how to teach problem solving to 1st graders

• Member Home
• My Bookmarks

Visual Models for Problem Solving in 1st Grade

May 10, 2020

As students enter 1st grade, they continue to work on math comprehension using early structures, like the Kindergarten journal we introduced last week, but now we begin to add visual models to the mix!

Let’s recap a child’s developmental journey through problem solving:

• In the early childhood years, a child needs lots of developmentally appropriate experience interacting with real objects in a physical world . 
• The physical world is captured in a quantitative picture , which young children observe and use as a springboard for mathematical conversations.
• We transition into a more structured math work mat to help young students be able to connect numbers to words and words to numbers, still using familiar situations from real life.
• The math work mat gives way to a formal math journal in Kindergarten that makes use of math comprehension skills. It provides a structure for students to explain their understanding of numbers within real world situations that will carry on throughout elementary school. 

Each of the stages of development builds on the skills developed in the previous step, so it is important that students aren’t rushed through these stages. The goal is to teach students the why behind the how so they aren’t just memorizing procedures but truly understand what is happening as they solve problems.

This 1st grade year is the last stage in the Math4Littles progression , in my opinion. After this, there isn’t much scaffolding, so we really want to carefully implement all the previous stages of problem solving before we turn the students loose, because we don’t want them to start guessing and checking. In taking students on this developmental journey, we are trying to build them a solid foundation for visual models to help them to understand problem solving. 

How We Used to Teach Problem Solving

When I was teaching 1st grade, I remember a strategy that we used for problem solving called the C.U.B.S. method. Each of those letters stood for a step in the problem solving process so students could remember what to do: C – circle the numbers, U – underline the word, B – box the operation, S – solve the problem. Seems like a simple process that gives kids a really great structure to start to understand what words problems are asking, right? But what I realized is that this strategy doesn’t hold up long term.

“Shannon has 5 lollipop and Scott has 4 more lollipops than Shannon. How many do they have all together?” 

I watched students follow that procedure with this type of problem. They circled the 4 and 5, underlined important information and put a box around the words all together , which means add because we’ve all seen the T-charts of addition/subtraction vocabulary – it says difference , it means we’re going to subtract, if you see all together , we’re going to add. But that strategy gives me 4, 5, and all together . If you go back to the question, you’ll realize the answer isn’t 9.

As I often do, I asked myself why ? Why isn’t it 9? A little more reading comprehension is required to decode that answer. The problem says I had 5 lollipops. Scott had 4 more than me, which means he also had 5. Adding that up, he had 9 and I had 5, so there were 14 all together.  

Why are we teaching kids procedures with concepts they don’t understand? Sometimes the strategies that we teach in math are conditional, meaning they only work for a certain amount of kids or a certain length of time. Then you have to worry about teaching them when to apply it and the rules for applying it, and what was meant to make things easier for students ends up being more complicated.

When we start working with strategies, I want to be able to find that vertical zip, meaning if I show you how this strategy might work in first grade, it has to work as the child gets older too so that they don’t have to learn a whole new set of strategies every year because every teacher teaches it differently. Honestly, the CUBS method would probably work for 75% of the problems in first grade. Students are doing more advanced part-whole addition problems, part-whole subtraction, part-whole missing addends, and they’ll start doing a few multi-step problems, all of which fit in the part-whole family, for which the CUBS method works well. But when you move out of that genre of problems, it falls apart. 

In the Kindergarten journal, we featured part-whole addition, part-whole subtraction, part-whole missing addend, a few problems with teen numbers, and a mixed review. The journal is very structured because it is intended to start students thinking about what they’re reading in the story problem: We have a story, a sentence form, a quick draw area, a number bond, a 10-frame, and a computation area. As they transition to 1st grade, how do we remove some of that scaffolding while still keeping it developmentally appropriate?

We have to be really careful with the way we make this transition, because very quickly, students can jump to the “circle the numbers, box the word” strategy and many times they just appeal to us because they don’t know what to do. It’s a word problem and it’s confusing, so they just add because we’re talking about adding that week. 

Additive Comparison Problems 

Additive comparison problems, where I have an amount and you have the same amount but you may have more or less than I do, are introduced after students have spent some time working on multi-step part-whole problems.

This type of problem is really a play on language, in my opinion, which makes it really confusing for kids to understand exactly what it is asking. So, we really want kids to take a step back to understand the additive comparison problems, which are coded AC in our journals. I find that building these problems with unfix cubes is a good way to start.

Let’s take this problem: Shannon has 10 pet rocks and Sherry has 4 pet rocks. How many more rocks does Shannon have than Sherry?

In some ways it seems like this might be a missing addend problem, but in fact we’re really comparing my pet rocks to Sherry’s pet rocks and we’re asking how many more does one have than the other. This really requires students to take it to the concrete level and make a bar model with unifix cubes.

I put 10 cubes to represent Shannon’s pet rocks, and then I’ll use different color cubes to show Sherry’s 4. Then, I want to compare the lengths of those two bars and figure out what the problem is really asking, which is the gap between where Sherry’s bar stops and Shannon’s bar stops. The question mark is asking for how many more does Shannon have? 

Sometimes, the language of an additive comparison problem might be reversed and say how many less does Sherry have? Since it is a play on words, which sometimes becomes confusing for students, we really need to put thought into how we go about teaching kids to do a problem like this.

Visual Models for Additive Comparison Problems

If I were to line up all the programs we work with, every one of them has bit of a different name for visual models: model drawings, tape diagrams, bar models, unit bars. We’re going to universally call them visual models for word problems. 

These aren’t the little quick draws we’ve been doing in Kindergarten because, as students get older and the problems get more complex, I’m not going to be able to draw 13 ducks and then 9 more because it will take too long! Instead, I want to put it into a visual model that has these units.

This first grade year is a transitional time where kids are going from the quick draw to what I’m going to call proportional bars, which have a length of individual cubes that are representative of the quantities we’re talking about in the problem.

I just was working with a first grade teacher last week on a Zoom call, and this teacher had not been able to attend our workshop on their campus about visual models. She, like most teachers I work with, didn’t understand why visual models were so important. She thought her students should be able to do quick draws and didn’t understand why they had to do boxes. She told me she was a big proponent of encouraging students to solve problems in different ways, so why would she possibly want to teach students a procedure like this and make them solve word problems in this way. 

After I took her through the same progression of problem solving we’ve been going through in our blog the past few weeks, she was sold! I took her up through fifth grade to help her see why it is that, in 1st grade, we’re asking students to stop doing quick draws and start to use a visual model that has a unit bar with different pieces. This proportional model is also a great transition into using a non-proportional bar.

Let’s say I had 92 pet rocks and Sherry has 45 pet rocks. A quick draw clearly won’t work for this problem, and I don’t have enough room on my paper to draw a proportional model for those numbers. But I can draw a longer bar that represents Shannon’s rocks, write in 92 rocks, and draw a shorter bar to show Sherry’s 45 rocks so I could see the proportionality. 

The hardest thing to remember when we do visual models for word problems is that it actually has nothing to do with math! We’re not actually solving the problem on the model; we are solely using a reading comprehension strategy.  

One of the biggest misconceptions we addressed when we started rolling out the 1st grade journal samples that I’ll be using in this video, was that the total doesn’t go on the line. If the problem asks for a total, we represent that in the visual model with a question mark. 

We also want to make sure that we label the visual model. For example, putting a B above the books that Erin had and an L above the books she got at the library. 

The whole point of this process is to provide a systematic way for students to work through problems that doesn’t stop working after 1st grade or when you start working on a different type of story problem. In fact, this strategy carries through multiplicative comparison problems and fractions, all the way into ratios and proportions in middle school. 

Step-by-Step Problem Solving

Read the problem. Then, have someone read it and repeat it, and every time a new piece of math information is presented, we’re going to put a chunk. So, as kids are reading the problem, they start to learn how to dissect what’s being asked. 

Not all first grade students will be able to read the story problem, but this process is modeled day after day after day in the first grade classroom, so eventually the child will become independent. 

I’m going to read a story problem: Mark has 9 strawberries, 6 of them are small. The rest are large. How many strawberries are large? 

Then, I’ll go back and read it in chunks: Mark has 9 strawberries . This is a new piece of mathematical information, so students will repeat that statement back and highlight or put a line there. The students also like to say chunk! Then we continue reading: Six of them were small. I’ll stop, repeat it, and the students say chunk! as they mark that chunk in their journals. Now we have two pieces of mathematical information. Let’s continue: The rest were large . Repeat and then chunk! So, we’ve got three sections of information that the problem has given us that we need to replicate in our visual model.  Finally, How many strawberries are large? Repeat that and then chunk!

By going through the problem slowly and methodically, students can really see these sections that they’re reading, and, as they’re going on to the subsequent steps of solving the problem, they can actually check off that they’ve included all the chunks of information in their visual model. 

In our problem, it asked me how many strawberries are large? To put it in a sentence form, I would say: Mark has ____ large strawberries. I like to say Hmm for the ____  as we’re reading it out loud.

In Kindergarten, we provide the sentence for students, leaving the blank space for their answer. But in 1st grade, we take some of the scaffolding away. It might say “There were _____ large ____” and the students have to fill in the blanks.

The sentence form is a great way to make sure that kids are comprehending what they’re reading. Generally, students in first grade have a difficult time trying to create a sentence form, because they aren’t yet developmentally ready to give you a complete answer in reading. But students will be required to do a sentence form in 2nd through 5th grade so we can be sure they understand the problems being asked, so it’s really great practice to start in 1st grade with the scaffolding.

Proportional model. We start the 1st grade year with a proportional model. We may scaffold here for the who or the what, and students will eventually start to learn what goes in that visual model. In this case, we’re talking about all of Mark’s strawberries, even though the question itself is only asking about how many of them are large.

In a proportional model, you might see the 9 squares. This is a missing addend problem so that title is going to have PWMA at the top, and there will be exactly nine squares. Some people might think that’s giving it away, but remember the goal of visual models? It’s not to solve the problem but understand what’s going on in the problem, so we’re more concerned about whether or not the student can label the drawing correctly. 

In this example, the student would total the bar at 9 and check off the first chunk of the problem that we read earlier –  Mark has nine strawberries.

The next part says “6 of them are small.” In 6 of my boxes, I’ll make six Xs, or I might make small circles, and at the top I can either write small or abbreviate with an s . 

Then it says “the rest are big.” I could label that other section of the boxes B for big, or write the whole word if I wanted. Then,  I need to put a question mark above that section between 9 (the total number of strawberries) and 6 (the number of small strawberries). That section represents the large strawberries, which is what my sentence form reminds me that I’m looking for. 

Technically, a student could just look at this easy proportional model and say there are 3 large strawberries because it’s right there in front of them. So some people might think this journal is just too easy, but at the end of the day, students are solidifying the process. They’re going back up to the problem and putting a check when they add Xs or circles for the six small strawberries. They’re putting in a check when they’ve talked about putting in the large strawberries. Then they put a question mark to show what we’re looking for. There’s a lot of detail that we’re looking for kids to have to interact with the text in math to show the comprehension. 

In some of our schools, we will do a unit bar at the bottom of the page. In the 1st grade journal we’ve created for Math4Littles, we’re going to leave the bar off and introduce the non-proportional bar a little bit later in the year. There is nothing wrong with having a model of the proportional bar and then underneath it having the non-proportional bar. In our journal, we plan to show the proportional bar, and then bring in both types of bars so that kids could see the relationship between the two. If where about this non proportional bar, where would I slice it to put the nine in? And then where’s my question mark? is it labeled? etc. 

The integral parts of visual models are: labelling the who or what, taking the bar and adjusting it based on the information that’s given, and writing in their question mark. Then it’s time to solve!

Computation. Although this step might not seem necessary because our sample problem is so simple, and to first graders after they do so many, it seems simple and both teachers and students might wonder why they’re even doing it, but I can promise that these problems will become more complex, very quickly. In our 1st grade journal, we will feature this look at the proportional bar, and then transition to having proportional and non proportional models, and then eventually just leaving it blank and having the student put in a non proportional bar to see that they can develop this progression. 

1st Grade Goals

The goal is, by the end of their first grade year, students should be able to solve problems with larger numbers and a non-proportional bar. You certainly don’t want to rush that progression. 1st grade is a really nice scaffold for students to get to that point of independence, because when we get to 2nd grade, we don’t do a whole lot of scaffolding. There are more open-ended sentences, more blanks, and students are doing more of the work.

Additionally, we want to mix up the types of problems we’re solving, give students time to understand them. You might do three days of part-whole addition to see if they can get it under their belt. Then do some part-whole subtraction, then mix the two to see if students are just following a pattern where we’re adding today or subtracting today. We want to know that they can really apply what they’re learning. Multi-step problems, where students have to add and then subtract, or vice versa, are next. Give students lots of good practice, and then mix it up again to see if they’re really following the words, or if they’re just learning a procedure. The last type of problem that we would integrate in the first grade is additive comparisons. 

Video Tutorials

In the video tutorials, you’ll see aspects of four different problems being displayed. Some will have the proportional bar, some will have the proportional and the non proportional and some just won’t have it just so you can get an overall idea of what this looks like as we go.

[yotuwp type=”playlist” id=”PL76vNL0J-a405ysBIwEwXfaMp5883yGh4″ ]

As you watch the videos, think about how you could set this up in your classroom, starting with some of the sample problems that we’re offering as a free download today. We will be releasing a full 1st grade journal soon, so stay tuned! 

Join us next week for problem solving in 2nd grade: What are the different problems that 2nd grade is going to encounter? How are journals coded?  As we start to look at how journals are coded, which you certainly could use these tutorial videos right away in your classroom or in your distance learning by thinking about story problems in a different way.

*Addition , *Subtraction , *Word Problems , Audience - Lower Elementary (K-2) , Series - Math4Littles | 0 comments

Related Posts

Screening for Numeracy Development

Dec 5, 2022

Ever feel like the years are flying by and standing still at the same time? Usually, it’s children that help us feel this odd sensation, but I also can’t believe it’s been TEN years since I first created my numeracy screeners!Ten years ago, I developed a set of...

Rekenrek Activities for Numeracy Development

Feb 28, 2022

This little-known math tool, the rekenrek, is a star when it comes to numeracy development!

Using Place Value Discs in the Math Classroom

Jan 27, 2022

I have all these place value discs - How am I supposed to use them across different areas of my mathematical instruction?? This is a question that we get from a lot of teachers and we know that having a Math Salad Bar full of tools but not knowing how to implement...

Developing Problem-Solving Skills for Kids | Strategies & Tips

We've made teaching problem-solving skills for kids a whole lot easier! Keep reading and comment below with any other tips you have for your classroom!

Problem-Solving Skills for Kids: The Real Deal

Picture this: You've carefully created an assignment for your class. The step-by-step instructions are crystal clear. During class time, you walk through all the directions, and the response is awesome. Your students are ready! It's finally time for them to start working individually and then... 8 hands shoot up with questions. You hear one student mumble in the distance, "Wait, I don't get this" followed by the dreaded, "What are we supposed to be doing again?"

When I was a new computer science teacher, I would have this exact situation happen. As a result, I would end up scrambling to help each individual student with their problems until half the class period was eaten up. I assumed that in order for my students to learn best, I needed to be there to help answer questions immediately so they could move forward and complete the assignment.

Here's what I wish I had known when I started teaching coding to elementary students - the process of grappling with an assignment's content can be more important than completing the assignment's product. That said, not every student knows how to grapple, or struggle, in order to get to the "aha!" moment and solve a problem independently. The good news is, the ability to creatively solve problems is not a fixed skill. It can be learned by students, nurtured by teachers, and practiced by everyone!

Your students are absolutely capable of navigating and solving problems on their own. Here are some strategies, tips, and resources that can help:

Problem-Solving Skills for Kids: Student Strategies

These are strategies your students can use during independent work time to become creative problem solvers.

1. Go Step-By-Step Through The Problem-Solving Sequence 

Post problem-solving anchor charts and references on your classroom wall or pin them to your Google Classroom - anything to make them accessible to students. When they ask for help, invite them to reference the charts first.

2. Revisit Past Problems

If a student gets stuck, they should ask themself, "Have I ever seen a problem like this before? If so, how did I solve it?" Chances are, your students have tackled something similar already and can recycle the same strategies they used before to solve the problem this time around.

3. Document What Doesn’t Work

Sometimes finding the answer to a problem requires the process of elimination. Have your students attempt to solve a problem at least two different ways before reaching out to you for help. Even better, encourage them write down their "Not-The-Answers" so you can see their thought process when you do step in to support. Cool thing is, you likely won't need to! By attempting to solve a problem in multiple different ways, students will often come across the answer on their own.

4. "3 Before Me"

Let's say your students have gone through the Problem Solving Process, revisited past problems, and documented what doesn't work. Now, they know it's time to ask someone for help. Great! But before you jump into save the day, practice "3 Before Me". This means students need to ask 3 other classmates their question before asking the teacher. By doing this, students practice helpful 21st century skills like collaboration and communication, and can usually find the info they're looking for on the way.

Problem-Solving Skills for Kids: Teacher Tips

These are tips that you, the teacher, can use to support students in developing creative problem-solving skills for kids.

1. Ask Open Ended Questions

When a student asks for help, it can be tempting to give them the answer they're looking for so you can both move on. But what this actually does is prevent the student from developing the skills needed to solve the problem on their own. Instead of giving answers, try using open-ended questions and prompts. Here are some examples:

2. Encourage Grappling

Grappling  is everything a student might do when faced with a problem that does not have a clear solution. As explained in this article from Edutopia , this doesn't just mean perseverance! Grappling is more than that - it includes critical thinking, asking questions, observing evidence, asking more questions, forming hypotheses, and constructing a deep understanding of an issue.

There are lots of ways to provide opportunities for grappling. Anything that includes the Engineering Design Process is a good one! Examples include:

• Engineering or Art Projects
• Design-thinking challenges
• Computer science projects
• Science experiments

3. Emphasize Process Over Product

For elementary students, reflecting on the process of solving a problem helps them develop a growth mindset . Getting an answer "wrong" doesn't need to be a bad thing! What matters most are the steps they took to get there and how they might change their approach next time. As a teacher, you can support students in learning this reflection process.

4. Model The Strategies Yourself! 

As creative problem-solving skills for kids are being learned, there will likely be moments where they are frustrated or unsure. Here are some easy ways you can model what creative problem-solving looks and sounds like.

• Ask clarifying questions if you don't understand something
• Admit when don't know the correct answer
• Talk through multiple possible outcomes for different situations 
• Verbalize how you’re feeling when you find a problem

Practicing these strategies with your students will help create a learning environment where grappling, failing, and growing is celebrated!

Problem-Solving Skill for Kids

Did we miss any of your favorites? Comment and share them below!

Looking to add creative problem solving to your class?

Learn more about Kodable's free educator plan or create your free account today to get your students coding!

Kodable has everything you need to teach kids to code!

In just a few minutes a day, kids can learn all about the fundamentals of Computer Science - and so much more! With lessons ranging from zero to JavaScript, Kodable equips children for a digital future.

Problem and Solution for First Grade

• Read Alouds , Reading & Literacy

Being able to easily identify the problem and solution in a story is a foundational reading comprehension skill for first grade students.

It's an activity that can be done with every single read aloud.

It can (and should) be done whole group, in small group, with partners, in literacy stations and during independent reading.

It's also a great skill for parents to work on at home. 

Describing the problem includes:

• Identifying the problem the character(s) is experiencing in the beginning of the story
• Asking questions and making predictions about possible upcoming events and about possible ways to solve the problem
• Understanding how the events and characters influence the problem throughout the story

Describing the solution includes: 

• Confirming or revising predictions about the resolution
• Explaining how the resolution solves the problem
• Describing what happens to the character(s) because of the resolution

Examples of Problem and Solution

You might be totally comfortable with the topic of problem and solution, but when we are in the moment in front of 22 little faces, sometime we blank! 

It's time to give our students examples of what Problem and Solution is…

but we've got nothing! 

It helps to think of a few examples ahead of time and jot them down. 

Examples of problem and solution work best if the are real life examples that the students can relate to! 

Here's a few examples from the school day: 

• Your pencil breaks
• You can't find your book
• You forgot your lunch
• You can't remember the directions
• You left your jacket on the playground
• You don't know how to tie your shoes
• You need a supply that another student is using

By using these real-life examples, you are not only teaching problem and solution, but you are reinforcing your classroom management as well!

How to Introduce Problem and Solution for First Grade

If you teach lower elementary, then you know that there is SO much that goes into the comprehension of a book. First grade students are learning so much at this age and even listening comprehension requires their little brains to work so hard.

Why do I bring this up?

Because I want you to think about how hard they are ALREADY working when they are listening to a read aloud and when you use a mentor text to introduce a NEW SKILL, most students’ brains go into overload!

So what should we do instead?

Start with a non-text activity. Let me introduce you to a new kind of “slideshow”. 

I like to use interactive slideshows/powerpoints. My slideshows always follow this order: 

• Teaching Slides: Introduces students to WHAT the skill is
• Guided Practice: Introduces students to HOW to apply the skill
• Interactive Practice: Gives students an example and allows them to PRACTICE the skill in an easy and concise way

Problem and Solution Non-Text Activities for First Grade

After we practice the slideshow, then we practice building our problem and solution muscles with some guided and independent practice using a NON-TEXT ACTIVITY such as a station game.

Non-text activities are a HUGE asset to students because it allows them to build and flex their problem and solution muscles before we ask them to apply those skills to a text! 

How to Complete the Activity

We will do this activity together as a group first, then it will move into our guided reading stations where students will complete it independently!

I've found the best and easiest way to do this is with images of problems/solutions that my first grade students know a lot about. 

My students do this Problem and Solution activity (seen on the right). We do one together as a class for guided practice. 

For this activity, students must correctly match the problem and solution. Then I have students write about the problem and solution with an emphasis on why the solution actually works for this problem.

After we do this activity together, it goes into their stations for Guided Reading. 

The best part about this activity is that you can leave it out for several weeks because each time students can choose a new set of pictures! 

Mentor Texts for Problem and Solution

A mentor text is an incredibly powerful tool for teaching reading comprehension skills! 

(make sure you keep reading to the end of this post to see a list of my favorite mentor texts for problem & solution)

The problem that many teachers run into with mentor texts is that there are SO MANY different skills you can teach with the same mentor text….

Sometimes we try to do TOO MUCH and we overwhelm our students! 

Let me introduce you to a Comprehension Focus Question (CFQ). 

A CFQ is one question that you focus on through the entire text! 

It simplifies things for you and your students. (more on that later)…

But let's take a minute to dispel so myths about mentor texts..

A mentor text is NOT a book that you read once and put it away.

A mentor text is a book that you read once, then refer back to again and again and again.

The greatest benefit of a good mentor text is that after you have read it once, when you refer back to it, you aren’t reading the entire book again, you are simply referring back to one or two pages.

It will save you SO much time.

AND students are already familiar with the story line meaning that already have a foundation for whatever comprehension skill you are about to dive into!

How to Boost Comprehension for Problem & Solution

Comprehension Focus Questions

As I mentioned, a Comprehension Focus Question (CFQ) is a very focused and intentional comprehension goal for an activity, a week or even a unit.

If you have done your research and you understand your learning standard, the vocabulary and what students need to know…

Then it becomes very easy to choose a goal (or a comprehension focus question).

But, why do you need a comprehension goal?

To stay FOCUSED!

Not just for you, but for your students also!

Let’s look at an example. Let’s say that this week you are focusing on how to make an inference. Well, there are about a hundred different ways you can make an inference and a CFQ allows you to focus on one area at a time.

Example CFQ: “How Did The Character Change From ___ To ____?”

In this comprehension focus question, you and your students are focusing in on the characters of the story.

The great thing about CFQ’s is that the next time you pull out this mentor text, you can choose a different CFQ to focus on while still practicing how to make an inference!

Sentence Stems

Another great strategy that falls right in long with mentor texts and comprehension focus questions is sentence stems.

A sentence stem is a phrase that your first grade students will use to answer a comprehension question.

Sentence stems are designed to get students to answer comprehension questions more fully rather than giving one word answers.

Sentence stems encourage students to explain their thinking.

I like to have a list of sentence stems next to my table that are specific to each comprehension skill. I stick to one or two stems per skill for the entire year because I want my students to be consistent. (This also makes it a lot easier for them)

If we are sticking with our Make an Inference example, I would use the following sentence stems:

I Think ___ Because____.   

I Read This ____ So I Think _____

Problem and Solution Activities for First Grade

All of the activities that you found in this post, both printable and digital, along with UNIT LESSON PLANS can be found in my Problem and Solution Bundle here.

You can save up to 20% by purchasing the items together, but you can also purchase individual items to better fit your needs!

Best Books for Problem and Solution

**You can use the recording sheet from the Problem and Solution station with all of these read alouds!

More First Grade Favorites

sign up for free stuff

Sign up to receive weekly emails with tips, free resources and info about upcoming sales.

Kristen Sullins

I am a current Elementary Librarian and Enrichment Teacher, mother of two, follower of Christ and Texas native. In my own classroom, I love to save time by finding unique ways to integrate writing, social studies and science into all parts of my day. I also love all things organization!

YOU MAY ALSO ENJOY...

©2019 Kristen Sullins.  All Rights Reserved

Site by Ashley Hughes

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.

• freebie , Math Workshop , Problem Solving

FIND IT NOW!

Check me out on tpt.

CHECK THESE OUT

Three Types of Rocks and Minerals with Rock Cycle Circle Book

Partitioning Shapes Equal Share Fractions Halves, Thirds, Fourths Math Puzzles

Want to save time?

COPYRIGHT © 2016-2024. The Owl Teacher | Privacy page | Disclosure Page | Shipping | Returns/Refunds

BOGO on EVERYTHING!

Center for Teaching

Teaching problem solving.

Print Version

Tips and Techniques

Expert vs. novice problem solvers, communicate.

• Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
• If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
• In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
• When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

• Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
• Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles.
• Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

• Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

• Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

Teaching Guides

• Online Course Development Resources
• Principles & Frameworks
• Pedagogies & Strategies
• Reflecting & Assessing
• Challenges & Opportunities
• Populations & Contexts

Quick Links

• Services for Departments and Schools
• Examples of Online Instructional Modules

• Skip to main content
• Skip to footer

Miss Kindergarten

Kindergarten Teacher Blog

Tips for Teaching Word Problems in 1st Grade

April 9, 2023 misskindergarten Leave a Comment

Learning how to solve word problems is an essential skill for first graders!  It’s also one of the more challenging math concepts that our young learners practice in first grade.  In this post, I want to share some helpful tips for teaching word problems in 1st grade.  With these tips and resources, you’ll be able to keep your students engaged in Word Problem Practice all year long!

Teaching Word Problems: 1st Grade Classroom

Understanding and solving word problems can help your students see that math is all around them every day.  Plus, there are many other skills that your first graders can practice as they solve story problems.

• Reading Skills:   First graders are growing in their reading skills by leaps and bounds all year!  Word problems are an excellent way to add some reading practice to other pockets of your daily routine. Not only are students putting their decoding skills to work, but they are also stretching those reading comprehension muscles!
• Fine Motor Practice:  While your young students have come very far in their fine motor skills since entering kindergarten, they likely need continued practice in this area.  Using manipulatives to model and solve story problems can be a great way for students to practice their hand-eye coordination, pincer grasp, and more!
• Math Strategies:   Students learn many addition and subtraction strategies in kindergarten!  However, if they don’t continue to use those strategies in first grade, they might forget about them!  Word problem practice is a great time to remind students to try different math strategies.

As teachers, we can see the importance of word problem practice for our young learners.  However, they might not be as excited about them! Here are some tips for teaching word problems in a way that keeps your students engaged in this important practice.

1. Dissect Word Problems Together

Since first graders are still developing their reading comprehension skills, they might draw a total blank after reading a math word problem on their own.  Instead, be sure to practice dissecting word problems together as a class!  Highlighters, crayons, or even see-through colored math counters can mark the important information in the problem.  You could also teach students hand signals to hold up when they hear important information in a word problem that’s being read as a whole class.  There are many ways that you can make the process of dissecting word problems more engaging and memorable for your students!

2. Spread It Out

A great way to bring variety to your word problem practice is to incorporate math story problems throughout your daily routine!  You could have a story problem written on the whiteboard for your morning meeting. You can also incorporate story problem practice into your math rotations!  When you find yourself with extra time before your next transition, you could read and dissect a story problem together as a class. You might even see an opportunity to do a quick math story problem from a book you’re reading out loud to your students! 

3. Incorporate Movement

Story problems can also be used for meaningful movement breaks in the classroom.  You could display a word problem and have students take turns playing the part of the objects.  Students love to be seashells, bubbles, and butterflies! 

4. Have Students Write Their Own Word Problems

As your first graders become more familiar with the structure of story problems, they’ll be ready to write their own!  You can use a template with sentence frames for students who need that level of support.  As students grow and develop their writing skills, they might want to try their hand at writing and illustrating their own word problems.  

No matter which method you use to have students write their own word problems, be sure to use the final product in some way.  You could put the papers in a pile and choose a few at a time to discuss as a class.  Depending on your students, you could also recirculate the completed papers and have each student solve a word problem written by a classmate. You could even put together a class book of student-generated word problems! Just put the pages in sheet protectors (or laminate) and have students use dry-erase markers to solve the problem on each page.

5. Use Seasonal Story Problems

One of my favorite ways to keep students engaged in story problem practice is to use seasonal problems.  Not only do students find these problems more interesting, but they also support comprehension!  When students are currently experiencing a season, it is easier for them to visualize and understand what the story problem is talking about.

Another fun reason to use seasonal story problems is that you can pull out all of those holiday mini-erasers and other seasonal manipulatives that you have on hand!  This is also a great way to help students channel their excitement about upcoming holidays into a meaningful learning activity.

Seasonal Word Problems for 1st Grade

If you could like to use seasonal word problems in your first grade classroom, I have the perfect solution for you!  I have put together a resource with over 150 seasonal story problems that you can use all year long! Each page comes with coordinating manipulatives that students can cut out to help them model the word problem.  This is great for fine motor practice, as well! 

Since everything you need for each word problem is included on the page, this is a no-prep resource that you can use to supplement your math practice.  These story problem worksheets are perfect for small group intervention, whole group instruction, centers, morning work, or even for homework!  If you’d like to take a closer look at this resource, you can find it in my shop .

Math Story Problems Seasonal Addition and Subtraction Pack

Save these tips for teaching word problems in first grade.

I hope that this post has given you some inspiration for teaching word problems in first grade!  If you’d like to come back to this post later, just add the pin below to your favorite teaching board on Pinterest.  You’ll be able to quickly find these tips and resources whenever you need them!

Number Formation Poems

You may also enjoy these posts.

Check Out These Resources

March Activity Bundle

Addition and Subtraction Practice Activities BUNDLE

Phonics Activities CVC Words MEGA BUNDLE!

St. Patricks Day Centers for Kindergarten

Shop All Resources

Hello, I’m Hadar

Welcome to Miss Kindergarten. I’m so happy you’re here!

If you are looking for hands-on, engaging kindergarten activities, you came to the right place! I’m here to save you time by sharing tried and true kindergarten resources, and hopefully spark some ideas for your own kindergarten lesson plans!

Whether you need ideas to teach reading, sight words, math, or even some fun crafts, I have you covered. My ultimate goal is to help passionate educators and parents to young kids gain their valuable time back!

If you want to stay connected with Miss Kindergarten, please follow me on social media and be sure to sign up for the newsletter below.

More About Me Contact Me

Follow Miss Kindergarten on Instagram!

Fun ideas at your fingertips! Get daily inspiration, tips, and ideas, plus special sales and freebies! Connect with Miss Kindergarten on Instagram.

Helpful Links

• Free Resources

Popular Posts

FREE Kindergarten Reading Fluency Passages

Sight Word Sentences for Kindergarten

Spring Fine Motor Centers for Kindergarten

New in the shop.

April Activity Bundle

April Low Prep Kindergarten Centers Math and Literacy Centers

April Morning Work for Kindergarten

Teaching Problem-Solving Skills

Many instructors design opportunities for students to solve “problems”. But are their students solving true problems or merely participating in practice exercises? The former stresses critical thinking and decision­ making skills whereas the latter requires only the application of previously learned procedures.

Problem solving is often broadly defined as "the ability to understand the environment, identify complex problems, review related information to develop, evaluate strategies and implement solutions to build the desired outcome" (Fissore, C. et al, 2021). True problem solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem solver has not seen before, in order to obtain a satisfactory solution.

Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.

Principles for teaching problem solving

• Model a useful problem-solving method . Problem solving can be difficult and sometimes tedious. Show students how to be patient and persistent, and how to follow a structured method, such as Woods’ model described below. Articulate your method as you use it so students see the connections.
• Teach within a specific context . Teach problem-solving skills in the context in which they will be used by students (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill.
• Help students understand the problem . In order to solve problems, students need to define the end goal. This step is crucial to successful learning of problem-solving skills. If you succeed at helping students answer the questions “what?” and “why?”, finding the answer to “how?” will be easier.
• Take enough time . When planning a lecture/tutorial, budget enough time for: understanding the problem and defining the goal (both individually and as a class); dealing with questions from you and your students; making, finding, and fixing mistakes; and solving entire problems in a single session.
• Ask questions and make suggestions . Ask students to predict “what would happen if …” or explain why something happened. This will help them to develop analytical and deductive thinking skills. Also, ask questions and make suggestions about strategies to encourage students to reflect on the problem-solving strategies that they use.
• Link errors to misconceptions . Use errors as evidence of misconceptions, not carelessness or random guessing. Make an effort to isolate the misconception and correct it, then teach students to do this by themselves. We can all learn from mistakes.

Woods’ problem-solving model

Define the problem.

• The system . Have students identify the system under study (e.g., a metal bridge subject to certain forces) by interpreting the information provided in the problem statement. Drawing a diagram is a great way to do this.
• Known(s) and concepts . List what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it.
• Unknown(s) . Once you have a list of knowns, identifying the unknown(s) becomes simpler. One unknown is generally the answer to the problem, but there may be other unknowns. Be sure that students understand what they are expected to find.
• Units and symbols . One key aspect in problem solving is teaching students how to select, interpret, and use units and symbols. Emphasize the use of units whenever applicable. Develop a habit of using appropriate units and symbols yourself at all times.
• Constraints . All problems have some stated or implied constraints. Teach students to look for the words "only", "must", "neglect", or "assume" to help identify the constraints.
• Criteria for success . Help students consider, from the beginning, what a logical type of answer would be. What characteristics will it possess? For example, a quantitative problem will require an answer in some form of numerical units (e.g., $/kg product, square cm, etc.) while an optimization problem requires an answer in the form of either a numerical maximum or minimum.

Think about it

• “Let it simmer”.  Use this stage to ponder the problem. Ideally, students will develop a mental image of the problem at hand during this stage.
• Identify specific pieces of knowledge . Students need to determine by themselves the required background knowledge from illustrations, examples and problems covered in the course.
• Collect information . Encourage students to collect pertinent information such as conversion factors, constants, and tables needed to solve the problem.

Plan a solution

• Consider possible strategies . Often, the type of solution will be determined by the type of problem. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards.
• Choose the best strategy . Help students to choose the best strategy by reminding them again what they are required to find or calculate.

Carry out the plan

• Be patient . Most problems are not solved quickly or on the first attempt. In other cases, executing the solution may be the easiest step.
• Be persistent . If a plan does not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying.

Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions:

• Does the answer make sense?
• Does it fit with the criteria established in step 1?
• Did I answer the question(s)?
• What did I learn by doing this?
• Could I have done the problem another way?

If you would like support applying these tips to your own teaching, CTE staff members are here to help.  View the  CTE Support  page to find the most relevant staff member to contact. 

• Fissore, C., Marchisio, M., Roman, F., & Sacchet, M. (2021). Development of problem solving skills with Maple in higher education. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_15
• Foshay, R., & Kirkley, J. (1998). Principles for Teaching Problem Solving. TRO Learning Inc., Edina MN.  (PDF) Principles for Teaching Problem Solving (researchgate.net)
• Hayes, J.R. (1989). The Complete Problem Solver. 2nd Edition. Hillsdale, NJ: Lawrence Erlbaum Associates.
• Woods, D.R., Wright, J.D., Hoffman, T.W., Swartman, R.K., Doig, I.D. (1975). Teaching Problem solving Skills.
• Engineering Education. Vol 1, No. 1. p. 238. Washington, DC: The American Society for Engineering Education.

Catalog search

Teaching tip categories.

• Assessment and feedback
• Blended Learning and Educational Technologies
• Career Development
• Course Design
• Course Implementation
• Inclusive Teaching and Learning
• Learning activities
• Support for Student Learning
• Support for TAs
• Learning activities ,

Powerful online learning at your pace

1st Grade Essentials: Basic Fact Strategies

With pages of math standards at each grade level, what is really considered essential learning? In this series of posts, I attempt to highlight the key skills at every grade level, explain those skills in layman’s terms, and provide activities and tasks for helping children build those skills. Please note that as this series grows, there will be multiple posts for each grade level.

This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally recommend.

Fact fluency actually begins in Kindergarten, when children learn the combinations for the numbers through 10 and are expected to fluently add and subtract within 5. First grade builds on those skills. While the standard shown below is from the Common Core State Standards, other state standards are very similar.

CCSS.MATH.CONTENT.1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

There are two important ideas buried in that standard.

• First, while 1st Graders are working on the facts within 20, the expectation for fluency by the end of 1st Grade is within 10 (remember that Kinder was fluent within 5). That’s an important distinction. It basically means they should have automatic recall for facts within 10, like 4 + 5, 7 + 1, or 2 + 8, but they should have successful strategies for adding single-digit numbers up through 20, such as 6 + 7, 4 + 9, or 8 + 6.
• Second, the acquisition of fluency with basic facts is based on learning and using strategies that emphasize the relationships between numbers, not memorization. Those strategies are actually listed in the standard, and I’ll explain them in more detail in the next section.

Learning Facts Using a Strategy-Based Approach

Foundational skills.

In order to use strategies for learning the basic facts within twenty, students need to have mastered the Kindergarten skill of knowing the combinations of all the numbers through ten. See this post for more on that topic. It’s a good idea to quickly assess a child’s fluency with the combinations to ten before trying to teach strategies based on those combinations. The post I just mentioned provides information on doing that assessment. If a 1st Grader needs work on this Kindergarten skill, it’s best to provide practice with number combinations prior to trying to introduce the strategies outlined below.

What is the progression for teaching and learning the fact strategies?

In their book  Math Fact Fluency , Jennifer Bay-Williams and Gina Kling have a great graphic that shows how all the different fact strategies are interconnected. The idea is that children need to master the facts at each level before they can tackle the strategies below. Think of it this way, I can’t use a strategy called Near Doubles if I don’t know my Doubles.

+/- 0, 1, and 2

While it may seem obvious, children need to know that when we add 0 to or subtract 0 from any number, the number does not change.  So 5 + 0 = 5 and 5 – 0 = 5 as well. This is also a good time to introduce the idea of the commutative property , which means that the order does not matter when adding. Of course, it’s not necessary for a 1st Grader to learn the mathematical term, but you want them to have the understanding. This will help them understand that 5 + 0 = 5 and 0 + 5 = 5 as well. Important to note that the commutative property works for addition but not subtraction. Concrete materials can be used to help children visualize the commutative property.

In Kindergarten, children practice counting forward and back from any number. This helps them develop an understanding of the next number and the previous number. This first set of facts uses that counting-on/counting-back strategy. Facts in this group include facts such as 6 + 1, 2 + 7, and 9 – 0. Because counting on or back becomes inefficient with larger numbers, we only really want children using it for adding or subtracting up to 2. By that I mean that it’s very inefficient to use counting on to find the sum of 7 + 8, and there are much better strategies for that fact.

Here’s a little game kiddos can play to practice the +/- 0, 1, and 2 facts. If you don’t have ten-sided dice you can use playing cards . Use only the Ace through 9 cards, and instead of rolling the dice, turn over a card. Click here to grab yours.

Doubles and Near Doubles

Children often have an easier time learning their doubles (e.g., 4 + 4, 6 + 6, 9 + 9, etc.). That said, it’s still helpful to use concrete and pictorial representations to support the development of automaticity. Using a familiar tool like a ten-frame helps children to use the benchmark of five to see that 6 + 6 = 5 + 5 + 2. Click here to download a double ten-frame mat.

Once children are fluent with the doubles facts, they can work on Near Doubles. This strategy is sometimes referred to as Doubles Plus One, Doubles Plus Two, or Using Doubles. Using this strategy emphasizes the relationship between facts. If a child knows that 6 + 6 = 12, we want them to understand that 6 + 7 is just one more, so it must be 13. Again, using concrete and pictorial representations helps build this understanding.

You will also see how the Kindergarten skill of being about to decompose numbers in different ways supports this strategy. In this little activity for Near Doubles, one addend is decomposed to make a double fact.

One important note. There’s not just one way to use doubles. For example, one child might think about one more than 6 + 6 to solve 6 + 7. But another might think of one less than 7 + 7 to solve the same problem. That’s the beauty of using a strategy-based approach–children will use them in the way that makes the most sense to them! We want to be careful about imposing structure and rules when using strategies for adding and subtracting.

Combinations for 10 and Make a 10

In Kindergarten, children should work extensively to master all the combinations for the numbers up through 10. Ten is a special number in our place value system, so knowing that 7 + 3 = 10 helps children understand that 17 + 3 = 20. And that if I have 47, it’s 3 more to the next ten (50). And 470 + 30 = 500. You get the idea.

My friend Kris Graham made several short videos showing math games that can be played with only a deck of cards. Kids will love this Pyramid Ten game!

Ten frames are designed to emphasize benchmarks of 5 and 10, so they are an invaluable tool for practicing combinations for 10. They also help children visualize the Make a 10 strategy. Take for example the problem 8 + 3. Using a double ten frame, build one addend on the top ten frame and the other on the bottom. Using two different colors of counters helps with visualization. To add the numbers together, slide counters from the second addend to fill in the top ten frame, making a ten. The Make a 10 strategy is best when one of the addends is close to 10. Children need lots of concrete practice like this before moving to a more abstract process. Be sure that sometimes the addend close to 10 is the second addend, so children realize that 3 + 8 is the same as 8 + 3. In the case of 3 + 8, with 3 on the top ten frame, you would want to move counters down to the bottom ten frame to make a ten.

Once students understand the Make a 10 strategy using concrete materials, they are ready to decompose and work with the numbers mentally. Check out this pos t to grab another freebie!

Plus 10 and Pretend a 10

Plus 10 is simply another way to say “teen numbers.” Children begin to understand how place value works when they learn that teen numbers consist of a ten (ten ones) and some leftovers. So in the number 13, for example, we can bundle ten of the ones and three will be leftover. Again, ten frames are the ideal tool for helping children visualize this concept. This understanding needs to go beyond just saying there is a 1 in the tens place . Very young children need to see what that means for it to make sense and have meaning.

Here’s another one of Kris’s games, this one for making teen numbers. You can download a sheet like the one shown in the video for kids to record their numbers here .

Once children know their Plus 10 facts, they can begin to use that understanding to solve nearby facts using a strategy called Pretend a 10. This strategy is very useful for the nines facts, like 9 + 5. Children simply think,  I know that 10 + 5 = 15, so 9 + 5 is just one less, or 14. 

These strategies might be very new for you and different from how you learned your math facts. Trust the process! Children who learn their facts using a strategy-based approach learn that numbers and math make sense, rather than just seeing it as a series of procedures that must be memorized.

I would love to read comments about your experiences with or thoughts about using a strategy-based approach! Drop a comment below or post one on Twitter! Be sure to tag me! @MathCoachCorner

Bay-Williams, J. M., & Kling, G. (2019). Math fact fluency: 60 games and assessment tools to support learning and retention . Alexandria, VA: ASCD.

OConnell, S., & SanGiovanni, J. (2015).  Mastering the basic math facts in addition and subtraction: strategies, activities & interventions to move students beyond memorization . Portsmouth, NH: Heinemann.

Conklin, Melissa. (2010). It Makes Sense!: Using Ten-Frames to Build Number Sense . Math Solutions.

Similar Posts

Counting by Tens off the Decade on a 100 Chart

I was planning with my Kinder team today, and the discussion turned to skip counting by tens off the decade. Traditionally, when skip counting by tens was taught, we asked…

Using Math Stretches for a Daily Warm-Up

If you are a Laney Sammons fan, then you probably already know about Math Stretches. Part of Laney’s Guided Math framework is Morning Math Warm-Ups. Sammons explains that just like…

Developing Fraction Sense

It all started with a question…where should I put 3/4 on the number line? I was starting a unit with my 4th-grade RTI kiddos on fractions, and the question was…

Target 20: A Math Game of Strategy and Computation

You can never have too many math games, right? Slip in a little strategy to boost problem-solving and limit the materials to four dice and a recording sheet, and this…

Teaching Numeracy, Components 4 & 5

Hard to believe this is our last week of the book study! I want to thank Margie for being such an active participant and spending part of her summer with…

Do This, Not That: Structuring Math Workshop

Whether you are just getting started with a workshop approach to math or you have already implemented your own version, I have some tips for structuring math workshop to maximize…

15 Comments

hello, great game using playing cards to identify teen numbers.

*I received an error message on some of the downloads that were listed on this page..

Hmm, I tested all of the links. Can you tell me specifically which ones you had trouble with?

Hi, Thanks for sharing the links. Great games!

Great post! I appreciate your description of the process of building number sense and practical advice on helping kids “get” the strategies. I will be tutoring my daughter this summer to fill in gaps in understanding from first grade math so this is invaluable for me!

I always enjoy reading your blog! Thank you for supporting us during these wild times!

Great article! Learning strategies is so important when it comes to fact fluency!!

I love the Pyramid Game and my students are always asking to play it. It can also be adapted to practice combinations for other numbers within 10. To practice combinations to make 7, remove 7, 8, 9 and 10.

*I found a typo, “This will help them understand that 5 + 0 = 0 and 0 + 5 = 0 as well.”

Thank you!!

Thanks for catching that! All fixed. 🙂

oops…still a typo…”This will help them understand that 5 + 0 = 0 and 0 + 5 = 5 as well.” Should say 5 + 0 = 5*

Love your blog 🙂

Good grief!! Finally fixed. Thanks for the assistance!

Such a great article – will definitely be sharing with parents in our K-2 school!

Thank you- with my 1st grader in online learning this Fall, I felt lost trying to understand the basics of common core and what she should know and be building on.

Just printed some ten frames and created some counters.

I really enjoy your blog. You do a great job of explaining concepts and creating lessons that uncover misconceptions and teach deep understanding. I very much believe in teaching for conceptual understanding and I think the above strategies are great for number sense and therefore very worthwhile. However, I don’t see how these strategies help kids memorize (for instant recall) math facts. It seems like they need to just know the answer quickly without jumping through mental hoops of “OK, I know 8+8 is 16 so 8+9 must be 17”. It’s true I’d much prefer them get the answer to 8+9 by the near doubles strategy than by counting on from 8, but what is even better is automaticity. In your experience do these strategies eventually lead to automaticity or is there another piece that needs to happen? (I hope this doesn’t come across as negative. It’s a question I’ve been thinking about for a while!) Thank you for your great posts and resources. When I am teaching a new math concept you’re my first stop!

Thank you for your question! Your concern is a very common one, actually. The short answer is, this is a step toward automaticity, not the end product. During this stage, children use reasoning to arrive at the answer. With repeated practice, they develop automaticity. That’s why most current standards are written to emphasize this strategy-based approach in 1st Grade with automaticity being the expectation in 2nd Grade.

wonderful blog Donna! love the way you explain things. Thank you so much 🙂

• Pingback: What Are Number Facts In Year 4? – Fallsgardencafe

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

• Trying to Conceive
• Signs & Symptoms
• Pregnancy Tests
• Fertility Testing
• Fertility Treatment
• Weeks & Trimesters
• Staying Healthy
• Preparing for Baby
• Complications & Concerns
• Pregnancy Loss
• Breastfeeding
• School-Aged Kids
• Raising Kids
• Personal Stories
• Everyday Wellness
• Safety & First Aid
• Immunizations
• Food & Nutrition
• Active Play
• Pregnancy Products
• Nursery & Sleep Products
• Nursing & Feeding Products
• Clothing & Accessories
• Toys & Gifts
• Ovulation Calculator
• Pregnancy Due Date Calculator
• How to Talk About Postpartum Depression
• Editorial Process
• Meet Our Review Board

How to Help a First-Grader Who's Struggling With Math

It's common for young children to need a bit of help with reading, writing, and math. The early grades are seeing increasing pressure from standardized tests and homework and more emphasis on academics. This is the reason why many parents and education experts are calling kindergarten "the new first grade ."

If your first-grader is struggling with math, take steps now to help them feel more confident and strengthen their math skills so that they can have a strong foundation from which to move forward.

Ways to Strengthen Their Math Skills

Here are some things to try:

Understand Math Milestones

By age 6, many children can do basic addition and subtraction of numbers in their heads with answers up to 10. They can answer some simple math word problems and they understand the concept of halves, thirds, and quarters. However, these skills develop through ages 6 and 7 and your child may grasp them at different points during first grade.

Get to the Bottom of the Issue

Is the teacher going too fast for your child? Does your child feel anxious about tests? Are they having trouble with one basic concept, such as subtraction or fractions, that's affecting all the math they're learning ? Or could it be something completely unrelated, like a change in vision that's affecting their ability to see the board clearly?

Talk to Your Child's Teacher

Schedule a meeting with your child's teacher at a convenient time. It's likely that they'll have a good sense of what might be going on with your child and may have some suggestions on how to help.

Make Math Fun

Play fun math-based games with kids so that they don't even realize that they're learning math. Is your child crazy about baseball stats? Do they love helping you in the kitchen? Take advantage of their favorite activities and look for ways to incorporate math into them. Some fun ways to play with math every day:

• At the grocery store : Have your first-grader look at prices and see which ones are higher. Older kids will be able to calculate the actual value by looking at the price per weight of an item, but younger kids can stick to this simpler comparison. Ask them to add certain items, such as apples and oranges, to see how many pieces of fruit you are buying.
• In the car : Whether you're taking a long trip or simply driving to school or soccer, you can play with numbers in the car. Since first-graders need to learn their numbers, you can play spot the number and have your child keep track of how many numbers she can see out the window on street signs, storefronts, houses, and more.
• In the kitchen : Talk about concepts like doubling ingredients in a recipe or cutting a recipe in half. Talk about concepts like which is more, 1/2 of a cup or 1/4 of a cup.
• Online : There are many great sites that feature computer math games for every grade and interest. Challenge them to games that use a timer to see how many math problems—such as simple addition problems—a child can do in a set number of minutes. Offer a prize at the end, like getting to choose the family games for your next family game night.

Math Muscles

As with so many things in life, practicing math will improve their skills. Reassure them that they will get better at math with practice. Tell them not to get discouraged since the only way to improve is by making mistakes or by not getting something right the first time.

All Kids Can Succeed at Math

Erase the idea that some people are not good at math. This is an unfortunate myth that often affects women and girls, but some boys may get that message, too. Having such an idea in their minds can lead to math anxiety and a dislike of math. The fact is, with practice, anyone can improve their math skills.

Assess Your Own Attitude Toward Math

Try not to say things like, "I'm not good at math" or, "I hate math." Play math games with your child and really make an effort to have fun. If none of these efforts seem to be making a difference, you may want to talk to your child's teacher or pediatrician about consulting a learning specialist or hiring a tutor who specializes in building kids' confidence about math.

By Katherine Lee Katherine Lee is a parenting writer and a former editor at Parenting and Working Mother magazines.

Math for 1st Graders

Explore our first grade math resources aligned to the 1st grade common core math curriculum. Enjoy learning key math concepts taught in the first grade, including counting, addition and subtraction strategies, word problems, picture graphs, telling time, counting money, comparing measurements, and much more. Perfect grade 1 math resources for teachers, parents, and kids! Start now for free!

CONTENT TYPE

• Lesson Plans
• Math (2,055)
• Number Sense (558)
• Number Recognition (220)
• Number Recognition Within 3 (3)
• Number Recognition Within 5 (2)
• Number Recognition Within 10 (5)
• Number Recognition Within 20 (210)
• Number Sequence (21)
• Number Sequence Within 20 (3)
• Number Sequence Within 50 (5)
• Number Sequence Within 100 (5)
• Number Sequence Within 120 (4)
• Backward Sequence from 20 (2)
• Counting (168)
• Counting Objects Within 3 (10)
• Counting Objects Within 5 (20)
• Counting Objects Within 10 (37)
• Counting Objects Within 20 (10)
• Writing Numbers (200)
• Writing Numbers Within 20 (200)
• Number Representation (46)
• Compare and Order Numbers (94)
• Compare Numbers (88)
• Compare Numbers within 10 (29)
• Compare Objects within 10 (10)
• Compare Without Visual Support (10)
• Compare Numbers within 20 (29)
• Compare Numbers Using Place Value Blocks (10)
• Compare Numbers Without Visual Support (10)
• Compare Numbers within 100 (30)
• Use Place Value Blocks to Compare Numbers (10)
• Compare Two 2-Digit Numbers (10)
• Order Numbers (6)
• Order Numbers within 10 (3)
• Order Numbers within 20 (3)
• Skip Counting (8)
• Skip Count by 10 (8)
• Place Value (68)
• Read and Write Numbers (42)
• Numbers up to 10 (5)
• Numbers up to 20 (6)
• Numbers up to 50 (7)
• Numbers up to 100 (17)
• Unit Form (5)
• Addition (768)
• Embedded Numbers (4)
• Addition Sentences (55)
• Addition Sentence within 5 (11)
• Addition Sentence within 10 (44)
• Add with Pictures (33)
• Add with Pictures within 5 (22)
• Add with Pictures within 10 (11)
• Model Addition (232)
• Addition Properties (14)
• Commutative Property of Addition (8)
• Add Using Models (10)
• Addition Strategies (410)
• Addition Strategies within 10 (262)
• Count On to Add Strategy (39)
• Add using number line (9)
• Compose and Decompose Numbers (212)
• Number Bonds (197)
• Addition Strategies within 20 (104)
• Anchor 5 and 10 (12)
• Count On Strategy (18)
• Add with 10 (13)
• Make 10 Strategy (18)
• Doubles and Near Doubles Strategy to Add (31)
• Doubles Facts (13)
• Add Three Whole Numbers (16)
• Addition Strategies within 100 (42)
• Add using multiples of 10 (12)
• Addition Strategies within 1000 (3)
• Add using multiples of 100 (3)
• Addition Facts (186)
• Fluently Add within 5 (9)
• Fluently Add within 10 (79)
• Fluently Add within 20 (105)
• Equal Expressions (31)
• Addition Without Regrouping (61)
• Add within 100 without Regrouping (61)
• Add 2-digit number to 1-digit (12)
• Add 2-digit number to 2-digit (48)
• Addition With Regrouping (25)
• Add within 100 with Regrouping (25)
• Regroup and add 2-digit number to 1-digit (12)
• Regroup and add 2-digit numbers (12)
• Subtraction (443)
• Subtraction Sentences (40)
• Subtraction Sentences within 5 (7)
• Subtraction Sentences within 10 (32)
• Subtract with Pictures (41)
• Subtract with Pictures within 5 (25)
• Subtract with Pictures within 10 (16)
• Model Subtraction (45)
• Subtract using Models (7)
• Subtraction Strategies (114)
• Subtraction Strategies within 10 (32)
• Count Back Strategy within 10 (25)
• Relate Addition and Subtraction within 10 (6)
• Subtraction Strategies within 20 (68)
• Count Back Strategy within 20 (40)
• Subtract using number line (10)
• Relate Addition and Subtraction within 20 (10)
• Doubles and Near Doubles Strategy to Subtract (4)
• Subtract from 10 Strategy (10)
• Subtraction Strategies within 100 (14)
• Subtract using multiples of 10 (14)
• Subtraction Facts (168)
• Fluently Subtract within 5 (4)
• Fluently Subtract within 10 (78)
• Fluently Subtract within 20 (97)
• Equal Expressions in Subtraction (26)
• Subtraction Without Regrouping (65)
• Subtract within 100 without Regrouping (65)
• Subtract Multiples of 10 (17)
• Subtraction With Regrouping (28)
• Subtract within 100 with Regrouping (28)
• Geometry (123)
• Sides and Corners (12)
• Corners (11)
• Shapes (108)
• 2d Shapes (80)
• Identify Quadrilaterals (10)
• Trapezoids (10)
• Identify triangles (7)
• Identify polygons (1)
• Attributes of 2D shapes (11)
• Sort 2D shapes (10)
• Partition 2D Shapes (17)
• Partition into equal parts (13)
• Halves, Thirds, and Fourths (10)
• 3d Shapes (16)
• Flat and Solid Shapes (12)
• Match 3D Shapes (10)
• 3D Shapes in real life (10)
• Measurement (77)
• Capacity (6)
• Comparing Measurements (42)
• Compare Weights (10)
• Compare Lengths (22)
• Compare Heights (10)
• Data Handling (25)
• Organize and Interpret Data (18)
• Sort Objects (6)
• Measure Lengths (2)
• AM and PM (8)
• Analog Clock (29)
• Hour hand (12)
• Set time (7)
• Digital Clock (9)
• Time in Half Hours (19)
• Time in Hours (17)
• Identify Coins (20)
• Value of the Coins (10)
• Counting Money (54)
• Compare Money (2)
• Count Money with Coins (25)
• Penny, Nickel, and Dime (17)
• Word Problems (141)
• Addition and Subtraction Word Problems (141)
• Addition Word Problems (68)
• Addition Word Problems within 10 (29)
• Addition Word Problems within 20 (26)
• Addition Word Problems within 100 (10)
• Add to Compare Word Problems (6)
• Subtraction Word Problems (43)
• Subtraction Word Problems within 10 (17)
• Subtraction Word Problems within 20 (14)
• Subtraction Word Problems within 100 (9)
• Subtract to Compare Word Problems (6)
• ELA (2,072)
• Reading (1,495)
• Phonics (1,456)
• Bossy R (27)
• Words with AR (10)
• Words with ER (8)
• Words With IR (8)
• Words with OR (7)
• Words with UR (8)
• Ending Consonant Blends (91)
• CK Blend (7)
• LF Blend (13)
• LK Blend (14)
• LT Blend (13)
• MP Blend (12)
• ND Blend (13)
• NK Blend (14)
• SK Blend (12)
• ST Blend (12)
• NG Blend (7)
• Beginning Consonant Blends (89)
• L Blend Words (40)
• BL Blend (14)
• CL Blend (13)
• FL Blend (13)
• GL Blend (10)
• PL Blend (11)
• SL Blend (10)
• R Blend Words (36)
• CR Blend (12)
• FR Blend (12)
• GR Blend (11)
• PR Blend (13)
• TR Blend (12)
• Letter Sounds (111)
• Letter Sound A (5)
• Letter Sound B (5)
• Letter Sound C (5)
• Letter Sound D (5)
• Letter Sound E (5)
• Letter Sound F (5)
• Letter Sound G (5)
• Letter Sound H (5)
• Letter Sound I (3)
• Letter Sound J (4)
• Letter Sound K (5)
• Letter Sound L (5)
• Letter Sound M (5)
• Letter Sound N (4)
• Letter Sound O (5)
• Letter Sound P (5)
• Letter Sound Q (3)
• Letter Sound R (5)
• Letter Sound S (5)
• Letter Sound T (5)
• Letter Sound U (2)
• Letter Sound V (3)
• Letter Sound W (4)
• Letter Sound X (2)
• Letter Sound Y (4)
• Letter Sound Z (2)
• Vowels (221)
• Long Vowel Sounds (124)
• Long A Vowel Sound (26)
• Long E Vowel Sound (27)
• Long I Vowel Sound (26)
• Long O Vowel Sound (24)
• Long U Vowel Sound (23)
• Magic - E (35)
• Magic E Words with Long Vowel A (12)
• Magic E Words with Long Vowel E (6)
• Magic E Words with Long Vowel I (12)
• Magic E Words with Long Vowel O (11)
• Magic E Words with Long Vowel U (11)
• Short Vowel Sounds (60)
• Short A Vowel Sound (16)
• Short E Vowel Sound (10)
• Short I Vowel Sound (16)
• Short O Vowel Sound (9)
• Short U Vowel Sound (9)
• Vowel Teams (47)
• Words with AI and AY (13)
• Words with EA and EE (13)
• Words with IE and Y (11)
• Words with OA and OW (13)
• Words with OO (10)
• Words with UE and UI (9)
• Blending (314)
• CCVC Words (34)
• CVCC Words (81)
• CCVC and CCVCC Words (28)
• CVCC and CCVCC Words (46)
• Words With Bossy R (45)
• Words With Vowel Teams (50)
• Consonant Digraphs (11)
• Digraph CH (2)
• Digraph CK (5)
• Digraph NG (5)
• Digraph SH (2)
• Digraph TH (2)
• Digraph WH (2)
• Rhyming Words (71)
• Trigraphs (1)
• Trigraph DGE (1)
• Trigraph IGH (1)
• Trigraph TCH (1)
• Soft Sounds (2)
• Words with Soft C (1)
• Words with Soft G (1)
• Sight Words (581)
• Dolch Sight Words (150)
• Fry Sight Words (84)
• Syllables (6)
• Hard and Soft Sounds of C and G (2)
• Reading Skills (30)
• Story Elements (3)
• Authors Purpose (3)
• Compare and Contrast (3)
• Ask and Answer Questions (2)
• Central Message (3)
• Point of View (3)
• Sensory Words (3)
• Reality and Fantasy (2)
• Using Illustrations (3)
• Using Text Features (3)
• Context Clues (3)
• Communication Skills (9)
• Listening Skills (3)
• Speaking Skills (6)
• Writing (378)
• Writing Sight Words (20)
• Creative Writing (6)
• Grammar (23)
• Adverbs and Adjectives (4)
• Nouns and Pronouns (10)
• Pronouns (2)
• Prepositions and Conjunctions (3)
• Conjunctions (1)
• Prepositions (2)
• Punctuation (1)
• Sentences (2)
• Verbs and Tenses (3)
• Determiners (2)
• Vocabulary (157)
• Affixes (3)
• Inflectional Endings (2)
• Synonyms and Antonyms (2)
• Word Puzzles (53)
• Shades of Meaning (3)
• Sorting Words into Categories (19)
• Making Connections in Reading (4)
• Flashcards (21)
• Phonics Flashcards (19)
• Grammar Flashcards (2)

Number Sense

• Count by 1s within 20 Game

Enter the madness of math-multiverse by exploring how to count by 1s within 20.

Missing Numbers on Hundred Chart Game

Dive deep into the world of math by finding the missing numbers on the hundred chart.

Counting Sequence Worksheet

Kids must practice counting sequence in this worksheet.

Count Numbers upto 20 Worksheet

Use this printable worksheet to count numbers upto 20 to strengthen your math skills.

Solve Addition Sentences Game

Learn how to solve math problems by solving addition sentences.

Identify the Total Game

Kids must identify the total to practice addition.

Find the Missing Numbers Worksheet

Assess your math skills by finding the missing numbers in this worksheet.

Guess the Missing Numbers Worksheet

Combine math learning with adventure by guessing the missing numbers.

Subtraction

Use Subtraction Sentences to find the difference Game

Dive deep into the world of subtraction by using subtraction sentences to find the difference.

Identify the Difference Game

Let your child see the world through math-colored shades with our 'Identify the Difference' game!

Identify the Correct Subtraction Sentence Worksheet

Focus on core math skills with this fun worksheet by identifying the correct subtraction sentence.

• Subtraction on 10-frames Worksheet

Use this printable worksheet to practice subtraction on 10-frames to strengthen your math skills.

Two Equal Shares Game

Dive deep into the world of geometry by learning about two equal shares.

Four Equal Shares Game

Ask your little one to select the option that shows four equal shares.

Color Shapes Divided into Equal Parts Worksheet

Focus on core math skills with this fun worksheet by coloring shapes divided into equal parts.

Identify and Color Equal Parts Worksheet

Put your skills to the test by identifying and coloring equal parts.

Measurement

Align and Compare Lengths Game

Enjoy the marvel of math-multiverse by exploring how to align and compare lengths.

Equal Lengths Game

Practice the concept of equal lengths with your little one through this game.

Which One is Longer Worksheet

Learn measurement at the speed of lightning by practicing to identify which one is longer.

Which One is Shorter Worksheet

In this worksheet, learners will get to identify the shorter one.

The Hour Hand Game

Add more arrows to your child’s math quiver by playing 'The Hour Hand' game.

• The Minute Hand Game

Take a look at the minute hand with this fun game about time.

Hour Hand and Minute Hand Worksheet

Be on your way to become a mathematician by practicing the hour hand and the minute hand.

Position of Hour and Minute Hand Worksheet

Make math practice a joyride by solving problems to position the hour and minute hand correctly.

Different Types of Coins Game

Explore different types of coins with your little one.

Count Coins of a Type Game

Have your own math-themed party by learning how to count coins of a type.

Count the Coins to Answer Worksheet

Learners must count the coins correctly to enhance their math skills.

Identify the Coin Worksheet

Dive into this fun-filled printable worksheet by practicing to identify the coin.

Word Problems

Solve Count On Scenarios Game

Begin the exciting journey of becoming a math wizard by learning how to solve count on scenarios.

Represent 'Add To' Scenarios Game

Learn to solve math problems through our 'Represent 'Add To' Scenarios' game.

Find the Sum Using Part-Part-Whole Model Worksheet

Combine math learning with adventure by solving to find the sum using 'Part-Part-Whole' model.

Write Equations Using Part-Part-Whole Model Worksheet

Learn number sense at the speed of lightning by writing equations using 'Part-Part-Whole' model.

All Math Resources

Complete the Number Sentence Worksheet

This downloadable worksheet is designed to help you complete the number sentence.

Squares and Trapezoids Game

Take a look at squares and trapezoids with this geometry game.

Complete Subtraction Sentence Using Pictures Worksheet

Help your child revise subtraction by completing subtraction sentences using pictures.

Shapes in Everyday Life Worksheet

Pack your math practice time with fun by exploring shapes in everyday life.

Time of Activities of the Day Worksheet

Look at the time of activities of the day by printing this playful worksheet.

Guess the Price Worksheet

Dive into this fun-filled printable worksheet by practicing to guess the price.

Add or Subtract within 10: Summer Word Problems Worksheet

Summer-themed worksheet challenging students to solve addition or subtraction problems within 10.

Guess the Odd One Out Worksheet

Focus on core math skills with this fun worksheet by solving to guess the odd one out.

Complete the Number Bond Worksheet

Complete the number bond to practice your math skills.

Triangles and Rectangles Game

Take a look at triangles and rectangles with this geometry game.

Represent Subtraction Sentences Worksheet

Make math practice a joyride by solving problems to represent subtraction sentences.

How Many Corners and Sides Worksheet

Learn geometry at the speed of lightning by practicing all about corners and sides.

Identify Coins & Values Worksheet

Solidify your math skills by practicing to identify coins & values.

Add or Subtract within 20: Summer Word Problems Worksheet

Engaging summer-themed worksheet to master addition and subtraction within 20 through word problems.

Missing Numbers on Number Line Game

Take a deep dive into the world of math by finding the missing numbers on the number line.

Find the Sum Game

Kids must find the sum to practice addition.

Counting Using 10-frames Worksheet

Put your skills to the test by counting using 10-frames.

Counting Dots on Ladybugs Worksheet

This downloadable worksheet is designed to practice math skills by counting dots on ladybugs.

Solve Word Problems to Find the Difference Game

Kids must solve word problems to find the difference to practice subtraction.

Identify Shapes by Name Game

Practice the superpower of mathematics by learning to identify shapes by their names.

Use Pictures to Subtract Worksheet

Learners must use pictures to subtract to enhance their math skills.

Identify the Flat Shapes Worksheet

Reinforce math concepts by practicing to identify the flat shapes.

Align and Compare Heights Game

Kids must align and compare heights to practice measurement.

Read Time in Half Hours Game

Shine bright in the math world by learning how to read time in half hours.

• Compare Lengths of Objects Worksheet

Reveal the secrets of math wizardry by practicing to compare the lengths of objects.

Separate Out the Coin Game

Take a deep dive into the world of math by correctly separating out the coin.

Solve 'Add To' Scenarios Game

Add more arrows to your child’s math quiver by solving 'Add To' scenarios.

Understanding Coins Worksheet

Reinforce math concepts by practicing to understand coins.

Add or Subtract within 10: Halloween Word Problems Worksheet

Engage in this Halloween-themed worksheet, solving fun addition and subtraction problems within 10.

Browse Our Fun Collection of 1st Grade Math Learning Resources!

We are happy to introduce SplashLearn's grade 1 math resources, designed for 6-7 year old kids. Our learning program includes interactive games , fun worksheets , detailed lesson plans , live classes, and more, all focusing on making math for first grade a fun learning experience.

These 1st grade resources help kids learn and practice math skills, such as counting, comparing and ordering numbers, place value models up to 100, addition and subtraction strategies, addition and subtraction word problems, comparing lengths, data handling with picture graphs, telling time using analog clocks, identifying coins, counting money, and much more! 

These resources encourage first graders' growing curiosity in math, turning common learning challenges into enjoyable learning experiences. Let’s help kids learn and master the grade 1 math curriculum in a fun and interactive way!

Types of Engaging 1st Grade Math Learning Resources

Let’s explore our wide range of engaging resources for 1st grade math online, all designed to make math fun and engaging.  

Key Features of 1st Grade Math Resources

Here are some amazing features of our 1st grade math learning resources.

• Curriculum-Aligned: 1st grade math resources are in line with the common core math 1st grade, with regular updates. This ensures kids learn essential skills from the first grade math curriculum through fun activities.
• Fun & Engaging: Features exciting activities, fun characters, attractive themes, and colorful visuals.
• Cross-Platform Compatibility: Games seamlessly work on various devices, including Windows, Mac, iOS, Android, and Chromebooks. Worksheets can be accessed easily through a PC or laptop.
• Flexible and Easy to Use: Ideal and convenient for 1st grade kids, parents, and teachers.

Best Tips for Teaching First Grade Math to Kids

Consider these useful tips to simplify math for 1st graders:

• Understand the curriculum : Learning about the 1st grade math curriculum and its key goals is crucial. This clarity helps focus on important concepts. Read Most Important Math Concepts Kids Learn in the First Grade to get an overview of math concepts taught in the 1st grade. A perfect blog for teachers and parents!
• Use different learning resources : Use different learning methods, such as games, worksheets, etc. This ensures students stay engaged and interested in the learning process. These resources go beyond traditional methods and offer fun learning experiences.
• Real-world connections : Make math fun and relatable for kids through everyday activities, such as counting steps on stairs, identifying positions of minute hand and hour hand, etc. These strategies help make learning math for 1st graders relevant, fun, and enjoyable.

What Are the Best 5 First Grade Math Resources for Kids?

Here are 5 fun 1st grade online math resources:

• Math Lesson Plan — Addition & Subtraction Word Problems Magic

How will our 1st grade math online educational resources benefit your child?

First grade math resources help make math learning convenient for children. Kids can practice important math skills at any time from any place by using these resources. They also allow children to practice at a pace they’re comfortable with, thus providing them with personalized, student-centered learning. First grade learning math resources promote critical thinking skills in children. Kids learn to use their analytical and logical skills to solve math problems which enhances their critical thinking. Practicing math for 1st graders becomes more fun and engaging through online educational resources. Kids can practice essential math concepts by playing interactive games and solving fun worksheets that make the process of learning enjoyable for them.

What are the important topics in math for first graders?

Some important topics in math for 1st graders include measurement, time, money, word problems, addition, subtraction, geometry and number sense.

How can we get first graders excited to learn math?

First grade learning math resources can be used to teach essential math topics to children. These resources, including math games and math worksheets , promote math talk in children which subsequently increases their interest in mathematics. Real-time activities can be used to teach first grade math to children. For example, clocks can be used to teach the concept of time, grocery shopping can be used to teach the concept of money, kids can sort different objects in the house to learn about 3D shapes like a ball is a sphere, a block is a cube, a party hat is a cone, etc. This helps children to get excited about practicing math as they learn to relate mathematical concepts to real life. You can set up various milestones for math learning with your child. This motivates children to practice as they start perceiving different topics as achievable areas for learning and succeeding.

Your one stop solution for all grade learning needs.

Home » 1st Grade Teaching Resources » 21 1st Grade Word Problems For Easy Math Skill Development

21 1st Grade Word Problems For Easy Math Skill Development

An important part of the curriculum, 1st grade word problems offer students an opportunity to apply the math concepts they have learned in class to everyday situations. 

Math class can be one of the most challenging subjects for children, so understanding and solving word problems about math in a practical way helps students practice math skills while applying different learning styles and understanding of math concepts in the real world. 

Table of Contents

Do 1st graders do word problems, best 1st grade word problem worksheets, how do you teach first grade word problems, about the author.

First grade students can do word problems by approaching them using what they already know: language skills like reading and listening, working together in teams, and manipulating objects to demonstrate and develop spatial sense. Word problems help students to understand the world around them, be able to solve real-world mathematical problems they can use in their everyday lives, and develop critical thinking skills, so it’s important to introduce word problems as early as 1st grade to help students think holistically about math.

In partnership with Teach Simple , whose marketplace is full of educational materials created by actual teachers (plus 50% of all revenues go to them), I have curated a list of 1st grade word problems on fantastic, interactive worksheets for teachers and parents to use to challenge students. They can be used in the classroom or at home . 

Children are often drawn to this kind of thinking, and there are lots of fun ways to make the experience playful and exciting for them. These worksheets and activities align with common core math standards for 1st grade, which include operations and algebraic thinking, numbers and operations, measurement and data, and geometry.  

Secret Word Problem Puzzles

These 5 sets of puzzles will help students add and subtract within word problems. Students solve the word puzzles and use their answers to figure out the code words. 

This bundle includes the secret code card, 8 word problems per set, response cards, and an answer key to check answers in 1 PDF file. 

Word Problems Solving Worksheet

With this worksheet, students can read the word problem and choose the correct operation to solve it. Simple yet effective, this printable sheet includes pictures and is available in 1 PDF file.  

Single Digit Addition Word Problem Activity

This printable worksheet has students solve single-digit addition word problems using colorful images and relatable situations. 

Math Strategy Cheat Sheet for Word Problems

This resource is a math strategy cheat sheet that students can utilize when solving word problems. When working on a problem, students can pull out this resource guide and determine which strategy will help them most. It includes 1 PDF with 2 ready-to-print pages.

Dental Math Word Problems Worksheet

This activity engages students by challenging them to solve word problems while learning all about the dentist! 

“ It’s Fall” Word Problems

These engaging math and literacy worksheet sets include word problems to be solved on a number line, as part-part-whole (number bonds), and in a drawing. This is an ebook download in PDF format.

Ocean Math Word Problems Activity

This activity engages students by asking them to solve word problems while learning about oceans. It contains 1 product file.  

Storytime Discoveries Math

The stories and activities in this book help make math fun through interesting folktales , poems, and original stories. Students learn about logical thinking, problem solving, and various mathematical concepts, such as measurement, shapes, telling time, addition, fractions, and map reading. 

”It’s Winter” Math Word Problems

When it’s cold outside, add some fun to your classroom with these engaging math problems. They have activities that can be used for morning work, homework, group work, or in learning centers. 

This product includes a word problem to be solved on a number line, as part-part-whole (number bonds), and in a drawing. 

Cut-and-Paste Math Word Problems

With this activity, students can practice word problems with cut-and-paste activities that provide hands-on practice for simple addition. Students read the problem, count out the amount they need, add them together, glue them onto their paper, then write their equation. 

2-Digit Addition, Subtraction, and Word Problems Workbook

This workbook provides practice for place value , two-digit addition and subtraction, odd and even numbers, and addition and subtraction word problems. It includes a 21-page printable packet with activities.

Frostyville Cinema Worksheets

These worksheets contain a variety of math skills that align with the curriculum. Students will work on reading a schedule and a menu, solving word problems, adding and subtracting money , and working on elapsed time. 

It has a fun wintertime theme and two different levels of problems, a color version, a black-and-white version, and the answer key.

Add and Subtract Word Problems Worksheet

This worksheet has add and subtract word problems ranging from 10 to 100.

10 Printable Word Problem Worksheets (Numbers 1–20)

This printable bundle has four word problems worksheets on addition, four on subtraction, and two worksheets on mixed operations.

Barnyard Math Word Problems

This activity engages students by asking them to solve word problems while learning about barnyard animals.

Harvest Theme Addition and Subtraction Word Problems

These materials are designed to be a follow-up activity after instruction on tens frame is presented. 

The word problems are presented on task cards. Students can answer the problems by using ten frames and apple-themed counters. Then, they can write their answers on a student recording sheet.

Math Word Problems Worksheet

These addition word problems include key words such as “in all,” “altogether,” “total number,” and “sum.” They have fun colorful pictures to make the problems interesting. These files are in a zipped folder with 8 sheets. 

First Grade Word Problems

This is a set of 30 math worksheets for first grade . They give students structured practice in solving addition and subtraction word problems, which involves both math and reading comprehension .

Addition Within 20 Word Problems Task Cards

These task cards each have an addition word problem with answers within 20. There are 20 cards, recording sheet, and answer key included.

Time Word Problems and Blank Clock Template

These printable worksheets are available in PDF format with 4 PDF worksheets with a blank template that includes analog clocks and empty boxes, to assist students practice giving varied times. Word problems are included in two worksheets for extra practice. Given certain time constraints, students must solve the problem and indicate when the event began and when it ends.

Multiplication for Primary Students

If you have any first graders that are ready to give multiplication a try, this resource contains 9 pages that will help your students understand multiplication.

The goal with 1st grade word problems is for students to develop skills like abstract and quantitative reasoning, applying mathematical tools they have already learned, and making sense of real-world mathematical scenarios. 

When teaching word problems to 1st grade students, we want to make sure we explain the problems clearly, note when students struggle with language comprehension (such as new vocabulary), and are available to provide support by talking out the problems with students. 

Here are some great tips for teaching word problems:

Tip 1: print them on good quality cardstock or laminate for durability and longevity, tip 2: print them on colored paper to engage students’, tip 3: remind students of different strategies they can use to solve word problems, tip 4: let students have access to the answer sheets once they have worked on the problem so they can self-correct, tip 5: have students work in groups, make the 1st grade word problems into a game, and get creative with your teaching style.

Jen Skolsky has a background in English, Psychology, and Creative Writing. She has taught for many years in international education, including ESL for all ages, middle school literature, speech and debate; high school AP Psychology, AP Language, AP Literature; university level Academic Writing, and Chinese Medicine Theory. She now works in marketing and book publishing.

Share Article:

Download unlimited teaching resources, join free today, teach simple.

The team behind Teach Simple is a small but dedicated group who are passionate about education and making a positive impact on the lives of teachers and students.

We have a lot of interesting articles and educational resources from a wide variety of authors and teaching professionals.

17 Of The Best First Grade Coin Worksheets

23 first grade grammar worksheets that teach the basics.

Last Updated on July 17, 2023 by Teach Simple

• ELEMENTARY TEACHING , SOCIAL EMOTIONAL LEARNING IN THE CLASSROOM

SEL Problem Solving: How to Teach Students to be Problem Solvers in 2024

If you are an elementary teacher looking to learn how to help your students solve problems independently, then you found the right place! Problem solving skills prepare kids to face dilemmas and obstacles with confidence. Students who have problem solving skills are more independent than students who do not. In this post, we’ll go into detail about what problem solving skills are and why they are important. In addition, we’ll share tips and ideas for how to teach problem solving skills in an elementary classroom setting. Read all about helping students solve problems in and out of the classroom below!

What Does Solving Problems Mean?

Solving problems means brainstorming solutions to the problem after identifying and analyzing the problem and why it occurred. It is important to brainstorm different solutions by looking at all angles of the problem and creating a list of possible solutions. Then you can pick the solution that fits the best.

Why is it Important for Kids to Solve Problems?

It is important for kids to solve problems by brainstorming different solutions so that they can pick the best solution. This teaches them that there can be many different solutions to a problem and they vary in effectiveness. Teaching kids to solve problems helps them be independent in making choices. 

How Do I Know If I Need to Teach Problem Solving in My Classroom?

The students in your 1st, 2nd, 3rd, 4th or 5th grade classroom would benefit from problem solving lessons and activities if any of these statements are true:

• Student confidence is lacking.
• Students are getting into conflicts with each other.
• They come to you to solve problems they could have solved on their own.
• Students are becoming easily frustrated.
• Recess is a hard time for your class.

5 Reasons To Promote Problem Solving In Your Elementary Classroom

Below are 5 reasons to promote problem solving in your elementary classroom.

1. Problem solving builds confidence 

Students’ confidence will grow as they learn problem solving skills because they will believe in their own abilities to solve problems. The more experience they have using their problem solving skills, the more confident they will become. Instead of going to others to solve problems for them, they will look inside themselves at their own abilities. 

2. Problem solving creates stronger friendships

Students who can problem solve create stronger friendships because they won’t let arguments or running into issues stop them from being friends with a person. Instead they work with their friend to get through their problem together and get through the bump in the road, instead of giving up on the friendship. 

3. Problem solving skills increase emotional intelligence 

Having emotional intelligence is incredibly helpful when solving problems. As students learn problem solving skills, they will use emotional intelligence to think about the feelings of others involved in the conflict. They will also think about how the problem is affecting others. 

4. Problem solving skills create more independent kids

Students who can problem solve become more independent than kids who cannot because they will try to solve their problems first instead of going to an adult. They won’t look at adults as being the only people who can solve their problems. They will be equipped with the skill set to tackle the problems they are experiencing by themselves or with peers. However, it is important to make the distinction with kids between problems they can solve on their own and problems they need an adult for. 

5. Teaching problem solving skills causes students to be more reflective 

Reflecting is part of the problem solving process. Students need to reflect on the problem and what caused it when deciding how to solve the problem. Once students choose the best solution to their problem, they need to reflect on whether or not the solution was effective. 

5 Tips and Ideas for Teaching Problem Solving Skills 

Below are tips and ideas for teaching problem solving.

1. Read Aloud Picture Books about Problem Solving Skills 

Picture books are a great way to introduce and teach an SEL topic. It gets students thinking about the topic and activating their background knowledge. Check out this list of picture books for teaching problem solving skills !

2. Watch Videos about Problem Solving Skills 

There are tons of free online videos out there that promote social emotional learning. It’s a fun and engaging way to teach SEL skills that your students will enjoy. Check out these videos for teaching problem solving skills !

3. Explicitly Teach Vocabulary Related to Problem Solving Skills 

Vocabulary words can help students develop understanding of problem solving and create connections through related words. Our problem solving SEL unit includes ten vocabulary cards with words related to the SEL topic. It is important for students to be able to see, hear, and use relevant vocabulary while learning. One idea for how to use them is to create an SEL word wall as students learn the words.

4. Provide Practice Opportunities

When learning any skill, students need time to practice. Social emotional learning skills are no different! Our problem solving SEL unit includes scenario cards, discussion cards, choice boards, games, and much more. These provide students with opportunities to practice the skills independently, with partners or small groups, or as a whole class.

5. Integrate Other Content Areas

Integrating other content areas with this topic is a great way to approach this SEL topic. Our problem solving SEL unit includes reading, writing, and art activities.

Skills Related to Problem Solving

Problem-solving, in the context of social emotional learning (SEL) or character education, refers to the process of identifying, analyzing, and resolving challenges or obstacles in a thoughtful and effective manner. While “problem-solving” is the commonly used term, there are other words and phrases that can convey a similar meaning. These alternative words highlight different aspects of finding solutions, critical thinking, and decision-making. Here are some other words used in the context of problem-solving:

• Troubleshooting: Identifying and resolving problems or difficulties by analyzing their root causes.
• Critical thinking: Applying logical and analytical reasoning to evaluate and solve problems.
• Decision-making: Considering options and making choices to address and solve problems effectively.
• Analytical problem-solving: Using data, evidence, and systematic thinking to address challenges and find solutions.
• Creative problem-solving: Generating innovative ideas and approaches to overcome obstacles and find solutions.
• Resourcefulness: Finding effective solutions using available resources and thinking outside the box.
• Solution-oriented: Focusing on identifying and implementing solutions rather than dwelling on problems.
• Adaptability: Adjusting strategies and approaches to fit changing circumstances and overcome challenges.
• Strategic thinking: Planning and organizing actions to achieve desired outcomes and resolve problems.
• Systems thinking: Considering the interconnectedness and relationships between different elements when solving problems.

These terms encompass the concept of problem-solving and reflect the qualities of critical thinking, decision-making, and finding effective solutions within the context of social emotional learning (SEL) or character education.

Download the SEL Activities

Click an image below to either get this individual problem solving unit or get ALL 30 SEL units

In closing, we hope you found this information about teaching problem solving skills helpful! If you did, then you may also be interested in these posts.

• SEL Best Practices for Elementary Teachers
• Social Emotional Learning Activities
• 75+ SEL Videos for Elementary Teachers
• Teaching SEL Skills with Picture Books
• How to Create a Social Emotional Learning Environment

You might also like...

5 Read Alouds about Respect for Elementary Teachers in 2024

8 Children’s Books about Worrying for Elementary Teachers in 2024

8 Self Regulation Books for Elementary Teachers – 2024

Join the newsletter.

• CLUTTER-FREE TEACHER CLUB
• FACEBOOK GROUPS
• EMAIL COMMUNITY
• OUR TEACHER STORE
• ALL-ACCESS MEMBERSHIPS
• OUR TPT SHOP
• JODI & COMPANY
• TERMS OF USE
• Privacy Policy

• Skip to primary navigation
• Skip to main content
• Skip to primary sidebar

Simply STEAM Education

Making STEAM education simple!

March 11, 2021

7 Fun Activities For Teaching Word Problems That Actually Work!

Word problems are an important part of math instruction because they show students how they can use the math they are learning in the classroom in real life. A skill they will be using constantly throughout their life!

For this reason, I try to make learning this skill as fun as possible so that students will be engaged enough to really learn and understand the concept!

Here are some of my favorite tips for teaching word problems!

• Use picture books – Model real-world problems using actual books. This is so easy to do with pretty much any picture book. All you need are pictures! While you’re reading, look for any changes with adding and subtracting in the pictures. For example: in Eric Carle’s The Very Hungry Caterpillar, you can point out the adding one concept using the food. This is a good start for helping students understand that word problems have a beginning, change, and an end. For modeling subtraction, I found this book One Big Pair of Underwear. It’s hilarious! The kids really liked the funny pictures and obviously, anything with underwear captures their attention.

• What do you know? 
• What do you need to solve? 
• How might you solve that?

 This supports your little learners by helping “read” the world problem and it integrates with your listening and speaking standards. 

• Use rewards – Motivate your students to complete word problems. You can use this FREE Word Problem pack to do that. When students complete a word problem, they simply color, stamp, or place a counter over a space. When they’ve completed a certain amount, they earn a reward of their choice. For example, if a student completes five word problems, then the student can take their shoes off. 

• Making Movies – is another way I like to teach my students how to solve word problems. Have them close their eyes and visualize what is happening in the story. Is the information missing in the beginning, middle, or end of the story?

• DIY Word Problems – Create your own math word problems. Have students roll dice to create their own math word problems. This helps engage them in learning and gets them to work independently. You can grab these by clicking here ! 

• Get Hands-on -Use math manipulatives to model word problems. My favorite math manipulative is using an abacus. I model with one row the first part of the story. Then, I model the second part on the second row. Finally, I model the third part on the third row. Wherever the missing information is (beginning, middle, or end), we don’t model it, and this is where we show our answer. You can also use a tens frame with counters. This hands on manipulative organizes the information for kids to see and it’s an essential tool that will appear over and over again in K – 2. 

• Play Games – There are so many benefits to doing this. You can read about those here. You can get extra practice with word problems using these games. I’ve made sure to create a balance with word problems that have a missing beginning, missing middle, and a missing end. There are some with a change and some that compare.

These activities have always been a hit in my classroom. Making learning fun is such a simple and great way to increase student engagement and learning outcomes!

What are your favorite ways to teach word problems? Let me know in the comments!

Share this:

Reader interactions, leave a reply cancel reply.

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Notify me of follow-up comments by email.

Notify me of new posts by email.

You Might Also Love

Get connected with Simply STEAM!

• Skip to main content

Use promo code: SJT15OFF to take an extra 15% off your first purchase!

Susan Jones Teaching

Teaching Resources

Story Problems in First Grade

susanjones March 8, 2016 Leave a Comment

This post may contain affiliate ads at no cost to you. See my disclosures for more information.

Addition Subtraction Place Value Time Missing Addend Fractions Money

Looking for more standards-based math games that will engage your learners and save you lots of time?!

Join hundreds of primary teachers over in the SJT Math Club:

You may also enjoy these posts...

Reader Interactions

Leave a comment cancel reply.

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed .

Free CVC Word Mapping Mats

Sign up for my free email newsletter and receive these free CVC Word Mapping Mats to help with your next lesson plan!

Check out these popular math resources!

We have loads of great math resources over in the shop. Here are just a few I pulled together for you!

Math Games for 1st Grade: Print, Play, LEARN!

Number Sense Activities (0-20)

Telling Time Games

Subtraction Games & Activities

Hello friends.

Welcome to Susan Jones Teaching. When it comes to the primary grades, learning *All Things* in the K-2 world has been my passion for many years! I just finished my M.Ed. in Curriculum and Instruction and love sharing all the latest and greatest strategies I learn with you through this blog and my YouTube channel! I hope you'll enjoy learning along with me :)

More About Me

• Our Mission

Shining a Light on Dyscalculia

Here’s how to recognize what might be behind a student’s difficulty with math as well as strategies for teaching them.

With reading research and methodology in the current spotlight, educators are learning more about dyslexia. Now, many are asking for the same support regarding math instruction and dyscalculia , which Dr. Honora Wall, founder of the Dyscalculia Training and Research Institute , defines as “a type of neurodivergence: a difference in brain development or function.”

There’s much less research, however, about dyscalculia than there is for dyslexia. In Dyscalculia: From Science to Education , cognitive neuropsychologist Brian Butterworth writes that since 2000, the National Institutes of Health has spent $107.2 million in funding for dyslexia research but only $2.3 million on dyscalculia. Consequently, students with dyscalculia are not getting the support they need, due to the lack of teachers’ knowledge about the disorder. 

Programs and approaches designed for the needs of learners who are dyslexic, such as Orton-Gillingham, Barton, S.P.I.R.E., and Fundations, just to name a few, are readily available. With no equivalent for dyscalculia, educators are scrambling for just the right tools to effectively address the needs of a vulnerable population. The good news is, there are several very concrete ways teachers can support these students.

What dyscalculia is not

It’s not dyslexia with numbers. Dyslexia typically involves difficulty learning how to read, which can interfere with math learning. However, dyscalculia impedes a person’s ability to make sense of numbers and math concepts in ways that are different from dyslexia. 

It’s not uncommon. Research suggests, according to Butterworth, that dyscalculia is just as prevalent as dyslexia. In fact, Butterworth maintains that it’s estimated that 50 to 60 percent of people with dyslexia also have dyscalculia. 

It’s not being bad at math. Studies have shown that babies demonstrate an innate understanding of numerosity, as Butterworth says in his book. Dyscalculia is a learning difference that requires specialized teaching and isn’t just “being bad at math.”

Indicators of dyscalculia

There are several behaviors that can present themselves in learners with dyscalculia. Just as dyslexia and ADHD (attention-deficit/hyperactivity disorder) present themselves on a spectrum, the same is true for dyscalculia. That means that each student brings with them a unique set of strengths and weaknesses. Below are behaviors that are typical for students with dyscalculia. 

Difficulties subitizing and estimating: Subitizing is the ability to “see” small numbers without actually counting them. For example, when rolling a die, a young student with dyscalculia will need to count the dots as opposed to automatically seeing that the number rolled was four.

Difficulties with patterns: Students with dyscalculia may have difficulty putting numbers in order from least to greatest or greatest to least. They also may struggle with skip counting or determining what number would come next in a sequence. 

Loss of previously acquired skills: Research, according to Wall, hasn’t quite determined why this happens, but it is very typical for students with dyscalculia to forget the math they learned, much to the dismay of their teachers. Some lose information quickly, others over time. This is why reference charts and a structured, spiraling curriculum are crucial. 

What kind of teaching do dyscalculic learners need? 

CRA Instructional Sequence: In The Dyscalculia Toolkit: Supporting Learning Difficulties in Maths , specialist teacher Ronit Bird agrees with Butterworth that a Concrete Representational Abstract instructional sequence is an approach that moves students from using concrete manipulatives to representational drawings to abstract numbers when learning new concepts and is a best practice for all learners. Dyscalculic learners will need to experience this sequence multiple times and gradually, when developing new skills and understandings. 

Visualization: Often the transition from the concrete stage to abstract is a bumpy one. Bird suggests that dyscalculic learners be explicitly taught how to picture numbers and operations in their mind’s eye. This is especially true when solving word problems. Drawings, open number lines, and area models are some of the ways she suggests to bridge the concrete and abstract stages. 

Quality over quantity: Bird and Butterworth both recommend limiting the demands on a learner’s working memory, allowing them to focus on the important skills of a task. Providing reference charts, reading directions, and using rubrics are just some of the ways to reduce the load placed on working memory. 

Explicit scaffolding: All learners must have a secure understanding of foundational concepts before building on them. This is especially true for learners with dyscalculia. Making explicit connections to previously taught skills and breaking tasks down into the smallest of steps are essential. This reduces the risk of taking students’ background knowledge for granted.

How to plan instruction

Focus on sets: Butterworth asserts that dyscalculics struggle with operations because of a deficit in the understanding of numbers as sets. Instruction needs to focus on supporting concepts such as counting, one-to-one correspondence, part-whole relationships, and cardinality in the early years. 

Diagnostics: There are assessments typically used by psychologists to diagnose dyscalculia, including the Wechsler Intelligence Scale for Children, KeyMath-3, Wechsler Individual Achievement Test for Math Fluency, and the Feifer Assessment of Mathematics. Educators, however, must first identify which students need additional support and then specifically which mathematical knowledge is in need of intervention. Acadience Math, the Early Childhood Assessment in Mathematics, Universal Screeners for Number Sense, and the Georgia Numeracy Project are widely used resources. 

Feedback: Because a loss of previously acquired skills is a hallmark of the disability, committing mathematical understanding to long-term memory is an arduous process. It is imperative that the information learned be accurate. Wall writes that research suggests that when the brain learns new information, it does not “overwrite” what it has already learned, even if that information is incorrect.

This speaks to the uphill battle that teachers face when having to undo a misconception that a student has committed to memory. In order to avoid this, students who struggle must be given consistent, real-time feedback as they learn. In addition to teacher input, Butterworth recommends adaptive digital platforms and games as great ways to provide feedback consistently.

Manipulatives: Numbers are abstract. Manipulatives make numbers concrete. Using blocks, Cuisenaire rods, ten frames, and counters are just some of the ways students can have hands-on experiences. Dyscalculic learners solidify the concept that numbers are made up of sets of smaller numbers with tactile input from manipulatives.

Joy: Fear of math is a reality for many and is a major obstacle to learning. Years of struggle reinforce math as unenjoyable and a source of anxiety. The frequent use of games modified to students’ current levels of understanding can have a disarming effect on those who experience math aversion. 

There is still much to learn about dyscalculia. When armed with the right information, however, educators can make small changes to their practice that will have a huge impact on the lives of those with dyscalculia.