiply fractions
  • Understand decimals
  • Plane figures
  • Measuring angles
  • Area and perimeter
  • Units of measurement
  • Decimal place value
  • Add decimals
  • Subtract decimals
  • Multi-digit multiplication and division
  • Divide fractions
  • Multiply decimals
  • Divide decimals
  • Powers of ten
  • Coordinate plane
  • Algebraic thinking
  • Converting units of measure
  • Properties of shapes
  • Ratios, rates, & percentages
  • Arithmetic operations
  • Negative numbers
  • Properties of numbers
  • Variables & expressions
  • Equations & inequalities introduction
  • Data and statistics
  • Negative numbers: addition and subtraction
  • Negative numbers: multiplication and division
  • Fractions, decimals, & percentages
  • Rates & proportional relationships
  • Expressions, equations, & inequalities
  • Numbers and operations
  • Solving equations with one unknown
  • Linear equations and functions
  • Systems of equations
  • Geometric transformations
  • Data and modeling
  • Volume and surface area
  • Pythagorean theorem
  • Transformations, congruence, and similarity
  • Arithmetic properties
  • Factors and multiples
  • Reading and interpreting data
  • Negative numbers and coordinate plane
  • Ratios, rates, proportions
  • Equations, expressions, and inequalities
  • Exponents, radicals, and scientific notation
  • Foundations
  • Algebraic expressions
  • Linear equations and inequalities
  • Graphing lines and slope
  • Expressions with exponents
  • Quadratics and polynomials
  • Equations and geometry
  • Algebra foundations
  • Solving equations & inequalities
  • Working with units
  • Linear equations & graphs
  • Forms of linear equations
  • Inequalities (systems & graphs)
  • Absolute value & piecewise functions
  • Exponents & radicals
  • Exponential growth & decay
  • Quadratics: Multiplying & factoring
  • Quadratic functions & equations
  • Irrational numbers
  • Performing transformations
  • Transformation properties and proofs
  • Right triangles & trigonometry
  • Non-right triangles & trigonometry (Advanced)
  • Analytic geometry
  • Conic sections
  • Solid geometry
  • Polynomial arithmetic
  • Complex numbers
  • Polynomial factorization
  • Polynomial division
  • Polynomial graphs
  • Rational exponents and radicals
  • Exponential models
  • Transformations of functions
  • Rational functions
  • Trigonometric functions
  • Non-right triangles & trigonometry
  • Trigonometric equations and identities
  • Analyzing categorical data
  • Displaying and comparing quantitative data
  • Summarizing quantitative data
  • Modeling data distributions
  • Exploring bivariate numerical data
  • Study design
  • Probability
  • Counting, permutations, and combinations
  • Random variables
  • Sampling distributions
  • Confidence intervals
  • Significance tests (hypothesis testing)
  • Two-sample inference for the difference between groups
  • Inference for categorical data (chi-square tests)
  • Advanced regression (inference and transforming)
  • Analysis of variance (ANOVA)
  • Scatterplots
  • Data distributions
  • Two-way tables
  • Binomial probability
  • Normal distributions
  • Displaying and describing quantitative data
  • Inference comparing two groups or populations
  • Chi-square tests for categorical data
  • More on regression
  • Prepare for the 2020 AP®︎ Statistics Exam
  • AP®︎ Statistics Standards mappings
  • Polynomials
  • Composite functions
  • Probability and combinatorics
  • Limits and continuity
  • Derivatives: definition and basic rules
  • Derivatives: chain rule and other advanced topics
  • Applications of derivatives
  • Analyzing functions
  • Parametric equations, polar coordinates, and vector-valued functions
  • Applications of integrals
  • Differentiation: definition and basic derivative rules
  • Differentiation: composite, implicit, and inverse functions
  • Contextual applications of differentiation
  • Applying derivatives to analyze functions
  • Integration and accumulation of change
  • Applications of integration
  • AP Calculus AB solved free response questions from past exams
  • AP®︎ Calculus AB Standards mappings
  • Infinite sequences and series
  • AP Calculus BC solved exams
  • AP®︎ Calculus BC Standards mappings
  • Integrals review
  • Integration techniques
  • Thinking about multivariable functions
  • Derivatives of multivariable functions
  • Applications of multivariable derivatives
  • Integrating multivariable functions
  • Green’s, Stokes’, and the divergence theorems
  • First order differential equations
  • Second order linear equations
  • Laplace transform
  • Vectors and spaces
  • Matrix transformations
  • Alternate coordinate systems (bases)

Frequently Asked Questions about Khan Academy and Math Worksheets

Why is khan academy even better than traditional math worksheets.

Khan Academy’s 100,000+ free practice questions give instant feedback, don’t need to be graded, and don’t require a printer.

Math WorksheetsKhan Academy
Math worksheets take forever to hunt down across the internetKhan Academy is your one-stop-shop for practice from arithmetic to calculus
Math worksheets can vary in quality from site to siteEvery Khan Academy question was written by a math expert with a strong education background
Math worksheets can have ads or cost moneyKhan Academy is a nonprofit whose resources are always free to teachers and learners – no ads, no subscriptions
Printing math worksheets use up a significant amount of paper and are hard to distribute during virtual learningKhan Academy practice requires no paper and can be distributed whether your students are in-person or online
Math worksheets can lead to cheating or a lack of differentiation since every student works on the same questionsKhan Academy has a full question bank to draw from, ensuring that each student works on different questions – and at their perfect skill level
Math worksheets can slow down student learning since they need to wait for feedbackKhan Academy gives instant feedback after every answer – including hints and video support if students are stuck
Math worksheets take up time to collect and take up valuable planning time to gradeKhan Academy questions are graded instantly and automatically for you

What do Khan Academy’s interactive math worksheets look like?

Here’s an example:

What are teachers saying about Khan Academy’s interactive math worksheets?

“My students love Khan Academy because they can immediately learn from their mistakes, unlike traditional worksheets.”

Is Khan Academy free?

Khan Academy’s practice questions are 100% free—with no ads or subscriptions.

What do Khan Academy’s interactive math worksheets cover?

Our 100,000+ practice questions cover every math topic from arithmetic to calculus, as well as ELA, Science, Social Studies, and more.

Is Khan Academy a company?

Khan Academy is a nonprofit with a mission to provide a free, world-class education to anyone, anywhere.

Want to get even more out of Khan Academy?

Then be sure to check out our teacher tools . They’ll help you assign the perfect practice for each student from our full math curriculum and track your students’ progress across the year. Plus, they’re also 100% free — with no subscriptions and no ads.

Get Khanmigo

The best way to learn and teach with AI is here. Ace the school year with our AI-powered guide, Khanmigo. 

For learners     For teachers     For parents

Pythagorean Theorem Exercises

Pythagorean theorem practice problems with answers.

There are eight (8) problems here about the Pythagorean Theorem for you to work on. When you do something a lot, you get better at it. Let’s get started!

Here’s the Pythagorean Theorem formula for your quick reference.

Pythagorean Theorem - a squared plus b squared is equal to c squared

Note: drawings not to scale

Problem 1: Find the value of [latex]x[/latex] in the right triangle.

the legs of a right triangle are 6 and 8

[latex]10[/latex]

Problem 2: Find the value of [latex]x[/latex] in the right triangle.

the leg of a right triangle is 12 and the hypotenuse is 16

[latex]4\sqrt 7 [/latex]

Problem 3: Find the value of [latex]x[/latex] in the right triangle.

right triangle with legs square root 3 and square root 6

[latex]3[/latex]

Problem 4: The legs of a right triangle are [latex]5[/latex] and [latex]12[/latex]. What is the length of the hypotenuse?

[latex]13[/latex]

Problem 5: The leg of a right triangle is [latex]8[/latex] and its hypotenuse is [latex]17[/latex]. What is the measure of its other leg?

[latex]15[/latex]

Problem 6: Suppose the shorter leg of a right triangle is [latex]\sqrt 2[/latex]. The longer leg is twice the shorter leg. Find the hypotenuse.

[latex]\sqrt {10} [/latex]

Problem 7: The hypotenuse of a right triangle is [latex]4\sqrt 2[/latex]. If the longest leg is half the hypotenuse, what is the length of the shortest leg?

[latex]2\sqrt 6[/latex]

Problem 8: Find the value of [latex]x[/latex] of the right isosceles triangle.

the hypotenuse of a right isosceles triangle is 2 times square root 3

[latex]\sqrt 6[/latex]

You might also like these tutorials:

  • Pythagorean Theorem
  • Pythagorean Triples
  • Generating Pythagorean Triples

We’re fighting to restore access to 500,000+ books in court this week. Join us!

Internet Archive Audio

practice and problem solving page 15

  • This Just In
  • Grateful Dead
  • Old Time Radio
  • 78 RPMs and Cylinder Recordings
  • Audio Books & Poetry
  • Computers, Technology and Science
  • Music, Arts & Culture
  • News & Public Affairs
  • Spirituality & Religion
  • Radio News Archive

practice and problem solving page 15

  • Flickr Commons
  • Occupy Wall Street Flickr
  • NASA Images
  • Solar System Collection
  • Ames Research Center

practice and problem solving page 15

  • All Software
  • Old School Emulation
  • MS-DOS Games
  • Historical Software
  • Classic PC Games
  • Software Library
  • Kodi Archive and Support File
  • Vintage Software
  • CD-ROM Software
  • CD-ROM Software Library
  • Software Sites
  • Tucows Software Library
  • Shareware CD-ROMs
  • Software Capsules Compilation
  • CD-ROM Images
  • ZX Spectrum
  • DOOM Level CD

practice and problem solving page 15

  • Smithsonian Libraries
  • FEDLINK (US)
  • Lincoln Collection
  • American Libraries
  • Canadian Libraries
  • Universal Library
  • Project Gutenberg
  • Children's Library
  • Biodiversity Heritage Library
  • Books by Language
  • Additional Collections

practice and problem solving page 15

  • Prelinger Archives
  • Democracy Now!
  • Occupy Wall Street
  • TV NSA Clip Library
  • Animation & Cartoons
  • Arts & Music
  • Computers & Technology
  • Cultural & Academic Films
  • Ephemeral Films
  • Sports Videos
  • Videogame Videos
  • Youth Media

Search the history of over 866 billion web pages on the Internet.

Mobile Apps

  • Wayback Machine (iOS)
  • Wayback Machine (Android)

Browser Extensions

Archive-it subscription.

  • Explore the Collections
  • Build Collections

Save Page Now

Capture a web page as it appears now for use as a trusted citation in the future.

Please enter a valid web address

  • Donate Donate icon An illustration of a heart shape

Algebra 1, grades 9-12 practice and problem solving workbook : holt mcdougal algebra 1

Bookreader item preview, share or embed this item, flag this item for.

  • Graphic Violence
  • Explicit Sexual Content
  • Hate Speech
  • Misinformation/Disinformation
  • Marketing/Phishing/Advertising
  • Misleading/Inaccurate/Missing Metadata

[WorldCat (this item)]

plus-circle Add Review comment Reviews

57 Previews

5 Favorites

DOWNLOAD OPTIONS

No suitable files to display here.

PDF access not available for this item.

IN COLLECTIONS

Uploaded by station18.cebu on November 3, 2021

SIMILAR ITEMS (based on metadata)

Mathwarehouse Logo

Algebra Worksheets

Free worksheets with answer keys.

Enjoy these free printable sheets . Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

  • Distance Formula
  • Equation of Circle
  • Factor Trinomials Worksheet
  • Domain and Range
  • Mixed Problems on Writing Equations of Lines
  • Slope Intercept Form Worksheet
  • Standard Form Worksheet
  • Point Slope Worksheet
  • Write Equation of Line from the Slope and 1 Point
  • Write Equation of Line from Two Points
  • Equation of Line Parallel to Another Line and Through a Point
  • Equation of Line Perpendicular to Another Line and Through a Point
  • Slope of a Line
  • Perpendicular Bisector of Segment
  • Write Equation of Line Mixed Review
  • Word Problems
  • Multiplying Monomials Worksheet
  • Multiplying and Dividing Monomials Sheet
  • Adding and Subtracting Polynomials Worksheet
  • Multiplying Monomials with Polynomials Worksheet
  • Multiplying Binomials Worksheet
  • Multiplying Polynomials
  • Simplifying Polynomials
  • Factoring Trinomials
  • Operations with Polynomials Worksheet
  • Dividing Radicals
  • Simplify Radicals Worksheet
  • Adding Radicals
  • Mulitplying Radicals Worksheet
  • Radicals Review (Mixed review worksheet on radicals and square roots)
  • Solve Systems of Equations Graphically
  • Solve Systems of Equations by Elimination
  • Solve by Substitution
  • Solve Systems of Equations (Mixed review)
  • Activity on Systems of Equations (Create an advertisement for your favorite method to Solve Systems of Equations )
  • Real World Connections (Compare cell phone plans)
  • Scientific Notation
  • Operations with Scientific Notation

Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there!

Popular pages @ mathwarehouse.com.

Surface area of a Cylinder

It's a new school year!   Make it the best yet   with our math, computer science, contest, and science courses!

Train With the World's Top Math Minds

Perfect for grades 5–12. Since 1993, our students have mastered the critical thinking and problem solving skills to excel in prestigious competitions, universities, and careers.

Student actively engaged and learning using the AoPS Online Classroom

Since 2015, all USA International Math Olympiad teammates have been AoPS students

Art of problem solving trains students to approach new challenges by breaking problems down into familiar parts., critical thinking.

Students focus on advanced problem solving and conceptual understanding—not rote memorization.

LIVE COLLABORATION

Discuss new problems with brilliant peers and mentors from the world's largest problem solving community.

Face new challenges every day and build the confidence to approach future problems without fear.

On Track to Prestigious Universities

Our students earn admission to the most prestigious universities in the nation, including:

UC BERKELEY

Many of our students who are mathematically inclined have found Art of Problem Solving (AoPS) an indispensable resource. – MIT Admissions Office

Olympiad Winners Train the Next Generation

AoPS curriculum is designed and taught by former math and science Olympians.

VIEW COURSES

Staff Spotlight

Richard Rusczyk headshot

Richard Rusczyk

Founder and CEO USAMO Winner Perfect AIME

David Patrick headshot

David Patrick

Principal Math Curriculum Editor USAMO Winner Putnam Top 10

Alex Song headshot

Principal Math Olympiad Curriculum   Developer 5-time IMO Gold Medalist

Naoki Sato headshot

Senior Math Curriculum Developer Winner of Canadian Mathematical   Olympiad 3-time Director of Canadian IMO Team

Ashley Ahlin headshot

Ashley Ahlin

Online Math Instructor MATHCOUNTS Problem Writer US Chem Olympiad Team Member

Mark Eichenlaub headshot

Mark Eichenlaub

Principal Physics Curriculum   Developer Coach of the US IPhO Team

AoPS Alumni Success

In the last 10 years, 59 USA International Math Olympiad team members have medaled and have taken over 360 AoPS Online courses.

USA IMO Team 2019

1 Million

problem solvers discuss and solve challenges together on AoPS Online—one of the largest online math communities in the world.

AoPS online school helps thousands of students each year develop tools needed for success in top-tier colleges and in prestigious math competitions. – Mathematical Association of America (MAA)

Ready to join our community? Pick a class that best fits your interests and schedule.

Something appears to not have loaded correctly.

Click to refresh .

practice and problem solving page 15

MathPapa Practice

MathPapa Practice has practice problems to help you learn algebra.

Basic Arithmetic

Subtraction, multiplication, basic arithmetic review, multi-digit arithmetic, addition (2-digit), subtraction (2-digit), multiplication (2-digit by 1-digit), division (2-digit answer), multiplication (2-digit by 2-digit), multi-digit division, negative numbers, addition: negative numbers, subtraction: negative numbers, multiplication: negative numbers, division: negative numbers, order of operations, order of operations 1, basic equations, equations: fill in the blank 1, equations: fill in the blank 2, equations: fill in the blank 3 (order of operations), fractions of measurements, fractions of measurements 2, adding fractions, subtracting fractions, adding fractions: fill in the blank, multiplication: fractions 1, multiplication: fractions 2, division: fractions 1, division: fractions 2, division: fractions 3, addition (decimals), subtraction (decimals), multiplication 2 (example problem: 3.5*8), multiplication 3 (example problem: 0.3*80), division (decimals), division (decimals 2), percentages, percentages 1, percentages 2, chain reaction, balance arithmetic, number balance, basic balance 1, basic balance 2, basic balance 3, basic balance 4, basic balance 5, basic algebra, basic algebra 1, basic algebra 2, basic algebra 3, basic algebra 4, basic algebra 5, algebra: basic fractions 1, algebra: basic fractions 2, algebra: basic fractions 3, algebra: basic fractions 4, algebra: basic fractions 5.

To get additional practice, check out the sample problems in each of the topic above. We provide full solutions with steps for all practice problems. There's no better way to find math help online than with Cymath, so also make sure you download our mobile app for and today! Learn more than what the answer is - with the math helper app, you'll learn the steps behind it too.

Even simple math problems become easier to solve when broken down into steps. From basic additions to calculus, the process of problem solving usually takes a lot of practice before answers could come easily. As problems become more complex, it becomes even more important to understand the step-by-step process by which we solve them. At Cymath, our goal is to take your understanding of math to a new level.

If you find Cymath useful, try today! It offers an ad-free experience and more detailed explanations. In short, goes into more depth than the standard version, giving students more resources to learn the step-by-step process of solving math problems.

practice and problem solving page 15

  • Teen & Young Adult
  • Education & Reference

Sorry, there was a problem.

Kindle app logo image

Download the free Kindle app and start reading Kindle books instantly on your smartphone, tablet, or computer - no Kindle device required .

Read instantly on your browser with Kindle for Web.

Using your mobile phone camera - scan the code below and download the Kindle app.

QR code to download the Kindle App

Image Unavailable

Holt McDougal Algebra 1 Practice and Problem Solving Workbook Algebra 1

  • To view this video download Flash Player

practice and problem solving page 15

Follow the author

HOLT MCDOUGAL

Holt McDougal Algebra 1 Practice and Problem Solving Workbook Algebra 1 Paperback – January 1, 2011

  • Print length 208 pages
  • Language English
  • Publisher Holt McDougal
  • Publication date January 1, 2011
  • Grade level 10 - 12
  • Dimensions 8 x 0.25 x 10.5 inches
  • ISBN-10 0554024047
  • ISBN-13 978-0554024042
  • See all details

Product details

  • Publisher ‏ : ‎ Holt McDougal; 1st edition (January 1, 2011)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 208 pages
  • ISBN-10 ‏ : ‎ 0554024047
  • ISBN-13 ‏ : ‎ 978-0554024042
  • Grade level ‏ : ‎ 10 - 12
  • Item Weight ‏ : ‎ 0.033 ounces
  • Dimensions ‏ : ‎ 8 x 0.25 x 10.5 inches
  • #370 in Teen & Young Adult Algebra

About the author

Holt mcdougal.

Discover more of the author’s books, see similar authors, read author blogs and more

Customer reviews

  • 5 star 4 star 3 star 2 star 1 star 5 star 64% 9% 10% 11% 6% 64%
  • 5 star 4 star 3 star 2 star 1 star 4 star 64% 9% 10% 11% 6% 9%
  • 5 star 4 star 3 star 2 star 1 star 3 star 64% 9% 10% 11% 6% 10%
  • 5 star 4 star 3 star 2 star 1 star 2 star 64% 9% 10% 11% 6% 11%
  • 5 star 4 star 3 star 2 star 1 star 1 star 64% 9% 10% 11% 6% 6%

Customer Reviews, including Product Star Ratings help customers to learn more about the product and decide whether it is the right product for them.

To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. It also analyzed reviews to verify trustworthiness.

  • Sort reviews by Top reviews Most recent Top reviews

Top reviews from the United States

There was a problem filtering reviews right now. please try again later..

practice and problem solving page 15

  • About Amazon
  • Investor Relations
  • Amazon Devices
  • Amazon Science
  • Sell products on Amazon
  • Sell on Amazon Business
  • Sell apps on Amazon
  • Become an Affiliate
  • Advertise Your Products
  • Self-Publish with Us
  • Host an Amazon Hub
  • › See More Make Money with Us
  • Amazon Business Card
  • Shop with Points
  • Reload Your Balance
  • Amazon Currency Converter
  • Amazon and COVID-19
  • Your Account
  • Your Orders
  • Shipping Rates & Policies
  • Returns & Replacements
  • Manage Your Content and Devices
 
 
 
 
  • Conditions of Use
  • Privacy Notice
  • Consumer Health Data Privacy Disclosure
  • Your Ads Privacy Choices

practice and problem solving page 15

Best Practices

Top 5 ways to practice problem-solving, practice problem-solving in your daily life. use our handy guide to improve this crucial workplace skill and boost your professional performance..

practice and problem solving page 15

Problem-solving is something we do every day. From deciding what to make for dinner when we haven’t grocery shopped to figuring out how to increase our sales by 30% by the end of the month, we constantly run into obstacles in our personal and professional lives. 

No one is a master problem-solver right away — it takes patience and time to develop this skill. Practicing problem-solving in low-stakes situations prepares us for when it really counts: a high-pressure setting. Luckily, we know the best ways to practice problem-solving, how to develop your problem-solving skills, and strategies for solving problems quickly and practically.

What is problem-solving?

We can break down the problem-solving process into three main parts: identifying a problem, brainstorming solutions, and taking action. Like any other skill, this process becomes easier with practice. Learning actionable problem-solving techniques can also help us to respond to difficult situations quickly and effectively.

Problem-solving skills are a great help in the workplace — especially for business owners responsible for running all aspects of a business. These skills empower us in both our professional and personal lives and give us the independence to tackle roadblocks on our own — a great asset for solopreneurs.

How to develop problem-solving skills

Practicing problem-solving doesn’t have to be a chore. Here are five exciting ways to flex your creativity and problem-solving muscles:

1. Puzzles and brainteasers

These are fantastic ways to exercise our brains in a controlled and relaxed environment. When we have ample time and no deadlines to brainstorm potential solutions, we’re more likely to try new methods, experiment, and find the problem-solving strategy that works best for us.

Practicing this skill can be as simple as picking up a book of sudoku or sitting down for a crossword every week. Choose activities that you enjoy and make you excited to learn.

Board games and video games provide both entertainment and complex problems to tackle. While immersed in the world or storyline of the game, we’re often required to overcome challenges by discovering a step-by-step journey to the solutions.

Strategy games in particular can strengthen our ability to plan and adapt to sudden changes. Because these games are just for fun, we can break down the problem with patience and take as many attempts as we need.

Starting a new hobby, like a craft or sport, encourages us to embrace a beginner’s mind and find creative solutions while we learn. Whether it’s knitting or basketball, each new journey is going to have hiccups we must persevere through and overcome. 

4. Case studies

If games and puzzles seem a little too abstract to help with professional problem-solving, reading case studies is a powerful alternative. Many case studies published by companies and authors break down the minutiae of problem-solving in real-world settings, including the stress and deadlines of an office environment .

By working through these cases from the comfort of our homes, we learn to consider problems from new perspectives and build the know-how to replicate these strategies — even under stress.

{{mid-cta-product}}

Mastering problem-solving 

Once we feel comfortable practicing our problem-solving, it’s time to put our skills into action to tackle real-world problems. Here are four ways you can work more quickly and efficiently in high-pressure situations:

  • Make sure you understand the problem and can explain it to others. The first step to solving a problem is knowing it inside and out, and an excellent way to test this is by explaining it to peers or team members. 
  • Lose the fear of making mistakes. The best solution is the one that works most quickly and effectively for you. There’s no “wrong” answer, and there are likely many viable strategies you could choose.
  • Use visual techniques. Good problem solvers understand the methods that work best for them. If staring at words on a page isn’t working, try visualizing the problem through diagrams, mind maps, and other visual tools.
  • Reframe the problem as a question you can answer. Thinking of problems as questions allows you to focus on their answers. For example, turn “My clients are upset we don’t communicate enough” into “How can I improve communication with my clients?”

Problem-solving strategies

If you’re looking to really level up your problem-solving, we have three strategies you can implement.

1. IDEAL problem solving

This 5-step process is easy to remember because it’s based on the acronym IDEAL:

  • Identify the problem at hand. Ensure you understand the scope of the problem, the facts you already have, and what you need to find out.
  • Define an outcome. What does a successful solution look like? Outline an objective that’s agreed upon by you and any other parties involved. 
  • Explore strategies. This step is where diagrams, mind maps, and brainstorming can come into play. It doesn’t matter how far-fetched an idea seems — write it down anyway.
  • Anticipate outcomes. Examine your best strategies and make your best guess at what the outcome of each will look like. Pick a solution from your list based on which you think will be most successful. You can never know for certain what will happen, but you must take a step forward to move the process along. If you fail, turn to your next best strategy.
  • Look back and learn. Reflection is crucial to becoming better at problem-solving. After you make a decision and act on it, reflect on the journey and the outcome. Did you achieve what you wanted to? Would another strategy have been more efficient?

2. Practical problem-solving

This 8-step method centers around solving problems in a team setting, though it can be adapted to individual use:

  • Clarify the problem . Ensure all your team members are on the same page by discussing the problem and landing on a definition.
  • Break down the problem. If a problem is complex, break it down into more manageable sections. This way, you can employ strategies for each facet of the problem rather than getting stuck on the big picture. You and your team are less likely to become discouraged if you can celebrate successes along the way.
  • Set a target. Agree on an end goal and deadline for solving the problem. This will keep everyone accountable to the same solution.
  • Analyze the source of the problem. Determine the crux of the problem by tracing back to its root cause. Try using a mind map and beginning at the root of issue and tracing backward.
  • Develop countermeasures to correct the problem. Brainstorm solutions with your peers and weigh what the most effective methods might be. Like the IDEAL strategy, this is the time to anticipate the outcomes of your solutions and choose the best step forward.
  • Act on the countermeasures. Once you’ve chosen your measures, it’s time to implement them. Delegate tasks amongst your team and offer each other support. 
  • Monitor your progress. Track your team’s progress with milestones or metrics so everyone’s on the same page about the problem’s status. 
  • Set a standard and share. How often should team members check in? Set clear expectations and ensure the team conducts regular follow-ups to keep everyone updated on the project's progress — and, of course, when the problem is solved. 

3. Lightning Decision Jam

This 9-step process focuses on speed and aims to efficiently generate a variety of solutions to a group of problems. The steps are quick and snappy:

  • Write down your problems. What issues are you looking to solve?
  • Present each problem to the team (if you’re not working alone). Outline a concise overview of each problem.
  • Vote on what problems are priorities (or rank them yourself). Number your problems based on urgency and importance.
  • Rewrite priority problems as challenges. Translate your top problems into concrete challenges you or your team must overcome. What are the causes and who do they affect?
  • Brainstorm solutions. Have a rapid-fire session and write everything down — there are no wrong answers.
  • Vote for the best solutions (or rank them yourself). What solutions from your brainstorming are the most practical, efficient, and promising?
  • Prioritize the most relevant solutions. Among the popular solutions, which are most relevant? Weigh effort versus impact and consider your individual or team strengths. 
  • Decide what to act on first. Tackle the easiest tasks with the highest impact first, then work your way to the most difficult actions that will be the least impactful.
  • Delegate actions and tasks (if you’re not working alone). You know what you have to do and how to get there, so assign work based on your team’s skillset. Who is the best fit for each task?

The best time to start is now

Unfortunately, there’s no recipe for solving every problem you come across. But practicing your problem-solving will unearth your strengths and weaknesses and teach you the necessary techniques to tackle whatever difficulties come your way head-on. So grab a puzzle, dust off a game, or turn your attention to that issue at work — it’s time to get problem-solving. 

Excellent communication is a crucial component of effective problem-solving. Try Practice’s all-in-one client management system today to streamline client conversations and give you back some time to focus on tackling client and business complications.

Give your clients a simple and professional experience

Simple client management designed for teams, free form templates from practice.

A comprehensive ADHD coaching client questionnaire for professionals to use with their clients. Get insights into your client's symptoms and needs!

Get your clients feedback with this professional Coaching Completion Survey Template. Get the insights you need to improve your services and keep your clients satisfied.

A professional Life Coaching Intake Form Template to help you gather the information you need from your clients. Get started now!

More articles from Practice

practice and problem solving page 15

How Leaders Can Use Coaching to Improve Performance

practice and problem solving page 15

4 Tips to Practice Effective, Professional Communication

practice and problem solving page 15

5 Tips to Start Coaching Your Team for Performance Improvement

practice and problem solving page 15

5 Ways to Practice Positive Thinking for Coaches

practice and problem solving page 15

How to Improve Your Emotional Intelligence in the Workplace

practice and problem solving page 15

How to Practice Mindfulness: 6 Easy Ways

practice and problem solving page 15

Feedback Best Practices: 6 Ways to Be Effective

practice and problem solving page 15

Professional Development

What is a life coach and how to become one.

practice and problem solving page 15

About Practice

4 ways practice helps coaches get organized.

practice and problem solving page 15

Guides & Templates

How to hire the right employees for your small business.

practice and problem solving page 15

Level Up and Become an Effective Coach With Our 6 Top Tips

practice and problem solving page 15

CRMs Versus CMs: Which One is Best for You?

practice and problem solving page 15

Here’s How to Create a Client Communication Plan Template

practice and problem solving page 15

21 Freelance Business Ideas You Can Start Today

practice and problem solving page 15

Key Benefits of Having Tutoring Business Insurance

IMAGES

  1. Five key problem solving skills for professionals

    practice and problem solving page 15

  2. Problem Solving Activities

    practice and problem solving page 15

  3. 3 Tips for Effective Problem Solving

    practice and problem solving page 15

  4. Problem Solving

    practice and problem solving page 15

  5. Lesson 6 Problem Solving Practice

    practice and problem solving page 15

  6. Add or Multiply

    practice and problem solving page 15

COMMENTS

  1. Algebra 1 Practice and Problem Solving Workbook

    Find step-by-step solutions and answers to Algebra 1 Practice and Problem Solving Workbook - 9780133688771, as well as thousands of textbooks so you can move forward with confidence. ... Page 15: Practice. Page 17: Standardized Test Prep. Page 18: Think About a Plan. Page 19: Practice. Page 21: Standardized Test Prep. Page 22: Think About a ...

  2. Ready Mathematics: Practice and Problem Solving Grade 7

    Find step-by-step solutions and answers to Ready Mathematics: Practice and Problem Solving Grade 7 - 9781495704840, as well as thousands of textbooks so you can move forward with confidence. ... Section 15: Writing Linear Expressions. Section 16: Solve Problems with Equations. Section 17: Solve Problems with Inequalities. Page 180: Unit ...

  3. High School Math 2012 Common-core Algebra 1 Practice And Problem

    FREE Answers for High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9. ... Write an algebraic expression for each word phrase. 8 minus the quotient of 15 and y. Problem 22P: Write an algebraic expression for each word phrase. A number q tripled plus z doubled.

  4. Free Math Worksheets

    Khan Academy's 100,000+ free practice questions give instant feedback, don't need to be graded, and don't require a printer. Math Worksheets. Khan Academy. Math worksheets take forever to hunt down across the internet. Khan Academy is your one-stop-shop for practice from arithmetic to calculus. Math worksheets can vary in quality from ...

  5. Pythagorean Theorem Practice Problems With Answers

    There are eight (8) problems here about the Pythagorean Theorem for you to work on. When you do something a lot, you get better at it. Let's get started! Here's the Pythagorean Theorem formula for your quick reference. The longer leg is twice the shorter leg. Find the hypotenuse. If the longest leg is half the hypotenuse, what is the length ...

  6. Algebra 1, grades 9-12 practice and problem solving workbook : holt

    Page_number_confidence 65 Page_number_module_version 1.0.5 Pages 212 Pdf_module_version 0.0.16 Ppi 360 Rcs_key 24143 Republisher_date 20211109140700 Republisher_operator [email protected] Republisher_time 329 Scandate

  7. Algebra Workshets -- free sheets(pdf) with answer keys

    Enjoy these free printable sheets. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key. Algebra. Distance Formula. Equation of Circle. Factoring. Factor Trinomials Worksheet. Functions and Relations.

  8. Practice and Problem Solving Workbook

    Write an algebraic expression that models each word phrase. 1. nine less than 5 multiplied by the number p 5p 2 9. 2. the product of 2 divided by the number h and 8 more than the number k Q h2 R (k 1 8) 3. two decreased by the quotient of the number a and 7 and increased by a. multiplied by 3. 2 2 a7 1 3a.

  9. Algebra 2 Practice and Problem Solving Workbook

    Find step-by-step solutions and answers to Algebra 2 Practice and Problem Solving Workbook - 9780133688894, as well as thousands of textbooks so you can move forward with confidence. ... Page 15: Practice. Page 17: Standardized Test Prep. Page 18: Think About a Plan. Page 19: Practice. Page 21: Standardized Test Prep. Page 22: Think About a ...

  10. PDF Homework Prractice and Problem-Solving Practice Workbook

    Visit us online at ca.gr5math.comISBN: 978--02-111969-1 MHID: -02-111969-4. Homework Practice and Problem-Solving Practice Workbook. Contents Include: • 100 Homework Practice worksheets- one for each lesson • 100 Problem-Solving Practice worksheets- one for each lesson to apply lesson concepts in a real-world situation.

  11. enVision Algebra 1

    Our resource for enVision Algebra 1 includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems, you can take the guesswork out of studying and move forward with confidence. Find step-by-step solutions and answers to enVision ...

  12. Art of Problem Solving

    Train With the World's Top Math Minds. Perfect for grades 5-12. Since 1993, our students have mastered the critical thinking and problem solving skills to excel in prestigious competitions, universities, and careers.

  13. Math Practice Problems

    MathPapa Practice has practice problems to help you learn algebra. Basic Arithmetic Addition Subtraction Multiplication Division ... (Example Problem: 3.5*8) Multiplication 3 (Example Problem: 0.3*80) Division (Decimals) Division (Decimals 2) Percentages Percentages 1 ...

  14. PDF LESSON 15-5 Practice and Problem Solving: A/B

    Practice and Problem Solving: A/B A parent function has equation 1 ()0.25 . Y = x For 1-4, find the equation for each Y 2. 1. Y 2 is a vertical stretch of Y 1. The values of Y 2 are 6 times those of Y ... 15-5 f1 7 9 O gcxi a.CI is O t.se f101 1 a 50 f 5 N 0.4 5. Created Date: 2/12/2019 7:43:30 PM ...

  15. Practice Math Problems with Answers

    From basic additions to calculus, the process of problem solving usually takes a lot of practice before answers could come easily. As problems become more complex, it becomes even more important to understand the step-by-step process by which we solve them. At Cymath, our goal is to take your understanding of math to a new level.

  16. Algebra 1, Geometry, Algebra 2 Common Core-Savvas Learning Company

    Practice and Problem Solving Workbook Teacher's Guide price: $32.50. isbn10: 0133188442 isbn13: 9780133188448 notes: † Quantity. Common Core Overview Implementation Guide price: $15.00. isbn10: 0133185583 isbn13: 9780133185584. Quantity. All-in-One Teaching Resources. price: $289.00.

  17. enVision Algebra 2

    Now, with expert-verified solutions from enVision Algebra 2 1st Edition, you'll learn how to solve your toughest homework problems. Our resource for enVision Algebra 2 includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems ...

  18. PDF The Pythagorean Theorem 12-1 Practice and Problem Solving: A/B

    Part is an alternate interior angle to a 45° angle, and part is an alternate interior angle to a 35° angle. I can use those measures to add because the angles are congruent. 4. m∠x = 70° − 30° = 40° The angle marked 70° and the angles marked x and 30° are alternate interior angles and therefore congruent.

  19. High School Math 2012 Common-Core Algebra 2 Practice and Problem

    Get it Aug 12 - 15. In Stock. Ships from and sold by All American Textbooks. + HIGH SCHOOL MATH 2015 COMMON CORE ALGEBRA 2 STUDENT EDITION GRADES 10/11 [$46.22 $ 46. 22. Get it Aug 8 - 12. ... HIGH SCHOOL MATH COMMON-CORE GEOMETRY PRACTICE/PROBLEM SOLVING WORKBOOK GRADE 9/10. Savvas Learning Co.

  20. Amazon.com: Holt McDougal Algebra 1 Practice and Problem Solving

    4.4 out of 5 stars 15. Hardcover. 23 offers from $4.47. Holt McDougal Algebra 1: Common Core Practice and Problem Solving Workbook Teacher's Guide ... The Practice and Problem Solving workbook did not provide any answers. Therefore, it unfortunately did not meet my expectations or my needs. Read more. 4 people found this helpful. Helpful. Report.

  21. Geometry Common Core Practice and Problem Solving Workbook

    Find step-by-step solutions and answers to Geometry Common Core Practice and Problem Solving Workbook - 9780133185966, as well as thousands of textbooks so you can move forward with confidence. ... Page 15: Practice. Page 16: Practice. Page 17: Standardized Test Prep. Page 18: Think About a Plan. Page 19: Practice. Page 20: Practice. Page 21 ...

  22. Top 5 Ways to Practice Problem-Solving

    How to develop problem-solving skills. Practicing problem-solving doesn't have to be a chore. Here are five exciting ways to flex your creativity and problem-solving muscles: 1. Puzzles and brainteasers. These are fantastic ways to exercise our brains in a controlled and relaxed environment.

  23. enVision Geometry

    Practice and Problem Solving. Exercise a. Exercise b. At Quizlet, we're giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from enVision Geometry 1st Edition, you'll learn how to solve your toughest homework problems.