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## Teaching Problem Solving in Math

• Freebies , Math , Planning

Every year my students can be fantastic at math…until they start to see math with words. For some reason, once math gets translated into reading, even my best readers start to panic. There is just something about word problems, or problem-solving, that causes children to think they don’t know how to complete them.

Every year in math, I start off by teaching my students problem-solving skills and strategies. Every year they moan and groan that they know them. Every year – paragraph one above. It was a vicious cycle. I needed something new.

I put together a problem-solving unit that would focus a bit more on strategies and steps in hopes that that would create problem-solving stars.

## The Problem Solving Strategies

First, I wanted to make sure my students all learned the different strategies to solve problems, such as guess-and-check, using visuals (draw a picture, act it out, and modeling it), working backward, and organizational methods (tables, charts, and lists). In the past, I had used worksheet pages that would introduce one and provide the students with plenty of problems practicing that one strategy. I did like that because students could focus more on practicing the strategy itself, but I also wanted students to know when to use it, too, so I made sure they had both to practice.

I provided students with plenty of practice of the strategies, such as in this guess-and-check game.

There’s also this visuals strategy wheel practice.

I also provided them with paper dolls and a variety of clothing to create an organized list to determine just how many outfits their “friend” would have.

Then, as I said above, we practiced in a variety of ways to make sure we knew exactly when to use them. I really wanted to make sure they had this down!

Anyway, after I knew they had down the various strategies and when to use them, then we went into the actual problem-solving steps.

## The Problem Solving Steps

I wanted students to understand that when they see a story problem, it isn’t scary. Really, it’s just the equation written out in words in a real-life situation. Then, I provided them with the “keys to success.”

S tep 1 – Understand the Problem.   To help students understand the problem, I provided them with sample problems, and together we did five important things:

• restated the problem in our own words
• crossed out unimportant information
• circled any important information
• stated the goal or question to be solved

We did this over and over with example problems.

Once I felt the students had it down, we practiced it in a game of problem-solving relay. Students raced one another to see how quickly they could get down to the nitty-gritty of the word problems. We weren’t solving the problems – yet.

Then, we were on to Step 2 – Make a Plan . We talked about how this was where we were going to choose which strategy we were going to use. We also discussed how this was where we were going to figure out what operation to use. I taught the students Sheila Melton’s operation concept map.

We talked about how if you know the total and know if it is equal or not, that will determine what operation you are doing. So, we took an example problem, such as:

Sheldon wants to make a cupcake for each of his 28 classmates. He can make 7 cupcakes with one box of cupcake mix. How many boxes will he need to buy?

We started off by asking ourselves, “Do we know the total?” We know there are a total of 28 classmates. So, yes, we are separating. Then, we ask, “Is it equal?” Yes, he wants to make a cupcake for EACH of his classmates. So, we are dividing: 28 divided by 7 = 4. He will need to buy 4 boxes. (I actually went ahead and solved it here – which is the next step, too.)

Step 3 – Solving the problem . We talked about how solving the problem involves the following:

• taking our time
• working the problem out
• showing all our work
• using thinking strategies

We talked specifically about thinking strategies. Just like in reading, there are thinking strategies in math. I wanted students to be aware that sometimes when we are working on a problem, a particular strategy may not be working, and we may need to switch strategies. We also discussed that sometimes we may need to rethink the problem, to think of related content, or to even start over. We discussed these thinking strategies:

• switch strategies or try a different one
• rethink the problem
• think of related content
• decide if you need to make changes
• but most important…don’t give up!

To make sure they were getting in practice utilizing these thinking strategies, I gave each group chart paper with a letter from a fellow “student” (not a real student), and they had to give advice on how to help them solve their problem using the thinking strategies above.

Finally, Step 4 – Check It.   This is the step that students often miss. I wanted to emphasize just how important it is! I went over it with them, discussing that when they check their problems, they should always look for these things:

• check for reasonableness
• restate the question in the answer
• explain how you solved the problem

Then, I gave students practice cards. I provided them with example cards of “students” who had completed their assignments already, and I wanted them to be the teacher. They needed to check the work and make sure it was completed correctly. If it wasn’t, then they needed to tell what they missed and correct it.

To demonstrate their understanding of the entire unit, we completed an adorable lap book (my first time ever putting together one or even creating one – I was surprised how well it turned out, actually). It was a great way to put everything we discussed in there.

Once we were all done, students were officially Problem Solving S.T.A.R.S. I just reminded students frequently of this acronym.

Stop – Don’t rush with any solution; just take your time and look everything over.

Think – Take your time to think about the problem and solution.

Act  – Act on a strategy and try it out.

Review – Look it over and see if you got all the parts.

Wow, you are a true trooper sticking it out in this lengthy post! To sum up the majority of what I have written here, I have some problem-solving bookmarks FREE to help you remember and to help your students!

You can grab these problem-solving bookmarks for FREE by clicking here .

You can do any of these ideas without having to purchase anything. However, if you are looking to save some time and energy, then they are all found in my Math Workshop Problem Solving Unit . The unit is for grade three, but it  may work for other grade levels. The practice problems are all for the early third-grade level.

• freebie , Math Workshop , Problem Solving

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## 6 Tips for Teaching Math Problem-Solving Skills

Solving word problems is tougher than computing with numbers, but elementary teachers can guide students to do the deep thinking involved.

A growing concern with students is the ability to problem-solve, especially with complex, multistep problems. Data shows that students struggle more when solving word problems than they do with computation , and so problem-solving should be considered separately from computation. Why?

Consider this. When we’re on the way to a new destination and we plug in our location to a map on our phone, it tells us what lane to be in and takes us around any detours or collisions, sometimes even buzzing our watch to remind us to turn. When I experience this as a driver, I don’t have to do the thinking. I can think about what I’m going to cook for dinner, not paying much attention to my surroundings other than to follow those directions. If I were to be asked to go there again, I wouldn’t be able to remember, and I would again seek help.

If we can switch to giving students strategies that require them to think instead of giving them too much support throughout the journey to the answer, we may be able to give them the ability to learn the skills to read a map and have several ways to get there.

Here are six ways we can start letting students do this thinking so that they can go through rigorous problem-solving again and again, paving their own way to the solution.

When we can remind students that they already have many comprehension skills and strategies they can easily use in math problem-solving, it can ease the anxiety surrounding the math problem. For example, providing them with strategies to practice, such as visualizing, acting out the problem with math tools like counters or base 10 blocks, drawing a quick sketch of the problem, retelling the story in their own words, etc., can really help them to utilize the skills they already have to make the task less daunting.

We can break these skills into specific short lessons so students have a bank of strategies to try on their own. Here's an example of an anchor chart that they can use for visualizing . Breaking up comprehension into specific skills can increase student independence and help teachers to be much more targeted in their problem-solving instruction. This allows students to build confidence and break down the barriers between reading and math to see they already have so many strengths that are transferable to all problems.

## 2. Avoid boxing students into choosing a specific operation

It can be so tempting to tell students to look for certain words that might mean a certain operation. This might even be thoroughly successful in kindergarten and first grade, but just like when our map tells us where to go, that limits students from becoming deep thinkers. It also expires once they get into the upper grades, where those words could be in a problem multiple times, creating more confusion when students are trying to follow a rule that may not exist in every problem.

We can encourage a variety of ways to solve problems instead of choosing the operation first. In first grade, a problem might say, “Joceline has 13 stuffed animals and Jordan has 17. How many more does Jordan have?” Some students might choose to subtract, but a lot of students might just count to find the amount in between. If we tell them that “how many more” means to subtract, we’re taking the thinking out of the problem altogether, allowing them to go on autopilot without truly solving the problem or using their comprehension skills to visualize it.

## 3. Revisit ‘representation’

The word “representation” can be misleading. It seems like something to do after the process of solving. When students think they have to go straight to solving, they may not realize that they need a step in between to be able to support their understanding of what’s actually happening in the problem first.

Using an anchor chart like one of these ( lower grade , upper grade ) can help students to choose a representation that most closely matches what they’re visualizing in their mind. Once they sketch it out, it can give them a clearer picture of different ways they could solve the problem.

Think about this problem: “Varush went on a trip with his family to his grandmother’s house. It was 710 miles away. On the way there, three people took turns driving. His mom drove 214 miles. His dad drove 358 miles. His older sister drove the rest. How many miles did his sister drive?”

If we were to show this student the anchor chart, they would probably choose a number line or a strip diagram to help them understand what’s happening.

If we tell students they must always draw base 10 blocks in a place value chart, that doesn’t necessarily match the concept of this problem. When we ask students to match our way of thinking, we rob them of critical thinking practice and sometimes confuse them in the process.

## 4. Give time to process

Sometimes as educators, we can feel rushed to get to everyone and everything that’s required. When solving a complex problem, students need time to just sit with a problem and wrestle with it, maybe even leaving it and coming back to it after a period of time.

This might mean we need to give them fewer problems but go deeper with those problems we give them. We can also speed up processing time when we allow for collaboration and talk time with peers on problem-solving tasks.

## 5. Ask questions that let Students do the thinking

Questions or prompts during problem-solving should be very open-ended to promote thinking. Telling a student to reread the problem or to think about what tools or resources would help them solve it is a way to get them to try something new but not take over their thinking.

These skills are also transferable across content, and students will be reminded, “Good readers and mathematicians reread.”

## 6. Spiral concepts so students frequently use problem-solving skills

When students don’t have to switch gears in between concepts, they’re not truly using deep problem-solving skills. They already kind of know what operation it might be or that it’s something they have at the forefront of their mind from recent learning. Being intentional within their learning stations and assessments about having a variety of rigorous problem-solving skills will refine their critical thinking abilities while building more and more resilience throughout the school year as they retain content learning in the process.

Problem-solving skills are so abstract, and it can be tough to pinpoint exactly what students need. Sometimes we have to go slow to go fast. Slowing down and helping students have tools when they get stuck and enabling them to be critical thinkers will prepare them for life and allow them multiple ways to get to their own destination.

## 5 Teaching Mathematics Through Problem Solving

Janet Stramel

In his book “How to Solve It,” George Pólya (1945) said, “One of the most important tasks of the teacher is to help his students. This task is not quite easy; it demands time, practice, devotion, and sound principles. The student should acquire as much experience of independent work as possible. But if he is left alone with his problem without any help, he may make no progress at all. If the teacher helps too much, nothing is left to the student. The teacher should help, but not too much and not too little, so that the student shall have a reasonable share of the work.” (page 1)

What is a problem  in mathematics? A problem is “any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method” (Hiebert, et. al., 1997). Problem solving in mathematics is one of the most important topics to teach; learning to problem solve helps students develop a sense of solving real-life problems and apply mathematics to real world situations. It is also used for a deeper understanding of mathematical concepts. Learning “math facts” is not enough; students must also learn how to use these facts to develop their thinking skills.

According to NCTM (2010), the term “problem solving” refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing students’ mathematical understanding and development. When you first hear “problem solving,” what do you think about? Story problems or word problems? Story problems may be limited to and not “problematic” enough. For example, you may ask students to find the area of a rectangle, given the length and width. This type of problem is an exercise in computation and can be completed mindlessly without understanding the concept of area. Worthwhile problems  includes problems that are truly problematic and have the potential to provide contexts for students’ mathematical development.

There are three ways to solve problems: teaching for problem solving, teaching about problem solving, and teaching through problem solving.

Teaching for problem solving begins with learning a skill. For example, students are learning how to multiply a two-digit number by a one-digit number, and the story problems you select are multiplication problems. Be sure when you are teaching for problem solving, you select or develop tasks that can promote the development of mathematical understanding.

Teaching about problem solving begins with suggested strategies to solve a problem. For example, “draw a picture,” “make a table,” etc. You may see posters in teachers’ classrooms of the “Problem Solving Method” such as: 1) Read the problem, 2) Devise a plan, 3) Solve the problem, and 4) Check your work. There is little or no evidence that students’ problem-solving abilities are improved when teaching about problem solving. Students will see a word problem as a separate endeavor and focus on the steps to follow rather than the mathematics. In addition, students will tend to use trial and error instead of focusing on sense making.

Teaching through problem solving  focuses students’ attention on ideas and sense making and develops mathematical practices. Teaching through problem solving also develops a student’s confidence and builds on their strengths. It allows for collaboration among students and engages students in their own learning.

Consider the following worthwhile-problem criteria developed by Lappan and Phillips (1998):

• The problem has important, useful mathematics embedded in it.
• The problem requires high-level thinking and problem solving.
• The problem contributes to the conceptual development of students.
• The problem creates an opportunity for the teacher to assess what his or her students are learning and where they are experiencing difficulty.
• The problem can be approached by students in multiple ways using different solution strategies.
• The problem has various solutions or allows different decisions or positions to be taken and defended.
• The problem encourages student engagement and discourse.
• The problem connects to other important mathematical ideas.
• The problem promotes the skillful use of mathematics.
• The problem provides an opportunity to practice important skills.

Of course, not every problem will include all of the above. Sometimes, you will choose a problem because your students need an opportunity to practice a certain skill.

Key features of a good mathematics problem includes:

• It must begin where the students are mathematically.
• The feature of the problem must be the mathematics that students are to learn.
• It must require justifications and explanations for both answers and methods of solving.

Problem solving is not a  neat and orderly process. Think about needlework. On the front side, it is neat and perfect and pretty.

But look at the b ack.

It is messy and full of knots and loops. Problem solving in mathematics is also like this and we need to help our students be “messy” with problem solving; they need to go through those knots and loops and learn how to solve problems with the teacher’s guidance.

When you teach through problem solving , your students are focused on ideas and sense-making and they develop confidence in mathematics!

## Mathematics Tasks and Activities that Promote Teaching through Problem Solving

Selecting activities and/or tasks is the most significant decision teachers make that will affect students’ learning. Consider the following questions:

• Teachers must do the activity first. What is problematic about the activity? What will you need to do BEFORE the activity and AFTER the activity? Additionally, think how your students would do the activity.
• What mathematical ideas will the activity develop? Are there connections to other related mathematics topics, or other content areas?
• Can the activity accomplish your learning objective/goals?

## Low Floor High Ceiling Tasks

By definition, a “ low floor/high ceiling task ” is a mathematical activity where everyone in the group can begin and then work on at their own level of engagement. Low Floor High Ceiling Tasks are activities that everyone can begin and work on based on their own level, and have many possibilities for students to do more challenging mathematics. One gauge of knowing whether an activity is a Low Floor High Ceiling Task is when the work on the problems becomes more important than the answer itself, and leads to rich mathematical discourse [Hover: ways of representing, thinking, talking, agreeing, and disagreeing; the way ideas are exchanged and what the ideas entail; and as being shaped by the tasks in which students engage as well as by the nature of the learning environment].

The strengths of using Low Floor High Ceiling Tasks:

• Allows students to show what they can do, not what they can’t.
• Provides differentiation to all students.
• Promotes a positive classroom environment.
• Advances a growth mindset in students
• Aligns with the Standards for Mathematical Practice

Examples of some Low Floor High Ceiling Tasks can be found at the following sites:

• YouCubed – under grades choose Low Floor High Ceiling
• NRICH Creating a Low Threshold High Ceiling Classroom
• Inside Mathematics Problems of the Month

## Math in 3-Acts

Math in 3-Acts was developed by Dan Meyer to spark an interest in and engage students in thought-provoking mathematical inquiry. Math in 3-Acts is a whole-group mathematics task consisting of three distinct parts:

Act One is about noticing and wondering. The teacher shares with students an image, video, or other situation that is engaging and perplexing. Students then generate questions about the situation.

In Act Two , the teacher offers some information for the students to use as they find the solutions to the problem.

Act Three is the “reveal.” Students share their thinking as well as their solutions.

“Math in 3 Acts” is a fun way to engage your students, there is a low entry point that gives students confidence, there are multiple paths to a solution, and it encourages students to work in groups to solve the problem. Some examples of Math in 3-Acts can be found at the following websites:

• Dan Meyer’s Three-Act Math Tasks
• Math in 3-Acts: Real World Math Problems to Make Math Contextual, Visual and Concrete

## Number Talks

Number talks are brief, 5-15 minute discussions that focus on student solutions for a mental math computation problem. Students share their different mental math processes aloud while the teacher records their thinking visually on a chart or board. In addition, students learn from each other’s strategies as they question, critique, or build on the strategies that are shared.. To use a “number talk,” you would include the following steps:

• The teacher presents a problem for students to solve mentally.
• Provide adequate “ wait time .”
• The teacher calls on a students and asks, “What were you thinking?” and “Explain your thinking.”
• For each student who volunteers to share their strategy, write their thinking on the board. Make sure to accurately record their thinking; do not correct their responses.
• Invite students to question each other about their strategies, compare and contrast the strategies, and ask for clarification about strategies that are confusing.

“Number Talks” can be used as an introduction, a warm up to a lesson, or an extension. Some examples of Number Talks can be found at the following websites:

• Inside Mathematics Number Talks
• Number Talks Build Numerical Reasoning

## Saying “This is Easy”

“This is easy.” Three little words that can have a big impact on students. What may be “easy” for one person, may be more “difficult” for someone else. And saying “this is easy” defeats the purpose of a growth mindset classroom, where students are comfortable making mistakes.

When the teacher says, “this is easy,” students may think,

• “Everyone else understands and I don’t. I can’t do this!”
• Students may just give up and surrender the mathematics to their classmates.
• Students may shut down.

• “I think I can do this.”
• “I have an idea I want to try.”
• “I’ve seen this kind of problem before.”

Tracy Zager wrote a short article, “This is easy”: The Little Phrase That Causes Big Problems” that can give you more information. Read Tracy Zager’s article here.

## Using “Worksheets”

Do you want your students to memorize concepts, or do you want them to understand and apply the mathematics for different situations?

What is a “worksheet” in mathematics? It is a paper and pencil assignment when no other materials are used. A worksheet does not allow your students to use hands-on materials/manipulatives [Hover: physical objects that are used as teaching tools to engage students in the hands-on learning of mathematics]; and worksheets are many times “naked number” with no context. And a worksheet should not be used to enhance a hands-on activity.

Students need time to explore and manipulate materials in order to learn the mathematics concept. Worksheets are just a test of rote memory. Students need to develop those higher-order thinking skills, and worksheets will not allow them to do that.

One productive belief from the NCTM publication, Principles to Action (2014), states, “Students at all grade levels can benefit from the use of physical and virtual manipulative materials to provide visual models of a range of mathematical ideas.”

You may need an “activity sheet,” a “graphic organizer,” etc. as you plan your mathematics activities/lessons, but be sure to include hands-on manipulatives. Using manipulatives can

• Provide your students a bridge between the concrete and abstract
• Serve as models that support students’ thinking
• Provide another representation
• Support student engagement
• Give students ownership of their own learning.

Adapted from “ The Top 5 Reasons for Using Manipulatives in the Classroom ”.

any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method

should be intriguing and contain a level of challenge that invites speculation and hard work, and directs students to investigate important mathematical ideas and ways of thinking toward the learning

involves teaching a skill so that a student can later solve a story problem

when we teach students how to problem solve

teaching mathematics content through real contexts, problems, situations, and models

a mathematical activity where everyone in the group can begin and then work on at their own level of engagement

20 seconds to 2 minutes for students to make sense of questions

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Answer: 9 $• If you take 30 mins to walk one mile, How long will it take to walk five miles? Answer: 1 hour 50 minutes • If a square has four sides, how many sides does a triangle have? Answer: Three • Fill the missing numbers given below: 25 + —–= 50 Answer: 25 • There are four vendors selling dry fruits across the street. One of the vendors packed his stuff and left the place. How many vendors did you see still selling the dry fruits? Answer: 3 vendors • How many sides does an octagon have? Answer: 8 Sides • There are 30 cotton balls stuffed in a soft toy. If you remove 20 cotton balls, how many will be remaining inside the toy? Answer: 10 cotton balls • Multiply the following number given below: 30 x 12 = 360 Answer: 360 • There are 250 bags of rice, 200 bags of corn and 300 bags of millets kept in the store. What is the total number of bags in the store? Answer: 750 Bags ## Benefits of Math Problems For Kids Some of the benefits of free math problems for kids are mentioned below: • Solving math problems will help your child become more confident in the subject and help them develop several skills. They are great tools through which kids learn to apply their math skills and solve a range of mathematical problems. Solving these math problems will also help them develop their critical thinking and problem-solving skills. • They start developing interest in acquiring math skills with utmost confidence and dedication. • Solving problems helps kids to think out of the box scenarios to come up with logical solutions to problems. • Math problems for kids improve their academic performance. • Kids become highly skilled in solving problems associated with any mathematical concepts accurately. • Math problems for kids enables them to manage time, speed and accuracy while solving any equations. Check Osmo for more activities, games to aid in your kids learning – math riddles for kids , coding games for kids and writing games for kids . ## Frequently Asked Questions on Math Problems for kids What are the math problems for kids. The Math Problems for kids are fill in the missing numbers, 10, 20, _, 40, _, _, 70, _, 90, _. What is the product of 5 x 6 x 7?, etc. ## How to teach Math Problems for kids? You can teach Math Problems for kids in the interesting and fun ways such as, helping kids identify the patterns, study the questions repeatedly and understand the problems, then help them to visualize on how to solve the problems. • » blog • » Mathematics • » 5 Best Free Math Problem Solvers ## 5 Best Free Math Problem Solvers By Casey Allen, 06 Jun 2023 Math problems allow students to learn new concepts and strengthen problem-solving skills. But many learners feel confused or frustrated if they can’t find the correct solution. A math problem solver is a handy tool that helps students doublecheck their work and identify errors. However, not all math problem solvers are created equal. Here are the top five math solvers for K-12 and college students. IntMath’s free online math solver offers comprehensive help for math and science problems. This innovative technology blends cutting-edge artificial intelligence language models with a mathematical computation engine. As a result, the math problem solver provides the quickest and most accurate answers. This math solver answers questions from every branch of math, from introductory algebra to calculus. It can also interpret and solve complex word problems. Plus, students can use the solver for other challenging subjects like chemistry and physics. IntMath’s solver also offers the most flexibility. The tool analyzes natural human language to answer questions a calculator wouldn’t understand. It’s also more accurate than standard AI interfaces, so users always get the correct answers. And the math equation solver can answer questions more quickly than a tutor at any time of the day. ## 2. Microsoft Math Solver The Microsoft Math Solver provides step-by-step answers for pre-algebra, algebra, trigonometry, and calculus problems. It also links video tutorials, worksheets, and similar math problems posted online. Users can manually type problems into the Microsoft Math Solver or take pictures of them with their smartphone. This tool also has a sketch calculator, which lets students handwrite problems using their fingers or a stylus. You can download the Microsoft Math Solver as a mobile application or use the built-in web application in Microsoft Edge. Mathway is a math equation solver developed by the online homework service Chegg. This mobile and web application answers many types of math problems, including calculus, finite math, graphing, and physics. Students can take a picture of the problem or manually input it with the built-in keyboard. The free version of the Mathway app only provides solutions. If you want to see the step-by-step process to answer problems, you’ll need to purchase an annual subscription for$9.99 monthly or $39.99 annually. ## 4. Photomath The Photomath mobile application allows students to take pictures of math problems with their smartphone camera and offers multiple solution methods. This tool is designed for K-12 students and covers subjects like geometry, statistics, and word problems. Math teachers vet all problem-solving methods. Photomath has a free version that provides answers but doesn’t explain how to solve the problems. Photomath Plus is a subscription plan that costs$9.99 monthly or $69.99 annually and gives animated tutorials for each solution. ## 5. Socratic By Google An honorable mention goes to Socratic by Google . This tool uses artificial intelligence to locate relevant online explanations and resources for math problems. However, Socratic doesn’t solve problems itself. As a result, Socratic works best for students who want to learn how to solve problems but get the answers on their own. ## Get More Help With IntMath Math word problem solvers are valuable homework aids, but live math tutoring can help students master challenging math subjects. IntMath’s expert tutors provide personalized online tutoring to help all learners excel and gain lifelong math skills. Contact us today to get started. Be the first to comment below. ## Related posts: • Microsoft Math 3.0 Review MS Math 3.0 is a well-designed computer-based math tool.... • Free math software downloads Wanting to use some math software but find it’s too expensive? Here are some free... • GraphSketch.com - free online math grapher GraphSketch is a free offering that allows the user to sketch graphs of math functions.... • Context Free math-based art Context Free is software you can use to produce some beautiful math-based art. Build STEM... • Free math resources Here is a list of math lessons and other resources that you may find useful.... Posted in Mathematics category - 06 Jun 2023 [ Permalink ] ## Leave a comment * Name (required) * E-Mail (required - will not be published) Your blog URL (can be left blank) Notify me of followup comments via e-mail Your comment: Preview comment ## Comment Preview HTML: You can use simple tags like <b>, <a href="...">, etc. To enter math , you can can either: • Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone): a^2 = sqrt(b^2 + c^2) (See more on ASCIIMath syntax ); or • Use simple LaTeX in the following format. Surround your math with $$and$$ . $$\int g dx = \sqrt{\frac{a}{b}}$$ (This is standard simple LaTeX.) NOTE: You can mix both types of math entry in your comment. • Ten Ways to Survive the Math Blues • How to understand math formulas • How to learn math formulas • How to make math class interesting? • SquareCirclez Sitemap • Mathematics (370) • Intmath Newsletters (180) • Learning mathematics (164) • Math movies (162) • Learning (general) (119) • Environmental math (66) • General (54) • Computers & Internet (40) • Math Supplies (23) • Contact (1) • Exam Guides (1) ## Most Commented • Is 0 a Natural Number? (162) • How do you find exact values for the sine of all angles? 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## Combination Locks - maths problem solving

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Last updated

22 February 2018

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A great resource to use with Y6 as a supply teacher after Sat's

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## clazzashazza

What a great idea! Thank you.

## AntoniaRebecca

This would be a useful resource for me when having to plan a lesson for an observation at a job interview.

Easy to use activity, especially for year5s

Super lesson, made a couple of tweaks and gave it to my yr7's who were really enthused. A great lesson for students not used to problem solving and thinking for themselves.

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OpenAI Made an AI Breakthrough Before Altman Firing, Stoking Excitement and Concern Save 25% and Read now

## OpenAI Made an AI Breakthrough Before Altman Firing, Stoking Excitement and Concern

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One day before he was fired by OpenAI’s board last week, Sam Altman alluded to a recent technical advance the company had made that allowed it to “push the veil of ignorance back and the frontier of discovery forward.” The cryptic remarks at the APEC CEO Summit went largely unnoticed as the company descended into turmoil.

But some OpenAI employees believe Altman’s comments referred to an innovation by the company’s researchers earlier this year that would allow them to develop far more powerful artificial intelligence models, a person familiar with the matter said. The technical breakthrough, spearheaded by OpenAI chief scientist Ilya Sutskever, raised concerns among some staff that the company didn’t have proper safeguards in place to commercialize such advanced AI models, this person said.

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## How to Solve Math Problems

Last Updated: May 16, 2023 Fact Checked

This article was co-authored by Daron Cam . Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary's College. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 574,843 times.

Although math problems may be solved in different ways, there is a general method of visualizing, approaching and solving math problems that may help you to solve even the most difficult problem. Using these strategies can also help you to improve your math skills overall. Keep reading to learn about some of these math problem solving strategies.

## Understanding the Problem

• Draw a Venn diagram. A Venn diagram shows the relationships among the numbers in your problem. Venn diagrams can be especially helpful with word problems.
• Draw a graph or chart.
• Arrange the components of the problem on a line.
• Draw simple shapes to represent more complex features of the problem.

## Expert Q&A

• Seek help from your teacher or a math tutor if you get stuck or if you have tried multiple strategies without success. Your teacher or a math tutor may be able to easily identify what is wrong and help you to understand how to correct it. Thanks Helpful 1 Not Helpful 1
• Keep practicing sums and diagrams. Go through the concept your class notes regularly. Write down your understanding of the methods and utilize it. Thanks Helpful 1 Not Helpful 0

## You Might Also Like

• ↑ Daron Cam. Math Tutor. Expert Interview. 29 May 2020.
• ↑ http://tutorial.math.lamar.edu/Extras/StudyMath/ProblemSolving.aspx
• ↑ https://math.berkeley.edu/~gmelvin/polya.pdf

To solve a math problem, try rewriting the problem in your own words so it's easier to solve. You can also make a drawing of the problem to help you figure out what it's asking you to do. If you're still completely stuck, try solving a different problem that's similar but easier and then use the same steps to solve the harder problem. Even if you can't figure out how to solve it, try to make an educated guess instead of leaving the question blank. To learn how to come up with a solid plan to use to help you solve a math problem, scroll down! Did this summary help you? Yes No

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6. Can You Solve This Problem?

1. Free Math Worksheets

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!

2. Teaching Problem Solving in Math

Step 1 - Understand the Problem. To help students understand the problem, I provided them with sample problems, and together we did five important things: read the problem carefully restated the problem in our own words crossed out unimportant information circled any important information stated the goal or question to be solved

3. Problem Solving Lessons

TED-Ed lessons on the subject Problem Solving. TED-Ed celebrates the ideas of teachers and students around the world. Discover hundreds of animated lessons, create customized lessons, and share your big ideas. ... Mathematics Can you solve the time traveling car riddle? Lesson duration 05:18 505,318 Views. 06:26. Health 4 epidemics that almost ...

4. 6 Tips for Teaching Math Problem-Solving Skills

1. Link problem-solving to reading. When we can remind students that they already have many comprehension skills and strategies they can easily use in math problem-solving, it can ease the anxiety surrounding the math problem. For example, providing them with strategies to practice, such as visualizing, acting out the problem with math tools ...

5. Problem-Solving Steps

(10 minutes) Bring students together in a circle, either seated or standing. Bring blocks with you to the circle. Show the student the blocks and ask them to watch you build a tall castle. After you build it, bring out two figurines that you would like to play with in the castle. Say out loud, "Hmm....there seems to be a problem.

6. Teaching Mathematics Through Problem Solving

in mathematics? A problem is "any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific 'correct' solution method" (Hiebert, et. al., 1997).

7. Microsoft Math Solver

Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app.

8. Algebraic word problems

To solve an algebraic word problem: Define a variable. Write an equation using the variable. Solve the equation. If the variable is not the answer to the word problem, use the variable to calculate the answer. It's important for us to keep in mind how we define our variables.

9. Mathway

Free math problem solver answers your algebra homework questions with step-by-step explanations.

10. Arithmetic patterns and problem solving

3rd grade 14 units · 141 skills. Unit 1 Intro to multiplication. Unit 2 1-digit multiplication. Unit 3 Addition, subtraction, and estimation. Unit 4 Intro to division. Unit 5 Understand fractions. Unit 6 Equivalent fractions and comparing fractions. Unit 7 More with multiplication and division. Unit 8 Arithmetic patterns and problem solving.

11. enVision Mathematics Middle School Math

MathXL for School: Practice & Problem Solving, during the lesson, includes personalized practice for the Practice & Problem Solving portion of the lesson, along with Additional Practice or Enrichment; auto‐scored with on‐screen help, including Help Me Solve This and View an Example tools, tutorial videos, Math Tools, and one‐click ...

12. Algebra 1

The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!

13. Step-by-Step Math Problem Solver

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. The algebra section allows you to expand, factor or simplify virtually any expression you choose.

14. Solving Algebra Problems

MathHelp.com - https://www.MathHelp.com - offers comprehensive help solving Algebra problems with over 1000 online math lessons featuring a personal math tea...

15. 10 Fun Math Problem Solving Activities

One way to use problem-solving activities in your math lessons is to help introduce a new concept. For example, when we were learning about even and odd numbers, we started our math lesson by playing the Odds vs. Evens game from Beast Academy Playground. This simple math problem solving activity is a variation on the game Rock Paper Scissors.

16. Fluency, Reasoning & Problem Solving: What They REALLY Are

But if problem solving depends on a deep knowledge of mathematics, this approach to lesson structure is going to be very ineffective. As mentioned earlier, the reasoning and problem solving questions were based on the same math content as the fluency exercises, making it more likely that students would solve problems correctly whether they ...

17. Math Lesson Plans for Teachers

Students learn how to solve music and math problems by finding patterns. Subjects Mathematics Music Music National Content Standard 8 Download Add to Favorites LESSON PLANS Odd and Even Numbers Lesson A hundreds chart is used to show the alternating pattern of odd and even numbers, and students are asked to extend the… Subjects Mathematics

18. Problem Solving Maths Lessons

Problem solving is at the heart of engaging and inspiring mathematics lessons. In the past couple of years, my faculty have gone through deep-dive OFSTED inspectionsâ€"a trial inspection with three HMIs and an actual inspection. The trial inspection showed all students have a love of maths.

19. Maths Problem Solving Booklets

pdf, 424.8 KB. pdf, 353.5 KB. Maths problem solving booklets covering a wide range of mathematical problems designed to improve problem solving strategies as well as numeracy and mathematical ability. Designed to be printed as A5 booklets. Disclaimer: These are free because the problems are from a wide variety of sources, most of which I have ...

20. Math Problems For Kids

Subtract 8 from 12. 12 - 8 = 4. Therefore, x = 4. Checking the solution is one of the most important parts of solving math problems for kids. Often, kids rush through the process of solving a problem to get an answer but forget to check if the solution is correct. And most often, this misstep causes errors.

21. 5 Best Free Math Problem Solvers

1. IntMath IntMath's free online math solver offers comprehensive help for math and science problems. This innovative technology blends cutting-edge artificial intelligence language models with a mathematical computation engine. As a result, the math problem solver provides the quickest and most accurate answers.

22. Combination Locks

Taught to Y5 & Y6 children, working between level 2 and 5. Differentiated questions - range of maths topics; LA/AA/MA. Combination locks resources - recording sheet for chn. Page 1: solve teacher's examples; Page 2: create own clues. **UPDATE (November 2015) - As per comment, there should be no "s" on the web address in the plan.

23. Math Problem Solving

Featuring original free math problem solving worksheets for teachers and parents to copy for their kids. Use these free math worksheets for teaching, reinforcement, and review. These math word problems are most appropriate for grades four and five, but many are designed to be challenging and informative to older and more advanced students as well.

24. An Innovator's Journey: 5 Lessons Learned

4. There's magic in metaphors. As a leader, it's important to be able to build rapport with a wide variety of people because many times you'll need to be able to communicate with someone who has ...

25. OpenAI Made an AI Breakthrough Before Altman Firing, Stoking Excitement

One day before he was fired by OpenAI's board last week, Sam Altman alluded to a recent technical advance the company had made that allowed it to "push the veil of ignorance back and the frontier of discovery forward." The cryptic remarks at the APEC CEO Summit went largely unnoticed as the ...

26. 3 Easy Ways to Solve Math Problems (with Pictures)

Draw a graph or chart. Arrange the components of the problem on a line. Draw simple shapes to represent more complex features of the problem. 5. Look for patterns. Sometimes you can identify a pattern or patterns in a math problem simply by reading the problem carefully.