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10 Best Strategies for Solving Math Word Problems

1. Understand the Problem by Paraphrasing

2. identify key information and variables, 3. translate words into mathematical symbols, 4. break down the problem into manageable parts, 5. draw diagrams or visual representations, 6. use estimation to predict answers, 7. apply logical reasoning for unknown variables, 8. leverage similar problems as templates, 9. check answers in the context of the problem, 10. reflect and learn from mistakes.

Have you ever observed the look of confusion on a student’s face when they encounter a math word problem ? It’s a common sight in classrooms worldwide, underscoring the need for effective strategies for solving math word problems . The main hurdle in solving math word problems is not just the math itself but understanding how to translate the words into mathematical equations that can be solved.

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Generic advice like “read the problem carefully” or “practice more” often falls short in addressing students’ specific difficulties with word problems. Students need targeted math word problem strategies that address the root of their struggles head-on. 

A Guide on Steps to Solving Word Problems: 10 Strategies 

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. This means they rewrite the problem using simpler language or break it down into more digestible parts. Paraphrasing helps students grasp the concept and focus on the problem’s core elements without getting lost in the complex wording.

Original Problem: “If a farmer has 15 apples and gives away 8, how many does he have left?”

Paraphrased: “A farmer had some apples. He gave some away. Now, how many apples does he have?”

This paraphrasing helps students identify the main action (giving away apples) and what they need to find out (how many apples are left).

Play these subtraction word problem games in the classroom for free:

Students often get overwhelmed by the details in word problems. Teach them to identify key information and variables essential for solving the problem. This includes numbers , operations ( addition , subtraction , multiplication , division ), and what the question is asking them to find. Highlighting or underlining can be very effective here. This visual differentiation can help students focus on what’s important, ignoring irrelevant details.

• Encourage students to underline numbers and circle keywords that indicate operations (like ‘total’ for addition and ‘left’ for subtraction).
• Teach them to write down what they’re solving for, such as “Find: Total apples left.”

Problem: “A classroom has 24 students. If 6 more students joined the class, how many students are there in total?”

Key Information:

• Original number of students (24)
• Students joined (6)
• Looking for the total number of students

Here are some fun addition word problems that your students can play for free:

The transition from the language of word problems to the language of mathematics is a critical skill. Teach your students to convert words into mathematical symbols and equations. This step is about recognizing keywords and phrases corresponding to mathematical operations and expressions .

Common Translations:

• “Total,” “sum,” “combined” → Addition (+)
• “Difference,” “less than,” “remain” → Subtraction (−)
• “Times,” “product of” → Multiplication (×)
• “Divided by,” “quotient of” → Division (÷)
• “Equals” → Equals sign (=)

Problem: “If one book costs $5, how much would 4 books cost?”

Translation: The word “costs” indicates a multiplication operation because we find the total cost of multiple items. Therefore, the equation is 4 × 5 = $20

Complex math word problems can often overwhelm students. Incorporating math strategies for problem solving, such as teaching them to break down the problem into smaller, more manageable parts, is a powerful approach to overcome this challenge. This means looking at the problem step by step rather than simultaneously trying to solve it. Breaking it down helps students focus on one aspect of the problem at a time, making finding the solution more straightforward.

Problem: “John has twice as many apples as Sarah. If Sarah has 5 apples, how many apples do they have together?”

Steps to Break Down the Problem:

Find out how many apples John has: Since John has twice as many apples as Sarah, and Sarah has 5, John has 5 × 2 = 10

Calculate the total number of apples: Add Sarah’s apples to John’s to find the total,  5 + 10 = 15

By splitting the problem into two parts, students can solve it without getting confused by all the details at once.

Explore these fun multiplication word problem games:

Diagrams and visual representations can be incredibly helpful for students, especially when dealing with spatial or quantity relationships in word problems. Encourage students to draw simple sketches or diagrams to represent the problem visually. This can include drawing bars for comparison, shapes for geometry problems, or even a simple distribution to better understand division or multiplication problems .

Problem: “A garden is 3 times as long as it is wide. If the width is 4 meters, how long is the garden?”

Visual Representation: Draw a rectangle and label the width as 4 meters. Then, sketch the length to represent it as three times the width visually, helping students see that the length is 4 × 3 = 12

Estimation is a valuable skill in solving math word problems, as it allows students to predict the answer’s ballpark figure before solving it precisely. Teaching students to use estimation can help them check their answers for reasonableness and avoid common mistakes.

Problem: “If a book costs $4.95 and you buy 3 books, approximately how much will you spend?”

Estimation Strategy: Round $4.95 to the nearest dollar ($5) and multiply by the number of books (3), so 5 × 3 = 15. Hence, the estimated total cost is about $15.

Estimation helps students understand whether their final answer is plausible, providing a quick way to check their work against a rough calculation.

Check out these fun estimation and prediction word problem worksheets that can be of great help:

When students encounter problems with unknown variables, it’s crucial to introduce them to logical reasoning. This strategy involves using the information in the problem to deduce the value of unknown variables logically. One of the most effective strategies for solving math word problems is working backward from the desired outcome. This means starting with the result and thinking about the steps leading to that result, which can be particularly useful in algebraic problems.

Problem: “A number added to three times itself equals 32. What is the number?”

Working Backward:

Let the unknown number be x.

The equation based on the problem is  x + 3x = 32

Solve for x by simplifying the equation to 4x=32, then dividing by 4 to find x=8.

By working backward, students can more easily connect the dots between the unknown variable and the information provided.

Practicing problems of similar structure can help students recognize patterns and apply known strategies to new situations. Encourage them to leverage similar problems as templates, analyzing how a solved problem’s strategy can apply to a new one. Creating a personal “problem bank”—a collection of solved problems—can be a valuable reference tool, helping students see the commonalities between different problems and reinforcing the strategies that work.

Suppose students have solved a problem about dividing a set of items among a group of people. In that case, they can use that strategy when encountering a similar problem, even if it’s about dividing money or sharing work equally.

It’s essential for students to learn the habit of checking their answers within the context of the problem to ensure their solutions make sense. This step involves going back to the original problem statement after solving it to verify that the answer fits logically with the given information. Providing a checklist for this process can help students systematically review their answers.

Checklist for Reviewing Answers:

• Re-read the problem: Ensure the question was understood correctly.
• Compare with the original problem: Does the answer make sense given the scenario?
• Use estimation: Does the precise answer align with an earlier estimation?
• Substitute back: If applicable, plug the answer into the problem to see if it works.

Problem: “If you divide 24 apples among 4 children, how many apples does each child get?”

After solving, students should check that they understood the problem (dividing apples equally).

Their answer (6 apples per child) fits logically with the number of apples and children.

Their estimation aligns with the actual calculation.

Substituting back 4×6=24 confirms the answer is correct.

Teaching students to apply logical reasoning, leverage solved problems as templates, and check their answers in context equips them with a robust toolkit for tackling math word problems efficiently and effectively.

One of the most effective ways for students to improve their problem-solving skills is by reflecting on their errors, especially with math word problems. Using word problem worksheets is one of the most effective strategies for solving word problems, and practicing word problems as it fosters a more thoughtful and reflective approach to problem-solving

These worksheets can provide a variety of problems that challenge students in different ways, allowing them to encounter and work through common pitfalls in a controlled setting. After completing a worksheet, students can review their answers, identify any mistakes, and then reflect on them in their mistake journal. This practice reinforces mathematical concepts and improves their math problem solving strategies over time.

3 Additional Tips for Enhancing Word Problem-Solving Skills

Before we dive into the importance of reflecting on mistakes, here are a few impactful tips to enhance students’ word problem-solving skills further:

1. Utilize Online Word Problem Games

Incorporate online games that focus on math word problems into your teaching. These interactive platforms make learning fun and engaging, allowing students to practice in a dynamic environment. Games can offer instant feedback and adaptive challenges, catering to individual learning speeds and styles.

Here are some word problem games that you can use for free:

2. Practice Regularly with Diverse Problems

Consistent practice with a wide range of word problems helps students become familiar with different questions and mathematical concepts. This exposure is crucial for building confidence and proficiency.

Start Practicing Word Problems with these Printable Word Problem Worksheets:

3. Encourage Group Work

Solving word problems in groups allows students to share strategies and learn from each other. A collaborative approach is one of the best strategies for solving math word problems that can unveil multiple methods for tackling the same problem, enriching students’ problem-solving toolkit.

Conclusion 

Mastering math word problems is a journey of small steps. Encourage your students to practice regularly, stay curious, and learn from their mistakes. These strategies for solving math word problems are stepping stones to turning challenges into achievements. Keep it simple, and watch your students grow their confidence and skills, one problem at a time.

Frequently Asked Questions (FAQs)

How can i help my students stay motivated when solving math word problems.

Encourage small victories and use engaging tools like online games to make practice fun and rewarding.

What's the best way to teach beginners word problems?

Begin with simple problems that integrate everyday scenarios to make the connection between math and real-life clear and relatable.

How often should students practice math word problems?

Regular, daily practice with various problems helps build confidence and problem-solving skills over time.

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Covering Innovation & Inequality in Education

Why schools are teaching math word problems all wrong

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CENTRAL FALLS, R.I. — When Natalia Molina began teaching her second grade students word problems earlier this school year, every lesson felt difficult. Most students were stymied by problems such as: “Sally went shopping. She spent $86 on groceries and $39 on clothing. How much more did Sally spend on groceries than on clothing?”

Both Molina, a first-year teacher, and her students had been trained to tackle word problems by zeroing in on key words like “and,” “more” and “total”  — a simplistic approach that Molina said too often led her students astray. After recognizing the word “and,” for instance, they might mistakenly assume that they needed to add two nearby numbers together to arrive at an answer.

Some weaker readers, lost in a sea of text, couldn’t recognize any words at all.

“I saw how overwhelmed they would get,” said Molina, who teaches at Segue Institute for Learning, a predominantly Hispanic charter school in this small city just north of Providence.

So, with the help of a trainer doing work in Rhode Island through a state grant, Molina and some of her colleagues revamped their approach to teaching word problems this winter — an effort that they said is already paying off in terms of increased student confidence and ability. “It has been a game changer for them,” Molina said.

Perhaps no single educational task encompasses as many different skills as the word problem. Between reading, executive functioning, problem solving, computation and vocabulary, there are a lot of ways for students to go wrong. And for that reason, students perform significantly worse overall on word problems compared to questions more narrowly focused on computation or shapes (for example: “Solve 7 + _ = 22” or “What is 64 x 3?”).

If a student excels at word problems, it’s a good sign that they’re generally excelling at school. “Word-problem solving in lower grades is one of the better indicators of overall school success in K-12,” said Lynn Fuchs, a research professor at Vanderbilt University. In a large national survey , for instance, algebra teachers rated word-problem solving as the most important among 15 skills required to excel in the subject.

Teacher takeaways

• Don’t instruct students to focus mainly on “key words” in word problems such as “and” or “more” 
• Mix question types in any lesson so that students don’t assume they just apply the same operation (addition, subtraction) again and again
• Teach students the underlying structure — or schema — of the word problem

Yet most experts and many educators agree that too many schools are doing it wrong, particularly in the elementary grades. And in a small but growing number of classrooms, teachers like Molina are working to change that. “With word problems, there are more struggling learners than non-struggling learners” because they are taught so poorly, said Nicole Bucka, who works with teachers throughout Rhode Island to provide strategies for struggling learners.

Too many teachers, particularly in the early grades, rely on key words to introduce math problems. Posters displaying the terms — sum, minus, fewer, etc. — tied to operations including addition and subtraction are a staple in elementary school classrooms across the country.

Key words can be a convenient crutch for both students and teachers, but they become virtually meaningless as the problems become harder, according to researchers. Key words can help first graders figure out whether to add or subtract more than half of the time, but the strategy rarely works for the multi-step problems students encounter starting in second and third grade. “With multi-step problems, key words don’t work 90 percent of the time,” said Sarah Powell, a professor at the University of Texas in Austin who studies word problems and whose research has highlighted the inefficacy of key words . “But the average kindergarten teacher is not thinking about that; they are teaching 5-year-olds, not 9-year-olds.”

Many teachers in the youngest grades hand out worksheets featuring the same type of word problem repeated over and over again. That’s what Molina’s colleague, Cassandra Santiago, did sometimes last year when leading a classroom on her own for the first time. “It was a mistake,” the first grade teacher said. “It’s really important to mix them up. It makes them think more critically about the parts they have to solve.”

Another flaw with word problem instruction is that the overwhelming majority of questions are divorced from the actual problem-solving a child might have to do outside the classroom in their daily life — or ever, really. “I’ve seen questions about two trains going on the same track,” said William Schmidt, a University Distinguished Professor at Michigan State University. “First, why would they be going on the same track and, second, who cares?”

Schmidt worked on an analysis of about 8,000 word problems used in 23 textbooks in 19 countries. He found that less than one percent had “real world applications” and involved “higher order math applications .”

“That is one of the reasons why children have problems with mathematics,” he said. “They don’t see the connection to the real world … We’re at this point in math right now where we are just teaching students how to manipulate numbers.”

He said a question, aimed at middle schoolers, that does have real world connections and involves more than manipulating numbers, might be: “Shopping at the new store in town includes a 43% discount on all items which are priced the same at $2. The state you live in has a 7% sales tax. You want to buy many things but only have a total of $52 to spend. Describe in words how many things you could buy.”

Schmidt added that relevancy of word problems is one area where few, if any, countries excel. “No one was a shining star leading the way,” he said. 

In her brightly decorated classroom one Tuesday afternoon, Santiago, the first grade teacher, gave each student a set of animal-shaped objects and a sheet of blue paper (the water) and green (the grass). “We’re going to work on a number story,” she told them. “I want you to use your animals to tell me the story.”

“ Once upon a time,” the story began. In this tale, three animals played in the water, and two animals played in the grass. Santiago allowed some time for the ducks, pigs and bears to frolic in the wilds of each student’s desk before she asked the children to write a number sentence that would tell them how many animals they have altogether.

Some of the students relied more on pictorial representations (three dots on one side of a line and two dots on the other) and others on the number sentence (3+2 = 5) but all of them eventually got to five. And Santiago made sure that her next question mixed up the order of operations (so students didn’t incorrectly assume that all they ever have to do is add): “Some more animals came and now there are seven. So how many more came?”

One approach to early elementary word problems that is taking off in some schools, including Segue Institute, has its origins in a special education intervention for struggling math students. Teachers avoid emphasizing key words and ask students instead to identify first the conceptual type of word problem (or schema, as many practitioners and researchers refer to it) they are dealing with: “Total problems,” for instance, involve combining two parts to find a new amount; “change problems” involve increasing or decreasing the amount of something. Total problems do not necessarily involve adding, however.

“The schemas that students learn in kindergarten will continue with them throughout their whole career,” said Powell, the word-problem researcher, who regularly works with districts across the country to help implement the approach. 

In Olathe, Kansas — a district inspired by Powell’s work — teachers had struggled for years with word problems, said Kelly Ulmer, a math support specialist whose goal is to assist in closing academic gaps that resulted from lost instruction time during the pandemic. “We’ve all tried these traditional approaches that weren’t working,” she said. “Sometimes you get pushback on new initiatives from veteran teachers and one of the things that showed us how badly this was needed is that the veteran teachers were the most excited and engaged — they have tried so many things” that haven’t worked.

In Rhode Island, many elementary schools initially used the strategy with students who required extra help, including those in special education, but expanded this use to make it part of the core instruction for all, said Bucka. In some respects, it’s similar to the recent, well publicized evolution of reading instruction in which some special education interventions for struggling readers  — most notably, a greater reliance on phonics in the early grades — have gone mainstream.

There is an extensive research bas e showing that focusing on the different conceptual types of word problems is an effective way of teaching math, although much of the research focuses specifically on students experiencing difficulties in the subject. 

Molina has found asking students to identify word problems by type to be a useful tool with nearly all of her second graders; next school year she hopes to introduce the strategy much earlier.

One recent afternoon, a lesson on word problems started with everyone standing up and chanting in unison: “Part plus part equals total” (they brought two hands together). “Total minus part equals part ” (they took one hand away) .

It’s a way to help students remember different conceptual frameworks for word problems. And it’s especially effective for the students who learn well through listening and repeating. For visual learners, the different types of word problems were mapped out on individual dry erase mats.

The real work began when Molina passed out questions, and the students— organized into the Penguin, Flower Bloom, Red Panda and Marshmallow teams — had to figure out which framework they were dealing with on their own and then work toward an answer. A few months ago, many of them would have automatically shut down when they saw the text on the page, Molina said.

For the Red Pandas, the question under scrutiny was: “The clothing store had 47 shirts. They sold 21, how many do they have now?”

“It’s a total problem,” one student said.

“No, it’s not total,” responded another.

“I think it’s about change,” said a third.

None of the students seemed worried about their lack of consensus, however. And neither was Molina. A correct answer is always nice but those come more often now that most of the students have made a crucial leap. “I notice them thinking more and more,” she said, “about what the question is actually asking.”

This story about word problems was produced by The Hechinger Report , a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the Hechinger newsletter .

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In the last example of the word problem involving the shirts would the teacher have been fine with either explanation. One thought would be that there is a total number of shirts (41) with one part being sold (21) leaving the other part on hand (26). Another way of thinking about the problem would be a change happening with the beginning number of (47) shirts being reduced or changed by the number being taken away (21), leaving the rest (26).

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If You Like Wordle, You Should Try These Puzzle and Word Games Next

These 10 word games are sure to give you a challenge.

• Apple software beta tester, "Helps make our computers and phones work!" - Zach's grandparents

Wordle  was 2022's biggest word game, and it continues to be a smash hit. It was created by Josh Wardle for his partner, and  it was later bought by the New York Times . CNET's  Gael Cooper  has loads of tips and tricks to tackle each Wordle puzzle, but if you're finished with today's game -- or just really enjoy puzzle games -- these options are well-worth your time.

Wordle asks players to figure out a five-letter word in six or fewer guesses (we have a two-step strategy to help you solve the puzzle every time ). After each guess, the game shows gray blocks for the wrong letters, yellow blocks for the right letters in the wrong spot and green blocks for the right letters in the correct spot. It's addictive, but after you solve the daily puzzle or use up all your guesses, you have to wait until the next day to play again.

You've likely already learned some tips, tricks and lessons from the popular word game , so why not apply your newly honed problem-solving skills to other puzzles, too? After all, Wordle isn't the only game in town. Here are 10 other puzzle games like Wordle you'll likely enjoy.

Connections

I know it's old, but i'm not even going to try to figure this out. screenshot by gael fashingbauer cooper/cnet.

Another NYT-owned puzzle,  Connections is a tricky word game. "Players must select four groups of four words without making more than four mistakes," the  NYT wrote on X, formerly Twitter . There are also four color-coded difficulty levels for each game; yellow is the easiest, then green, the blue and finally purple. The game is also similar to the BBC quiz show Only Connect, and the show's host took to  X  to point out the connection -- see what I did there?

You can play  Connections on any web browser, but you need a NYT subscription ( which starts at $1 a week ) to play.

Quartiles is a new word game Apple News Plus subscribers can access on their iPhone or iPad that's running iOS 17.5 or later. In this word game, you're given 20 tiles with letters on them, and you're trying to put them together to form different words. The longest words are four-tiles long, and these are called Quartiles. The game can be tough, but finding just one of the Quartiles is as satisfying as remembering something that was just on the tip of your tongue.

You can play Quartiles on an iPhone or iPad, but you need an Apple News subscription ( which starts at $13 a month ) to play.

Multiple word Wordle spinoffs: Dordle, Quordle, Octordle and Sedecordle

Quordle has you solve four word puzzles at once which sounds daunting.

Are you up for a challenge? If you love Wordle and want puzzle games that take more brain power, you'll want to check out either  Dordle ,  Quordle , Octordle  or  Sedecordle . Each of these word games resembles Wordle, but add more rows, columns and words to solve. Each requires you to simultaneously solve a different number of words at once: Dordle has you solving two words, Quordle four at once, Octordle eight at once, and Sedecordle a whopping 16. Good luck. 

You can play  Dordle ,  Quordle ,  Octordle  or  Sedecordle  on any web browser.

Word Master

This Wordle remake  functions almost exactly like the original but with a small tweak. Word Master uses gray, yellow and green blocks in the same way as Wordle, but Word Master lets you play unlimited games at a time so you don't have to wait 24 hours for the next puzzle. 

You can play Word Master on any web browser. 

"Lewdle is a game about rude words," this game's content advisory reads. "If you're likely to be offended by the use of profanity, vulgarity or obscenity, it likely isn't for you." Translation: It's Wordle, but with bad words. The words range from mild -- like poopy -- to words that would make a sailor blush. Thankfully, despite this game's content warning,  slurs are not included . Like Wordle, gray, yellow and green blocks are used in the same way and there's only one puzzle per day. So go forth and let the bad words flow!

You can play Lewdle on any web browser. You can also download this title from Apple's App Store or the Google Play store.

Not off to a great start with this Antiwordle puzzle.

Tired of seeing those grey, yellow and green blocks plastered all over your social media feed? Give Antiwordle a try. While Wordle wants you to guess a word in as few tries as possible, Antiwordle wants you to avoid the word by guessing as many times as possible. When you guess, letters will turn gray, yellow or red. Gray means the letter isn't in the word and can't be used again, yellow means the letter is in the word and must be included in each subsequent guess and red means the letter is in the exact position within the word and is locked in place. If you can use every letter on the keyboard without getting the word correct, you win. Honestly, I've found this version of Wordle to be much harder than the original. 

You can play  Antiwordle  on any web browser.

Absurdle bills itself as the "adversarial version" of Wordle. While Wordle nudges you in the right direction with each guess, Absurdle is trying to avoid giving you the correct answer. According to the game's website, "With each guess, Absurdle reveals as little information as possible, changing the secret word if need be." Absurdle doesn't pick a word at the beginning of the game for the player to guess. Instead, it uses the player's guesses to narrow its list of words down in an effort to make the game go as long as possible. The final word might not even include a yellow letter from one of your earlier guesses either. You can guess as many times as you want, which is helpful, and the best score you can get is four. Have fun!

You can play Absurdle on any web browser.

For more word game fun, check out CNET's Wordle tips , the best Wordle jokes and how to play past Wordle puzzles . If you're still confused about the word game, here's everything to know about the word game .

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The Supreme Court says cities can punish people for sleeping in public places

Jennifer Ludden

U.S. Supreme Court says cities can punish people for sleeping in public places

A homeless person walks near an elementary school in Grants Pass, Ore., on March 23. The rural city became the unlikely face of the nation's homelessness crisis when it asked the U.S. Supreme Court to uphold its anti-camping laws. Jenny Kane/AP hide caption

In its biggest decision on homelessness in decades, the U.S. Supreme Court today ruled that cities can ban people from sleeping and camping in public places. The justices, in a 6-3 decision along ideological lines, overturned lower court rulings that deemed it cruel and unusual under the Eighth Amendment to punish people for sleeping outside if they had nowhere else to go.

Writing for the majority, Justice Gorsuch said, “Homelessness is complex. Its causes are many.” But he said federal judges do not have any “special competence” to decide how cities should deal with this.

“The Constitution’s Eighth Amendment serves many important functions, but it does not authorize federal judges to wrest those rights and responsibilities from the American people and in their place dictate this Nation’s homelessness policy,” he wrote.

In a dissent, Justice Sotomayor said the decision focused only on the needs of cities but not the most vulnerable. She said sleep is a biological necessity, but this decision leaves a homeless person with “an impossible choice — either stay awake or be arrested.”

The court's decision is a win not only for the small Oregon city of Grants Pass, which brought the case, but also for dozens of Western localities that had urged the high court to grant them more enforcement powers as they grapple with record high rates of homelessness. They said the lower court rulings had tied their hands in trying to keep public spaces open and safe for everyone.

Supreme Court appears to side with an Oregon city's crackdown on homelessness

But advocates for the unhoused say the decision won’t solve the bigger problem, and could make life much harder for the quarter of a million people living on streets, in parks and in their cars. “Where do people experiencing homelessness go if every community decides to punish them for their homelessness?” says Diane Yentel, president of the National Low Income Housing Coalition.

Today’s ruling only changes current law in the 9th Circuit Court of Appeals, which includes California and eight other Western states where the bulk of America’s unhoused population lives. But it will also determine whether similar policies elsewhere are permissible; and it will almost certainly influence homelessness policy in cities around the country.

Cities complained they were hamstrung in managing a public safety crisis

Grants Pass and other cities argued that lower court rulings fueled the spread of homeless encampments, endangering public health and safety. Those decisions did allow cities to restrict when and where people could sleep and even to shut down encampments – but they said cities first had to offer people adequate shelter.

That’s a challenge in many places that don’t have nearly enough shelter beds. In briefs filed by local officials, cities and town also expressed frustration that many unhoused people reject shelter when it is available; they may not want to go if a facility bans pets, for example, or prohibits drugs and alcohol.

Critics also said lower court rulings were ambiguous, making them unworkable in practice. Localities have faced dozens of lawsuits over the details of what’s allowed. And they argued that homelessness is a complex problem that requires balancing competing interests, something local officials are better equipped to do than the courts.

"We are trying to show there's respect for the public areas that we all need to have," Seattle City Attorney Ann Davison told NPR earlier this year. She wrote a legal brief on behalf of more than a dozen other cities. "We care for people, and we're engaging and being involved in the long-term solution for them."

The decision will not solve the larger problem of rising homelessness

Attorneys for homeless people in Grants Pass argued that the city’s regulations were so sweeping, they effectively made it illegal for someone without a home to exist. To discourage sleeping in public spaces, the city banned the use of stoves and sleeping bags, pillows or other bedding. But Grants Pass has no public shelter, only a Christian mission that imposes various restrictions and requires people to attend religious service.

"It's sort of the bare minimum in what a just society should expect, is that you're not going to punish someone for something they have no ability to control," said Ed Johnson of the Oregon Law Center, which represents those who sued the city.

He also said saddling people with fines and a criminal record makes it even harder for them to eventually get into housing.

Johnson and other advocates say today’s decision won’t change the core problem behind rising homelessness: a severe housing shortage, and rents that have become unaffordable for a record half of all tenants. The only real solution, they say, is to create lots more housing people can afford – and that will take years.

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Practice Word Problems 4+

Practice word problems, yonggao yang, designed for ipad.

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Want to practice math word problems? This app accesses the question library with about 10,000 questions, answers, and step-by-step solutions. Word problem is one of the most challenging topics in math. SAT math sections always have such questions with a high difficulty level. Solving math word problems requires executing a series of arithmetic operations to obtain a final answer, which is a formidable challenge to students.
 This app is a tool for users to practice word problems (in different difficulty levels) from a library of 30447 questions. Each question comes with a step-by-step solution, and the user can review all the questions he/she practiced within the report card tab.

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Move the database to Firebase platform. Make the app to run on the latest iOS platform.

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The developer, Yonggao Yang , indicated that the app’s privacy practices may include handling of data as described below. For more information, see the developer’s privacy policy .

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Up to six family members can use this app with family sharing enabled., more by this developer.

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E.U. Charges Microsoft With Antitrust Violations Over Teams Bundling

The tech giant has been accused of stifling competition by packaging its video conferencing app with other tools like Word and Excel.

By Adam Satariano

Reporting from London

European Union regulators on Tuesday charged Microsoft with breaking antitrust rules by bundling its Teams video conferencing and collaboration software with a suite of other productivity tools, giving it an unfair advantage over rivals.

Regulators said Microsoft’s packaging of Teams with other well-established software tools in Office 365 and Microsoft 365, which includes programs like Word, Excel, PowerPoint and Outlook, amounted to an illegal abuse of market dominance that rival companies like Zoom and Slack could not match. Regulators said businesses essentially had little choice but to take Teams if they wanted other software made by Microsoft.

The charges are just the latest in a barrage of announcements by the European Union in recent months in its effort to crack down on the world’s largest tech platforms. On Monday, regulators accused Apple of violating competition rules because of its App Store policies. Amazon, Google, Meta, TikTok and X are also facing investigations related to their business practices and services.

The Microsoft case has its roots in the Covid-19 pandemic, when videoconferencing and collaboration tools like Zoom, Slack and Teams became essential for remote workforces. In 2020, Slack, now owned by Salesforce, complained to regulators that Microsoft’s bundling of Teams with other productivity software was anticompetitive, setting off the initial E.U. investigation.

E.U. regulators said Microsoft had an unfair “distribution advantage” by not giving customers a choice of whether to buy Teams when purchasing other software. Rivals makers of videoconferencing tools also face challenges making their services work with other Microsoft software, regulators said.

“The conduct may have prevented Teams’ rivals from competing, and in turn innovating, to the detriment of customers,” the European Commission, the European Union’s executive branch conducting the investigation, said in a statement.

The charges brought on Tuesday are one step in a long process. Microsoft can now respond to the complaint, but if the two sides do not reach an agreement, the company could face a fine of up to 10 percent of its annual global revenue.

The case has parallels to the antitrust charges brought decades ago by the U.S. Justice Department against Microsoft for bundling Internet Explorer inside its Windows operating system, a case that was eventually resolved.

On Tuesday, Microsoft said it had taken steps to resolve the dispute. Last year, Microsoft agreed to sell Teams separately from Office products.

“Having unbundled Teams and taken initial interoperability steps, we appreciate the additional clarity provided today and will work to find solutions to address the commission‘s remaining concerns.” Brad Smith, Microsoft’s president, said in a statement.

The European Commission said Microsoft’s changes were “insufficient” and called for more changes to be made to “restore competition,” without specifying what those changes should be.

Adam Satariano is a technology correspondent for The Times, based in London. More about Adam Satariano