math problem solving cards

Flash Math Cards

Flash Math Cards helps you practice math in a natural and fun way, with interactive flash cards to build your memory and recall of addition, subtraction, multiplication, and division.

In practice mode, swipe down to reveal a new card, then think carefully about the right answer. Check yourself by swiping sideways to flip the card over.

Once you're ready to test your skills, start the challenge mode. Enter your answer with the on-screen numbers, or you can even tap the voice button and say your answer out loud! But hurry, each problem has a timer -- the faster you answer, the more points you get!

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Problem Solving Practice Cards

Built for rigor and carefully aligned to the standards, these activity card sets will help students develop a variety of problem-solving strategies. Featuring classroom-tested problems, each card also suggests a specific strategy to be used such as drawing a picture, using a model or solving an equation. There are three sets available – for grades 3, 4 and 5. Each set contains 100 cards – 20 for each of the five domains and detailed teacher activity guide.

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Macmillan Maths: Problem Solving Boxes

Our problem-solving boxes are designed to take learners on a creative journey! Students are encouraged to use real contexts to apply the mathematics they have learned in lessons. Presented in a flexible, supplementary format, they are an easy, out-of-the box resource that are perfect for immediate lessons. The problem-solving boxes challenge students to think deeply and laterally to develop a full understanding and firm grasp of mathematical concepts and include extension activities for high achievers.

At a glance

• Each box contains 150 enticing cards to develop and strengthen problem-solving strategies across number and algebra, measurement and geometry and statistics and probability
• The digital offering provides ISWB-friendly PDFs of all cards and blank card templates, a teaching guide, assessment guidelines and rubric, posters, record sheets, answers and index

About the series

• Presented in a flexible, supplementary format
• easy, out-of-the-box resource for additional practice
• challenges students to develop a full understanding and firm grasp of mathematical concepts

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An Easy Way To Boost Math Problem Solving Skills

Math Problem Solving Task Cards are one of the most productive tools for helping students build a deeper understanding of math concepts. These unique task cards include a variety of word problems that require students to utilize problem solving skills, critical thinking, precise modeling, and get routine practice with explaining their reasoning. Each day during Math Workshop , students are given time to work on these rigorous task so they can connect the math skills they are learning to real world situations.

This post contains affiliate links for which I may make a small commission at no extra cost to you should you make a purchase.

To make the most of this tool, and rapidly build your students’ problem solving skills, it is essential that students are given time to engage with these tasks on a routine basis. This post includes a break down of the math task card routines and expectations I have used for years in my second and third grade classes, which can be adapted and used in your elementary classroom this coming week.

When Do Students Work On Task Cards?

During the At Your Seat rotation of Math Workshop each day, students are given time to work on their task cards. First, students complete a short exit slip-style assignment that directly aligns to the mini lesson taught that day. In my classroom, this assignment has always come directly from our district-adopted curriculum. That assignment is completed, checked, and placed in the homework folder (the backside of this sheet is nightly homework due the following day).

Then, students move on to their task card work. On average, students spend about ten minutes working on task cards each day before it is time to move on to the second rotation of Math Workshop.

How Do Students Select Their Task Card?

At the back of our classroom, there is a small display that serves as the designated task card board. Each week, four Making Meaning Tasks and four Challenge Tasks are displayed.

Making Meaning Tasks require students to apply grade-level math concepts to solve complex word problems. Challenge Tasks are designed to provide enrichment opportunities to students who have mastered the math concepts introduced. Each Challenge Task requires critical thinking and the ability to apply known skills to solve more advanced and complex situations.

Individual students make their own decision as to which type of task they wish to complete. Two copies of each task are printed, laminated, and placed in the pockets on our task card board. This allows more than one student to work on the same task simultaneously.

What Do Students Do Once They’ve Selected A Task Card?

After a task card is selected, a student also picks up a blank problem solving recording sheet , and heads back to his desk to begin solving. The problem solving process used to solve each task is outlined on the side of the recording sheet, which serves as a checklist for students.

If a student runs out of time and needs to prepare for their next Math Workshop rotation, or needs to tidy up because Math Workshop has ended, they tuck the task card back into its pocket on the task card board, and place their recording sheet in their math binder to continue the following day.

If a student completes a task card, she submits it to our rubric drawers (described in detail below), then heads back to the board to select another task card and recording sheet.

Are Students Required To Solve Task Cards Independently?

For the most part, students complete task cards independently during the At Your Seat rotation of Math Workshop. They do have the option of working with a partner to solve a task card (each partner must submit their own recording sheet), or to ask members of their Math Triad for help as needed.

Challenge tasks are also an excellent tool for small group instruction with advanced learners. In this case, I recommend starting with a math talk-style conversation, then moving on to have each member of the small group record their model and explanation on a recording sheet.   

How Many Problem Solving Task Cards Do Students Complete Each Week?

Due to the fact that these tasks cards require a great deal of modeling, labeling, and a written explanation of math reasoning, students usually complete one task card every two days, and two task cards every week.

Once students complete a task, they will walk over to our rubric drawers, reflect on their level of understanding for that task, and place their recording sheet in the drawer that corresponds with that level of understanding. Any task submitted to these drawers can be quickly checked and stamped to be sent home. Each week, students get to select one of their tasks to submit to the bin sitting on top of the rubric drawer tower. This task will be closely checked by me, scored, entered in the gradebook, and given written feedback before bring sent home.

When a task card is submitted to the rubric drawers for feedback, students draw a star next to their name on our Weekly Task Card Record poster using a Vis-A-Vis pen. This allows me to quickly check who is on track to meet their weekly goal, and who needs to work on task cards as an early finisher option after bellwork or word work. This poster is wiped clean at the beginning of each week for a fresh record-keeping start.  

If a student needs a custom task card goal that is modified to meet their unique learning strengths or needs, I let them know one-on-one what their weekly goal will be.     

How Are Task Cards Scored?

Scoring task cards daily is highly recommended because the process will be quick, and you can share your feedback with students in a very timely manner. In a general education classroom the reality is you may only have time to score tasks weekly, and share your feedback with students on a set day each week…nothing wrong with that!

To save your grading sanity, I recommend spending time completing in-depth scoring for one task card per student per week. Having a special bin where students submit the task they are most proud of (as described above) can help you organize this system. You may even want to have students use this rubric and reflection freebie to score their own work in depth, and provide a consistent feedback format. Taking an extra minute to enter this weekly score as a formative assessment data point makes this process even more worthwhile.

For the other tasks students have self-scored using the rubric drawers, do a quick glance for accuracy, stamp, and file. The only exception is if students score themselves at a level of understanding of 1 or 2 using the rubric drawers. You may want to pull those tasks aside, and use them for small group instruction during the Meet the Teacher rotation.

CORE INSPIRATION MATH RUBRIC & REFLECTION FREEBIES

Applying these routines in your classroom.

If you are ready to boost your students’ ability to solve word problems, and deepen their math understanding, here are all the task card-related supplies I use in my classroom to help you get started. I have listed these supplies in order from most essential to least essential to help you get started.

• Problem Solving Task Cards
• Problem Solving Recording Sheets
• Problem Solving Reflection and Feedback Freebie (submit form above)
• Task Card Board Labels Freebie (submit form above)
• Weekly Task Card Tracker Freebie (submit linked above)
• Cardstock for task card pockets
• Feedback bin
• Rubric drawer bins
• Rubric drawer towers

I’d love to hear about your experience with introducing these routines in your classroom, and any questions you may have in the comments below.

INTERESTED IN LEARNING MORE ABOUT MATH WORKSHOP?

For more details about Math Workshop, check out my other posts about this instructional approach.

HOW TO INTRODUCE MATH WORKSHOP IN YOUR CLASSROOM:

Details about m.a.t.h. rotations:.

• Overview: Differentiate Instruction with Math Workshop
• Warm Up: Number of the Day Binder
• Mini Lesson: 3 Approaches To Formatting Lessons for Math Workshop
• Meet with the Teacher: How To Organize Small Groups for Math Workshop
• Meet with the Teacher: 5 Steps To Efficient Data Tracking
• At Your Seat: Top 5 Ideas for Math Workshop At Your Seat
• At Your Seat: Boost Problem Solving Skills
• Hands On: Tips for Making Math Games A Success

MATH WORKSHOP CLASSROOM MANAGEMENT TIPS:

• How To Boost Student Independence With Math Triads
• Incorporating Project Based Learning Into Math Workshop
• How To Make Transitions Efficient During Math Workshop

This post contains Amazon Affiliate links to make it easier for you find the problem solving task card supplies shared in this post. To see all my favorite Amazon finds, visit my  Amazon Influencer page here .

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13 Responses

I love the idea of task cards . I would love to use these with my first graders. Do you have first grade task cards for sale, and if not, do you know of a resource that could be easily used? Thanks!

Hi Martine, Thank you for reaching out. I would love to tell you I have task cards for first grade, but I don’t currently have those available. I would check in with the store called The Brown Bag Teacher. She may have something similar because I know her content is quite rigorous. Wishing you and your students all the best! Laura

I love this idea and want to apply it with my middle school students. I see that students are required to do two of these per week. How do you handle this with students who are chronically absent? Also, do you have any task cards for middle school (grades 6-8)?

Hi Teresa, Thank you for reaching out. I don’t have much experience with chronic absence, but my gut would be to assign it as makeup work completed for homework. I don’t have any middle school task cards, but I believe Lindsay Perro has some rigorous middle school math resources. Warmly,Laura

This seems like such a simple process! Where would you suggest for 5th grade resources, or is it that any task cards will work with the recording sheet? In other words, is the rigor from the cards or the breakdown/process of answering them? What is your approach for those who do not complete or work well independently? Thanks so much!!

Hi Christi, thank you for the kind message. 🙂 The recording sheets are designed to work well with any task card. The task cards in my store are specifically designed for second and third grade standards. Teaching With A Mountain View has great task cards for fifth grade. For those who struggle with independence, I usually have them complete one task card per week instead of 2. For some, I also write the task card question for them as we talk through the process they will use to solve. Then they complete the modeling and solution with independence.

Hi Laura, Couple of questions…where did you get the small storage boxes for task cards that have the task label on them? I’ve been trying to find the perfect size. Do you have a file available with those box labels? I can’t seem to access anything through PicMonkey…am I missing something? When I click on the link, I am taken to a page but I can’t enter my email address. Thanks for all you help! Hope

Hi Hope, Thank you for reaching out. 🙂 The small storage boxes are from The Container Store, but they can also be found on Amazon here . (affiliate link) The box labels are an exclusive freebie when you purchase the year long math enrichment bundle for third grade. I’m a bit unclear on what you are referring to when you mention the PicMonkey link. Can you clarify which link you are clicking on? I appreciate your help. 🙂 Warmly, Laura

oops, it’s the mailchimp link for Problem Solving Reflection and Feedback Freebie. The link asks for my contact info, but then there is no where to enter it. I’m sure, I’m doing something wrong, I just don’t know what it is. HAHA

I notice that the page for Week 3 of starting the Math Workshop gives a 404 error (page no longer exists). Is that post available somewhere else? I would like to know how to introduce the small group component of math workshop.

Hi Carolee, Thank you for reaching out. I had posted the link in several of the Math Workshop posts before the third week post went live. 🙂 It is now available, and you can find it here . Sorry for the inconvenience. Warmly, Laura

I’ve been trying to get the task card board labels freebie sent to my email, but it’s not working.????Any way you could check it out? I’m obsessed with your classroom, management, and organization!!!

Hi Amy, Please make sure to check your junk/spam folder for the email. 🙂 Warmly, Laura

I’m Laura Santos

I’ve been an elementary teacher for ten years, and love sharing tips and resources that make differentiated learning more manageable for you. Thank you for visiting. Learn More

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9 Fun And Engaging Math Problem Solving Activities Your Students Will Enjoy

Are you looking for math problem solving activities that are fun and engaging? Then continue reading on! I will be sharing with you 9 fun math problem solving activities that you can use in your class.  

What are mathematics problem-solving activities?

According to the National Council Of Teachers Of Mathematics, Mathematics problem solving refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing students’ mathematical understanding and development. 

Problem-solving is a skill that we try to teach to our students in math class. A lot of times we will use word problems as problem-solving tasks. But there are actually more activities that do not involve story problems. 

You can use these problem-solving activities as a lesson themselves, math starters, review, fast finishers, with small groups or a large group.  

9 Fun Math Problem Solving Activities

Students often dread doing math word problems and tasks that are challenging. And forcing them down their throat is not the long-term solution as it can lead to math anxiety.

There must be a better way!

And the solution is…to find a fun way to tackle them!

Here is a list of 9 different ways to do problem-solving tasks. And I even gave some educational materials that you can grab if you are interested to use them in your class.

• Online Word Problems Practice
• Short Video
• Non-Routine Word Problems
• Hands-On Math Problem Solving Activities
• Math Puzzles
• Mystery Puzzles
• Scavenger Hunt
• Digital Treasure Hunt
• Escape Room

1) Online Word Problems Practice

Children love to go online. So by giving them a chance to play with the tablet or computer, they will already be more interested in the task on hand than usual. 

Consider the digital interactive task cards available on the Boom Learning site. They are often self-checking and require no preparation. This means they do not require much time from you and students can accomplish the mathematical practice independently.  

Furthermore, if you assign the Boom Cards to students, you can look through the reports of your student’s progress and results.   

These digital versions of word problems not only add a bit more fun to them but also help to develop a deeper understanding of mathematical concepts.

2) Short Video

Video provides a multisensory experience that helps to capture students’ attention. It is also great for memory retention and can enhance their learning experience. 

A) Show short videos that help them build their problem-solving skills. 

For example, matchstick puzzle examples. 

Related read: 3 Free Math Puzzles With Answer For You To Enjoy This Summer

B) Show them videos that teach them math skills or review math skills. 

This can be just a short review or a math hook for more math practice. 

Related read: 5 Hooks For Math Lessons That Will Engage Your Students Easily & Quickly

C) Show them a real-life problem and ask them to solve it using math.

Linking math to a real-life issue can always help to make math lessons more exciting. 

You can show them an existing issue and let them brainstorm on how to solve them. How can we use our math knowledge or other knowledge to solve it? (Sounds familiar? Consider project-based learning.)

Or you can show how real-life problems were solved due to our knowledge of math. Will they be the next mathematicians that make an impact on the world? 

3) Non-Routine Word Problems

What is more challenging and interesting than word problems? It’s non-routine word problems! 

They can be tricky and require different problem-solving strategies than the usual problem-solving approach. 

It requires some critical thinking to get to the correct answer. Sometimes there may also be different solutions to these challenging problems.

4) Hands-On Math Problem Solving Activities

By incorporating hands-on activities with word problems, word problems look more attractive now! 

Furthermore, kinesthetic learners will benefit greatly from math craft or math craftivity. Hands-on activities are engaging. 

Be aware of the suitability of the craft as young children or older students may require different sets of activities. One way to differentiate is by grade level. 

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5) Math Puzzles

There are many types of math puzzles. For example, logic puzzles, sudoku puzzles, and magic squares.

These math puzzles can help build logical reasoning. 

6) Mystery Puzzles

Students get to practice rigorous word problems and develop a deep conceptual understanding with these mystery puzzles!  

Students now have to solve word problems to know which are the correct clues. 

Furthermore, these worksheets are differentiated which means students of different standards can also utilize them. There are different culprits for the different sets which means students can do all of them if needed. 

7) Scavenger Hunt

Scavenger hunts are great movement activities for students. However, to incorporate word problems with a scavenger hunt, I would prefer to use them for lower elementary students. 

That’s because word problems for lower grades are usually shorter and require less time to solve. 

After all, if students have to stand for very long at a spot, it lowers the fun factors of the scavenger hunts.   

8) Digital Treasure Hunt

Treasure hunt is similar to a scavenger hunt. But what I have in mind for you is a digital treasure hunt that requires students to solve word problems prior to “digging” the spot. 

These digital versions of treasure hunting help you save some hassle but still engage students. 

9) Escape Room

Escape room is great for practicing problem solving skills as it usually includes a variety of problems and puzzles. The types of problems will vary, depending on the creator. So choose the ones that suit your students’ needs. 

Some elaborate escape rooms let students practice decision-making skills, collaboration skills, spatial reasoning, logical reasoning, deductive reasoning, and/or a variety of mathematical knowledge. 

Of course, we can always stick to the less fussy way and make students solve logic problems.

Final Thoughts

To make math problem-solving activity fun and engaging, the questions must be either interesting enough or within the student’s ability. 

The fun part of any puzzle is always those that we can solve if we think harder or out of the box. 

If it is too hard, students will get discouraged very soon and all of us will not meet our goals.

However, we also need to develop students’ growth mindset so that even if they can’t solve complex tasks, they will have the correct mindset facing their “failure”.

Hopefully, by using these ideas and tips mentioned above, your class will start looking forward to problem-solving activities. And we can also start looking forward to an increase in their math abilities and test scores! 

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6 tips for supporting   problem-based learning in your math classroom

Most math teachers have been here before. We’ve all transposed the names of our own students for those in a word problem. We’ve all used our school community goings-on as fodder for plot lines: “If 89 middle schoolers are traveling on buses to Outdoor School, and each bus can transport 35 students and four chaperones.…” But how “real world” are we really getting?

We—Kailey Rhodes and Kristen Tsutsui, math teachers and authors of this blog post—wanted to know teachers’ experience with real-world problem-solving, what’s going well, and what’s in their way. So we surveyed some. In this post, we’ll walk you through what we asked, learned, and think as we move forward—and we’ll also share the resources our teachers shared with us. But first, let us introduce you to an official definition of real-world context in the math classroom.

The PISA Mathematics Framework

PISA is an international assessment administered to 15-year-olds globally. In their 2022 Mathematics Framework , PISA explains the underpinnings of their assessment as it relates to math literacy, reasoning, and problem-solving. It also stipulates that to uplift these underpinnings, mathematics problems should be presented in real-world contexts: personal, occupational, societal, and scientific.

Educators, take a moment to read the descriptions of these contexts . As you read, ask yourself the question we asked in our survey: “Which do you naturally find yourself gravitating toward in your classroom?”

• Personal: “Problems classified in the personal context category focus on activities of one’s self, one’s family, or one’s peer group. Personal contexts include (but are not limited to) those involving food preparation, shopping, games, personal health, personal transportation, sports, travel, personal scheduling, and personal finance.”
• Occupational: “Problems classified in the occupational context category are centered on the world of work. Items categorized as occupational may involve (but are not limited to) such things as measuring, costing, and ordering materials for building, payroll/accounting, quality control, scheduling/inventory, design/architecture, and job-related decision-making. Occupational contexts may relate to any level of the workforce, from unskilled work to the highest levels of professional work, although items in the PISA survey must be accessible to 15-year-old students.”
• Societal: “Problems classified in the societal context category focus on one’s community (whether local, national, or global). They may involve (but are not limited to) such things as voting systems, public transport, government, public policies, demographics, advertising, national statistics, and economics. Although individuals are involved in all of these things in a personal way, in the societal context category, the focus of problems is on the community perspective.”
• Scientific: “Problems classified in the scientific category relate to the application of mathematics to the natural world and issues and topics related to science and technology. Particular contexts might include (but are not limited to) such areas as weather or climate, ecology, medicine, space science, genetics, measurement, and the world of mathematics itself. Items that are intra-mathematical, where all the elements involved belong in the world of mathematics, fall within the scientific context.”

Which context did you most resonate with? If you were to focus on one context per quarter, how would you order them? What is your biggest struggle with real-world context and problem-based learning? How do you bring the “real world” inside your classroom?

We surveyed a focus group of math teachers, from kindergarten to IB, to see what they thought.

Survey says!

When we asked our teachers, “Which do you naturally find yourself gravitating toward in your classroom?” personal and scientific contexts were the winners, with societal coming in fourth. Our guess for this is that societal is not only ever-changing but is also often politically adjacent, something educators can, understandably, be wary of approaching.

Naturally, personal real-world math context offers an entry point into students’ interests, which is paramount in the math classroom. One teacher said, “Good projects that connect to the curriculum and also interest the students are worth their weight in gold. I really wish publishers did a better job of planning good projects; in most books I’ve used, the projects, if they exist at all, are an afterthought and poorly done.”

When it comes to other contexts, like societal, the bullseye of curriculum connection, student interest level, and math teacher time is a hard one to hit. As one teacher said, “With more time I would like to start new math topics with ‘real world problems’ and have the students brainstorm what knowledge would be useful to solve them, building resilience in the face of complex problems. However, these kinds of freeform explorations take time that I often feel like I don’t have in my class.”

This theme of “not enough time” appeared often, with teachers expressing a desire for more real-world presence, including cross-collaboration with other colleagues. A teacher said, “I have tried to coordinate with science classes to talk about the mathematical aspects of science concepts they are learning, but it can be hard to coordinate and map those kinds of things onto my own curriculum.”

This was echoed in the teachers’ comments, along with many wishful statements about what they “would do…if.”

With all the time and resources, what would teachers do?

We asked teachers to describe their dream scenario: what they would do if they had more resources, time, and permission. In most responses, what stood out was teachers’ love for math’s interconnectedness and innate curiosity. Some dreamed big:

• “An interdisciplinary project across all subjects that would allow students to see how math applies to all facets of the world”
• “Something like ‘a history of mathematical thought,’ bringing history, culture, psychology, ecology, science, and engineering into the curriculum”
• “Students being given the opportunity to explore a problem they are passionate about and explore ways that mathematics can be used to help solve it”
• “Students working alongside professionals in various math-related fields so they can see, firsthand, how the math they are learning is currently being used”

It’s clear that teachers want to provide classroom experiences that both underscore math’s omnipresence in the world around us and ignite students’ interests. It’s also clear that when your survey takers have to type qualifiers like, “But this would take a lot of time” and “We don’t have the resources for this,” the “real world” is actually what’s in the way. So, what can be done?

From ideal to real: Helpful tips & a relaxing thought on problem-based learning

No one knows better than math teachers that you can’t add time to your school day.  But, through our interactions with teachers, we walked away with some resources and tips to share with you. Here are the gems:

• Split it into quadrants. Most teachers surveyed would order their quarters and contexts like this: first quarter, personal; second quarter, societal; third quarter, scientific; fourth quarter, occupational.
• Switch with science. One teacher said this: “Actually switch classes with a science teacher to reiterate how what they are learning in science is related to what we do in math. And then they can come to my class to do the same so they can really understand the connection.”
• Draw a parallel. “Have a project that seems like it might belong in an arts classroom, like creating a piece of clothing,” another teacher suggested. “They have to use multiple modes of mathematical knowledge to do this, like unit conversions (centimeters to inches to yards), spatial constraints (if fabric is a certain size, can I fit my pattern in it? How big do the pieces have to be to fit on the body?), and area (how much fabric do I need?).”
• Estimate. “I use Estimation 180 , but I gamify it to address average, mean, median, and mode. I have students secretly record their estimations, and I write them all on the board. We discuss the average classroom guess and how close our range is. Estimation is everywhere.”
• Level up. “I’ve been using Skew the Script to heighten engagement for all my students and teach them about larger global issues affecting society. Their After The AP Data Science Challenge aims to solve the real (unsolved) problem of finding a model to predict the best and worst colleges for conquering student debt.”
• Build the roster: “Try to arrange a handful of yearly speakers and field trips you can count on to bring the math to life. My husband is a civil engineer and uses the Pythagorean theorem. You’d be surprised how many folks would love to come in and talk to a math class—with your teacher guidance and enthusiasm, of course.”

And now for the relaxing thought: Start small. As with any endeavor in the classroom, no matter the discipline, the key is to work incrementally. We already know how important increments are, right, math teachers?

What is “real,” anyway?

Let’s return to the age-old question of, “When will we ever use this?” It plagues math teachers perhaps more than any other discipline, and the task of “real-world” problem-solving often feels like a “gotcha” moment. The fact is, sometimes, we math teachers don’t have a great real-world example of dividing negative fractions in our back pocket. But does that mean that it isn’t worth learning? Must every concept in math be nested perfectly within the “real” world?

In one particular mic-drop moment, one of our teachers shared, “I think the label ‘real-world’ has been used extensively in math education, and I’ve found it a bit frustrating. In many regards, math is the least ‘real’ discipline we teach children. It is, largely, the art of abstraction! That it is ‘real’ is in many ways the least interesting and important thing about it as a system of thinking, and this is often lost when continually looked at with the question ‘When will we ever use this?’”

Maybe when we’ll “use this” is when we’re thinking through a problem with many facets and variables. Math is, after all, less of a “what” and more of a “how.” How should we go about solving this? How do we use computational thinking to solve problems? How do we spiral what we already know with what we don’t?

We’re teaching kids how to think —and isn’t that the most real-world skill we can possibly teach?

To learn more about how NWEA can support you in teaching math, visit our website .

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Developing Logical Mathematical Intelligence

How to unlock your problem-solving potential

• Characteristics and Examples
• Develop Logical Mathematical Intelligence
• Tips and Strategies

Logical mathematical intelligence is one of eight intelligences that Howard Gardner, a professor of cognition and education at Harvard University, proposed in his theory of multiple intelligences , which he outlined in his book Frames of Mind . Gardner's theory posited these types of intelligence:

• Visual-spatial
• Linguistic-verbal
• Logical-mathematical
• Body-kinesthetic
• Interpersonal
• Intrapersonal
• Naturalistic

According to Rebecca Mannis, PhD and founder and learning specialist at Ivy Prep, for a long time American psychologists viewed intelligence as a single factor, typified by Lewis Terman in the early to mid-1900s, who referred to intelligence as “g.” Similarly,  Kimberly Nix Berens, PhD , founder of Fit Learning and author of "Blind Spots: Why Students Fail and the Science That Can Save Them," explains that intelligence is often viewed as an innate ability, but there is a lack of scientific evidence to support this.

Instead, Gardner theorized that there are a number of kinds of intelligence that we each may have, that we may vary in the degree we have of each one, and that we may have more or less of each of these throughout our lifetimes. Logical mathematical intelligence is one of the intelligences he described, and it represents the ability to use numbers effectively, to reason well, and to recognize and solve problems using logical patterns.

In this article, we’ll review the characteristics of logical mathematical intelligence, discover how to develop it, explore strategies to enhance it, and look at the benefits of this kind of intelligence.

Anchiy / E+ / Getty

Characteristics and Examples of Logical Mathematical Intelligence

People who have logical mathematical intelligence solve problems using logic, can quickly calculate math problems , and like when things are categorized in a rational way. They’re also good at understanding patterns, the relationships between things, and understanding complex ideas.

Thus, logical-mathematical intelligence encompasses the following:

• Being good with numbers
• Understanding logical concepts
• Having good reasoning skills
• Enjoying experiments
• Enjoying solving puzzles and mysteries
• Being good at manipulating numbers and operations
• Being good at understanding and applying scientific principles

According to Berens, examples of logical mathematical intelligence include “fluently solving multi-step equations, [solving] language-based math problems , interpreting and analyzing scientific findings, and designing experiments.”

Mannis explains that mastery of basic facts and concepts that leads to the ability to adapt those facts and concepts into more complex tasks and to new settings is a hallmark of logical mathematical intelligence.

For instance, Mannis gives the example of a third grader with strong logical mathematical intelligence who not only knows how to distinguish between perimeter and area but can also use those formulas for other things. The child can apply “that information to a math challenge to design a playground… where they are tasked with determining what the area of a complex shape would be if there were sections of semicircles or squares within that figure ‘cut out.’ They would also be able to then identify the cost of paving the entire play area given a particular per foot fee.”

For those of us who are more inclined toward verbal linguistics or another type of intelligence, this may seem beyond our reach, but it is possible to build your strength in the more mathematical areas of intelligence.

How to Develop Logical Mathematical Intelligence

Decades of research indicate that higher-level skills, such as those seen in logical mathematical intelligence, require the mastery of foundational skills, says Berens. As a result, “Young learners require explicit instruction and repeated practice to fluency in core math skills such as numeracy, basic computation, fractions, decimals, percents, and ratios," she says. "They also require fluent reading skills and fluent comprehension, problem-solving, and critical thinking skills.”

Mannis explains that some children are better at memorizing facts and drawing connections between concepts than others, but there are ways to develop these skills.

These methods include:

• Teacher education: According to Mannis, teachers must have a “strong understanding of how children develop these skills and methods [by] first teaching this content systematically and then gradually ‘scaffolding’ or adding complexity and integration."
• Focusing on basic math: As Berens indicates students must attain fluency in the basics before they can begin applying these core skills for mastery of highly complex skills, including algebra, geometry, and calculus.
• Engagement beyond the classroom: Encouraging children to see how mathematical concepts can be part of their real lives can help develop logical mathematical intelligence skills.

Mannis provides an example of the last point: “A child usually reads a book in four days and would like to borrow the series to read during the three weeks between the end of the school year and sleep away camp. How can they estimate how many books they will get through? How does being free of homework shift their estimate? That is an example of living math that offers a chance to systematize, use concepts such as ratios and estimating, and also encourage them to engage through creating a system to make their estimate.”

Strategies for Enhancing Logical Mathematical Intelligence

To enhance logical mathematical intelligence you first have to learn the basics, so explicit instruction and repeated practice in math skills is essential, says Berens.

Moreover, per Mannis, to enhance skills in logical mathematical intelligence further:

• Provide opportunities to create systems and patterns, and solve logic problems
• Encourage ‘metacognitive awareness,’ or being aware of how you think, and talk through this approach
• Balance learning facts and math operations with real-world problem-solving

For example, Mannis speaks of a middle school class she consulted with that timed its geometry unit so it was right before the school carnival. “After completing the basics of the course, the students were put in charge of designing, creating, and manning some of the carnival stations using” what they learned. This allowed them to use the skills they got from the course and enhance their logical mathematical intelligence.

Benefits of Logical Mathematical Intelligence

People with logical mathematical intelligence are good at rational thinking, analyzing problems logically, and thinking about issues scientifically. “Not only does mastery of high-level math skills produce long-term academic success," says Berens, "but it also gives learners access to careers in science, technology, and engineering.”

We have a lot of complex problems in these fields to solve, such as climate change, and we need people with logical mathematical intelligence to solve them, she says.

While some people may have more innate ability with logical mathematical intelligence, anyone can enhance their abilities. Developing math skills, engaging in strategy games and logic problems, explaining your thinking, and using your skills in the real world can help develop your logical mathematical intelligence and have you on your way to unlocking your problem-solving potential.

Gardner H.  Frames of Mind: The Theory of Multiple Intelligences . 10th anniversary ed. BasicBooks; 1993.

Arani HK, Mobarakeh SD. Metacognitive strategies and logical/mathematical intelligence in EFL context: Investigating possible relationships. TPLS . 2012;2(2):304-313. doi:10.4304/tpls.2.2.304-313

Šafranj J. Logical/mathematical intelligence in teaching English as a second language .  Procedia - Social and Behavioral Sciences . 2016;232:75-82. doi: 10.1016/j.sbspro.2016.10.019

By Cynthia Vinney, PhD Cynthia Vinney, PhD is an expert in media psychology and a published scholar whose work has been published in peer-reviewed psychology journals.

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10 Problem Solving Strategy Cards

Updated:  09 Mar 2021

A set of 10 problem solving strategy cards.

Non-Editable:  PDF

Pages:  3 Pages

Grades:  2 - 3

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The 10 problem-solving strategies include:

• Guess and check
• Make a table or chart
• Draw a picture or diagram
• Act out the problem
• Find a pattern or use a rule
• Check for relevant or irrelevant information
• Find smaller parts of a large problem
• Make an organized list
• Solve a simpler problem
• Work backward

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