math problem solving steps elementary

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Problem Solving

Problem Solving Strategies

Think back to the first problem in this chapter, the ABC Problem . What did you do to solve it? Even if you did not figure it out completely by yourself, you probably worked towards a solution and figured out some things that did not work.

Unlike exercises, there is never a simple recipe for solving a problem. You can get better and better at solving problems, both by building up your background knowledge and by simply practicing. As you solve more problems (and learn how other people solved them), you learn strategies and techniques that can be useful. But no single strategy works every time.

Pólya’s How to Solve It

George Pólya was a great champion in the field of teaching effective problem solving skills.  He was born in Hungary in 1887, received his Ph.D. at the University of Budapest, and was a professor at Stanford University (among other universities).  He wrote many mathematical papers along with three books, most famously, “How to Solve it.” Pólya died at the age 98 in 1985. [1]

 In 1945, Pólya published the short book How to Solve It , which gave a four-step method for solving mathematical problems:

• First, you have to understand the problem.
• After understanding, then make a plan.
• Carry out the plan.
• Look back on your work. How could it be better?

This is all well and good, but how do you actually do these steps?!?! Steps 1. and 2. are particularly mysterious! How do you “make a plan?” That is where you need some tools in your toolbox, and some experience to draw upon.

Much has been written since 1945 to explain these steps in more detail, but the truth is that they are more art than science. This is where math becomes a creative endeavor (and where it becomes so much fun). We will articulate some useful problem solving strategies, but no such list will ever be complete. This is really just a start to help you on your way. The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems!

We have already seen one problem solving strategy, which we call “Wishful Thinking.” Do not be afraid to change the problem! Ask yourself “what if” questions:

• What if the picture was different?
• What if the numbers were simpler?
• What if I just made up some numbers?

You need to be sure to go back to the original problem at the end, but wishful thinking can be a powerful strategy for getting started.

This brings us to the most important problem solving strategy of all:

Problem Solving Strategy 2 (Try Something!). If you are really trying to solve a problem, the whole point is that you do not know what to do right out of the starting gate. You need to just try something! Put pencil to paper (or stylus to screen or chalk to board or whatever!) and try something. This is often an important step in understanding the problem; just mess around with it a bit to understand the situation and figure out what is going on.

And equally important: If what you tried first does not work, try something else! Play around with the problem until you have a feel for what is going on.

Problem 2 (Payback)

Last week, Alex borrowed money from several of his friends. He finally got paid at work, so he brought cash to school to pay back his debts. First he saw Brianna, and he gave her 1/4 of the money he had brought to school. Then Alex saw Chris and gave him 1/3 of what he had left after paying Brianna. Finally, Alex saw David and gave him 1/2 of what he had remaining. Who got the most money from Alex?

Think/Pair/Share

After you have worked on the problem on your own for a while, talk through your ideas with a partner (even if you have not solved it). What did you try? What did you figure out about the problem?

This problem lends itself to two particular strategies. Did you try either of these as you worked on the problem? If not, read about the strategy and then try it out before watching the solution.

Problem Solving Strategy 3 (Draw a Picture). Some problems are obviously about a geometric situation, and it is clear you want to draw a picture and mark down all of the given information before you try to solve it. But even for a problem that is not geometric, like this one, thinking visually can help! Can you represent something in the situation by a picture?

Draw a square to represent all of Alex’s money. Then shade 1/4 of the square — that’s what he gave away to Brianna. How can the picture help you finish the problem?

After you have worked on the problem yourself using this strategy (or if you are completely stuck), you can watch someone else’s solution.

Problem Solving Strategy 4 (Make Up Numbers). Part of what makes this problem difficult is that it is about money, but there are no numbers given. That means the numbers must not be important. So just make them up!

You can work forwards: Assume Alex had some specific amount of money when he showed up at school, say $100. Then figure out how much he gives to each person. Or you can work backwards: suppose he has some specific amount left at the end, like $10. Since he gave Chris half of what he had left, that means he had $20 before running into Chris. Now, work backwards and figure out how much each person got.

Watch the solution only after you tried this strategy for yourself.

If you use the “Make Up Numbers” strategy, it is really important to remember what the original problem was asking! You do not want to answer something like “Everyone got $10.” That is not true in the original problem; that is an artifact of the numbers you made up. So after you work everything out, be sure to re-read the problem and answer what was asked!

Problem 3 (Squares on a Chess Board)

How many squares, of any possible size, are on a 8 × 8 chess board? (The answer is not 64… It’s a lot bigger!)

Remember Pólya’s first step is to understand the problem. If you are not sure what is being asked, or why the answer is not just 64, be sure to ask someone!

Think / Pair / Share

After you have worked on the problem on your own for a while, talk through your ideas with a partner (even if you have not solved it). What did you try? What did you figure out about the problem, even if you have not solved it completely?

It is clear that you want to draw a picture for this problem, but even with the picture it can be hard to know if you have found the correct answer. The numbers get big, and it can be hard to keep track of your work. Your goal at the end is to be absolutely positive that you found the right answer. You should never ask the teacher, “Is this right?” Instead, you should declare, “Here’s my answer, and here is why I know it is correct!”

Problem Solving Strategy 5 (Try a Simpler Problem). Pólya suggested this strategy: “If you can’t solve a problem, then there is an easier problem you can solve: find it.” He also said: “If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?” In this case, an 8 × 8 chess board is pretty big. Can you solve the problem for smaller boards? Like 1 × 1? 2 × 2? 3 × 3?

Of course the ultimate goal is to solve the original problem. But working with smaller boards might give you some insight and help you devise your plan (that is Pólya’s step (2)).

Problem Solving Strategy 6 (Work Systematically). If you are working on simpler problems, it is useful to keep track of what you have figured out and what changes as the problem gets more complicated.

For example, in this problem you might keep track of how many 1 × 1 squares are on each board, how many 2 × 2 squares on are each board, how many 3 × 3 squares are on each board, and so on. You could keep track of the information in a table:

Problem Solving Strategy 7 (Use Manipulatives to Help You Investigate). Sometimes even drawing a picture may not be enough to help you investigate a problem. Having actual materials that you move around can sometimes help a lot!

For example, in this problem it can be difficult to keep track of which squares you have already counted. You might want to cut out 1 × 1 squares, 2 × 2 squares, 3 × 3 squares, and so on. You can actually move the smaller squares across the chess board in a systematic way, making sure that you count everything once and do not count anything twice.

Problem Solving Strategy 8 (Look for and Explain Patterns). Sometimes the numbers in a problem are so big, there is no way you will actually count everything up by hand. For example, if the problem in this section were about a 100 × 100 chess board, you would not want to go through counting all the squares by hand! It would be much more appealing to find a pattern in the smaller boards and then extend that pattern to solve the problem for a 100 × 100 chess board just with a calculation.

If you have not done so already, extend the table above all the way to an 8 × 8 chess board, filling in all the rows and columns. Use your table to find the total number of squares in an 8 × 8 chess board. Then:

• Describe all of the patterns you see in the table.
• Can you explain and justify any of the patterns you see? How can you be sure they will continue?
• What calculation would you do to find the total number of squares on a 100 × 100 chess board?

(We will come back to this question soon. So if you are not sure right now how to explain and justify the patterns you found, that is OK.)

Problem 4 (Broken Clock)

This clock has been broken into three pieces. If you add the numbers in each piece, the sums are consecutive numbers. ( Consecutive numbers are whole numbers that appear one after the other, such as 1, 2, 3, 4 or 13, 14, 15.)

Can you break another clock into a different number of pieces so that the sums are consecutive numbers? Assume that each piece has at least two numbers and that no number is damaged (e.g. 12 isn’t split into two digits 1 and 2.)

Remember that your first step is to understand the problem. Work out what is going on here. What are the sums of the numbers on each piece? Are they consecutive?

After you have worked on the problem on your own for a while, talk through your ideas with a partner (even if you have not solved it). What did you try? What progress have you made?

Problem Solving Strategy 9 (Find the Math, Remove the Context). Sometimes the problem has a lot of details in it that are unimportant, or at least unimportant for getting started. The goal is to find the underlying math problem, then come back to the original question and see if you can solve it using the math.

In this case, worrying about the clock and exactly how the pieces break is less important than worrying about finding consecutive numbers that sum to the correct total. Ask yourself:

• What is the sum of all the numbers on the clock’s face?
• Can I find two consecutive numbers that give the correct sum? Or four consecutive numbers? Or some other amount?
• How do I know when I am done? When should I stop looking?

Of course, solving the question about consecutive numbers is not the same as solving the original problem. You have to go back and see if the clock can actually break apart so that each piece gives you one of those consecutive numbers. Maybe you can solve the math problem, but it does not translate into solving the clock problem.

Problem Solving Strategy 10 (Check Your Assumptions). When solving problems, it is easy to limit your thinking by adding extra assumptions that are not in the problem. Be sure you ask yourself: Am I constraining my thinking too much?

In the clock problem, because the first solution has the clock broken radially (all three pieces meet at the center, so it looks like slicing a pie), many people assume that is how the clock must break. But the problem does not require the clock to break radially. It might break into pieces like this:

Were you assuming the clock would break in a specific way? Try to solve the problem now, if you have not already.

• Image of Pólya by Thane Plambeck from Palo Alto, California (Flickr) [CC BY 2.0 (http://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons ↵

Mathematics for Elementary Teachers Copyright © 2018 by Michelle Manes is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License , except where otherwise noted.

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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. 

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 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.

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:

• 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

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
• estimating the answer
• 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
• check your work
• 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:

• compare your answer to your estimate
• check for reasonableness
• check your calculations
• add the units
• 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.

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Problem Solving Activities: 7 Strategies

• Critical Thinking

Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.

In the middle of our problem solving lesson, my district math coordinator stopped by for a surprise walkthrough. 

I was so excited!

We were in the middle of what I thought was the most brilliant math lesson– teaching my students how to solve problem solving tasks using specific problem solving strategies. 

It was a proud moment for me!

Each week, I presented a new problem solving strategy and the students completed problems that emphasized the strategy. 

Genius right? 

After observing my class, my district coordinator pulled me aside to chat. I was excited to talk to her about my brilliant plan, but she told me I should provide the tasks and let my students come up with ways to solve the problems. Then, as students shared their work, I could revoice the student’s strategies and give them an official name. 

What a crushing blow! Just when I thought I did something special, I find out I did it all wrong. 

I took some time to consider her advice. Once I acknowledged she was right, I was able to make BIG changes to the way I taught problem solving in the classroom. 

When I Finally Saw the Light

To give my students an opportunity to engage in more authentic problem solving which would lead them to use a larger variety of problem solving strategies, I decided to vary the activities and the way I approached problem solving with my students. 

Problem Solving Activities

Here are seven ways to strategically reinforce problem solving skills in your classroom. 

Seasonal Problem Solving

Many teachers use word problems as problem solving tasks. Instead, try engaging your students with non-routine tasks that look like word problems but require more than the use of addition, subtraction, multiplication, and division to complete. Seasonal problem solving tasks and daily challenges are a perfect way to celebrate the season and have a little fun too!

Cooperative Problem Solving Tasks

Go cooperative! If you’ve got a few extra minutes, have students work on problem solving tasks in small groups. After working through the task, students create a poster to help explain their solution process and then post their poster around the classroom. Students then complete a gallery walk of the posters in the classroom and provide feedback via sticky notes or during a math talk session.

Notice and Wonder

Before beginning a problem solving task, such as a seasonal problem solving task, conduct a Notice and Wonder session. To do this, ask students what they notice about the problem. Then, ask them what they wonder about the problem. This will give students an opportunity to highlight the unique characteristics and conditions of the problem as they try to make sense of it. 

Want a better experience? Remove the stimulus, or question, and allow students to wonder about the problem. Try it! You’ll gain some great insight into how your students think about a problem.

Math Starters

Start your math block with a math starter, critical thinking activities designed to get your students thinking about math and provide opportunities to “sneak” in grade-level content and skills in a fun and engaging way. These tasks are quick, designed to take no more than five minutes, and provide a great way to turn-on your students’ brains. Read more about math starters here ! 

Create your own puzzle box! The puzzle box is a set of puzzles and math challenges I use as fast finisher tasks for my students when they finish an assignment or need an extra challenge. The box can be a file box, file crate, or even a wall chart. It includes a variety of activities so all students can find a challenge that suits their interests and ability level.

Calculators

Use calculators! For some reason, this tool is not one many students get to use frequently; however, it’s important students have a chance to practice using it in the classroom. After all, almost everyone has access to a calculator on their cell phones. There are also some standardized tests that allow students to use them, so it’s important for us to practice using calculators in the classroom. Plus, calculators can be fun learning tools all by themselves!

Three-Act Math Tasks

Use a three-act math task to engage students with a content-focused, real-world problem! These math tasks were created with math modeling in mind– students are presented with a scenario and then given clues and hints to help them solve the problem. There are several sites where you can find these awesome math tasks, including Dan Meyer’s Three-Act Math Tasks and Graham Fletcher’s 3-Acts Lessons . 

Getting the Most from Each of the Problem Solving Activities

When students participate in problem solving activities, it is important to ask guiding, not leading, questions. This provides students with the support necessary to move forward in their thinking and it provides teachers with a more in-depth understanding of student thinking. Selecting an initial question and then analyzing a student’s response tells teachers where to go next. 

Ready to jump in? Grab a free set of problem solving challenges like the ones pictured using the form below. 

Which of the problem solving activities will you try first? Respond in the comments below.

Shametria Routt Banks

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2 Responses

This is a very cool site. I hope it takes off and is well received by teachers. I work in mathematical problem solving and help prepare pre-service teachers in mathematics.

Thank you, Scott! Best wishes to you and your pre-service teachers this year!

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Math Problem Solving Strategies That Make Students Say “I Get It!”

Even students who are quick with math facts can get stuck when it comes to problem solving.

As soon as a concept is translated to a word problem, or a simple mathematical sentence contains an unknown, they’re stumped.

That’s because problem solving requires us to  consciously choose the strategies most appropriate for the problem   at hand . And not all students have this metacognitive ability.

But you can teach these strategies for problem solving.  You just need to know what they are.

We’ve compiled them here divided into four categories:

Strategies for understanding a problem

Strategies for solving the problem, strategies for working out, strategies for checking the solution.

Get to know these strategies and then model them explicitly to your students. Next time they dive into a rich problem, they’ll be filling up their working out paper faster than ever!

Before students can solve a problem, they need to know what it’s asking them. This is often the first hurdle with word problems that don’t specify a particular mathematical operation.

Encourage your students to:

Read and reread the question

They say they’ve read it, but have they  really ? Sometimes students will skip ahead as soon as they’ve noticed one familiar piece of information or give up trying to understand it if the problem doesn’t make sense at first glance.

Teach students to interpret a question by using self-monitoring strategies such as:

• Rereading a question more slowly if it doesn’t make sense the first time
• Asking for help
• Highlighting or underlining important pieces of information.

Identify important and extraneous information

John is collecting money for his friend Ari’s birthday. He starts with $5 of his own, then Marcus gives him another $5. How much does he have now?

As adults looking at the above problem, we can instantly look past the names and the birthday scenario to see a simple addition problem. Students, however, can struggle to determine what’s relevant in the information that’s been given to them.

Teach students to sort and sift the information in a problem to find what’s relevant. A good way to do this is to have them swap out pieces of information to see if the solution changes. If changing names, items or scenarios has no impact on the end result, they’ll realize that it doesn’t need to be a point of focus while solving the problem.

Schema approach

This is a math intervention strategy that can make problem solving easier for all students, regardless of ability.

Compare different word problems of the same type and construct a formula, or mathematical sentence stem, that applies to them all. For example, a simple subtraction problems could be expressed as:

[Number/Quantity A] with [Number/Quantity B] removed becomes [end result].

This is the underlying procedure or  schema  students are being asked to use. Once they have a list of schema for different mathematical operations (addition, multiplication and so on), they can take turns to apply them to an unfamiliar word problem and see which one fits.

Struggling students often believe math is something you either do automatically or don’t do at all. But that’s not true. Help your students understand that they have a choice of problem-solving strategies to use, and if one doesn’t work, they can try another.

Here are four common strategies students can use for problem solving.

Visualizing

Visualizing an abstract problem often makes it easier to solve. Students could draw a picture or simply draw tally marks on a piece of working out paper.

Encourage visualization by modeling it on the whiteboard and providing graphic organizers that have space for students to draw before they write down the final number.

Guess and check

Show students how to make an educated guess and then plug this answer back into the original problem. If it doesn’t work, they can adjust their initial guess higher or lower accordingly.

Find a pattern

To find patterns, show students how to extract and list all the relevant facts in a problem so they can be easily compared. If they find a pattern, they’ll be able to locate the missing piece of information.

Work backward

Working backward is useful if students are tasked with finding an unknown number in a problem or mathematical sentence. For example, if the problem is 8 + x = 12, students can find x by:

• Starting with 12
• Taking the 8 from the 12
• Being left with 4
• Checking that 4 works when used instead of x

Now students have understood the problem and formulated a strategy, it’s time to put it into practice. But if they just launch in and do it, they might make it harder for themselves. Show them how to work through a problem effectively by:

Documenting working out

Model the process of writing down every step you take to complete a math problem and provide working out paper when students are solving a problem. This will allow students to keep track of their thoughts and pick up errors before they reach a final solution.

Check along the way

Checking work as you go is another crucial self-monitoring strategy for math learners. Model it to them with think aloud questions such as:

• Does that last step look right?
• Does this follow on from the step I took before?
• Have I done any ‘smaller’ sums within the bigger problem that need checking?

Students often make the mistake of thinking that speed is everything in math — so they’ll rush to get an answer down and move on without checking.

But checking is important too. It allows them to pinpoint areas of difficulty as they come up, and it enables them to tackle more complex problems that require multiple checks  before  arriving at a final answer.

Here are some checking strategies you can promote:

Check with a partner

Comparing answers with a peer leads is a more reflective process than just receiving a tick from the teacher. If students have two different answers, encourage them to talk about how they arrived at them and compare working out methods. They’ll figure out exactly where they went wrong, and what they got right.

Reread the problem with your solution

Most of the time, students will be able to tell whether or not their answer is correct by putting it back into the initial problem. If it doesn’t work or it just ‘looks wrong’, it’s time to go back and fix it up.

Fixing mistakes

Show students how to backtrack through their working out to find the exact point where they made a mistake. Emphasize that they can’t do this if they haven’t written down everything in the first place — so a single answer with no working out isn’t as impressive as they might think!

Need more help developing problem solving skills?

Read up on  how to set a problem solving and reasoning activity  or explore Mathseeds and Mathletics, our award winning online math programs. They’ve got over 900 teacher tested problem solving activities between them!

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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

Choosing the Right Task

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
• Graham Fletcher3-Act 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.

Instead, you and your students could say the following:

• “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

Mathematics Methods for Early Childhood Copyright © 2021 by Janet Stramel is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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K-5 Math Centers

K-5 math ideas, 3rd grade math, need help organizing your k-5 math block, 5 ways to include math problem solving activities in your classroom.

Are you looking for math problem solving activities that are not too easy and not too hard, but juuust right? I’ve got something just for you and your students.

Solve and Explain Problem Solving Tasks are open-ended math tasks that provide just the right amount of challenge for your kids. Here’s a little more about them.

Open-ended math problem solving tasks:

• promote multiple solution paths and/or multiple solutions
• boost critical thinking and math reasoning skills
• increase opportunities for developing perseverance
• provide opportunities to justify answer choices
• strengthen kids written and oral communication skills

What Makes These So Great?

• All Common Core Standards are covered for your grade level
• 180+ Quality questions that are rigorous yet engaging
• They are SUPER easy to assemble
• Provide opportunities for meaningful math discussions
• Perfect for developing a growth mindset
• Easily identify student misconceptions so you can provide assistance
• Very versatile (check out the different ways to use them below)

You can find out more details for your grade level by clicking on the buttons below.

I’m sure you really want to know how can you use these with your kids. Check out the top 5 ideas on how to use Solve and Explain Problem Solving Tasks in your classroom.

How and When Can I Use Them?

Solve and Explain Tasks Cards are very versatile. You can use them for:

• Math Centers  – This is my favorite way to use these! Depending on your grade level, there are at least two (Kinder – 2nd) or three (3rd-5th) tasks types per Common Core standard. And each task type has 6 different questions. Print out each of the different tasks types on different color paper. Then, let students choose which one question from each task type they want to solve.

• Problem of the Day  – Use them as a daily math journal prompt. Print out the recording sheet and project one of the problems on your white board or wall.  Students solve the problem and then glue it in their spiral or composition notebooks.

• Early Finisher Activities  -No more wondering what to do next!Create an early finishers notebook where students can grab a task and a recording sheet. Place the cards in sheet protectors and make copies of the Early Finisher Activity Check-Off card for your kids to fill out BEFORE they pull a card out to work on. We want to make sure kids are not rushing through there first assignment before moving on to an early finisher activity.

• Weekly Math Challenges  – Kids LOVE challenges! Give students copies of one of the problems for homework. Then give them a week to complete it. Since many of the questions have multiple solutions and students have to explain how they got their answers, you can have a rich whole group discussion at the end of the week (even with your kindergarten and 1st grade students).

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• Formative Assessments  – Give your students a problem to solve. Then use the Teacher Scoring Rubric to see how your kids are doing with each standard. Since they have to explain their thinking, this is a great way to catch any misconceptions and give feedback to individual students.

So this wraps up the top 5 ways that you can use problem solving tasks in your classroom.  Click your grade level below to get Solve and Explain problem solving tasks for your classroom.

• Read more about: K-5 Math Ideas

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10 Strategies for Problem Solving in Math

Created on May 19, 2022

Updated on January 6, 2024

When faced with problem-solving, children often get stuck. Word puzzles and math questions with an unknown variable, like x, usually confuse them. Therefore, this article discusses math strategies and how your students may use them since instructors often have to lead students through this problem-solving maze.

What Are Problem Solving Strategies in Math?

If you want to fix a problem, you need a solid plan. Math strategies for problem solving are ways of tackling math in a way that guarantees better outcomes. These strategies simplify math for kids so that less time is spent figuring out the problem. Both those new to mathematics and those more knowledgeable about the subject may benefit from these methods.

There are several methods to apply problem-solving procedures in math, and each strategy is different. While none of these methods failsafe, they may help your student become a better problem solver, particularly when paired with practice and examples. The more math problems kids tackle, the more math problem solving skills they acquire, and practice is the key.

Strategies for Problem-solving in Math

Even if a student is not a math wiz, a suitable solution to mathematical problems in math may help them discover answers. There is no one best method for helping students solve arithmetic problems, but the following ten approaches have shown to be very effective.

Understand the Problem

Understanding the nature of math problems is a prerequisite to solving them. They need to specify what kind of issue it is ( fraction problem , word problem, quadratic equation, etc.). Searching for keywords in the math problem, revisiting similar questions, or consulting the internet are all great ways to strengthen their grasp of the material. This step keeps the pupil on track.

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Guess and check.

One of the time-intensive strategies for resolving mathematical problems is the guess and check method. In this approach, students keep guessing until they get the answer right.

After assuming how to solve a math issue, students should reintroduce that assumption to check for correctness. While the approach may appear cumbersome, it is typically successful in revealing patterns in a child’s thought process.

Work It Out

Encourage pupils to record their thinking process as they go through a math problem. Since this technique requires an initial comprehension of the topic, it serves as a self-monitoring method for mathematics students. If they immediately start solving the problem, they risk making mistakes.

Students may keep track of their ideas and fix their math problems as they go along using this method. A youngster may still need you to explain their methods of solving the arithmetic questions on the extra page. This confirmation stage etches the steps they took to solve the problem in their minds.

Work Backwards

In mathematics, a fresh perspective is sometimes the key to a successful solution. Young people need to know that the ability to recreate math problems is valuable in many professional fields, including project management and engineering.

Students may better prepare for difficulties in real-world circumstances by using the “Work Backwards” technique. The end product may be used as a start-off point to identify the underlying issue.

In most cases, a visual representation of a math problem may help youngsters understand it better. Some of the most helpful math tactics for kids include having them play out the issue and picture how to solve it.

One way to visualize a workout is to use a blank piece of paper to draw a picture or make tally marks. Students might also use a marker and a whiteboard to draw as they demonstrate the technique before writing it down.

Find a Pattern

Kids who use pattern recognition techniques can better grasp math concepts and retain formulae. The most remarkable technique for problem solving in mathematics is to help students see patterns in math problems by instructing them how to extract and list relevant details. This method may be used by students when learning shapes and other topics that need repetition.

Students may use this strategy to spot patterns and fill in the blanks. Over time, this strategy will help kids answer math problems quickly.

When faced with a math word problem, it might be helpful to ask, “What are some possible solutions to this issue?” It encourages you to give the problem more thought, develop creative solutions, and prevent you from being stuck in a rut. So, tell the pupils to think about the math problems and not just go with the first solution that comes to mind.

Draw a Picture or Diagram

Drawing a picture of a math problem can help kids understand how to solve it, just like picturing it can help them see it. Shapes or numbers could be used to show the forms to keep things easy. Kids might learn how to use dots or letters to show the parts of a pattern or graph if you teach them.

Charts and graphs can be useful even when math isn’t involved. Kids can draw pictures of the ideas they read about to help them remember them after they’ve learned them. The plan for how to solve the mathematical problem will help kids understand what the problem is and how to solve it.

Trial and Error Method

The trial and error method may be one of the most common problem solving strategies for kids to figure out how to solve problems. But how well this strategy is used will determine how well it works. Students have a hard time figuring out math questions if they don’t have clear formulas or instructions.

They have a better chance of getting the correct answer, though, if they first make a list of possible answers based on rules they already know and then try each one. Don’t be too quick to tell kids they shouldn’t learn by making mistakes.

Review Answers with Peers

It’s fun to work on your math skills with friends by reviewing the answers to math questions together. If different students have different ideas about how to solve the same problem, get them to share their thoughts with the class.

During class time, kids’ ways of working might be compared. Then, students can make their points stronger by fixing these problems.

Check out the Printable Math Worksheets for Your Kids!

There are different ways to solve problems that can affect how fast and well students do on math tests. That’s why they need to learn the best ways to do things. If students follow the steps in this piece, they will have better experiences with solving math questions.

Jessica is a a seasoned math tutor with over a decade of experience in the field. With a BSc and Master’s degree in Mathematics, she enjoys nurturing math geniuses, regardless of their age, grade, and skills. Apart from tutoring, Jessica blogs at Brighterly. She also has experience in child psychology, homeschooling and curriculum consultation for schools and EdTech websites.

As adults, we take numbers for granted, but preschoolers and kindergartners have no idea what these symbols mean. Yet, we often demand instant understanding and flawless performance when we start teaching numbers to our children. If you don’t have a clue about how to teach numbers for kids, browse no more. You will get four […]

May 19, 2022

Teaching children is a complex process because they require more attention than an adult person. You may need to employ different teaching strategies when teaching kids. But what are teaching strategies? Teaching strategies are the methods to ensure your kids or students learn efficiently. But not all strategies yield similarly, and if the one you […]

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Maneuvering the Middle

Student-Centered Math Lessons

Math Problem Solving Strategies

How many times have you been teaching a concept that students are feeling confident in, only for them to completely shut down when faced with a word problem?  For me, the answer is too many to count.  Word problems require problem solving strategies. And more than anything, word problems require decoding, eliminating extra information, and opportunities for students to solve for something that the question is not asking for .  There are so many places for students to make errors! Let’s talk about some problem solving strategies that can help guide and encourage students!

1. C.U.B.E.S.

C.U.B.E.S stands for circle the important numbers, underline the question, box the words that are keywords, eliminate extra information, and solve by showing work.  

• Why I like it: Gives students a very specific ‘what to do.’
• Why I don’t like it: With all of the annotating of the problem, I’m not sure that students are actually reading the problem.  None of the steps emphasize reading the problem but maybe that is a given.

2. R.U.N.S.

R.U.N.S. stands for read the problem, underline the question, name the problem type, and write a strategy sentence. 

• Why I like it: Students are forced to think about what type of problem it is (factoring, division, etc) and then come up with a plan to solve it using a strategy sentence.  This is a great strategy to teach when you are tackling various types of problems.
• Why I don’t like it: Though I love the opportunity for students to write in math, writing a strategy statement for every problem can eat up a lot of time.

3. U.P.S. CHECK

U.P.S. Check stands for understand, plan, solve, and check.

• Why I like it: I love that there is a check step in this problem solving strategy.  Students having to defend the reasonableness of their answer is essential for students’ number sense.
• Why I don’t like it: It can be a little vague and doesn’t give concrete ‘what to dos.’ Checking that students completed the ‘understand’ step can be hard to see.

4. Maneuvering the Middle Strategy AKA K.N.O.W.S.

Here is the strategy that I adopted a few years ago.  It doesn’t have a name yet nor an acronym, (so can it even be considered a strategy…?)

UPDATE: IT DOES HAVE A NAME! Thanks to our lovely readers, Wendi and Natalie!

• Know: This will help students find the important information.
• Need to Know: This will force students to reread the question and write down what they are trying to solve for.
• Organize:   I think this would be a great place for teachers to emphasize drawing a model or picture.
• Work: Students show their calculations here.
• Solution: This is where students will ask themselves if the answer is reasonable and whether it answered the question.

Ideas for Promoting Showing Your Work

• White boards are a helpful resource that make (extra) writing engaging!
• Celebrating when students show their work. Create a bulletin board that says ***I showed my work*** with student exemplars.
• Take a picture that shows your expectation for how work should look and post it on the board like Marissa did here.

Show Work Digitally

Many teachers are facing how to have students show their work or their problem solving strategy when tasked with submitting work online. Platforms like Kami make this possible. Go Formative has a feature where students can use their mouse to “draw” their work. 

If you want to spend your energy teaching student problem solving instead of writing and finding math problems, look no further than our All Access membership . Click the button to learn more. 

Students who plan succeed at a higher rate than students who do not plan.   Do you have a go to problem solving strategy that you teach your students? 

Editor’s Note: Maneuvering the Middle has been publishing blog posts for nearly 8 years! This post was originally published in September of 2017. It has been revamped for relevancy and accuracy.

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Reader Interactions

18 comments.

October 4, 2017 at 7:55 pm

As a reading specialist, I love your strategy. It’s flexible, “portable” for any problem, and DOES get kids to read and understand the problem by 1) summarizing what they know and 2) asking a question for what they don’t yet know — two key comprehension strategies! How about: “Make a Plan for the Problem”? That’s the core of your rationale for using it, and I bet you’re already saying this all the time in class. Kids will get it even more because it’s a statement, not an acronym to remember. This is coming to my reading class tomorrow with word problems — thank you!

October 4, 2017 at 8:59 pm

Hi Nora! I have never thought about this as a reading strategy, genius! Please let me know how it goes. I would love to hear more!

December 15, 2017 at 7:57 am

Hi! I am a middle school teacher in New York state and my district is “gung ho” on CUBES. I completely agree with you that kids are not really reading the problem when using CUBES and only circling and boxing stuff then “doing something” with it without regard for whether or not they are doing the right thing (just a shot in the dark!). I have adopted what I call a “no fear word problems” procedure because several of my students told me they are scared of word problems and I thought, “let’s take the scary out of it then by figuring out how to dissect it and attack it! Our class strategy is nearly identical to your strategy:

1. Pre-Read the problem (do so at your normal reading speed just so you basically know what it says) 2. Active Read: Make a short list of: DK (what I Definitely Know), TK (what I Think I Know and should do), and WK (what I Want to Know– what is the question?) 3. Draw and Solve 4. State the answer in a complete sentence.

This procedure keep kids for “surfacely” reading and just trying something that doesn’t make sense with the context and implications of the word problem. I adapted some of it from Harvey Silver strategies (from Strategic Teacher) and incorporated the “Read-Draw-Write” component of the Eureka Math program. One thing that Harvey Silver says is, “Unlike other problems in math, word problems combine quantitative problem solving with inferential reading, and this combination can bring out the impulsive side in students.” (The Strategic Teacher, page 90, Silver, et al.; 2007). I found that CUBES perpetuates the impulsive side of middle school students, especially when the math seems particularly difficult. Math word problems are packed full of words and every word means something to about the intent and the mathematics in the problem, especially in middle school and high school. Reading has to be done both at the literal and inferential levels to actually correctly determine what needs to be done and execute the proper mathematics. So far this method is going really well with my students and they are experiencing higher levels of confidence and greater success in solving.

October 5, 2017 at 6:27 am

Hi! Another teacher and I came up with a strategy we call RUBY a few years ago. We modeled this very closely after close reading strategies that are language arts department was using, but tailored it to math. R-Read the problem (I tell kids to do this without a pencil in hand otherwise they are tempted to start underlining and circling before they read) U-Underline key words and circle important numbers B-Box the questions (I always have student’s box their answer so we figured this was a way for them to relate the question and answer) Y-You ask yourself: Did you answer the question? Does your answer make sense (mathematically)

I have anchor charts that we have made for classrooms and interactive notebooks if you would like them let me me know….

October 5, 2017 at 9:46 am

Great idea! Thanks so much for sharing with our readers!

October 8, 2017 at 6:51 pm

LOVE this idea! Will definitely use it this year! Thank you!

December 18, 2019 at 7:48 am

I would love an anchor chart for RUBY

October 15, 2017 at 11:05 am

I will definitely use this concept in my Pre-Algebra classes this year; I especially like the graphic organizer to help students organize their thought process in solving the problems too.

April 20, 2018 at 7:36 am

I love the process you’ve come up with, and think it definitely balances the benefits of simplicity and thoroughness. At the risk of sounding nitpicky, I want to point out that the examples you provide are all ‘processes’ rather than strategies. For the most part, they are all based on the Polya’s, the Hungarian mathematician, 4-step approach to problem solving (Understand/Plan/Solve/Reflect). It’s a process because it defines the steps we take to approach any word problem without getting into the specific mathematical ‘strategy’ we will use to solve it. Step 2 of the process is where they choose the best strategy (guess and check, draw a picture, make a table, etc) for the given problem. We should start by teaching the strategies one at a time by choosing problems that fit that strategy. Eventually, once they have added multiple strategies to their toolkit, we can present them with problems and let them choose the right strategy.

June 22, 2018 at 12:19 pm

That’s brilliant! Thank you for sharing!

May 31, 2018 at 12:15 pm

Mrs. Brack is setting up her second Christmas tree. Her tree consists of 30% red and 70% gold ornaments. If there are 40 red ornaments, then how many ornaments are on the tree? What is the answer to this question?

June 22, 2018 at 10:46 am

Whoops! I guess the answer would not result in a whole number (133.333…) Thanks for catching that error.

July 28, 2018 at 6:53 pm

I used to teach elementary math and now I run my own learning center, and we teach a lot of middle school math. The strategy you outlined sounds a little like the strategy I use, called KFCS (like the fast-food restaurant). K stands for “What do I know,” F stands for “What do I need to Find,” C stands for “Come up with a plan” [which includes 2 parts: the operation (+, -, x, and /) and the problem-solving strategy], and lastly, the S stands for “solve the problem” (which includes all the work that is involved in solving the problem and the answer statement). I find the same struggles with being consistent with modeling clearly all of the parts of the strategy as well, but I’ve found that the more the student practices the strategy, the more intrinsic it becomes for them; of course, it takes a lot more for those students who struggle with understanding word problems. I did create a worksheet to make it easier for the students to follow the steps as well. If you’d like a copy, please let me know, and I will be glad to send it.

February 3, 2019 at 3:56 pm

This is a supportive and encouraging site. Several of the comments and post are spot on! Especially, the “What I like/don’t like” comparisons.

March 7, 2019 at 6:59 am

Have you named your unnamed strategy yet? I’ve been using this strategy for years. I think you should call it K.N.O.W.S. K – Know N – Need OW – (Organise) Plan and Work S – Solution

September 2, 2019 at 11:18 am

Going off of your idea, Natalie, how about the following?

K now N eed to find out O rganize (a plan – may involve a picture, a graphic organizer…) W ork S ee if you’re right (does it make sense, is the math done correctly…)

I love the K & N steps…so much more tangible than just “Read” or even “Understand,” as I’ve been seeing is most common in the processes I’ve been researching. I like separating the “Work” and “See” steps. I feel like just “Solve” May lead to forgetting the checking step.

March 16, 2020 at 4:44 pm

I’m doing this one. Love it. Thank you!!

September 17, 2019 at 7:14 am

Hi, I wanted to tell you how amazing and kind you are to share with all of us. I especially like your word problem graphic organizer that you created yourself! I am adopting it this week. We have a meeting with all administrators to discuss algebra. I am going to share with all the people at the meeting.

I had filled out the paperwork for the number line. Is it supposed to go to my email address? Thank you again. I am going to read everything you ahve given to us. Have a wonderful Tuesday!

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How to Ace Math Problem Solving

When your kids struggle with their math, it’s time to take a step back and take a deep breath. They need to slow down and take their time. Here’s a step by step guide that will help your kids get through those tough math problems.

We’ll use a grade 3 addition word problem as an example to clarify:

Pinky the Pig bought 36 apples while Danny the Duck bought 73 apples and 14 bananas. How many apples do they have altogether?

Read the problem

Carefully read through the problem to make sure you understand what is being asked.

Pinky the pig and Danny the duck bought apples and bananas. The question is how many apples they have together.

Re-read the problem

Read through the problem again and as you read through it, make notes.

Pinky the pig –36 apples. Danny the duck –73 apples and 14 bananas. How many apples together?

What is the problem asking

In your own words, say or write down exactly what the question is asking you to solve.

The question is asking how many apples the pig and the duck bought together.

Write it down in detail

Go through the problem and write out the information in an organized fashion. A diagram or table might help.

Turn it into math

Figure out what math operation(s) or formula(s) you need to use in order to solve this problem.

The problem wants us to add the number of apples Pinky the Pig and Danny the Duck have together. That means we need to make use of addition to add the apples.

Find an example

Are you still struggling? Sometimes it’s hard to work out the solution, especially if the math problem involves several steps. It’s time to present the problem in an easier way. As teachers and parents we can often help our kids simplify the problem from our own math knowledge. If the problem is a bit harder, there are lots of resources online that you can look up for similar problems that have been worked out on paper or a video tutorial to watch.

In our example, let’s say the double-digit numbers are intimidating our student, so we’re going to simplify the equation for the sake of helping our student understand the operation needed.

Let’s say Pinky the Pig bought 3 apples and Danny the Duck 7 apples and 1 banana. Now, how many apples have they bought together? With 3 apples and 7 apples bought, the total number of apples is 10.

Work out the problem

Now that we have got to the bottom of what is being asked and know what operation to use, it’s time to work out the problem.

Pinky the Pig bought 36 apples. Danny the Duck bought 73 apples. (The 14 bananas do not matter) We need to add up the apples. 36 + 73 = 109

Check and review your answer

Check that your answer is correct. Always ask: does this answer make sense?  You can use estimation using mental math, for example.

Let’s round the numbers: 30 + 70 = 100. That is close to the exact number so it’s in the correct range.

The beauty of the basic operations is that addition and subtraction can be used to check answers too.

If we use the sum and take away one of the numbers, it should equal the other number.

109 – 73 = 36 109 – 36 = 73

If our student did not work out the sum correctly, we would not come to these sums.

(By the way, the same can be done with multiplication and division.)

Finally, go back and review the problem one last time. By going over the concepts, operations and formulas, it will help your kids to internalize the process and help them tackle harder math problems in the future.

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4 Math Word Problem Solving Strategies

5 Strategies to Learn to Solve Math Word Problems

A critical step in math fluency is the ability to solve math word problems. The funny thing about solving math word problems is that it isn’t just about math. Students need to have strong reading skills as well as the growth mindset needed for problem-solving. Strong problem solving skills need to be taught as well. In this article, let’s go over some strategies to help students improve their math problem solving skills when it comes to math word problems. These skills are great for students of all levels but especially important for students that struggle with math anxiety or students with animosity toward math.

Signs of Students Struggling with Math Word Problems

It is important to look at the root cause of what is causing the student to struggle with math problems. If you are in a tutoring situation, you can check your students reading level to see if that is contributing to the issue. You can also support the student in understanding math keywords and key phrases that they might need unpacked. Next, students might need to slow their thinking down and be taught to tackle the word problem bit by bit.

How to Help Students Solve Math Word Problems

Focus on math keywords and mathematical key phrases.

The first step in helping students with math word problems is focusing on keywords and phrases. For example, the words combined or increased by can mean addition. If you teach keywords and phrases they should watch out for students will gain the cues needed to go about solving a word problem. It might be a good idea to have them underline or highlight these words.

Cross out Extra Information

Along with highlighting important keywords students should also try to decipher the important from unimportant information. To help emphasize what is important in the problem, ask your students to cross out the unimportant distracting information.  This way, it will allow them to focus on what they can use to solve the problem.

Encourage Asking Questions

As you give them time to read, allow them to have time to ask questions on what they just read. Asking questions will help them understand what to focus on and what to ignore. Once they get through that, they can figure out the right math questions and add another item under their problem-solving strategies.

Draw the Problem

A fun way to help your students understand the problem is through letting them draw it on graph paper. For example, if a math problem asks a student to count the number of fruits that Farmer John has, ask them to draw each fruit while counting them. This is a great strategy for visual learners.

Check Back Once They Answer

Once they figured out the answer to the math problem, ask them to recheck their answer. Checking their answer is a good habit for learning and one that should be encouraged but students need to be taught how to check their answer. So the first step would be to review the word problem to make sure that they are solving the correct problem. Then to make sure that they set it up right. This is important because sometimes students will check their equation but will not reread the word problem and make sure that the equation is set up right. So always have them do this first! Once students believe that they have read and set up the correct equation, they should be taught to check their work and redo the problem, I also like to teach them to use the opposite to double check, for example if their equation is 2+3=5, I will show them how to take 5 which is the whole and check their work backwards 5-3 and that should equal 2. This is an important step and solidifies mathematical thinking in children.

Mnemonic Devices

Mnemonic devices are a great way to remember all of the types of math strategy in this post. The following are ones that I have heard of and wanted to share:

CUBES Word Problem Strategy

Cubes is a mnemonic to remember the following steps in solving math word problems:

C: Circle the numbers

U: Underline the question

B: Box in the key words

E: Eliminate the information

S: Solve the problem & show your work

RISE Word Problem Strategy

Rise is another way to explain the steps needed to solve problems:

R: Read and reread

I: Illustrate what is being asked

S: Solve by writing your equation or number sentences

E: Explain your thinking

COINS Word Problem Strategy

C: Comprehend the questions

O: Observe the data

I: Illustrate the problem

N: Write the number sentence (equation)

Understand -Plan – Solve – Check Word Problem Strategy

This is a simple step solution to show students the big picture. I think this along with one of the mnemonic devices helps students with better understanding of the approach.

Understand: What is the question asking? Do you understand all the words?

Plan: What would be a reasonable answer? In this stage students are formulating their approach to the word problem. 

Solve: What strategies will I use to solve this problem? Am I showing my thinking? Here students use the strategies outlined in this post to attack the problem.

Check: Students will ask themselves if they answered the question and if their answer makes sense. 

If you need word problems to use with your classroom, you can check out my word problems resource below.

Teaching students how to approach and solve math word problems is an important skill. Solving word problems is the closest math skill that resembles math in the real world. Encouraging students to slow their thinking, examine and analyze the word problem and encourage the habit of answer checking will give your students the learning skills that can be applied not only to math but to all learning. I also wrote a blog post on a specific type of math word problem called cognitively guided instruction you can read information on that too. It is just a different way that math problems are written and worth understanding to teach problem solving, click here to read .

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19 Best Math Problem-Solving Strategies for elementary students

• Author: Noreen Niazi
• Last Updated on: January 12, 2024

Do you know problem-solving strategies that help you to solve every hardest math problem? If you are finding such math problem-solving strategies, this article is for you. Let’s explore different strategies for solving math problems and enjoy teaching and learning mathematics.

What is Polya’s method for solving math problems?

George Polya is a mathematician who provides the basis for how to solve complex math problems. He writes different books on Math Problem-Solving Strategies. His book “ How to solve it ”  provides the foundation for every efficient problem-solving method in the Modern World.

Polya’s method for solving math problems involves four steps:

• Recognizing the issue,
• Making a plan,
• Executing the plan and
• Assessing the solution.

There are different specific math problem-solving strategies and techniques that you can use to solve the problem.

These include drawing diagrams, making a list or table, working backward, and looking for patterns.

Problem-Solving Strategies in Mathematics

Most students face the problem of problem-solving in math. Whether it’s a word problem or a simple math problem of finding the unknown, they all have unique problem-solving methods. So, math problem-solving strategies are the method and techniques to solve a math problem that leads to accurate answers.

There are numerous ways to find the solution, and methods depend upon the nature of the questions. Here we discuss the top 19 math problem-solving strategies that are helpful in every math question.

According to Polya’s method , we also divide our math problem solving strategies into four categories.

PART 1: Understanding the Problem

PART 2:  Devising a plan

PART 3: Carrying Out the Plan 

PART 4: Evaluating the Plan.

PART: 1 Understand the problem

Understanding is the key to the problem.  If you properly understand the problem,  you solve 50% of your problems. Keep the following question in your mind while working on your math problem-solving. 

• What are the keywords in the math problem?
• Ask students if they understand what is given and what they must find.
• Now check whether students can define the problem in their own words.
• Can students divide the problem into a mind map or pictorial form?
• What are the things that need to understand the problem?
• Encourage students to list down the relevant and irrelevant information from the question.
• Give time to students to read the problem. Once they read and understand it, they move on to the common math problem-solving strategies.

PART: 2 Devising a plan

Now it’s clear what the problem is and what we must find. Now move on to making a plan to solve the problem.  According to Polya’s method, here we discuss the top 14 strategies to devise a plan or problem-solving. You can choose anyone according to the problem’s nature and interest.

Be ingenious

Be ingenious and use your creativity to splash complex math problems. Encourage students to create new ideas for problem-solving and then choose the accurate one.

Consider special cases

Consider exceptional cases for your problem. Working on special issues simplifies the problem and helps solve it completely.

Eliminate possibilities

Convert your problem into a pictorial form and then solve each step individually. It helps you better understand the method and gives you the confidence to solve the problem.

Draw a picture

Divide your problem into different steps and solve it to find all the possible solutions. When there is a wrong answer, eliminate this possibility and move to other steps.

Guess and check

Guess the solution to the problem and then check it by putting it back into the equations.

Look for a pattern

Most of the tricky math questions have the same pattern. If you find a way to solve questions, you can solve the whole problem quickly.

Make an Orderly list

Making an orderly list of questions saves a lot of time and gives you a way to tackle the difficult task. Break down your job into a simple list and work on the final solution.

Solve a simpler problem.

Need help understanding the hard problem, start with a more straightforward problem. A simpler Problem makes a base in the method and creates interest in students. Moving from more superficial to harder is the best strategy for teaching math at the elementary level.

Solve an equation

Convert the problem into the form of an equation. It is easy to solve equations. When you solve the equation, you get the final solution to your problem.

Use a formula

Find the relative formula for your problem. Then put your given data into the procedure and calculate the answer.

Use a model

When a maths problem is represented visually, it usually becomes simpler for children, even if it initially seems complex. Some of the best math tactics for problem resolution involve having youngsters visualize and act out the arithmetic problem.

An alternative to visualization is to make tally marks or a picture on a working-out paper. You may also have students use a marker to doodle before writing down the answer as you demonstrate the procedure on the whiteboard.

o the procedure and calculate the answer.

Use direct reasoning

Direct reasoning, sometimes referred to as top-down or forward reasoning, starts with what you already know and uses that knowledge to attempt to solve the problem. This is frequently used when a lot of information is provided about the problem.

By segmenting the issue, you can begin to see how the many elements fit together and ultimately come up with a solution.

Use symmetry

Find the symmetry of the problem. Work or one part and another part will be solved automatically without long calculations.

Work backward

Working backward is also a powerful problem-solving strategy. In this, you know what the solution is. Take the key and then move back and create the original problem.

Working backward is helpful if pupils are required to identify an unknown number in a problem or mathematical language. If the equation is, for instance, 8 + x = 12, students can determine x by:

• beginning with 12
• subtracting eight from 12
• having four leftover
• Verifying that using 4 in place of x works

PART: 3 Carrying out the Plan

Now your plan is ready, move to the next step and use your problem-solving skills to execute the plan. Typically, this stage is more straightforward than creating the strategy.

 You only need care and patience because you have the essential abilities. Stick to the strategy you’ve picked. If it doesn’t stop failing, throw it away and choose another. Don’t be fooled; this is how maths is done, even by experts.

PART: 4 Evaluating the solution

Once you get the solution now, it is time to verify it. Cross-check your solution by answering the following questions.

• Take a look at the outcome.
• Please verify the outcome.
• Could you verify the argument?
• Can you come up with an alternate solution?
• Can you quickly recognize it?

If you can answer all the above questions, that shows you have selected the right math problem-solving strategies.

Some Practice problems of math problem-solving strategies.

Here are some examples of math problems that can be solved using these strategies for elementary students:

• Understand the Problem : If there are 10 apples and 5 are eaten, how many apples are left?
• Guess and Check: If a student has 10 pencils and gives away 3, how many pencils does the student have left?
• Work It Out : If a student has 10 apples and gives away 3, how many apples does the student have left?
•  Work Backwards : If a student has 10 apples and wants to give away 3, how many apples does the student need to start with
• Visualize : If a student has 10 apples and wants to give away 3, what does the picture look like?
• Find a Pattern : If a student has 10 apples and wants to give away 3, what is the pattern.
• Think: If a student has 10 apples and wants to give away 3, what is the easiest way to solve this problem
• Draw a Picture or Diagram: Draw a picture of a problem that involves adding two numbers together.

What are some examples of math problem-solving strategies?

Some examples of math problem-solving strategies include: guessing and checking, drawing a picture or diagram, making a table or chart, working backward, using logical reasoning, breaking the problem down into smaller parts, and looking for patterns or relationships.

How do you get better at solving problems?

There are numerous methods for enhancing problem-solving abilities. The following advice may be useful to you:

1. Clearly state the issue and your aim or purpose.

2. Compile as many facts regarding the issue as you can, then arrange it by rephrasing, compressing, or summarizing it.

3. Examine the data you’ve acquired, looking for significant relationships, trends, and links.

4. Generate a list of potential remedies for the issue.

5. Determine the viability and efficacy of each prospective option.

6. Decide on the best course of action and create a plan of action to carry it out.

7. Keep track of your development and modify your strategy as necessary.

Additionally, you can engage in brainstorming exercises like mind mapping, approach everyday situations with a “what if” mindset, routinely test new strategies, keep an idea journal in which you jot down all of your ideas, even the ones that seem implausible, play logic games and solve puzzles like sudoku or Wordle , and read trade publications that cover the most recent software and solutions to common problems.

Final Verdict:

You need multiple strategies to solve math word problems . Regardless of your methods, you will end up with an accurate answer. But most power math problem-solving strategies are drawing the picture and making models. And at the end, verify your answer by moving backward.

Do you want to explore more problem-solving strategies, go through the book , and find an accurate way to solve your problem?

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Word Problems Explained For Elementary School Teachers & Parents

Sophie Bartlett

Solving word problems in elementary school is an essential part of the math curriculum. Here are over 30 math word problems to practice with children, plus expert guidance on how to solve them.

This blog is part of our series of blogs designed for teachers, schools, and parents supporting home learning .

What is a word problem?

A word problem in math is a math question written as one sentence or more that requires children to apply their math knowledge to a ‘real-life’ scenario. 

This means that children must be familiar with the vocabulary associated with the mathematical symbols they are used to, in order to make sense of the word problem. 

For example:

Word Problems Grade 4 Number and Base 10

11 grade 4 number and base 10 questions to develop your students' reasoning and problem solving skills.

Isn’t brilliant arithmetic enough?

In short, no. Students need to build good reading comprehension, even in math. Overtime math problems become increasingly complex and require students to possess deep conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. 

As students progress through their mathematical education, they will need to be able to apply mathematical reasoning and develop mathematical arguments and proofs using math language. They will also need to be dynamic, applying their math knowledge to a variety of increasingly sophisticated problems. 

To support this schools are adopting a ‘mastery’ approach to math

“Teaching for mastery”, is defined with these components: 

• Math teaching for mastery rejects the idea that a large proportion of people ‘just can’t do math’.  
• All students are encouraged by the belief that by working hard at math they can succeed. 
• Procedural fluency and conceptual understanding are developed in tandem because each supports the development of the other. 
• Significant time is spent developing deep knowledge of the key ideas that are needed to support future learning. The structure and connections within the mathematics are emphasized, so that students develop deep learning that can be sustained.

(The Essence of Maths Teaching for Mastery, 2016)

Mastery helps children to explore math in greater depth

Fluency in arithmetic is important; however, with this often lies the common misconception that once a child has learned the number skills appropriate to their grade level/age, they should be progressed to the next grade level/age of number skills. 

The mastery approach encourages exploring the breadth and depth of these math concepts (once fluency is secure) through reasoning and problem solving. 

How to teach children to solve word problems? 

Here are two simple math strategies for problem solving that can be applied to many word problems before solving them.

• What do you already know?
• How can this problem be drawn/represented pictorially?

Let’s see how this can be applied to word problems to help achieve the answer.

Solving a simple word problem

There are 28 students in a class.

The teacher has 8 liters of orange juice.

She pours 225 milliliters of orange juice for every student.

How much orange juice is left over?

1. What do you already know?

• There are 1,000ml in 1 liter
• Pours = liquid leaving the bottle = subtraction
• For every = multiply
• Left over = requires subtraction at some point

2. How can this problem be drawn/represented pictorially?

The bar model , also known as strip diagram , is always a great way of representing problems. However, if you are not familiar with this, there are always other ways of drawing it out. 

Read more: What is a bar model

For example, for this question, you could draw 28 students (or stick man x 28) with ‘225 ml’ above each one and then a half-empty bottle with ‘8 liters’ marked at the top.

Now to put the math to work. This is a 5th grade multi-step problem, so we need to use what we already know and what we’ve drawn to break down the steps.

Solving a more complex, mixed word problem

Mara is in a bookshop.

She buys one book for $6.99 and another that costs $3.40 more than the first book.

She pays using a $20 bill.

What change does Mara get? (What is the remainder?)

• More than = add
• Using decimals means I will have to line up the decimal points correctly in calculations
• Change from money = subtract

See this example of bar modelling for this question:

Now to put the math to work using what we already know and what we’ve drawn to break down the steps.

Mara is in a bookshop. 

She buys one book for $6.99 and another that costs $3.40 more than the first book. 1) $6.99 + ($6.99 + $3.40) = $17.38

What change does Mara get? 2) $20 – $17.38 = $2.62

Math word problems for Kindergarten to Grade 5

The more children learn about math as they go through elementary school, the trickier the word problems they face will become.

Below you will find some information about the types of word problems your child will be coming up against on a year by year basis, and how word problems apply to each elementary grade. 

Word problems in kindergarten

Throughout kindergarten a child is likely to be introduced to word problems with the help of concrete resources (manipulatives, such as pieces of physical apparatus like coins, cards, counters or number lines) to help them understand the problem.

An example of a word problem for kindergarten would be

Chris has 3 red bounce balls and 2 green bounce balls. How many bounce balls does Chris have in all?

Word problems in 1st grade

First grade is a continuation of kindergarten when it comes to word problems, with children still using concrete resources to help them understand and visualize the problems they are working on

An example of a word problem for first grade would be:

A class of 10 children each have 5 pencils in their pencil cases. How many pencils are there in total?

Word problems in 2nd grade

In second grade, children will move away from using concrete resources when solving word problems, and move towards using written methods. Teachers will begin to demonstrate the adding and subtracting within 100, adding up to 4- two-digit numbers at a time.

This is also the year in which 2-step word problems will be introduced. This is a problem which requires two individual calculations to be completed.

2nd grade word problem: geometry properties of shape

Shaun is making shapes out of plastic straws.

At the vertices where the straws meet, he uses blobs of modeling clay to fix them together

Here are some of the shapes he makes:

One of Sean’s shapes is a triangle. Which is it? Explain your answer.

Answer: shape B as a triangle has 3 sides (straws) and 3 vertices, or angles (clay)

2nd grade word problem: statistics

2nd grade is collecting pebbles. This pictogram shows the different numbers of pebbles each group finds.

Word problems in 3rd grade

At this stage of their elementary school career, children should feel confident using the written method for addition and subtraction. They will begin multiplying and dividing within 100. 

This year children will be presented with a variety of problems, including 2-step problems and be expected to work out the appropriate method required to solve each one. 

3rd grade word problem: number and place value

My number has four digits and has a 7 in the hundreds place.

The digit which has the highest value in my number is 2.

The digit which has the lowest value in my number is 6.

My number has 3 fewer tens than hundreds.

What is my number?

Answer: 2,746

Word problems in 4th grade

One and two-step word problems continue in fourth grade, but this is also the year that children will be introduced to word problems containing decimals.

4th grade word problem: fractions and decimals

Stan, Frank and John are washing their cars outside their houses.

Stan has washed 0.5 of his car.

Frank has washed 1/5 of his car.

Norm has washed 2/5 of his car.

Who has washed the most?

Explain your answer.

Answer: Stan (he has washed 0.5 whereas Frank has only washed 0.2 and Norm 0.4)

Word problems in 5th grade

In fifth grade children move on from 2-step word problems to multi-step word problems . These will include fractions and decimals.

Here are some examples of the types of math word problems in fifth grade will have to solve.

5th grade word problem: ratio and proportion

The Angel of the North is a large statue in England. It is 20 meters tall and 54 meters wide. 

Ally makes a scale model of the Angel of the North. Her model is 40 centimeters tall. How wide is her model?

Answer: 108cm

5th grade word problem: algebra

Amina is making designs with two different shapes.

She gives each shape a value.

Calculate the value of each shape.

Answer: 36 (hexagon) and 25. 

5th grade word problem: measurement

Answer: 1.7 liters or 1,700ml

Topic based word problems

The following examples give you an idea of the kinds of math word problems your child will encounter in elementary school

4th grade word problem: place value

This machine subtracts one hundredth each time the button is pressed. The starting number is 8.43. What number will the machine show if the button is pressed six times? Answer: 8.37

Download free number and place value word problems for grades 2, 3, 4 and 5

2nd grade word problem: addition and subtraction

Sam has 64 sweets. He gets given 12 more. He then gives 22 away. How many sweets is he left with? Answer: 54

Download free addition and subtraction word problems for for grades 2, 3, 4 and 5

2nd grade word problem: addition

Sammy thinks of a number. He subtracts 70. His new number is 12. What was the number Sammy thought of? Answer: 82

5th grade word problem: subtraction

The temperature at 7pm was 4oC. By midnight, it had dropped by 9 degrees. What was the temperature at midnight? Answer: -5oC

3rd grade word problem: multiplication

Eggs are sold in boxes of 12. The egg boxes are delivered to stores in crates. Each crate holds 9 boxes. How many eggs are in a crate? Answer: 108

Download free multiplication word problems for grades 2, 3, 4 and 5. 

5th grade word problem: division

A factory produces 3,572 paint brushes every day. They are packaged into boxes of 19. How many boxes does the factory produce every day? Answer: 188

Download free division word problems for grades 2, 3, 4 and 5. 

Free resource: Use these four operations word problems to practice addition, subtraction, multiplication and division all together.

4th grade word problem: fractions

At the end of every day, a chocolate factory has 1 and 2/6 boxes of chocolates left over. How many boxes of chocolates are left over by the end of a week? Answer: 9 and 2/6 or 9 and 1/3

Download free fractions and decimals word problems for grades 2, 3, 4 and 5. 

2nd grade word problem: money

Lucy and Noor found some money on the playground at recess. Lucy found 2 dimes and 1 penny, and Noor found 2 quarters and a dime. How many cents did Lucy and Noor find? Answer: Lucy = $0.21, Noor = $0.60; $0.21 + $0.61 = $0.81

3rd grade word problem: area

A rectangle measures 6cm by 5cm.

What is its area? Answer: 30cm2

3rd grade word problem: perimeter

The swimming pool at the Sunshine Inn hotel is 20m long and 7m wide. Mary swims around the edge of the pool twice. How many meters has she swum? Answer: 108m

5th grade word problem: ratio (crossover with measurement)

A local council has spent the day painting double yellow lines. They use 1 pot of yellow paint for every 100m of road they paint. How many pots of paint will they need to paint a 2km stretch of road? Answer: 20 pots

5th grade word problem: PEMDAS

Draw a pair of parentheses in one of these calculations so that they make two different answers. What are the answers?

50 – 10 × 5 =

5th grade word problem: volume

This large cuboid has been made by stacking shipping containers on a boat. Each individual shipping container has a length of 6m, a width of 4m and a height of 3m. What is the volume of the large cuboid? Answer: 864m3

Remember: The word problems can change but the math won’t 

It can be easy for children to get overwhelmed when they first come across word problems, but it is important that you remind them that while the context of the problem may be presented in a different way, the math behind it remains the same. 

Word problems are a good way to bring math into the real world and make math more relevant for your child. So help them practice, or even ask them to turn the tables and make up some word problems for you to solve. 

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

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44 Powerful Problem Solving Activities for Kids

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Inside: Tons of activities that will help boost kids’ problem-solving skills and make them super critical thinkers!

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Who doesn’t love a little challenge now and then? Especially if it’s for our kiddos! 

You see, problem-solving isn’t just for the puzzles and math sheets. It’s the magic stuff that shapes our little ones into big thinkers and doers. 

Yep, it’s pretty important!

With the right activities, we aren’t just sharpening kids’ brain muscles; we’re also enhancing their creativity, boosting their confidence and critical thinking skills, and (just maybe) buying ourselves five minutes to sip that coffee while it’s still hot. 

Stick around, and let’s dive into 44 simple activities to boost your child’s problem-solving skills while having a blast! 🚀💡

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Because we all want our kids to be happy and healthy — not just for right now, but for the rest of their lives.

Why is it Important to Learn Problem-Solving Strategies?

Importance of problem-solving abilities:

Navigating the maze of life requires many skills; it requires the ability to face challenges, find solutions, and adapt. 

This is where problem-solving enters the picture, and here’s why it’s so crucial for our kiddos:

Life is Full of Puzzles:  From tying shoes to understanding a new math concept, life constantly presents us with puzzles. Equipping our children with problem-solving skills ensures they can tackle each one confidently.

Boosts Independence:  As parents or educators, we won’t always be there to hand-hold. When kids can solve problems on their own, they gain a sense of independence, which is essential for their personal growth.

Develops Resilience:  Not every attempt to solve a problem will be successful. But with each try, children learn resilience, understanding that it’s okay to fail and important to try again.

Prepares for Real-World Challenges:  The real world isn’t a scripted playground. It’s unpredictable. By honing their problem-solving abilities, we’re preparing kids to face the unforeseen challenges of the world outside.

Enhances Cognitive Growth:  Otherwise known as cognitive development. Problem-solving isn’t just about finding solutions. It’s about thinking critically, analyzing situations, and making decisions. This cognitive workout helps in the overall brain development of our children.

Fosters Creativity:  There’s often more than one way to solve a problem. Encouraging kids to think outside the box helps them see things from different perspectives and nurtures their creative spirit, letting them see possibilities where others might see roadblocks.

Encourages Adaptability:  In the face of challenges, it’s important not just to find solutions but to be adaptable. As the world changes, kids with strong problem-solving skills can change with it, learning and growing along the way.

Builds Confidence :  Every problem solved is a victory, a testament to their capabilities. This builds a child’s self-esteem, making them believe in their ability to face and overcome obstacles.

So, while it may seem like just another skill on the list, problem-solving is a cornerstone for a well-rounded, resilient, and successful individual.

4 Simple Problem-Solving Steps We Should Know at a Young Age

Problem-solving steps can be thought of as the building blocks for tackling challenges. 

They’re like a set of instructions that  guide us  on our journey to finding different solutions. These steps provide a  roadmap  for kids, helping them break down big problems into smaller, more manageable pieces. 

By following these steps, children can learn  how  to think critically, make smart decisions, and even discover their own creative problem-solving superpowers. 

• First, we need to understand the problem, just like examining the pieces before we start building. 
• Next, we brainstorm – this is where we think of different solutions, like trying out various block combinations. Then comes the important part – evaluating the options. We must determine the best solution ,  just like choosing the right blocks for our structure. 
• After that, it’s time to put the plan into action, just like assembling the blocks to create something amazing. 
• Finally, we review and see if our solution works, making adjustments if needed. 

These problem-solving steps are like our trusty toolkit, helping us build our way to success with creativity and ingenuity.

Whether it’s figuring out a math puzzle, resolving a conflict with a friend, or coming up with a new game, these problem-solving steps will be a guide to helping kids take their next steps.

Featured resource

HeartSmart Social Emotional Curriculum

If you want a program that guides you on how to teach problem-solving along with other essential skills like self-regulation, respect, teamwork, conflict resolution, and more, check this out!

Best Problem-Solving Activities for Kids

In this guide, we have a cool mix of fun problem-solving activities. There are activities for inside, outside, playing in groups, and even on the computer! So take deep breaths, and let’s get to it!

44 Problem-Solving Activities for Kids

Problem-solving games for kids:, card games:.

These are more than just fun; they are brain boosters. In  Go Fish , the hunt for matching cards sharpens memory. While in the classic game  Uno , it’s all about plotting the right move to take the lead.

The Memory Game:

This game isn’t just about remembering; it’s about strategizing. Matching pairs means we’re not just recalling but also paying close attention. This boosts concentration, focus, and, of course, memory – essential skills for everyday challenges!

Try this animal matching memory game.

Classic  Board Games:

Whether it’s Chess , where every move counts, or  Monopoly ,  where every decision can make or break your game, these games teach foresight and strategy.

Maze Games :

Navigating a maze isn’t just about reaching the end; it’s about strategizing the route. These games enhance our ability to plan and foresee, invaluable skills in real-life situations.

Brain-Teasing Sudoku :

Sudoku   isn’t merely filling in numbers; it’s about using logic to deduce the correct sequence.

Tangram Puzzles: 

These aren’t your average puzzles. With Tangram, you shape a story, crafting images using geometric pieces.

Chess & Strategy-Based Games:

Think of these as mental workouts. Here, every step is a calculated decision, honing your ability to think multiple steps ahead.

For more fun:

• 20 Best Games for 4-Year-Olds
• 15 Board Games Every 9-Year-Old Will Love

Indoor Problem-Solving Activities for Kids

Complete simple tasks:.

Simple tasks are little jobs that you can do to practice problem-solving. 

• Matching Socks:  Sort through a pile of laundry to pair up matching socks.
• Grocery List Planning:  Help create a list for the week’s meals, considering everyone’s preferences.
• Toy Organization:  Sort toys into designated bins by type, size, or color.
• Packing Their School Bag:  Ensure they have all the necessary items for the next school day.
• Setting the Table:  Consider where each plate, fork, and glass should go.

Ask Open-Ended Questions:

Open-ended questions are special questions that don’t have just one answer. They make you think! For instance, instead of asking, “What color is the sky?” you might ask, “Why do you think the sky changes colors?”

Puzzle Games:

Try simple puzzles with fewer pieces for younger kids and more complex puzzles with more pieces for older kids! You figure out how to fit the pieces together, which helps your brain get stronger!

Puzzle games are also great for hand-eye coordination!

Pattern Recognition:

This is all about finding the special patterns in things. Imagine a puzzle with colors or shapes. You have to figure out the pattern to solve it.

Dress-Up and Role-Play:

When you dress up and pretend to be someone else, it’s like stepping into their shoes. You have to think about how they would act and problem-solve what they would say if you were them.

Shape Sorters:

Shape sorters  are super fun for young kids. You have to match each shape to the right hole. It’s like a puzzle for shapes! This helps you learn about different shapes and how they fit together.

Building Challenges:

Use Wooden blocks or legos and give kids a theme or structure to replicate. Great for all age groups!

Cooking or Baking:

Cooking and baking are like yummy science experiments! You follow recipes, mix ingredients, and even get to taste your creations. You must figure out how to follow and “solve” the recipe so that your creation tastes delicious!

“What If?” Scenarios:

Present hypothetical situations (e.g., “What if you were invisible for a day?”) and discuss possible solutions or actions.

Homemade Science Experiments:

Homemade science experiments are like being a scientist in your own lab! You get to try out cool experiments and discover how things work. 

Quick Experiment example:

Make Dancing Raisins:

• Clear soda (like Sprite or 7-Up)
• A clear glass
• Fill the glass with the soda.
• Drop a few raisins into the glass.

Result:  The raisins will initially sink, then start “dancing” up and down due to the carbon dioxide bubbles attaching and detaching from them.

Coding Activities: 

Coding is like giving a computer a set of clues to follow. Think of it as telling a story where the computer plays the main character, and your instructions guide its every move. It’s our way of communicating with machines to make them do amazing tasks!

Crossword Puzzles:

Crossword puzzles are fun little word challenges. You must fill in the blanks with the right words and use your smarts to solve tricky clues!

Complex Problems like Brain Teasers:

Brain teasers are like mental gymnastics, making you stretch and flex your thinking muscles. What’s fun about them? There’s often more than one way to reach an answer, so your imagination and logic both get a workout!

Goal Setting Activities:

Goal setting  is like making a special plan for what you want to achieve. 

Think of goal setting as charting out your very own treasure map, with no wrong answers! 

By laying out what you aim to achieve, you’re setting the course toward your treasure: success!

Goals, be they immediate or down the road, act like our personal compasses. They keep you on track and motivated. And every time you hit a goal? That’s you cracking a code and unlocking a new achievement in your adventure!

Setting SMART Goals

This engaging kit focuses on teaching essential skills for setting and  achieving smart goals,  just like breaking down that LEGO set into manageable sections. We help kids understand the importance of clear objectives, staying motivated, overcoming obstacles, embracing adaptability and more.

Math Challenges:

Think of math challenges as your brain’s personal gym session. These aren’t just any puzzles; they’re crafted to push those thinking caps to the limit. 

Debates (Best for older children):

Debates are friendly arguments where you defend your ideas with strong reasons. They’re excellent for problem-solving and for our social skills because they teach us how to think critically and consider different viewpoints. By defending our thoughts in a debate, we learn how to express ourselves clearly, listen to others, and find strong arguments to support our ideas!

Use Worksheets (Teach the Size of the Problem Concepts)

Teach concepts like the size of the problem to help kids determine if their reactions to problems are appropriate and what suitable solutions might be. Use fun visuals and problem-solving worksheets.

You can get this worksheet and more in our HeartSmart curriculum.

STEM Challenges: 

STEM challenges are games that use science, technology, engineering, and math to solve problems. They’re awesome for problem-solving because they let us be like inventors and builders. Kids can engage in creative play and design and create things, like bridges or machines, using our smarts and creativity. 

Outdoor Problem-Solving Activities for Kids

Nature scavenger hunt or treasure hunt: .

Create a list of natural items for kids to find. For added difficulty, give riddles as clues.

We have some awesome free Scavenger Hunt Bundles you can snag!

Free Scavenger Hunt Bundle

Download this set now, which includes four unique scavenger hunt games

Outdoor Obstacle Course: 

Use items like ropes, cones, and hula hoops to design a course that requires navigation.

Garden Planning & Planting :

Design a garden patch, deciding what to plant based on sunlight and spacing needs.

Map & Compass Orienteering:

Teach kids to use a map and compass, then set waypoints for them to find.

Water Relay Challenges:

Carry water from one bucket to another using a sponge or cup, navigating hurdles.

Campsite Setup Simulation Challenge:

Set up a mock campsite considering factors like wind direction, incline, and resource proximity.

Nature Art & Patterns:

Using twigs, leaves, stones, and more, create mosaic patterns or depictions.

Group Problem-Solving Activities for Kids

Tower of spaghetti:.

Using only spaghetti and marshmallows, groups compete to build the tallest stable tower.

Egg Drop Challenge:

Groups are provided with a set of materials (e.g., straws, tape, cotton) to create a protective casing for an egg, which is then dropped from a height.

Silent Line-Up:

Without speaking, kids must line up according to their birthdays or another criterion.

Group Story Time:

One child starts a story with a sentence or two, and each subsequent child adds on, weaving in unexpected twists and turns.

The Human Knot:

Kids stand in a circle, reach across, and grasp two different hands. The challenge is to untangle the knot without releasing hands.

Escape Room:

Everyone is ‘locked’ in a themed room and has to solve a series of clues and puzzles to ‘escape’ within a set time. It’s fantastic for problem-solving because it challenges critical thinking, teamwork, and creativity. Everyone must work together, think outside the box, and use their wits to solve the puzzles and complete the mission before time runs out!

Role-Playing Social Situations:

Role-playing helps you practice how to react and solve problems in different situations. Present the group with a fictional but realistic scenario (e.g., stranded on an island) and brainstorm and act out solutions.

By pretending to be in different roles, you can figure out the best ways to communicate, understand others, and find solutions to problems in a safe and fun way!

Blindfolded Obstacle Course:

In pairs, one blindfolded child is guided through an obstacle course by their partner using only verbal instructions.

Online and App-Based Problem Solving Activities

When tech meets intellect, the digital realm becomes a treasure trove of problem-solving wonder!

Educational Apps:

Best Apps by Age:

• Younger Kids : Dive into the mathematical world with “Moose Math” or kick-start programming concepts playfully with “Bee-Bot.”
• Older Kids: Amp up programming skills with “Cargo-Bot” or embark on a critical thinking journey with “Rush: A Disney Pixar Adventure.”

Online Escape Rooms:

Just like physical escape rooms, but from the comfort of your home! They’re digital adventures, demanding clues to be solved to advance to the next level.

Check out these 10 Family Friendly Online Escape rooms here! I’m especially looking forward to Hogwarts Harry Potter Escape Room .

Virtual Logic Puzzles:

Websites that present logic problems and puzzles, leveling up in complexity as kids solve them.

Top Picks:  “Conceptis Puzzles,” “Math Playground Logic Games.”

Benefits: Perfect for sharpening deductive reasoning and pattern recognition.

Interactive E-Books:

These are not your everyday e-books. They demand interaction, choices, and decision-making to progress the story.

Suggestions:  “This Book is Perfect” or I love this big list of the best interactive books for kids.

Benefits: Enhance comprehension, decision-making, and experience of how choices shape outcomes.

Online Strategy Games:

These games demand planning, strategic thinking, and foresight.

Check out: “Fish Sticks Strategy Game”

Benefits: Apart from being immensely fun, they teach patience, strategy formulation, and long-term planning.

10 Examples of Problem-Solving Skills Young Children Should Have

Each of these skills not only helps kids tackle problems effectively but also equips them with abilities they’ll use throughout their lives.

• Critical Thinking:  Encourage young thinkers to examine situations, ask questions, and view things from different angles before reaching a conclusion.
• Decision-Making Skills:  Help children practice making choices by offering them options and discussing the potential outcomes of each decision.
• Creative Thinking:  Cultivate creativity by providing opportunities for imaginative play, artistic expression, and activities that encourage thinking outside the box.
• Communication Skills:  Show children how to express their thoughts,  feelings , and ideas clearly and effectively – a vital skill for problem-solving in social situations.
• Teamwork and Collaboration:  Foster the spirit of cooperation by encouraging children to work together on group activities or projects, which helps develop problem-solving skills as a team.
• Resourcefulness:  Challenge children to find alternative solutions using the available resources rather than relying solely on adult guidance.
• Flexibility and Adaptability:  Teach children how to adapt to changes and unexpected situations, which is crucial for effective problem-solving in real-world scenarios.
• Persistence:  Staying determined, even when faced with challenges, and continuing to try until a solution is found.
• Self-reflection:  Recognizing one’s own mistakes or misunderstandings in a situation and learning from them for future problem-solving.
• Active Listening:  Paying close attention to details when others speak, helping them understand problems more fully and respond effectively. 

Must read post:

How to Help Kids with Inflexible Thinking THRIVE

Tips for Parents and Educators: Nurturing Problem-Solving in Kids

When it comes to fostering problem-solving skills in children, both parents and educators play pivotal roles. It’s less about giving the right answers and more about asking the right questions. 

Encourage Curiosity.  Let kids explore questions like, “What do you think would happen if…?” or “How would you do it differently next time?”.

Embracing mistakes as learning opportunities can be a game-changer.

Set Up Scenarios.  Create environments or situations where kids can think and act independently. Whether it’s setting up a puzzle station at home or a role-play corner in the classroom, these controlled scenarios can stimulate their problem-solving faculties. Remember, it’s okay for them to struggle a bit. It’s through overcoming challenges that real learning occurs.

Lastly,  Be a Guide, Not a Director.  Instead of directing them step-by-step, guide them by providing hints or asking probing questions. This helps them develop the ability to analyze situations and think critically. As they grow, they’ll be more equipped to approach challenges with confidence and creativity. 

So, whether you’re a parent or an educator, remember that each day presents countless opportunities to bolster these invaluable skills. Embrace them!

Final Thoughts: Problem Solving Activities for Kids

Being a pro at problem-solving helps us face all types of curveballs life throws at us.

From untangling math puzzles to making big decisions, this skill is our trusty sidekick. And when life changes? No sweat! We can adapt and shine.

In short, mastering problem-solving helps us face challenges, make wise choices, and truly succeed in whatever we tackle!

I hope you enjoyed these problem-solving activities for kids. Tell me, what one is your favorite?

Because we all want our kids to be happy and healthy — not just for right now, but for the rest of their lives.

Tina Williamson is the published author of the growth mindset activity journal for kids - “ Amazing Me ” and the writer and founder here at Mindfulmazing. Passionate about raising mindful, resilient, and compassionate kids we are committed to sharing calming strategies, positive parenting tips, and growth mindset resources. Our resources are now used in over 10,000 homes, schools and counseling offices! Visit the shop here.  

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Best iPad Math Notes Like Calculator Apps for Android

Ipados math notes calculator's feature is an old trick in android's book.

The recently concluded Apple’s WWDC 2024 event grabbed eyeballs worldwide. While iOS 18 has been the talk of the town with features like the ability to move app icons anywhere on the iPhone’s home screen, the ability to apply light/dark or tint to the app icons, the fully customizable Control Center, the option to change the focus of the flashlight , etc., one app also managed to grab headlines, called the Calculator app introduced for iPadOS 18.

However, the newly introduced iPad Calculator app isn’t just any other calculator app. The Math Notes is the main highlighting feature of the iPadOS 18 Calculator app, which auto-completes the calculation as soon as you write the equals sign after your equation. In this guide, we will show you the best iPad Math Notes calculator alternatives for Android. Of course, if it’s there for iOS, Android users may want it for themselves. Let’s jump right into it.

Table of Contents

What’s so good about the iPad Calculator?

So, iPads debuted back in 2010, and ever since their debut, they have been calculator-less. Thankfully, the iPadOS 18 update, announced at WWDC 2024 , added the Calculator app, and not just a simple calculation app; it does more than that. The iPad Calculator app has an interface similar to that of calculator apps across Apple platforms.

The app boasts round buttons in black and orange and features an improved unit conversion system, a history tape sidebar, and the most talked about Math Notes feature. The iPad Math Notes feature can be accessed from the Calculator app by using the dedicated button in the bottom left corner of the app screen.

Once you are in, simply write the equation, and as soon as you write equals to the (=) sign, the iPad Math Notes feature will automatically solve the problem for you. The iPad Math Notes feature in the Calculator app supports graphical expressions and gets answers by inputting various values into variables. The Math Notes are automatically stored in the new Math Notes folder.

If you loved the new iPad Math Notes and other features of the Calculator app for the iPad, let us take a look at the iPad Math Notes calculator app’s Android alternatives that offer a similar experience.

4 Best iPad Math Notes Calculator App Alternatives for Android

Microsoft Maths Solver – Offers step-by-step explanation

One of the best, or it is safe to say, advanced calculator apps that can easily be a great alternative to the iPadOS 18’s Calculator app is Microsoft Maths Solver. The app offers various similar features to the iPad Math Notes feature. You can easily handwrite your math problem or equations on the screen by tapping Send, and then the Microsoft Maths Solver will automatically solve the problem for you.

It can solve a variety of math problems, including arithmetic, algebra, trigonometry, calculus, statistics, and other topics, and makes use of AI to provide you with solutions. One of the best features of this app that I liked was the option to “Scan and Solve.” Notably, the feature lets you scan a math problem using your device’s camera to snap a photo and helps you solve it with step-by-step instructions. The feature also provides interactive graphs for a proper explanation.

The Microsoft Math Solver comes with support for advanced scientific math calculators, scanning and solving math problems in multiple worksheets, searching the web for similar problems or video lectures, supporting linear and non-linear functions, and also the ability to solve math problems in your language, including Chinese, French, German, Hindi, Italian, Japanese, Portuguese, Russian, Spanish, and many more.

• It supports advanced math problems, including elementary, pre-algebra, basic calculus, statistics, and more.
• Gives answers in multiple languages
• Support for linear/non-linear functions
• Lets you scan and solve a math problem
• The step-by-step solutions provided are not in real-time

Download Microsoft Math Solver

MyScript Calculator 2 – Solves multi-step problems quickly

Another popular iPad Math Notes Calculator alternative for Android is the MyScript Calculator 2. It is a paid app, but it is very close to how the iPad’s calculator app works. When you open the app, it turns into a virtual paper, where all you need to do is write down your equation and get the answers in real-time.

You can easily scratch and rewrite the correct equation as you would on an actual piece of paper. You can write down equations and problems, extending to several lines. One of the best parts about the MyScript Calculator 2 is that you can mix calculations, i.e., your equations or problems can include multiplication, division, subtraction, etc.

It also supports dragging and dropping numbers and equations; multi-step problems can be rearranged, and you can choose how your answers are displayed: as decimals, fractions, or mixed numbers. The app supports problem-solving related to logs, Trigonometry, inverse trigonometry, power, roots, exponentials, and much more.

• Lets you write or scratch equations or numbers on the screen
• Provides instant solutions to your problems
• Support solving complex multi-step calculations
• Keeps your calculation history
• Doesn’t support graphs
• There is no option for variables

Download MyScript Calculator 2

Maple Calculator – Visualize your problems and solutions in 2D and 3D

The Maple Calculator is an all-in-one calculator app that can help you visualize your problems and solutions in 2D and 3D. This app goes beyond being a simple calculator that solves your equations. You can write your equations on the screen, and the app, using the world’s most powerful math engine, Maple, will recognize your handwriting and give you step-by-step solutions.

The app provides 2D and 3D graphs just like iPad Math Notes, and you can see the graph change as the expressions are changed in real-time. You can also take a picture of your problem and upload it to the Maple Calculator to see the final answer or get a step-by-step solution.

It supports multiple languages and helps solve complex math disciplines such as algebra, calculus, trigonometry, linear algebra, differential equations, etc.

• Lets you visualize your problems and solutions in 2D and 3D
• Gives you step-by-step solutions to your written problems or captured problems
• Support complex math disciplines to be solved
• Step-by-step solutions may not be generated for most of the questions

Download Maple Calculator

Photomath – Google’s answer to Apple

Photomath from Google lets you scan any problem using the camera on your phone. The solutions are teacher-approved, and Photomath breaks your problem into step-by-step explanations to help you understand the solution better. Photomath supports solving problems from elementary arithmetic to advanced geometry, even to advanced calculus.

This calculator app can help you solve any handwritten or textbook-based problems. The animated steps negate the need for guessing to understand how the solution was achieved. There is a 24/7 virtual tutor as well, whom you can reach and get solutions to your questions. The app can even solve word problems and offer solutions in graphs. The app offers multiple solutions for a problem as well.

Google has included step-by-step explanations in the free version itself, and you can ask questions from various math disciplines, including numbers and quantity, algebra, functions, trigonometry and angles, sequences, geometry, and calculus. The app also explains the formulas and equations that have been applied to solve the problem with proper definitions.

• Lets you solve equations and word problems
• Animated step-by-step answers, even in the free version
• Interactive graphs and video learning
• Supports solving advanced math problems
• Scanning of problems may not always be accurate

Download Photomath

Make your Android do the math

The above apps are some of the best iPad Calculator app alternatives for Android that have features similar to Math Notes. Some of them even have more features than the iPad’s calculator app. If you are a Motorola user, then here’s a bonus tip: you can use the Handwriting Calculator app. It was introduced for the Moto G Stylus phone, but you can grab the APK from APKMirror and install it on any Motorola phone. You need to install it and create a home screen shortcut using the Activity Launcher app, and that’s it.

Since iPadOS 18 is expected to roll out to the public this fall, you can take a look at some of the best iPad calculator apps for the time being.